id	sid	tid	token	lemma	pos
american_scientific_journal-4814	1	1	50	50	NUM
american_scientific_journal-4814	1	2	american	american	ADJ
american_scientific_journal-4814	1	3	scientific	scientific	ADJ
american_scientific_journal-4814	1	4	research	research	NOUN
american_scientific_journal-4814	1	5	journal	journal	NOUN
american_scientific_journal-4814	1	6	for	for	ADP
american_scientific_journal-4814	1	7	engineering	engineering	NOUN
american_scientific_journal-4814	1	8	,	,	PUNCT
american_scientific_journal-4814	1	9	technology	technology	NOUN
american_scientific_journal-4814	1	10	,	,	PUNCT
american_scientific_journal-4814	1	11	and	and	CCONJ
american_scientific_journal-4814	1	12	sciences	science	NOUN
american_scientific_journal-4814	1	13	(	(	PUNCT
american_scientific_journal-4814	1	14	asrjets	asrjet	NOUN
american_scientific_journal-4814	1	15	)	)	PUNCT
american_scientific_journal-4814	1	16	issn	issn	PROPN
american_scientific_journal-4814	1	17	(	(	PUNCT
american_scientific_journal-4814	1	18	print	print	NOUN
american_scientific_journal-4814	1	19	)	)	PUNCT
american_scientific_journal-4814	1	20	2313	2313	NUM
american_scientific_journal-4814	1	21	-	-	SYM
american_scientific_journal-4814	1	22	4410	4410	NUM
american_scientific_journal-4814	1	23	,	,	PUNCT
american_scientific_journal-4814	1	24	issn	issn	PROPN
american_scientific_journal-4814	1	25	(	(	PUNCT
american_scientific_journal-4814	1	26	online	online	ADJ
american_scientific_journal-4814	1	27	)	)	PUNCT
american_scientific_journal-4814	1	28	2313	2313	NUM
american_scientific_journal-4814	1	29	-	-	SYM
american_scientific_journal-4814	1	30	4402	4402	NUM
american_scientific_journal-4814	1	31	©	©	PROPN
american_scientific_journal-4814	1	32	global	global	ADJ
american_scientific_journal-4814	1	33	society	society	NOUN
american_scientific_journal-4814	1	34	of	of	ADP
american_scientific_journal-4814	1	35	scientific	scientific	ADJ
american_scientific_journal-4814	1	36	research	research	NOUN
american_scientific_journal-4814	1	37	and	and	CCONJ
american_scientific_journal-4814	1	38	researchers	researcher	NOUN
american_scientific_journal-4814	1	39	http://asrjetsjournal.org/	http://asrjetsjournal.org/	PROPN
american_scientific_journal-4814	1	40	mathematical	mathematical	ADJ
american_scientific_journal-4814	1	41	modelling	modelling	NOUN
american_scientific_journal-4814	1	42	of	of	ADP
american_scientific_journal-4814	1	43	a	a	DET
american_scientific_journal-4814	1	44	rotating	rotate	VERB
american_scientific_journal-4814	1	45	deformable	deformable	ADJ
american_scientific_journal-4814	1	46	space	space	NOUN
american_scientific_journal-4814	1	47	vehicle	vehicle	NOUN
american_scientific_journal-4814	1	48	lace	lace	NOUN
american_scientific_journal-4814	1	49	attitude	attitude	NOUN
american_scientific_journal-4814	1	50	motions	motion	NOUN
american_scientific_journal-4814	1	51	saraka	saraka	ADV
american_scientific_journal-4814	1	52	jean	jean	PROPN
american_scientific_journal-4814	1	53	modeste	modeste	PROPN
american_scientific_journal-4814	1	54	kouassia	kouassia	PROPN
american_scientific_journal-4814	1	55	,	,	PUNCT
american_scientific_journal-4814	1	56	moussa	moussa	PROPN
american_scientific_journal-4814	1	57	syllab	syllab	NOUN
american_scientific_journal-4814	1	58	*	*	PUNCT
american_scientific_journal-4814	1	59	aufr	aufr	PROPN
american_scientific_journal-4814	1	60	mathématiques	mathématiques	PROPN
american_scientific_journal-4814	1	61	et	et	PROPN
american_scientific_journal-4814	1	62	informatique	informatique	PROPN
american_scientific_journal-4814	1	63	université	université	PROPN
american_scientific_journal-4814	1	64	félix	félix	PROPN
american_scientific_journal-4814	1	65	houphouët	houphouët	PROPN
american_scientific_journal-4814	1	66	-	-	PUNCT
american_scientific_journal-4814	1	67	boigny	boigny	PROPN
american_scientific_journal-4814	1	68	laboratoire	laboratoire	PROPN
american_scientific_journal-4814	1	69	de	de	X
american_scientific_journal-4814	1	70	mécanique	mécanique	X
american_scientific_journal-4814	1	71	bufr	bufr	PROPN
american_scientific_journal-4814	1	72	mathématiques	mathématiques	PROPN
american_scientific_journal-4814	1	73	et	et	PROPN
american_scientific_journal-4814	1	74	informatique	informatique	PROPN
american_scientific_journal-4814	1	75	université	université	PROPN
american_scientific_journal-4814	1	76	félix	félix	PROPN
american_scientific_journal-4814	1	77	houphouët	houphouët	PROPN
american_scientific_journal-4814	1	78	-	-	PUNCT
american_scientific_journal-4814	1	79	boigny	boigny	PROPN
american_scientific_journal-4814	1	80	laboratoire	laboratoire	PROPN
american_scientific_journal-4814	1	81	de	de	X
american_scientific_journal-4814	1	82	mécanique	mécanique	PROPN
american_scientific_journal-4814	1	83	,	,	PUNCT
american_scientific_journal-4814	1	84	abidjan	abidjan	PROPN
american_scientific_journal-4814	1	85	,	,	PUNCT
american_scientific_journal-4814	1	86	22	22	NUM
american_scientific_journal-4814	1	87	bp	bp	PROPN
american_scientific_journal-4814	1	88	582	582	NUM
american_scientific_journal-4814	1	89	,	,	PUNCT
american_scientific_journal-4814	1	90	côte	côte	NOUN
american_scientific_journal-4814	1	91	d’ivoire	d’ivoire	NOUN
american_scientific_journal-4814	1	92	aemail	aemail	NOUN
american_scientific_journal-4814	1	93	:	:	PUNCT
american_scientific_journal-4814	1	94	ksarakajm@yahoo.fr	ksarakajm@yahoo.fr	PROPN
american_scientific_journal-4814	1	95	bemail	bemail	NOUN
american_scientific_journal-4814	1	96	:	:	PUNCT
american_scientific_journal-4814	1	97	ba_mouss@yahoo.fr	ba_mouss@yahoo.fr	PROPN
american_scientific_journal-4814	1	98	abstract	abstract	ADJ
american_scientific_journal-4814	1	99	a	a	DET
american_scientific_journal-4814	1	100	rotating	rotate	VERB
american_scientific_journal-4814	1	101	elastic	elastic	ADJ
american_scientific_journal-4814	1	102	space	space	NOUN
american_scientific_journal-4814	1	103	vehicle	vehicle	NOUN
american_scientific_journal-4814	1	104	composed	compose	VERB
american_scientific_journal-4814	1	105	of	of	ADP
american_scientific_journal-4814	1	106	a	a	DET
american_scientific_journal-4814	1	107	central	central	ADJ
american_scientific_journal-4814	1	108	rigid	rigid	ADJ
american_scientific_journal-4814	1	109	body	body	NOUN
american_scientific_journal-4814	1	110	connected	connect	VERB
american_scientific_journal-4814	1	111	to	to	ADP
american_scientific_journal-4814	1	112	two	two	NUM
american_scientific_journal-4814	1	113	solar	solar	ADJ
american_scientific_journal-4814	1	114	arrays	array	NOUN
american_scientific_journal-4814	1	115	,	,	PUNCT
american_scientific_journal-4814	1	116	subjected	subject	VERB
american_scientific_journal-4814	1	117	to	to	ADP
american_scientific_journal-4814	1	118	external	external	ADJ
american_scientific_journal-4814	1	119	torques	torque	NOUN
american_scientific_journal-4814	1	120	,	,	PUNCT
american_scientific_journal-4814	1	121	is	be	AUX
american_scientific_journal-4814	1	122	studied	study	VERB
american_scientific_journal-4814	1	123	using	use	VERB
american_scientific_journal-4814	1	124	the	the	DET
american_scientific_journal-4814	1	125	spectral	spectral	ADJ
american_scientific_journal-4814	1	126	expansion	expansion	NOUN
american_scientific_journal-4814	1	127	continuum	continuum	ADJ
american_scientific_journal-4814	1	128	method	method	NOUN
american_scientific_journal-4814	1	129	of	of	ADP
american_scientific_journal-4814	1	130	rayleigh	rayleigh	PROPN
american_scientific_journal-4814	1	131	-	-	PUNCT
american_scientific_journal-4814	1	132	ritz	ritz	PROPN
american_scientific_journal-4814	1	133	.	.	PUNCT
american_scientific_journal-4814	2	1	the	the	DET
american_scientific_journal-4814	2	2	lace	lace	NOUN
american_scientific_journal-4814	2	3	attitudes	attitude	VERB
american_scientific_journal-4814	2	4	motion	motion	NOUN
american_scientific_journal-4814	2	5	of	of	ADP
american_scientific_journal-4814	2	6	the	the	DET
american_scientific_journal-4814	2	7	rotating	rotate	VERB
american_scientific_journal-4814	2	8	space	space	NOUN
american_scientific_journal-4814	2	9	vehicle	vehicle	NOUN
american_scientific_journal-4814	2	10	can	can	AUX
american_scientific_journal-4814	2	11	be	be	AUX
american_scientific_journal-4814	2	12	described	describe	VERB
american_scientific_journal-4814	2	13	by	by	ADP
american_scientific_journal-4814	2	14	a	a	DET
american_scientific_journal-4814	2	15	linear	linear	ADJ
american_scientific_journal-4814	2	16	combination	combination	NOUN
american_scientific_journal-4814	2	17	of	of	ADP
american_scientific_journal-4814	2	18	the	the	DET
american_scientific_journal-4814	2	19	global	global	ADJ
american_scientific_journal-4814	2	20	modes	mode	NOUN
american_scientific_journal-4814	2	21	different	different	ADJ
american_scientific_journal-4814	2	22	from	from	ADP
american_scientific_journal-4814	2	23	the	the	DET
american_scientific_journal-4814	2	24	usual	usual	ADJ
american_scientific_journal-4814	2	25	ordinary	ordinary	ADJ
american_scientific_journal-4814	2	26	modes	mode	NOUN
american_scientific_journal-4814	2	27	.	.	PUNCT
american_scientific_journal-4814	3	1	by	by	ADP
american_scientific_journal-4814	3	2	application	application	NOUN
american_scientific_journal-4814	3	3	of	of	ADP
american_scientific_journal-4814	3	4	the	the	DET
american_scientific_journal-4814	3	5	spectral	spectral	ADJ
american_scientific_journal-4814	3	6	expansion	expansion	NOUN
american_scientific_journal-4814	3	7	continuum	continuum	ADJ
american_scientific_journal-4814	3	8	approach	approach	NOUN
american_scientific_journal-4814	3	9	of	of	ADP
american_scientific_journal-4814	3	10	rayleigh	rayleigh	PROPN
american_scientific_journal-4814	3	11	-	-	PUNCT
american_scientific_journal-4814	3	12	ritz	ritz	PROPN
american_scientific_journal-4814	3	13	,	,	PUNCT
american_scientific_journal-4814	3	14	the	the	DET
american_scientific_journal-4814	3	15	impedance	impedance	NOUN
american_scientific_journal-4814	3	16	function	function	NOUN
american_scientific_journal-4814	3	17	of	of	ADP
american_scientific_journal-4814	3	18	the	the	DET
american_scientific_journal-4814	3	19	space	space	NOUN
american_scientific_journal-4814	3	20	vehicle	vehicle	NOUN
american_scientific_journal-4814	3	21	in	in	ADP
american_scientific_journal-4814	3	22	terms	term	NOUN
american_scientific_journal-4814	3	23	of	of	ADP
american_scientific_journal-4814	3	24	the	the	DET
american_scientific_journal-4814	3	25	global	global	ADJ
american_scientific_journal-4814	3	26	modes	mode	NOUN
american_scientific_journal-4814	3	27	of	of	ADP
american_scientific_journal-4814	3	28	the	the	DET
american_scientific_journal-4814	3	29	whole	whole	ADJ
american_scientific_journal-4814	3	30	system	system	NOUN
american_scientific_journal-4814	3	31	is	be	AUX
american_scientific_journal-4814	3	32	derived	derive	VERB
american_scientific_journal-4814	3	33	.	.	PUNCT
american_scientific_journal-4814	4	1	the	the	DET
american_scientific_journal-4814	4	2	numerical	numerical	PROPN
american_scientific_journal-4814	4	3	simulation	simulation	NOUN
american_scientific_journal-4814	4	4	of	of	ADP
american_scientific_journal-4814	4	5	these	these	DET
american_scientific_journal-4814	4	6	global	global	ADJ
american_scientific_journal-4814	4	7	modes	mode	NOUN
american_scientific_journal-4814	4	8	of	of	ADP
american_scientific_journal-4814	4	9	great	great	ADJ
american_scientific_journal-4814	4	10	interest	interest	NOUN
american_scientific_journal-4814	4	11	in	in	ADP
american_scientific_journal-4814	4	12	this	this	DET
american_scientific_journal-4814	4	13	study	study	NOUN
american_scientific_journal-4814	4	14	,	,	PUNCT
american_scientific_journal-4814	4	15	are	be	AUX
american_scientific_journal-4814	4	16	performed	perform	VERB
american_scientific_journal-4814	4	17	by	by	ADP
american_scientific_journal-4814	4	18	means	mean	NOUN
american_scientific_journal-4814	4	19	of	of	ADP
american_scientific_journal-4814	4	20	this	this	DET
american_scientific_journal-4814	4	21	impedance	impedance	NOUN
american_scientific_journal-4814	4	22	function	function	NOUN
american_scientific_journal-4814	4	23	relating	relate	VERB
american_scientific_journal-4814	4	24	the	the	DET
american_scientific_journal-4814	4	25	external	external	ADJ
american_scientific_journal-4814	4	26	torques	torque	NOUN
american_scientific_journal-4814	4	27	to	to	ADP
american_scientific_journal-4814	4	28	the	the	DET
american_scientific_journal-4814	4	29	rotating	rotate	VERB
american_scientific_journal-4814	4	30	space	space	NOUN
american_scientific_journal-4814	4	31	vehicle	vehicle	NOUN
american_scientific_journal-4814	4	32	lace	lace	NOUN
american_scientific_journal-4814	4	33	attitudes	attitude	NOUN
american_scientific_journal-4814	4	34	.	.	PUNCT
american_scientific_journal-4814	5	1	keywords	keyword	NOUN
american_scientific_journal-4814	5	2	:	:	PUNCT
american_scientific_journal-4814	5	3	vibration	vibration	NOUN
american_scientific_journal-4814	5	4	;	;	PUNCT
american_scientific_journal-4814	5	5	global	global	ADJ
american_scientific_journal-4814	5	6	mode	mode	NOUN
american_scientific_journal-4814	5	7	;	;	PUNCT
american_scientific_journal-4814	5	8	spectral	spectral	ADJ
american_scientific_journal-4814	5	9	expansion	expansion	NOUN
american_scientific_journal-4814	5	10	;	;	PUNCT
american_scientific_journal-4814	5	11	impedance	impedance	NOUN
american_scientific_journal-4814	5	12	function	function	NOUN
american_scientific_journal-4814	5	13	.	.	PUNCT
american_scientific_journal-4814	6	1	1	1	X
american_scientific_journal-4814	6	2	.	.	X
american_scientific_journal-4814	6	3	introduction	introduction	NOUN
american_scientific_journal-4814	6	4	several	several	ADJ
american_scientific_journal-4814	6	5	papers	paper	NOUN
american_scientific_journal-4814	6	6	using	use	VERB
american_scientific_journal-4814	6	7	the	the	DET
american_scientific_journal-4814	6	8	spectral	spectral	ADJ
american_scientific_journal-4814	6	9	decomposition	decomposition	NOUN
american_scientific_journal-4814	6	10	continuum	continuum	ADJ
american_scientific_journal-4814	6	11	approach	approach	NOUN
american_scientific_journal-4814	6	12	of	of	ADP
american_scientific_journal-4814	6	13	rayleigh	rayleigh	PROPN
american_scientific_journal-4814	6	14	-	-	PUNCT
american_scientific_journal-4814	6	15	ritz	ritz	PROPN
american_scientific_journal-4814	7	1	[	[	X
american_scientific_journal-4814	7	2	1	1	NUM
american_scientific_journal-4814	7	3	-	-	SYM
american_scientific_journal-4814	7	4	12	12	NUM
american_scientific_journal-4814	7	5	]	]	PUNCT
american_scientific_journal-4814	7	6	are	be	AUX
american_scientific_journal-4814	7	7	interested	interested	ADJ
american_scientific_journal-4814	7	8	by	by	ADP
american_scientific_journal-4814	7	9	the	the	DET
american_scientific_journal-4814	7	10	attitudes	attitude	NOUN
american_scientific_journal-4814	7	11	motions	motion	NOUN
american_scientific_journal-4814	7	12	of	of	ADP
american_scientific_journal-4814	7	13	elastic	elastic	ADJ
american_scientific_journal-4814	7	14	multibody	multibody	ADJ
american_scientific_journal-4814	7	15	system	system	NOUN
american_scientific_journal-4814	7	16	in	in	ADP
american_scientific_journal-4814	7	17	dynamics	dynamic	NOUN
american_scientific_journal-4814	7	18	.	.	PUNCT
american_scientific_journal-4814	8	1	many	many	ADJ
american_scientific_journal-4814	8	2	authors	author	NOUN
american_scientific_journal-4814	8	3	use	use	VERB
american_scientific_journal-4814	8	4	different	different	ADJ
american_scientific_journal-4814	8	5	mathematical	mathematical	ADJ
american_scientific_journal-4814	8	6	models	model	NOUN
american_scientific_journal-4814	8	7	to	to	PART
american_scientific_journal-4814	8	8	perform	perform	VERB
american_scientific_journal-4814	8	9	the	the	DET
american_scientific_journal-4814	8	10	modal	modal	ADJ
american_scientific_journal-4814	8	11	analysis	analysis	NOUN
american_scientific_journal-4814	8	12	of	of	ADP
american_scientific_journal-4814	8	13	the	the	DET
american_scientific_journal-4814	8	14	mechanical	mechanical	ADJ
american_scientific_journal-4814	8	15	system	system	NOUN
american_scientific_journal-4814	8	16	attitudes	attitude	VERB
american_scientific_journal-4814	8	17	motion	motion	NOUN
american_scientific_journal-4814	8	18	.	.	PUNCT
american_scientific_journal-4814	9	1	these	these	DET
american_scientific_journal-4814	9	2	attitudes	attitude	NOUN
american_scientific_journal-4814	9	3	motions	motion	NOUN
american_scientific_journal-4814	9	4	are	be	AUX
american_scientific_journal-4814	9	5	supposed	suppose	VERB
american_scientific_journal-4814	9	6	to	to	PART
american_scientific_journal-4814	9	7	be	be	AUX
american_scientific_journal-4814	9	8	coupled	couple	VERB
american_scientific_journal-4814	9	9	and	and	CCONJ
american_scientific_journal-4814	9	10	expanded	expand	VERB
american_scientific_journal-4814	9	11	generally	generally	ADV
american_scientific_journal-4814	9	12	with	with	ADP
american_scientific_journal-4814	9	13	the	the	DET
american_scientific_journal-4814	9	14	choice	choice	NOUN
american_scientific_journal-4814	9	15	of	of	ADP
american_scientific_journal-4814	9	16	the	the	DET
american_scientific_journal-4814	9	17	non	non	ADJ
american_scientific_journal-4814	9	18	-	-	ADJ
american_scientific_journal-4814	9	19	rotating	rotating	ADJ
american_scientific_journal-4814	9	20	base	base	NOUN
american_scientific_journal-4814	9	21	cantilever	cantilever	NOUN
american_scientific_journal-4814	9	22	modes	mode	NOUN
american_scientific_journal-4814	9	23	[	[	X
american_scientific_journal-4814	9	24	2	2	NUM
american_scientific_journal-4814	9	25	,	,	PUNCT
american_scientific_journal-4814	9	26	3	3	NUM
american_scientific_journal-4814	9	27	,	,	PUNCT
american_scientific_journal-4814	9	28	5	5	NUM
american_scientific_journal-4814	9	29	,	,	PUNCT
american_scientific_journal-4814	9	30	7	7	NUM
american_scientific_journal-4814	9	31	,	,	PUNCT
american_scientific_journal-4814	9	32	8	8	NUM
american_scientific_journal-4814	9	33	,	,	PUNCT
american_scientific_journal-4814	9	34	9	9	NUM
american_scientific_journal-4814	9	35	,	,	PUNCT
american_scientific_journal-4814	9	36	11	11	NUM
american_scientific_journal-4814	9	37	,	,	PUNCT
american_scientific_journal-4814	9	38	12	12	NUM
american_scientific_journal-4814	9	39	]	]	PUNCT
american_scientific_journal-4814	9	40	or	or	CCONJ
american_scientific_journal-4814	9	41	the	the	DET
american_scientific_journal-4814	9	42	rotating	rotate	VERB
american_scientific_journal-4814	9	43	base	base	NOUN
american_scientific_journal-4814	9	44	cantilever	cantilever	NOUN
american_scientific_journal-4814	9	45	modes	mode	NOUN
american_scientific_journal-4814	9	46	[	[	X
american_scientific_journal-4814	9	47	1	1	NUM
american_scientific_journal-4814	9	48	,	,	PUNCT
american_scientific_journal-4814	9	49	4	4	NUM
american_scientific_journal-4814	9	50	,	,	PUNCT
american_scientific_journal-4814	9	51	6	6	NUM
american_scientific_journal-4814	9	52	,	,	PUNCT
american_scientific_journal-4814	9	53	7	7	NUM
american_scientific_journal-4814	9	54	,	,	PUNCT
american_scientific_journal-4814	9	55	10	10	NUM
american_scientific_journal-4814	9	56	]	]	PUNCT
american_scientific_journal-4814	9	57	.	.	PUNCT
american_scientific_journal-4814	10	1	the	the	DET
american_scientific_journal-4814	10	2	modes	mode	NOUN
american_scientific_journal-4814	10	3	used	use	VERB
american_scientific_journal-4814	10	4	by	by	ADP
american_scientific_journal-4814	10	5	the	the	DET
american_scientific_journal-4814	10	6	authors	author	NOUN
american_scientific_journal-4814	10	7	to	to	PART
american_scientific_journal-4814	10	8	describe	describe	VERB
american_scientific_journal-4814	10	9	the	the	DET
american_scientific_journal-4814	10	10	distributed	distribute	VERB
american_scientific_journal-4814	10	11	flexibility	flexibility	NOUN
american_scientific_journal-4814	10	12	of	of	ADP
american_scientific_journal-4814	10	13	the	the	DET
american_scientific_journal-4814	10	14	mechanical	mechanical	ADJ
american_scientific_journal-4814	10	15	system	system	NOUN
american_scientific_journal-4814	10	16	,	,	PUNCT
american_scientific_journal-4814	10	17	leads	lead	VERB
american_scientific_journal-4814	10	18	to	to	ADP
american_scientific_journal-4814	10	19	the	the	DET
american_scientific_journal-4814	10	20	spectral	spectral	ADJ
american_scientific_journal-4814	10	21	expansion	expansion	NOUN
american_scientific_journal-4814	10	22	of	of	ADP
american_scientific_journal-4814	10	23	the	the	DET
american_scientific_journal-4814	10	24	reduced	reduce	VERB
american_scientific_journal-4814	10	25	impedance	impedance	NOUN
american_scientific_journal-4814	10	26	matrix	matrix	NOUN
american_scientific_journal-4814	10	27	of	of	ADP
american_scientific_journal-4814	10	28	the	the	DET
american_scientific_journal-4814	10	29	multibody	multibody	ADJ
american_scientific_journal-4814	10	30	system	system	NOUN
american_scientific_journal-4814	10	31	deriving	derive	VERB
american_scientific_journal-4814	10	32	from	from	ADP
american_scientific_journal-4814	10	33	this	this	DET
american_scientific_journal-4814	10	34	analysis	analysis	NOUN
american_scientific_journal-4814	10	35	.	.	PUNCT
american_scientific_journal-4814	11	1	the	the	DET
american_scientific_journal-4814	11	2	external	external	ADJ
american_scientific_journal-4814	11	3	torques	torque	NOUN
american_scientific_journal-4814	11	4	exerted	exert	VERB
american_scientific_journal-4814	11	5	on	on	ADP
american_scientific_journal-4814	11	6	the	the	DET
american_scientific_journal-4814	11	7	multibody	multibody	ADJ
american_scientific_journal-4814	11	8	system	system	NOUN
american_scientific_journal-4814	11	9	are	be	AUX
american_scientific_journal-4814	11	10	related	relate	VERB
american_scientific_journal-4814	11	11	to	to	ADP
american_scientific_journal-4814	11	12	its	its	PRON
american_scientific_journal-4814	11	13	coupled	couple	VERB
american_scientific_journal-4814	11	14	attitudes	attitude	NOUN
american_scientific_journal-4814	11	15	by	by	ADP
american_scientific_journal-4814	11	16	means	mean	NOUN
american_scientific_journal-4814	11	17	of	of	ADP
american_scientific_journal-4814	11	18	this	this	DET
american_scientific_journal-4814	11	19	matrix	matrix	NOUN
american_scientific_journal-4814	11	20	.	.	PUNCT
american_scientific_journal-4814	12	1	----------------------------------------------------------------------	----------------------------------------------------------------------	PUNCT
american_scientific_journal-4814	13	1	*	*	PUNCT
american_scientific_journal-4814	13	2	corresponding	correspond	VERB
american_scientific_journal-4814	13	3	author	author	NOUN
american_scientific_journal-4814	13	4	.	.	PUNCT
american_scientific_journal-4814	14	1	http://asrjetsjournal.org/	http://asrjetsjournal.org/	NOUN
american_scientific_journal-4814	14	2	mailto:%20aemail	mailto:%20aemail	NOUN
american_scientific_journal-4814	14	3	:	:	PUNCT
american_scientific_journal-4814	15	1	mailto:%20bemail	mailto:%20bemail	NUM
american_scientific_journal-4814	15	2	:	:	PUNCT
american_scientific_journal-4814	15	3	american	american	ADJ
american_scientific_journal-4814	15	4	scientific	scientific	ADJ
american_scientific_journal-4814	15	5	research	research	PROPN
american_scientific_journal-4814	15	6	journal	journal	NOUN
american_scientific_journal-4814	15	7	for	for	ADP
american_scientific_journal-4814	15	8	engineering	engineering	NOUN
american_scientific_journal-4814	15	9	,	,	PUNCT
american_scientific_journal-4814	15	10	technology	technology	NOUN
american_scientific_journal-4814	15	11	,	,	PUNCT
american_scientific_journal-4814	15	12	and	and	CCONJ
american_scientific_journal-4814	15	13	sciences	science	NOUN
american_scientific_journal-4814	15	14	(	(	PUNCT
american_scientific_journal-4814	15	15	asrjets	asrjet	NOUN
american_scientific_journal-4814	15	16	)	)	PUNCT
american_scientific_journal-4814	15	17	(	(	PUNCT
american_scientific_journal-4814	15	18	2019	2019	NUM
american_scientific_journal-4814	15	19	)	)	PUNCT
american_scientific_journal-4814	15	20	volume	volume	NOUN
american_scientific_journal-4814	15	21	55	55	NUM
american_scientific_journal-4814	15	22	,	,	PUNCT
american_scientific_journal-4814	15	23	no	no	DET
american_scientific_journal-4814	15	24	1	1	NUM
american_scientific_journal-4814	15	25	,	,	PUNCT
american_scientific_journal-4814	15	26	pp	pp	ADP
american_scientific_journal-4814	15	27	50	50	NUM
american_scientific_journal-4814	15	28	-	-	SYM
american_scientific_journal-4814	15	29	68	68	NUM
american_scientific_journal-4814	15	30	51	51	NUM
american_scientific_journal-4814	15	31	the	the	DET
american_scientific_journal-4814	15	32	present	present	ADJ
american_scientific_journal-4814	15	33	investigation	investigation	NOUN
american_scientific_journal-4814	15	34	uses	use	VERB
american_scientific_journal-4814	15	35	the	the	DET
american_scientific_journal-4814	15	36	spectral	spectral	ADJ
american_scientific_journal-4814	15	37	decomposition	decomposition	NOUN
american_scientific_journal-4814	15	38	continuum	continuum	ADJ
american_scientific_journal-4814	15	39	approach	approach	NOUN
american_scientific_journal-4814	15	40	of	of	ADP
american_scientific_journal-4814	15	41	rayleigh	rayleigh	PROPN
american_scientific_journal-4814	15	42	-	-	PUNCT
american_scientific_journal-4814	15	43	ritz	ritz	PROPN
american_scientific_journal-4814	15	44	.	.	PUNCT
american_scientific_journal-4814	16	1	one	one	NUM
american_scientific_journal-4814	16	2	describes	describe	VERB
american_scientific_journal-4814	16	3	the	the	DET
american_scientific_journal-4814	16	4	dynamics	dynamic	NOUN
american_scientific_journal-4814	16	5	of	of	ADP
american_scientific_journal-4814	16	6	a	a	DET
american_scientific_journal-4814	16	7	simplified	simplified	ADJ
american_scientific_journal-4814	16	8	elastic	elastic	ADJ
american_scientific_journal-4814	16	9	space	space	NOUN
american_scientific_journal-4814	16	10	vehicle	vehicle	NOUN
american_scientific_journal-4814	16	11	composed	compose	VERB
american_scientific_journal-4814	16	12	of	of	ADP
american_scientific_journal-4814	16	13	a	a	DET
american_scientific_journal-4814	16	14	central	central	ADJ
american_scientific_journal-4814	16	15	rigid	rigid	ADJ
american_scientific_journal-4814	16	16	body	body	NOUN
american_scientific_journal-4814	16	17	connected	connect	VERB
american_scientific_journal-4814	16	18	to	to	ADP
american_scientific_journal-4814	16	19	two	two	NUM
american_scientific_journal-4814	16	20	flexible	flexible	ADJ
american_scientific_journal-4814	16	21	solar	solar	NOUN
american_scientific_journal-4814	16	22	arrays	array	VERB
american_scientific_journal-4814	16	23	.	.	PUNCT
american_scientific_journal-4814	17	1	the	the	DET
american_scientific_journal-4814	17	2	particularity	particularity	NOUN
american_scientific_journal-4814	17	3	in	in	ADP
american_scientific_journal-4814	17	4	this	this	DET
american_scientific_journal-4814	17	5	work	work	NOUN
american_scientific_journal-4814	17	6	,	,	PUNCT
american_scientific_journal-4814	17	7	is	be	AUX
american_scientific_journal-4814	17	8	the	the	DET
american_scientific_journal-4814	17	9	decoupling	decoupling	NOUN
american_scientific_journal-4814	17	10	between	between	ADP
american_scientific_journal-4814	17	11	the	the	DET
american_scientific_journal-4814	17	12	attitudes	attitude	NOUN
american_scientific_journal-4814	17	13	motions	motion	NOUN
american_scientific_journal-4814	17	14	of	of	ADP
american_scientific_journal-4814	17	15	the	the	DET
american_scientific_journal-4814	17	16	spacecraft	spacecraft	NOUN
american_scientific_journal-4814	17	17	,	,	PUNCT
american_scientific_journal-4814	17	18	which	which	PRON
american_scientific_journal-4814	17	19	phenomena	phenomenon	NOUN
american_scientific_journal-4814	17	20	can	can	AUX
american_scientific_journal-4814	17	21	be	be	AUX
american_scientific_journal-4814	17	22	observed	observe	VERB
american_scientific_journal-4814	17	23	physically	physically	ADV
american_scientific_journal-4814	17	24	due	due	ADJ
american_scientific_journal-4814	17	25	to	to	ADP
american_scientific_journal-4814	17	26	the	the	DET
american_scientific_journal-4814	17	27	effect	effect	NOUN
american_scientific_journal-4814	17	28	of	of	ADP
american_scientific_journal-4814	17	29	attitudes	attitude	NOUN
american_scientific_journal-4814	17	30	control	control	NOUN
american_scientific_journal-4814	17	31	.	.	PUNCT
american_scientific_journal-4814	18	1	in	in	ADP
american_scientific_journal-4814	18	2	this	this	DET
american_scientific_journal-4814	18	3	case	case	NOUN
american_scientific_journal-4814	18	4	,	,	PUNCT
american_scientific_journal-4814	18	5	the	the	DET
american_scientific_journal-4814	18	6	interest	interest	NOUN
american_scientific_journal-4814	18	7	is	be	AUX
american_scientific_journal-4814	18	8	put	put	VERB
american_scientific_journal-4814	18	9	on	on	ADP
american_scientific_journal-4814	18	10	the	the	DET
american_scientific_journal-4814	18	11	lace	lace	NOUN
american_scientific_journal-4814	18	12	attitude	attitude	NOUN
american_scientific_journal-4814	18	13	motions	motion	NOUN
american_scientific_journal-4814	18	14	interacting	interact	VERB
american_scientific_journal-4814	18	15	with	with	ADP
american_scientific_journal-4814	18	16	the	the	DET
american_scientific_journal-4814	18	17	flexible	flexible	ADJ
american_scientific_journal-4814	18	18	parts	part	NOUN
american_scientific_journal-4814	18	19	global	global	ADJ
american_scientific_journal-4814	18	20	modes	mode	NOUN
american_scientific_journal-4814	18	21	[	[	X
american_scientific_journal-4814	18	22	12	12	NUM
american_scientific_journal-4814	18	23	]	]	PUNCT
american_scientific_journal-4814	18	24	.	.	PUNCT
american_scientific_journal-4814	19	1	from	from	ADP
american_scientific_journal-4814	19	2	the	the	DET
american_scientific_journal-4814	19	3	spectral	spectral	ADJ
american_scientific_journal-4814	19	4	decomposition	decomposition	NOUN
american_scientific_journal-4814	19	5	theory	theory	NOUN
american_scientific_journal-4814	19	6	performed	perform	VERB
american_scientific_journal-4814	19	7	,	,	PUNCT
american_scientific_journal-4814	19	8	one	one	PRON
american_scientific_journal-4814	19	9	gets	get	VERB
american_scientific_journal-4814	19	10	the	the	DET
american_scientific_journal-4814	19	11	impedance	impedance	NOUN
american_scientific_journal-4814	19	12	function	function	NOUN
american_scientific_journal-4814	19	13	of	of	ADP
american_scientific_journal-4814	19	14	the	the	DET
american_scientific_journal-4814	19	15	whole	whole	ADJ
american_scientific_journal-4814	19	16	system	system	NOUN
american_scientific_journal-4814	19	17	.	.	PUNCT
american_scientific_journal-4814	20	1	hence	hence	ADV
american_scientific_journal-4814	20	2	,	,	PUNCT
american_scientific_journal-4814	20	3	by	by	ADP
american_scientific_journal-4814	20	4	means	mean	NOUN
american_scientific_journal-4814	20	5	of	of	ADP
american_scientific_journal-4814	20	6	numerical	numerical	ADJ
american_scientific_journal-4814	20	7	algorithm	algorithm	NOUN
american_scientific_journal-4814	20	8	using	use	VERB
american_scientific_journal-4814	20	9	this	this	DET
american_scientific_journal-4814	20	10	impedance	impedance	NOUN
american_scientific_journal-4814	20	11	function	function	NOUN
american_scientific_journal-4814	20	12	,	,	PUNCT
american_scientific_journal-4814	20	13	the	the	DET
american_scientific_journal-4814	20	14	global	global	ADJ
american_scientific_journal-4814	20	15	modes	mode	NOUN
american_scientific_journal-4814	20	16	frequencies	frequency	NOUN
american_scientific_journal-4814	20	17	and	and	CCONJ
american_scientific_journal-4814	20	18	the	the	DET
american_scientific_journal-4814	20	19	natural	natural	ADJ
american_scientific_journal-4814	20	20	vibrations	vibration	NOUN
american_scientific_journal-4814	20	21	frequencies	frequency	NOUN
american_scientific_journal-4814	20	22	of	of	ADP
american_scientific_journal-4814	20	23	the	the	DET
american_scientific_journal-4814	20	24	whole	whole	ADJ
american_scientific_journal-4814	20	25	space	space	NOUN
american_scientific_journal-4814	20	26	vehicle	vehicle	NOUN
american_scientific_journal-4814	20	27	are	be	AUX
american_scientific_journal-4814	20	28	computed	compute	VERB
american_scientific_journal-4814	20	29	.	.	PUNCT
american_scientific_journal-4814	21	1	in	in	ADP
american_scientific_journal-4814	21	2	the	the	DET
american_scientific_journal-4814	21	3	modal	modal	ADJ
american_scientific_journal-4814	21	4	analysis	analysis	NOUN
american_scientific_journal-4814	21	5	,	,	PUNCT
american_scientific_journal-4814	21	6	one	one	PRON
american_scientific_journal-4814	21	7	supposes	suppose	VERB
american_scientific_journal-4814	21	8	that	that	SCONJ
american_scientific_journal-4814	21	9	the	the	DET
american_scientific_journal-4814	21	10	elastic	elastic	ADJ
american_scientific_journal-4814	21	11	space	space	NOUN
american_scientific_journal-4814	21	12	vehicle	vehicle	NOUN
american_scientific_journal-4814	21	13	undergoes	undergo	VERB
american_scientific_journal-4814	21	14	small	small	ADJ
american_scientific_journal-4814	21	15	lace	lace	NOUN
american_scientific_journal-4814	21	16	attitudes	attitude	NOUN
american_scientific_journal-4814	21	17	motions	motion	NOUN
american_scientific_journal-4814	21	18	and	and	CCONJ
american_scientific_journal-4814	21	19	elastic	elastic	ADJ
american_scientific_journal-4814	21	20	vibrations	vibration	NOUN
american_scientific_journal-4814	21	21	motions	motion	NOUN
american_scientific_journal-4814	21	22	interacting	interact	VERB
american_scientific_journal-4814	21	23	with	with	ADP
american_scientific_journal-4814	21	24	its	its	PRON
american_scientific_journal-4814	21	25	rotating	rotate	VERB
american_scientific_journal-4814	21	26	orbital	orbital	ADJ
american_scientific_journal-4814	21	27	motion	motion	NOUN
american_scientific_journal-4814	21	28	,	,	PUNCT
american_scientific_journal-4814	21	29	around	around	ADP
american_scientific_journal-4814	21	30	an	an	DET
american_scientific_journal-4814	21	31	equilibrium	equilibrium	NOUN
american_scientific_journal-4814	21	32	corresponding	correspond	VERB
american_scientific_journal-4814	21	33	to	to	ADP
american_scientific_journal-4814	21	34	some	some	DET
american_scientific_journal-4814	21	35	gravity	gravity	NOUN
american_scientific_journal-4814	21	36	-	-	PUNCT
american_scientific_journal-4814	21	37	gradient	gradient	NOUN
american_scientific_journal-4814	21	38	stabilized	stabilize	VERB
american_scientific_journal-4814	21	39	position	position	NOUN
american_scientific_journal-4814	21	40	where	where	SCONJ
american_scientific_journal-4814	21	41	the	the	DET
american_scientific_journal-4814	21	42	flexible	flexible	ADJ
american_scientific_journal-4814	21	43	appendages	appendage	NOUN
american_scientific_journal-4814	21	44	are	be	AUX
american_scientific_journal-4814	21	45	undeformed	undeformed	ADJ
american_scientific_journal-4814	21	46	[	[	X
american_scientific_journal-4814	21	47	7	7	NUM
american_scientific_journal-4814	21	48	,	,	PUNCT
american_scientific_journal-4814	21	49	13	13	NUM
american_scientific_journal-4814	21	50	]	]	PUNCT
american_scientific_journal-4814	21	51	.	.	PUNCT
american_scientific_journal-4814	22	1	2	2	X
american_scientific_journal-4814	22	2	.	.	X
american_scientific_journal-4814	22	3	dynamical	dynamical	ADJ
american_scientific_journal-4814	22	4	equations	equation	NOUN
american_scientific_journal-4814	22	5	of	of	ADP
american_scientific_journal-4814	22	6	the	the	DET
american_scientific_journal-4814	22	7	space	space	NOUN
american_scientific_journal-4814	22	8	vehicle	vehicle	NOUN
american_scientific_journal-4814	22	9	2.1	2.1	NUM
american_scientific_journal-4814	22	10	.	.	PUNCT
american_scientific_journal-4814	23	1	formulation	formulation	NOUN
american_scientific_journal-4814	23	2	and	and	CCONJ
american_scientific_journal-4814	23	3	parameterization	parameterization	NOUN
american_scientific_journal-4814	23	4	of	of	ADP
american_scientific_journal-4814	23	5	the	the	DET
american_scientific_journal-4814	23	6	space	space	NOUN
american_scientific_journal-4814	23	7	vehicle	vehicle	NOUN
american_scientific_journal-4814	23	8	motion	motion	NOUN
american_scientific_journal-4814	23	9	the	the	DET
american_scientific_journal-4814	23	10	mechanical	mechanical	ADJ
american_scientific_journal-4814	23	11	system	system	NOUN
american_scientific_journal-4814	23	12	(	(	PUNCT
american_scientific_journal-4814	23	13	𝔅𝔅	𝔅𝔅	PROPN
american_scientific_journal-4814	23	14	)	)	PUNCT
american_scientific_journal-4814	23	15	studied	study	VERB
american_scientific_journal-4814	23	16	is	be	AUX
american_scientific_journal-4814	23	17	composed	compose	VERB
american_scientific_journal-4814	23	18	of	of	ADP
american_scientific_journal-4814	23	19	a	a	DET
american_scientific_journal-4814	23	20	central	central	ADJ
american_scientific_journal-4814	23	21	rigid	rigid	ADJ
american_scientific_journal-4814	23	22	body	body	NOUN
american_scientific_journal-4814	23	23	(	(	PUNCT
american_scientific_journal-4814	23	24	𝔅𝔅0	𝔅𝔅0	PROPN
american_scientific_journal-4814	23	25	)	)	PUNCT
american_scientific_journal-4814	23	26	linked	link	VERB
american_scientific_journal-4814	23	27	symmetrically	symmetrically	ADV
american_scientific_journal-4814	23	28	to	to	ADP
american_scientific_journal-4814	23	29	two	two	NUM
american_scientific_journal-4814	23	30	solar	solar	ADJ
american_scientific_journal-4814	23	31	arrays	array	NOUN
american_scientific_journal-4814	23	32	(	(	PUNCT
american_scientific_journal-4814	23	33	𝔅𝔅1	𝔅𝔅1	PROPN
american_scientific_journal-4814	23	34	)	)	PUNCT
american_scientific_journal-4814	23	35	and	and	CCONJ
american_scientific_journal-4814	23	36	(	(	PUNCT
american_scientific_journal-4814	23	37	𝔅𝔅2	𝔅𝔅2	PROPN
american_scientific_journal-4814	23	38	)	)	PUNCT
american_scientific_journal-4814	23	39	by	by	ADP
american_scientific_journal-4814	23	40	means	mean	NOUN
american_scientific_journal-4814	23	41	of	of	ADP
american_scientific_journal-4814	23	42	two	two	NUM
american_scientific_journal-4814	23	43	rigid	rigid	ADJ
american_scientific_journal-4814	23	44	pieces	piece	NOUN
american_scientific_journal-4814	23	45	(	(	PUNCT
american_scientific_journal-4814	23	46	𝛾𝛾1	𝛾𝛾1	NOUN
american_scientific_journal-4814	23	47	)	)	PUNCT
american_scientific_journal-4814	23	48	and	and	CCONJ
american_scientific_journal-4814	23	49	(	(	PUNCT
american_scientific_journal-4814	23	50	𝛾𝛾2	𝛾𝛾2	NOUN
american_scientific_journal-4814	23	51	)	)	PUNCT
american_scientific_journal-4814	23	52	in	in	ADP
american_scientific_journal-4814	23	53	two	two	NUM
american_scientific_journal-4814	23	54	points	point	NOUN
american_scientific_journal-4814	23	55	𝑂𝑂1and	𝑂𝑂1and	VERB
american_scientific_journal-4814	23	56	𝑂𝑂2	𝑂𝑂2	PROPN
american_scientific_journal-4814	23	57	respectively	respectively	ADV
american_scientific_journal-4814	23	58	.	.	PUNCT
american_scientific_journal-4814	24	1	each	each	DET
american_scientific_journal-4814	24	2	array	array	NOUN
american_scientific_journal-4814	24	3	(	(	PUNCT
american_scientific_journal-4814	24	4	𝔅𝔅𝑖𝑖	𝔅𝔅𝑖𝑖	PROPN
american_scientific_journal-4814	24	5	)	)	PUNCT
american_scientific_journal-4814	24	6	(	(	PUNCT
american_scientific_journal-4814	24	7	𝑖𝑖	𝑖𝑖	NOUN
american_scientific_journal-4814	24	8	=	=	SYM
american_scientific_journal-4814	24	9	1	1	NUM
american_scientific_journal-4814	24	10	or	or	CCONJ
american_scientific_journal-4814	24	11	2	2	NUM
american_scientific_journal-4814	24	12	)	)	PUNCT
american_scientific_journal-4814	24	13	is	be	AUX
american_scientific_journal-4814	24	14	composed	compose	VERB
american_scientific_journal-4814	24	15	of	of	ADP
american_scientific_journal-4814	24	16	a	a	DET
american_scientific_journal-4814	24	17	supporting	support	VERB
american_scientific_journal-4814	24	18	piece	piece	NOUN
american_scientific_journal-4814	24	19	(	(	PUNCT
american_scientific_journal-4814	24	20	𝑆𝑆𝑆𝑆𝑖𝑖	𝑆𝑆𝑆𝑆𝑖𝑖	PROPN
american_scientific_journal-4814	24	21	)	)	PUNCT
american_scientific_journal-4814	24	22	,	,	PUNCT
american_scientific_journal-4814	24	23	a	a	DET
american_scientific_journal-4814	24	24	membrane	membrane	NOUN
american_scientific_journal-4814	24	25	(	(	PUNCT
american_scientific_journal-4814	24	26	𝐵𝐵𝐵𝐵𝑖𝑖	𝐵𝐵𝐵𝐵𝑖𝑖	PROPN
american_scientific_journal-4814	24	27	)	)	PUNCT
american_scientific_journal-4814	24	28	and	and	CCONJ
american_scientific_journal-4814	24	29	a	a	DET
american_scientific_journal-4814	24	30	tip	tip	NOUN
american_scientific_journal-4814	24	31	piece	piece	NOUN
american_scientific_journal-4814	24	32	(	(	PUNCT
american_scientific_journal-4814	24	33	𝑇𝑇𝑆𝑆𝑖𝑖	𝑇𝑇𝑆𝑆𝑖𝑖	NUM
american_scientific_journal-4814	24	34	)	)	PUNCT
american_scientific_journal-4814	24	35	.	.	PUNCT
american_scientific_journal-4814	25	1	the	the	DET
american_scientific_journal-4814	25	2	solar	solar	ADJ
american_scientific_journal-4814	25	3	arrays	array	NOUN
american_scientific_journal-4814	25	4	have	have	VERB
american_scientific_journal-4814	25	5	the	the	DET
american_scientific_journal-4814	25	6	same	same	ADJ
american_scientific_journal-4814	25	7	physical	physical	ADJ
american_scientific_journal-4814	25	8	characteristics	characteristic	NOUN
american_scientific_journal-4814	25	9	.	.	PUNCT
american_scientific_journal-4814	26	1	one	one	NUM
american_scientific_journal-4814	26	2	notes	note	VERB
american_scientific_journal-4814	26	3	ℜ(𝑡𝑡	ℜ(𝑡𝑡	NOUN
american_scientific_journal-4814	26	4	)	)	PUNCT
american_scientific_journal-4814	26	5	=	=	SYM
american_scientific_journal-4814	26	6	�	�	PROPN
american_scientific_journal-4814	26	7	𝑂𝑂0	𝑂𝑂0	PROPN
american_scientific_journal-4814	26	8	;	;	PUNCT
american_scientific_journal-4814	26	9	�	�	PROPN
american_scientific_journal-4814	26	10	⃗	⃗	PROPN
american_scientific_journal-4814	26	11	�	�	PROPN
american_scientific_journal-4814	26	12	𝑋0,𝑌𝑌	𝑋0,𝑌𝑌	NOUN
american_scientific_journal-4814	26	13	�	�	PROPN
american_scientific_journal-4814	26	14	⃗0,𝑍𝑍0	⃗0,𝑍𝑍0	NOUN
american_scientific_journal-4814	26	15	�	�	NOUN
american_scientific_journal-4814	26	16	the	the	DET
american_scientific_journal-4814	26	17	central	central	ADJ
american_scientific_journal-4814	26	18	reference	reference	NOUN
american_scientific_journal-4814	26	19	frame	frame	NOUN
american_scientific_journal-4814	26	20	which	which	PRON
american_scientific_journal-4814	26	21	is	be	AUX
american_scientific_journal-4814	26	22	rigidly	rigidly	ADV
american_scientific_journal-4814	26	23	joined	join	VERB
american_scientific_journal-4814	26	24	to	to	ADP
american_scientific_journal-4814	26	25	(	(	PUNCT
american_scientific_journal-4814	26	26	𝔅𝔅0	𝔅𝔅0	PROPN
american_scientific_journal-4814	26	27	)	)	PUNCT
american_scientific_journal-4814	26	28	of	of	ADP
american_scientific_journal-4814	26	29	mass	mass	PROPN
american_scientific_journal-4814	26	30	center	center	PROPN
american_scientific_journal-4814	26	31	𝑂𝑂0	𝑂𝑂0	PROPN
american_scientific_journal-4814	26	32	.	.	PUNCT
american_scientific_journal-4814	27	1	ℜ𝐺𝐺	ℜ𝐺𝐺	PROPN
american_scientific_journal-4814	27	2	=	=	SYM
american_scientific_journal-4814	27	3	�	�	PROPN
american_scientific_journal-4814	27	4	𝐺𝐺	𝐺𝐺	PROPN
american_scientific_journal-4814	27	5	;	;	PUNCT
american_scientific_journal-4814	27	6	�	�	PROPN
american_scientific_journal-4814	27	7	⃗	⃗	PROPN
american_scientific_journal-4814	27	8	�	�	PROPN
american_scientific_journal-4814	27	9	𝑎	𝑎	NOUN
american_scientific_journal-4814	27	10	,	,	PUNCT
american_scientific_journal-4814	27	11	𝑏𝑏	𝑏𝑏	PRON
american_scientific_journal-4814	27	12	�	�	NOUN
american_scientific_journal-4814	27	13	⃗	⃗	PROPN
american_scientific_journal-4814	27	14	,	,	PUNCT
american_scientific_journal-4814	27	15	𝑐𝑐	𝑐𝑐	PROPN
american_scientific_journal-4814	27	16	�	�	PROPN
american_scientific_journal-4814	27	17	is	be	AUX
american_scientific_journal-4814	27	18	the	the	DET
american_scientific_journal-4814	27	19	orthonormal	orthonormal	ADJ
american_scientific_journal-4814	27	20	orbiting	orbiting	ADJ
american_scientific_journal-4814	27	21	reference	reference	NOUN
american_scientific_journal-4814	27	22	of	of	ADP
american_scientific_journal-4814	27	23	origin	origin	NOUN
american_scientific_journal-4814	27	24	𝐺𝐺	𝐺𝐺	PROPN
american_scientific_journal-4814	27	25	which	which	PRON
american_scientific_journal-4814	27	26	is	be	AUX
american_scientific_journal-4814	27	27	the	the	DET
american_scientific_journal-4814	27	28	mass	mass	ADJ
american_scientific_journal-4814	27	29	center	center	NOUN
american_scientific_journal-4814	27	30	of	of	ADP
american_scientific_journal-4814	27	31	the	the	DET
american_scientific_journal-4814	27	32	whole	whole	ADJ
american_scientific_journal-4814	27	33	system	system	NOUN
american_scientific_journal-4814	27	34	deformed	deform	VERB
american_scientific_journal-4814	27	35	.	.	PUNCT
american_scientific_journal-4814	28	1	the	the	DET
american_scientific_journal-4814	28	2	solar	solar	ADJ
american_scientific_journal-4814	28	3	arrays	array	NOUN
american_scientific_journal-4814	28	4	are	be	AUX
american_scientific_journal-4814	28	5	modelled	model	VERB
american_scientific_journal-4814	28	6	by	by	ADP
american_scientific_journal-4814	28	7	rectangular	rectangular	ADJ
american_scientific_journal-4814	28	8	membranes	membrane	NOUN
american_scientific_journal-4814	28	9	of	of	ADP
american_scientific_journal-4814	28	10	constant	constant	ADJ
american_scientific_journal-4814	28	11	surface	surface	NOUN
american_scientific_journal-4814	28	12	density	density	NOUN
american_scientific_journal-4814	28	13	𝜎𝜎.	𝜎𝜎.	NOUN
american_scientific_journal-4814	28	14	the	the	DET
american_scientific_journal-4814	28	15	width	width	NOUN
american_scientific_journal-4814	28	16	and	and	CCONJ
american_scientific_journal-4814	28	17	length	length	NOUN
american_scientific_journal-4814	28	18	of	of	ADP
american_scientific_journal-4814	28	19	each	each	DET
american_scientific_journal-4814	28	20	solar	solar	ADJ
american_scientific_journal-4814	28	21	array	array	NOUN
american_scientific_journal-4814	28	22	in	in	ADP
american_scientific_journal-4814	28	23	its	its	PRON
american_scientific_journal-4814	28	24	underformed	underformed	ADJ
american_scientific_journal-4814	28	25	position	position	NOUN
american_scientific_journal-4814	28	26	are	be	AUX
american_scientific_journal-4814	28	27	denoted	denote	VERB
american_scientific_journal-4814	28	28	by	by	ADP
american_scientific_journal-4814	28	29	𝑒𝑒	𝑒𝑒	NOUN
american_scientific_journal-4814	28	30	and	and	CCONJ
american_scientific_journal-4814	28	31	𝑙𝑙	𝑙𝑙	X
american_scientific_journal-4814	28	32	respectively	respectively	ADV
american_scientific_journal-4814	28	33	.	.	PUNCT
american_scientific_journal-4814	29	1	the	the	DET
american_scientific_journal-4814	29	2	plane	plane	NOUN
american_scientific_journal-4814	29	3	�	�	PROPN
american_scientific_journal-4814	29	4	𝑂𝑂0	𝑂𝑂0	PROPN
american_scientific_journal-4814	29	5	;	;	PUNCT
american_scientific_journal-4814	29	6	�	�	PROPN
american_scientific_journal-4814	29	7	⃗	⃗	NOUN
american_scientific_journal-4814	29	8	�	�	PROPN
american_scientific_journal-4814	29	9	𝑋0,𝑍𝑍0	𝑋0,𝑍𝑍0	NOUN
american_scientific_journal-4814	29	10	�	�	PROPN
american_scientific_journal-4814	29	11	designates	designate	VERB
american_scientific_journal-4814	29	12	the	the	DET
american_scientific_journal-4814	29	13	whole	whole	ADJ
american_scientific_journal-4814	29	14	system	system	NOUN
american_scientific_journal-4814	29	15	symmetric	symmetric	ADJ
american_scientific_journal-4814	29	16	plane	plane	NOUN
american_scientific_journal-4814	29	17	in	in	ADP
american_scientific_journal-4814	29	18	its	its	PRON
american_scientific_journal-4814	29	19	underformed	underformed	ADJ
american_scientific_journal-4814	29	20	position	position	NOUN
american_scientific_journal-4814	29	21	(	(	PUNCT
american_scientific_journal-4814	29	22	see	see	VERB
american_scientific_journal-4814	29	23	figure	figure	NOUN
american_scientific_journal-4814	29	24	1	1	NUM
american_scientific_journal-4814	29	25	)	)	PUNCT
american_scientific_journal-4814	29	26	.	.	PUNCT
american_scientific_journal-4814	30	1	the	the	DET
american_scientific_journal-4814	30	2	inertial	inertial	ADJ
american_scientific_journal-4814	30	3	frame	frame	NOUN
american_scientific_journal-4814	30	4	reference	reference	NOUN
american_scientific_journal-4814	30	5	is	be	AUX
american_scientific_journal-4814	30	6	denoted	denote	VERB
american_scientific_journal-4814	30	7	by	by	ADP
american_scientific_journal-4814	30	8	ℜ𝑇𝑇	ℜ𝑇𝑇	PROPN
american_scientific_journal-4814	30	9	=	=	SYM
american_scientific_journal-4814	30	10	�	�	PROPN
american_scientific_journal-4814	30	11	𝑇𝑇	𝑇𝑇	PROPN
american_scientific_journal-4814	30	12	;	;	PUNCT
american_scientific_journal-4814	30	13	�	�	PROPN
american_scientific_journal-4814	30	14	⃗	⃗	PROPN
american_scientific_journal-4814	30	15	�	�	PROPN
american_scientific_journal-4814	30	16	𝑋,𝑌𝑌	𝑋,𝑌𝑌	NOUN
american_scientific_journal-4814	30	17	�	�	NOUN
american_scientific_journal-4814	30	18	⃗	⃗	PROPN
american_scientific_journal-4814	30	19	,	,	PUNCT
american_scientific_journal-4814	30	20	𝑍𝑍	𝑍𝑍	PROPN
american_scientific_journal-4814	30	21	�	�	PROPN
american_scientific_journal-4814	30	22	.	.	PROPN
american_scientific_journal-4814	31	1	relative	relative	ADJ
american_scientific_journal-4814	31	2	to	to	ADP
american_scientific_journal-4814	31	3	ℜ𝑇𝑇	ℜ𝑇𝑇	PROPN
american_scientific_journal-4814	31	4	,	,	PUNCT
american_scientific_journal-4814	31	5	the	the	DET
american_scientific_journal-4814	31	6	frame	frame	NOUN
american_scientific_journal-4814	31	7	ℜ𝐺𝐺	ℜ𝐺𝐺	PROPN
american_scientific_journal-4814	31	8	is	be	AUX
american_scientific_journal-4814	31	9	spinning	spin	VERB
american_scientific_journal-4814	31	10	around	around	ADP
american_scientific_journal-4814	31	11	the	the	DET
american_scientific_journal-4814	31	12	axis	axis	PROPN
american_scientific_journal-4814	31	13	�	�	PROPN
american_scientific_journal-4814	31	14	𝑇𝑇;𝑍𝑍	𝑇𝑇;𝑍𝑍	PROPN
american_scientific_journal-4814	31	15	�	�	PROPN
american_scientific_journal-4814	31	16	with	with	ADP
american_scientific_journal-4814	31	17	a	a	DET
american_scientific_journal-4814	31	18	constant	constant	ADJ
american_scientific_journal-4814	31	19	angular	angular	ADJ
american_scientific_journal-4814	31	20	speed	speed	NOUN
american_scientific_journal-4814	31	21	𝑛𝑛0	𝑛𝑛0	NOUN
american_scientific_journal-4814	31	22	.	.	PUNCT
american_scientific_journal-4814	32	1	during	during	ADP
american_scientific_journal-4814	32	2	its	its	PRON
american_scientific_journal-4814	32	3	orbital	orbital	ADJ
american_scientific_journal-4814	32	4	motion	motion	NOUN
american_scientific_journal-4814	32	5	,	,	PUNCT
american_scientific_journal-4814	32	6	the	the	DET
american_scientific_journal-4814	32	7	frame	frame	NOUN
american_scientific_journal-4814	32	8	ℜ𝐺𝐺	ℜ𝐺𝐺	PROPN
american_scientific_journal-4814	32	9	drives	drive	VERB
american_scientific_journal-4814	32	10	the	the	DET
american_scientific_journal-4814	32	11	whole	whole	ADJ
american_scientific_journal-4814	32	12	space	space	NOUN
american_scientific_journal-4814	32	13	vehicle	vehicle	NOUN
american_scientific_journal-4814	32	14	(	(	PUNCT
american_scientific_journal-4814	32	15	𝔅𝔅	𝔅𝔅	PROPN
american_scientific_journal-4814	32	16	)	)	PUNCT
american_scientific_journal-4814	32	17	which	which	PRON
american_scientific_journal-4814	32	18	mass	mass	ADJ
american_scientific_journal-4814	32	19	center	center	NOUN
american_scientific_journal-4814	32	20	𝐺𝐺	𝐺𝐺	NOUN
american_scientific_journal-4814	32	21	is	be	AUX
american_scientific_journal-4814	32	22	supposed	suppose	VERB
american_scientific_journal-4814	32	23	to	to	PART
american_scientific_journal-4814	32	24	describe	describe	VERB
american_scientific_journal-4814	32	25	a	a	DET
american_scientific_journal-4814	32	26	circular	circular	ADJ
american_scientific_journal-4814	32	27	orbit	orbit	NOUN
american_scientific_journal-4814	32	28	of	of	ADP
american_scientific_journal-4814	32	29	center	center	NOUN
american_scientific_journal-4814	32	30	𝑇𝑇	𝑇𝑇	PROPN
american_scientific_journal-4814	32	31	in	in	ADP
american_scientific_journal-4814	32	32	the	the	DET
american_scientific_journal-4814	32	33	plane	plane	NOUN
american_scientific_journal-4814	32	34	�	�	NOUN
american_scientific_journal-4814	32	35	𝑇𝑇	𝑇𝑇	PROPN
american_scientific_journal-4814	32	36	;	;	PUNCT
american_scientific_journal-4814	32	37	�	�	PROPN
american_scientific_journal-4814	32	38	⃗	⃗	PROPN
american_scientific_journal-4814	32	39	�	�	PROPN
american_scientific_journal-4814	32	40	𝑋,𝑌𝑌	𝑋,𝑌𝑌	NUM
american_scientific_journal-4814	32	41	�	�	PROPN
american_scientific_journal-4814	32	42	⃗	⃗	PROPN
american_scientific_journal-4814	32	43	�	�	PROPN
american_scientific_journal-4814	32	44	(	(	PUNCT
american_scientific_journal-4814	32	45	see	see	VERB
american_scientific_journal-4814	32	46	figure	figure	NOUN
american_scientific_journal-4814	32	47	2	2	NUM
american_scientific_journal-4814	32	48	)	)	PUNCT
american_scientific_journal-4814	32	49	.	.	PUNCT
american_scientific_journal-4814	33	1	the	the	DET
american_scientific_journal-4814	33	2	equilibrium	equilibrium	NOUN
american_scientific_journal-4814	33	3	position	position	NOUN
american_scientific_journal-4814	33	4	of	of	ADP
american_scientific_journal-4814	33	5	the	the	DET
american_scientific_journal-4814	33	6	space	space	NOUN
american_scientific_journal-4814	33	7	vehicle	vehicle	NOUN
american_scientific_journal-4814	33	8	(	(	PUNCT
american_scientific_journal-4814	33	9	𝔅𝔅	𝔅𝔅	PROPN
american_scientific_journal-4814	33	10	)	)	PUNCT
american_scientific_journal-4814	33	11	with	with	ADP
american_scientific_journal-4814	33	12	respect	respect	NOUN
american_scientific_journal-4814	33	13	to	to	ADP
american_scientific_journal-4814	33	14	the	the	DET
american_scientific_journal-4814	33	15	orbital	orbital	ADJ
american_scientific_journal-4814	33	16	reference	reference	NOUN
american_scientific_journal-4814	33	17	frame	frame	NOUN
american_scientific_journal-4814	33	18	is	be	AUX
american_scientific_journal-4814	33	19	perturbed	perturb	VERB
american_scientific_journal-4814	33	20	by	by	ADP
american_scientific_journal-4814	33	21	its	its	PRON
american_scientific_journal-4814	33	22	small	small	ADJ
american_scientific_journal-4814	33	23	lace	lace	NOUN
american_scientific_journal-4814	33	24	attitude	attitude	NOUN
american_scientific_journal-4814	33	25	motions	motion	NOUN
american_scientific_journal-4814	33	26	of	of	ADP
american_scientific_journal-4814	33	27	angle	angle	NOUN
american_scientific_journal-4814	33	28	𝜃𝜃(𝑡𝑡	𝜃𝜃(𝑡𝑡	NOUN
american_scientific_journal-4814	33	29	)	)	PUNCT
american_scientific_journal-4814	33	30	interacting	interact	VERB
american_scientific_journal-4814	33	31	with	with	ADP
american_scientific_journal-4814	33	32	the	the	DET
american_scientific_journal-4814	33	33	solar	solar	ADJ
american_scientific_journal-4814	33	34	arrays	array	VERB
american_scientific_journal-4814	33	35	elastic	elastic	ADJ
american_scientific_journal-4814	33	36	deformations	deformation	NOUN
american_scientific_journal-4814	33	37	,	,	PUNCT
american_scientific_journal-4814	33	38	represented	represent	VERB
american_scientific_journal-4814	33	39	by	by	ADP
american_scientific_journal-4814	33	40	the	the	DET
american_scientific_journal-4814	33	41	vector	vector	NOUN
american_scientific_journal-4814	33	42	𝑑𝑑𝑖𝑖	𝑑𝑑𝑖𝑖	NOUN
american_scientific_journal-4814	33	43	(	(	PUNCT
american_scientific_journal-4814	33	44	see	see	VERB
american_scientific_journal-4814	33	45	figure	figure	NOUN
american_scientific_journal-4814	33	46	4	4	NUM
american_scientific_journal-4814	33	47	):	):	PUNCT
american_scientific_journal-4814	33	48	𝑑𝑑𝑖𝑖(𝑀𝑀	𝑑𝑑𝑖𝑖(𝑀𝑀	NOUN
american_scientific_journal-4814	33	49	,	,	PUNCT
american_scientific_journal-4814	33	50	𝑡𝑡	𝑡𝑡	PROPN
american_scientific_journal-4814	33	51	)	)	PUNCT
american_scientific_journal-4814	33	52	=	=	SYM
american_scientific_journal-4814	34	1	(	(	PUNCT
american_scientific_journal-4814	34	2	𝑢𝑢𝑖𝑖(𝑠𝑠	𝑢𝑢𝑖𝑖(𝑠𝑠	NOUN
american_scientific_journal-4814	34	3	,	,	PUNCT
american_scientific_journal-4814	34	4	𝑡𝑡	𝑡𝑡	NOUN
american_scientific_journal-4814	34	5	)	)	PUNCT
american_scientific_journal-4814	34	6	,	,	PUNCT
american_scientific_journal-4814	34	7	0	0	NUM
american_scientific_journal-4814	34	8	,	,	PUNCT
american_scientific_journal-4814	34	9	0)𝑇𝑇	0)𝑇𝑇	NOUN
american_scientific_journal-4814	34	10	;	;	PUNCT
american_scientific_journal-4814	34	11	𝑠𝑠	𝑠𝑠	PRON
american_scientific_journal-4814	34	12	∈	∈	PROPN
american_scientific_journal-4814	35	1	[	[	X
american_scientific_journal-4814	35	2	0	0	NUM
american_scientific_journal-4814	35	3	;	;	PUNCT
american_scientific_journal-4814	35	4	𝑙𝑙	𝑙𝑙	X
american_scientific_journal-4814	35	5	]	]	PUNCT
american_scientific_journal-4814	35	6	;	;	PUNCT
american_scientific_journal-4814	35	7	on	on	ADP
american_scientific_journal-4814	35	8	(	(	PUNCT
american_scientific_journal-4814	35	9	𝑆𝑆𝑆𝑆𝑖𝑖	𝑆𝑆𝑆𝑆𝑖𝑖	PROPN
american_scientific_journal-4814	35	10	)	)	PUNCT
american_scientific_journal-4814	35	11	;	;	PUNCT
american_scientific_journal-4814	35	12	𝑑𝑑𝑖𝑖(𝑀𝑀	𝑑𝑑𝑖𝑖(𝑀𝑀	NOUN
american_scientific_journal-4814	35	13	,	,	PUNCT
american_scientific_journal-4814	35	14	𝑡𝑡	𝑡𝑡	PROPN
american_scientific_journal-4814	35	15	)	)	PUNCT
american_scientific_journal-4814	35	16	=	=	SYM
american_scientific_journal-4814	35	17	(	(	PUNCT
american_scientific_journal-4814	35	18	𝛼𝛼𝑖𝑖(𝑥𝑥	𝛼𝛼𝑖𝑖(𝑥𝑥	PROPN
american_scientific_journal-4814	35	19	,	,	PUNCT
american_scientific_journal-4814	35	20	𝑠𝑠	𝑠𝑠	ADP
american_scientific_journal-4814	35	21	,	,	PUNCT
american_scientific_journal-4814	35	22	𝑡𝑡	𝑡𝑡	ADJ
american_scientific_journal-4814	35	23	)	)	PUNCT
american_scientific_journal-4814	35	24	,	,	PUNCT
american_scientific_journal-4814	35	25	0	0	NUM
american_scientific_journal-4814	35	26	,	,	PUNCT
american_scientific_journal-4814	35	27	0)𝑇𝑇	0)𝑇𝑇	NOUN
american_scientific_journal-4814	35	28	(	(	PUNCT
american_scientific_journal-4814	35	29	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-4814	35	30	,	,	PUNCT
american_scientific_journal-4814	35	31	𝑠𝑠	𝑠𝑠	PRON
american_scientific_journal-4814	35	32	)	)	PUNCT
american_scientific_journal-4814	35	33	∈	∈	PROPN
american_scientific_journal-4814	35	34	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-4814	35	35	;	;	PUNCT
american_scientific_journal-4814	35	36	on	on	ADP
american_scientific_journal-4814	35	37	(	(	PUNCT
american_scientific_journal-4814	35	38	𝐵𝐵𝐵𝐵𝑖𝑖	𝐵𝐵𝐵𝐵𝑖𝑖	PROPN
american_scientific_journal-4814	35	39	)	)	PUNCT
american_scientific_journal-4814	35	40	.	.	PUNCT
american_scientific_journal-4814	36	1	on	on	ADP
american_scientific_journal-4814	36	2	(	(	PUNCT
american_scientific_journal-4814	36	3	𝑇𝑇𝑆𝑆𝑖𝑖	𝑇𝑇𝑆𝑆𝑖𝑖	NUM
american_scientific_journal-4814	36	4	)	)	PUNCT
american_scientific_journal-4814	36	5	the	the	DET
american_scientific_journal-4814	36	6	displacements	displacement	NOUN
american_scientific_journal-4814	36	7	field	field	NOUN
american_scientific_journal-4814	36	8	𝑑𝑑𝑖𝑖	𝑑𝑑𝑖𝑖	NOUN
american_scientific_journal-4814	36	9	are	be	AUX
american_scientific_journal-4814	36	10	obtained	obtain	VERB
american_scientific_journal-4814	36	11	by	by	ADP
american_scientific_journal-4814	36	12	the	the	DET
american_scientific_journal-4814	36	13	boundary	boundary	ADJ
american_scientific_journal-4814	36	14	condition	condition	NOUN
american_scientific_journal-4814	36	15	applied	apply	VERB
american_scientific_journal-4814	36	16	on	on	ADP
american_scientific_journal-4814	36	17	(	(	PUNCT
american_scientific_journal-4814	36	18	𝐵𝐵𝐵𝐵𝑖𝑖	𝐵𝐵𝐵𝐵𝑖𝑖	PROPN
american_scientific_journal-4814	36	19	)	)	PUNCT
american_scientific_journal-4814	36	20	and	and	CCONJ
american_scientific_journal-4814	36	21	(	(	PUNCT
american_scientific_journal-4814	36	22	𝑆𝑆𝑆𝑆𝑖𝑖	𝑆𝑆𝑆𝑆𝑖𝑖	PROPN
american_scientific_journal-4814	36	23	)	)	PUNCT
american_scientific_journal-4814	36	24	.	.	PUNCT
american_scientific_journal-4814	37	1	the	the	DET
american_scientific_journal-4814	37	2	vector	vector	NOUN
american_scientific_journal-4814	37	3	𝑑𝑑𝑖𝑖	𝑑𝑑𝑖𝑖	NOUN
american_scientific_journal-4814	37	4	is	be	AUX
american_scientific_journal-4814	37	5	measured	measure	VERB
american_scientific_journal-4814	37	6	in	in	ADP
american_scientific_journal-4814	37	7	the	the	DET
american_scientific_journal-4814	37	8	frame	frame	NOUN
american_scientific_journal-4814	37	9	components	component	NOUN
american_scientific_journal-4814	37	10	ℜ(𝑡𝑡	ℜ(𝑡𝑡	NOUN
american_scientific_journal-4814	37	11	)	)	PUNCT
american_scientific_journal-4814	37	12	.	.	PUNCT
american_scientific_journal-4814	38	1	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-4814	38	2	is	be	AUX
american_scientific_journal-4814	38	3	the	the	DET
american_scientific_journal-4814	38	4	integration	integration	NOUN
american_scientific_journal-4814	38	5	domain	domain	NOUN
american_scientific_journal-4814	38	6	representing	represent	VERB
american_scientific_journal-4814	38	7	the	the	DET
american_scientific_journal-4814	38	8	rectangular	rectangular	ADJ
american_scientific_journal-4814	38	9	membrane	membrane	NOUN
american_scientific_journal-4814	38	10	(	(	PUNCT
american_scientific_journal-4814	38	11	𝐵𝐵𝐵𝐵𝑖𝑖	𝐵𝐵𝐵𝐵𝑖𝑖	NOUN
american_scientific_journal-4814	38	12	)	)	PUNCT
american_scientific_journal-4814	38	13	defined	define	VERB
american_scientific_journal-4814	38	14	as	as	SCONJ
american_scientific_journal-4814	38	15	follows	follow	VERB
american_scientific_journal-4814	38	16	:	:	PUNCT
american_scientific_journal-4814	38	17	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-4814	38	18	=	=	SYM
american_scientific_journal-4814	38	19	�	�	PROPN
american_scientific_journal-4814	38	20	(	(	PUNCT
american_scientific_journal-4814	38	21	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-4814	38	22	,	,	PUNCT
american_scientific_journal-4814	38	23	𝑠𝑠	𝑠𝑠	PRON
american_scientific_journal-4814	38	24	)	)	PUNCT
american_scientific_journal-4814	38	25	/	/	SYM
american_scientific_journal-4814	38	26	−𝑒𝑒	−𝑒𝑒	PROPN
american_scientific_journal-4814	38	27	2	2	NUM
american_scientific_journal-4814	38	28	≤	≤	NOUN
american_scientific_journal-4814	38	29	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-4814	38	30	≤	≤	NOUN
american_scientific_journal-4814	38	31	+	+	PROPN
american_scientific_journal-4814	38	32	𝑒𝑒	𝑒𝑒	X
american_scientific_journal-4814	38	33	2	2	NUM
american_scientific_journal-4814	38	34	,	,	PUNCT
american_scientific_journal-4814	38	35	0	0	NUM
american_scientific_journal-4814	38	36	≤	≤	NUM
american_scientific_journal-4814	38	37	𝑠𝑠	𝑠𝑠	ADV
american_scientific_journal-4814	38	38	≤	≤	NUM
american_scientific_journal-4814	38	39	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-4814	38	40	�	�	PROPN
american_scientific_journal-4814	38	41	.	.	PUNCT
american_scientific_journal-4814	39	1	for	for	ADP
american_scientific_journal-4814	39	2	the	the	DET
american_scientific_journal-4814	39	3	remainder	remainder	NOUN
american_scientific_journal-4814	39	4	,	,	PUNCT
american_scientific_journal-4814	39	5	for	for	ADP
american_scientific_journal-4814	39	6	any	any	DET
american_scientific_journal-4814	39	7	function	function	NOUN
american_scientific_journal-4814	39	8	f	f	NOUN
american_scientific_journal-4814	39	9	depending	depend	VERB
american_scientific_journal-4814	39	10	on	on	ADP
american_scientific_journal-4814	39	11	the	the	DET
american_scientific_journal-4814	39	12	spatial	spatial	ADJ
american_scientific_journal-4814	39	13	variable	variable	NOUN
american_scientific_journal-4814	39	14	𝑠𝑠	𝑠𝑠	ADP
american_scientific_journal-4814	39	15	and	and	CCONJ
american_scientific_journal-4814	39	16	the	the	DET
american_scientific_journal-4814	39	17	time	time	NOUN
american_scientific_journal-4814	39	18	𝑡𝑡	𝑡𝑡	PROPN
american_scientific_journal-4814	39	19	,	,	PUNCT
american_scientific_journal-4814	39	20	one	one	NUM
american_scientific_journal-4814	39	21	notes	note	VERB
american_scientific_journal-4814	39	22	:	:	PUNCT
american_scientific_journal-4814	39	23	american	american	ADJ
american_scientific_journal-4814	39	24	scientific	scientific	ADJ
american_scientific_journal-4814	39	25	research	research	PROPN
american_scientific_journal-4814	39	26	journal	journal	NOUN
american_scientific_journal-4814	39	27	for	for	ADP
american_scientific_journal-4814	39	28	engineering	engineering	NOUN
american_scientific_journal-4814	39	29	,	,	PUNCT
american_scientific_journal-4814	39	30	technology	technology	NOUN
american_scientific_journal-4814	39	31	,	,	PUNCT
american_scientific_journal-4814	39	32	and	and	CCONJ
american_scientific_journal-4814	39	33	sciences	science	NOUN
american_scientific_journal-4814	39	34	(	(	PUNCT
american_scientific_journal-4814	39	35	asrjets	asrjet	NOUN
american_scientific_journal-4814	39	36	)	)	PUNCT
american_scientific_journal-4814	39	37	(	(	PUNCT
american_scientific_journal-4814	39	38	2019	2019	NUM
american_scientific_journal-4814	39	39	)	)	PUNCT
american_scientific_journal-4814	39	40	volume	volume	NOUN
american_scientific_journal-4814	39	41	55	55	NUM
american_scientific_journal-4814	39	42	,	,	PUNCT
american_scientific_journal-4814	39	43	no	no	DET
american_scientific_journal-4814	39	44	1	1	NUM
american_scientific_journal-4814	39	45	,	,	PUNCT
american_scientific_journal-4814	39	46	pp	pp	ADP
american_scientific_journal-4814	39	47	50	50	NUM
american_scientific_journal-4814	39	48	-	-	SYM
american_scientific_journal-4814	39	49	68	68	NUM
american_scientific_journal-4814	39	50	52	52	NUM
american_scientific_journal-4814	39	51	�	�	PROPN
american_scientific_journal-4814	39	52	̇	̇	PROPN
american_scientific_journal-4814	39	53	�	�	PROPN
american_scientific_journal-4814	39	54	𝐹	𝐹	NOUN
american_scientific_journal-4814	39	55	=	=	PUNCT
american_scientific_journal-4814	39	56	𝜕𝜕𝐹𝐹	𝜕𝜕𝐹𝐹	PROPN
american_scientific_journal-4814	39	57	𝜕𝜕𝑡𝑡	𝜕𝜕𝑡𝑡	NUM
american_scientific_journal-4814	39	58	,	,	PUNCT
american_scientific_journal-4814	39	59	�	�	PROPN
american_scientific_journal-4814	39	60	̈	̈	NOUN
american_scientific_journal-4814	39	61	�	�	NOUN
american_scientific_journal-4814	39	62	𝐹	𝐹	NOUN
american_scientific_journal-4814	39	63	=	=	PRON
american_scientific_journal-4814	39	64	𝜕𝜕2𝐹𝐹	𝜕𝜕2𝐹𝐹	NOUN
american_scientific_journal-4814	39	65	𝜕𝜕𝑡𝑡2	𝜕𝜕𝑡𝑡2	NOUN
american_scientific_journal-4814	39	66	,	,	PUNCT
american_scientific_journal-4814	40	1	𝐹𝐹′	𝐹𝐹′	NOUN
american_scientific_journal-4814	40	2	=	=	SYM
american_scientific_journal-4814	40	3	𝜕𝜕𝐹𝐹	𝜕𝜕𝐹𝐹	VERB
american_scientific_journal-4814	40	4	𝜕𝜕𝑠𝑠	𝜕𝜕𝑠𝑠	NOUN
american_scientific_journal-4814	40	5	,	,	PUNCT
american_scientific_journal-4814	40	6	𝐹𝐹′′	𝐹𝐹′′	NOUN
american_scientific_journal-4814	40	7	=	=	SYM
american_scientific_journal-4814	40	8	𝜕𝜕2𝐹𝐹	𝜕𝜕2𝐹𝐹	ADJ
american_scientific_journal-4814	40	9	𝜕𝜕𝑠𝑠2	𝜕𝜕𝑠𝑠2	NOUN
american_scientific_journal-4814	40	10	.	.	PUNCT
american_scientific_journal-4814	41	1	2.2	2.2	NUM
american_scientific_journal-4814	41	2	.	.	PUNCT
american_scientific_journal-4814	41	3	equations	equation	NOUN
american_scientific_journal-4814	41	4	of	of	ADP
american_scientific_journal-4814	41	5	the	the	DET
american_scientific_journal-4814	41	6	space	space	NOUN
american_scientific_journal-4814	41	7	vehicle	vehicle	NOUN
american_scientific_journal-4814	41	8	motion	motion	NOUN
american_scientific_journal-4814	41	9	by	by	ADP
american_scientific_journal-4814	41	10	the	the	DET
american_scientific_journal-4814	41	11	use	use	NOUN
american_scientific_journal-4814	41	12	of	of	ADP
american_scientific_journal-4814	41	13	the	the	DET
american_scientific_journal-4814	41	14	variational	variational	ADJ
american_scientific_journal-4814	41	15	principle	principle	NOUN
american_scientific_journal-4814	41	16	of	of	ADP
american_scientific_journal-4814	41	17	hamilton	hamilton	PROPN
american_scientific_journal-4814	41	18	,	,	PUNCT
american_scientific_journal-4814	41	19	one	one	PRON
american_scientific_journal-4814	41	20	gets	get	VERB
american_scientific_journal-4814	41	21	the	the	DET
american_scientific_journal-4814	41	22	equation	equation	NOUN
american_scientific_journal-4814	41	23	of	of	ADP
american_scientific_journal-4814	41	24	the	the	DET
american_scientific_journal-4814	41	25	global	global	ADJ
american_scientific_journal-4814	41	26	motion	motion	NOUN
american_scientific_journal-4814	41	27	and	and	CCONJ
american_scientific_journal-4814	41	28	the	the	DET
american_scientific_journal-4814	41	29	local	local	ADJ
american_scientific_journal-4814	41	30	equations	equation	NOUN
american_scientific_journal-4814	41	31	of	of	ADP
american_scientific_journal-4814	41	32	the	the	DET
american_scientific_journal-4814	41	33	flexible	flexible	ADJ
american_scientific_journal-4814	41	34	appendages	appendage	NOUN
american_scientific_journal-4814	41	35	motion	motion	NOUN
american_scientific_journal-4814	41	36	(	(	PUNCT
american_scientific_journal-4814	41	37	see	see	VERB
american_scientific_journal-4814	41	38	appendix	appendix	NOUN
american_scientific_journal-4814	41	39	2	2	NUM
american_scientific_journal-4814	41	40	):	):	PUNCT
american_scientific_journal-4814	41	41	•	•	NUM
american_scientific_journal-4814	41	42	equation	equation	NOUN
american_scientific_journal-4814	41	43	of	of	ADP
american_scientific_journal-4814	41	44	the	the	DET
american_scientific_journal-4814	41	45	global	global	ADJ
american_scientific_journal-4814	41	46	motion	motion	PROPN
american_scientific_journal-4814	41	47	𝐶𝐶	𝐶𝐶	PROPN
american_scientific_journal-4814	41	48	�	�	PROPN
american_scientific_journal-4814	41	49	̈	̈	X
american_scientific_journal-4814	41	50	�	�	NOUN
american_scientific_journal-4814	41	51	𝜃	𝜃	NOUN
american_scientific_journal-4814	41	52	+	+	NUM
american_scientific_journal-4814	41	53	3𝑛𝑛02(𝐵𝐵	3𝑛𝑛02(𝐵𝐵	NUM
american_scientific_journal-4814	41	54	−	−	NOUN
american_scientific_journal-4814	41	55	𝐴𝐴)𝜃𝜃	𝐴𝐴)𝜃𝜃	NOUN
american_scientific_journal-4814	41	56	+	+	CCONJ
american_scientific_journal-4814	41	57	�	�	PROPN
american_scientific_journal-4814	41	58	̈	̈	X
american_scientific_journal-4814	41	59	�	�	PROPN
american_scientific_journal-4814	41	60	𝑁𝑢𝑢∗	𝑁𝑢𝑢∗	ADJ
american_scientific_journal-4814	41	61	+	+	NUM
american_scientific_journal-4814	41	62	𝑛𝑛0	𝑛𝑛0	PROPN
american_scientific_journal-4814	41	63	�	�	NOUN
american_scientific_journal-4814	41	64	̇	̇	NOUN
american_scientific_journal-4814	41	65	�	�	PROPN
american_scientific_journal-4814	41	66	𝑁𝛼𝛼∗	𝑁𝛼𝛼∗	NOUN
american_scientific_journal-4814	41	67	+	+	PROPN
american_scientific_journal-4814	41	68	3𝑛𝑛02𝑁𝑁𝑢𝑢∗	3𝑛𝑛02𝑁𝑁𝑢𝑢∗	NUM
american_scientific_journal-4814	41	69	=	=	SYM
american_scientific_journal-4814	41	70	υ	υ	NOUN
american_scientific_journal-4814	41	71	.	.	PUNCT
american_scientific_journal-4814	42	1	(	(	PUNCT
american_scientific_journal-4814	42	2	1	1	X
american_scientific_journal-4814	42	3	)	)	PUNCT
american_scientific_journal-4814	42	4	where	where	SCONJ
american_scientific_journal-4814	42	5	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-4814	42	6	,	,	PUNCT
american_scientific_journal-4814	42	7	𝐵𝐵	𝐵𝐵	PROPN
american_scientific_journal-4814	42	8	and	and	CCONJ
american_scientific_journal-4814	42	9	𝐶𝐶	𝐶𝐶	PROPN
american_scientific_journal-4814	42	10	are	be	AUX
american_scientific_journal-4814	42	11	moments	moment	NOUN
american_scientific_journal-4814	42	12	of	of	ADP
american_scientific_journal-4814	42	13	inertia	inertia	NOUN
american_scientific_journal-4814	42	14	of	of	ADP
american_scientific_journal-4814	42	15	the	the	DET
american_scientific_journal-4814	42	16	space	space	NOUN
american_scientific_journal-4814	42	17	vehicle	vehicle	NOUN
american_scientific_journal-4814	42	18	and	and	CCONJ
american_scientific_journal-4814	42	19	υ	υ	NOUN
american_scientific_journal-4814	42	20	is	be	AUX
american_scientific_journal-4814	42	21	the	the	DET
american_scientific_journal-4814	42	22	external	external	ADJ
american_scientific_journal-4814	42	23	forces	force	NOUN
american_scientific_journal-4814	42	24	applied	apply	VERB
american_scientific_journal-4814	42	25	to	to	ADP
american_scientific_journal-4814	42	26	the	the	DET
american_scientific_journal-4814	42	27	space	space	NOUN
american_scientific_journal-4814	42	28	vehicle	vehicle	NOUN
american_scientific_journal-4814	42	29	:	:	PUNCT
american_scientific_journal-4814	42	30	�	�	PROPN
american_scientific_journal-4814	42	31	𝑁𝑁𝛼𝛼∗	𝑁𝑁𝛼𝛼∗	NOUN
american_scientific_journal-4814	42	32	=	=	NOUN
american_scientific_journal-4814	42	33	2∑	2∑	NUM
american_scientific_journal-4814	42	34	�	�	PROPN
american_scientific_journal-4814	42	35	∫	∫	NOUN
american_scientific_journal-4814	42	36	𝜎𝜎𝑥𝑥𝛼𝛼𝑖𝑖(𝑥𝑥	𝜎𝜎𝑥𝑥𝛼𝛼𝑖𝑖(𝑥𝑥	NOUN
american_scientific_journal-4814	42	37	,	,	PUNCT
american_scientific_journal-4814	42	38	𝑠𝑠	𝑠𝑠	ADP
american_scientific_journal-4814	42	39	,	,	PUNCT
american_scientific_journal-4814	42	40	𝑡𝑡)𝑑𝑑𝑠𝑠𝑙𝑙	𝑡𝑡)𝑑𝑑𝑠𝑠𝑙𝑙	NOUN
american_scientific_journal-4814	42	41	0	0	SYM
american_scientific_journal-4814	42	42	�	�	SYM
american_scientific_journal-4814	42	43	2	2	NUM
american_scientific_journal-4814	42	44	𝑖𝑖=1	𝑖𝑖=1	SYM
american_scientific_journal-4814	43	1	𝑁𝑁𝑢𝑢∗	𝑁𝑁𝑢𝑢∗	PROPN
american_scientific_journal-4814	43	2	=	=	SYM
american_scientific_journal-4814	43	3	∑	∑	PUNCT
american_scientific_journal-4814	43	4	(	(	PUNCT
american_scientific_journal-4814	43	5	−1)𝑖𝑖	−1)𝑖𝑖	PROPN
american_scientific_journal-4814	43	6	�	�	PROPN
american_scientific_journal-4814	43	7	∫	∫	PROPN
american_scientific_journal-4814	43	8	𝜌𝜌(𝑏𝑏	𝜌𝜌(𝑏𝑏	PROPN
american_scientific_journal-4814	43	9	+	+	CCONJ
american_scientific_journal-4814	43	10	𝑠𝑠)𝑢𝑢𝑖𝑖(𝑠𝑠	𝑠𝑠)𝑢𝑢𝑖𝑖(𝑠𝑠	NOUN
american_scientific_journal-4814	43	11	,	,	PUNCT
american_scientific_journal-4814	43	12	𝑡𝑡)𝑑𝑑𝑠𝑠	𝑡𝑡)𝑑𝑑𝑠𝑠	NOUN
american_scientific_journal-4814	43	13	+	+	CCONJ
american_scientific_journal-4814	43	14	𝜎𝜎∬	𝜎𝜎∬	NOUN
american_scientific_journal-4814	43	15	(	(	PUNCT
american_scientific_journal-4814	43	16	𝑏𝑏	𝑏𝑏	NOUN
american_scientific_journal-4814	43	17	+	+	CCONJ
american_scientific_journal-4814	43	18	𝑠𝑠)𝛼𝛼𝑖𝑖(𝑥𝑥	𝑠𝑠)𝛼𝛼𝑖𝑖(𝑥𝑥	PROPN
american_scientific_journal-4814	43	19	,	,	PUNCT
american_scientific_journal-4814	43	20	𝑠𝑠	𝑠𝑠	ADP
american_scientific_journal-4814	43	21	,	,	PUNCT
american_scientific_journal-4814	43	22	𝑡𝑡)𝑑𝑑𝑥𝑥𝑑𝑑𝑠𝑠	𝑡𝑡)𝑑𝑑𝑥𝑥𝑑𝑑𝑠𝑠	PROPN
american_scientific_journal-4814	43	23	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-4814	43	24	+	+	CCONJ
american_scientific_journal-4814	43	25	𝑚𝑚	𝑚𝑚	PROPN
american_scientific_journal-4814	43	26	�	�	PROPN
american_scientific_journal-4814	43	27	(𝑏𝑏	(𝑏𝑏	SYM
american_scientific_journal-4814	43	28	+	+	NUM
american_scientific_journal-4814	43	29	𝑙𝑙)𝑢𝑢𝑖𝑖(𝑙𝑙	𝑙𝑙)𝑢𝑢𝑖𝑖(𝑙𝑙	PROPN
american_scientific_journal-4814	43	30	,	,	PUNCT
american_scientific_journal-4814	43	31	𝑡𝑡	𝑡𝑡	ADJ
american_scientific_journal-4814	43	32	)	)	PUNCT
american_scientific_journal-4814	43	33	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-4814	43	34	0	0	NUM
american_scientific_journal-4814	43	35	�	�	PROPN
american_scientific_journal-4814	43	36	2	2	NUM
american_scientific_journal-4814	43	37	𝑖𝑖=1	𝑖𝑖=1	NUM
american_scientific_journal-4814	43	38	.	.	PUNCT
american_scientific_journal-4814	44	1	(	(	PUNCT
american_scientific_journal-4814	44	2	2	2	X
american_scientific_journal-4814	44	3	)	)	PUNCT
american_scientific_journal-4814	44	4	•	•	NOUN
american_scientific_journal-4814	44	5	local	local	ADJ
american_scientific_journal-4814	44	6	motions	motion	NOUN
american_scientific_journal-4814	44	7	equations	equation	NOUN
american_scientific_journal-4814	44	8	of	of	ADP
american_scientific_journal-4814	44	9	each	each	DET
american_scientific_journal-4814	44	10	solar	solar	ADJ
american_scientific_journal-4814	44	11	array	array	NOUN
american_scientific_journal-4814	44	12	(	(	PUNCT
american_scientific_journal-4814	44	13	𝐵𝐵𝑖𝑖	𝐵𝐵𝑖𝑖	NOUN
american_scientific_journal-4814	44	14	,	,	PUNCT
american_scientific_journal-4814	44	15	𝑖𝑖	𝑖𝑖	X
american_scientific_journal-4814	44	16	=	=	SYM
american_scientific_journal-4814	44	17	1,2	1,2	NUM
american_scientific_journal-4814	44	18	)	)	PUNCT
american_scientific_journal-4814	44	19	𝜌𝜌	𝜌𝜌	ADP
american_scientific_journal-4814	44	20	�	�	PROPN
american_scientific_journal-4814	44	21	�	�	PROPN
american_scientific_journal-4814	44	22	̈	̈	X
american_scientific_journal-4814	44	23	�	�	NOUN
american_scientific_journal-4814	44	24	𝑢𝑖𝑖	𝑢𝑖𝑖	NOUN
american_scientific_journal-4814	44	25	+	+	CCONJ
american_scientific_journal-4814	44	26	(	(	PUNCT
american_scientific_journal-4814	44	27	−1)𝑖𝑖(𝑏𝑏	−1)𝑖𝑖(𝑏𝑏	PUNCT
american_scientific_journal-4814	44	28	+	+	CCONJ
american_scientific_journal-4814	44	29	𝑠𝑠)	𝑠𝑠)	PROPN
american_scientific_journal-4814	44	30	�	�	NOUN
american_scientific_journal-4814	44	31	�	�	PROPN
american_scientific_journal-4814	44	32	̈	̈	X
american_scientific_journal-4814	44	33	�	�	NOUN
american_scientific_journal-4814	44	34	𝜃	𝜃	NOUN
american_scientific_journal-4814	44	35	+	+	NOUN
american_scientific_journal-4814	44	36	3𝑛𝑛02𝜃𝜃	3𝑛𝑛02𝜃𝜃	NUM
american_scientific_journal-4814	44	37	�	�	NOUN
american_scientific_journal-4814	44	38	�	�	PROPN
american_scientific_journal-4814	44	39	+	+	CCONJ
american_scientific_journal-4814	44	40	[	[	X
american_scientific_journal-4814	44	41	𝑆𝑆	𝑆𝑆	PROPN
american_scientific_journal-4814	44	42	�	�	PROPN
american_scientific_journal-4814	44	43	(𝑠𝑠)𝑢𝑢𝑖𝑖′]′	(𝑠𝑠)𝑢𝑢𝑖𝑖′]′	NOUN
american_scientific_journal-4814	44	44	+	+	CCONJ
american_scientific_journal-4814	44	45	𝐸𝐸𝐸𝐸𝑢𝑢𝑖𝑖	𝐸𝐸𝐸𝐸𝑢𝑢𝑖𝑖	PROPN
american_scientific_journal-4814	44	46	(	(	PUNCT
american_scientific_journal-4814	44	47	4	4	NUM
american_scientific_journal-4814	44	48	)	)	PUNCT
american_scientific_journal-4814	44	49	=	=	SYM
american_scientific_journal-4814	44	50	0	0	PUNCT
american_scientific_journal-4814	44	51	into	into	ADP
american_scientific_journal-4814	44	52	(	(	PUNCT
american_scientific_journal-4814	44	53	𝑆𝑆𝑆𝑆𝑖𝑖	𝑆𝑆𝑆𝑆𝑖𝑖	PROPN
american_scientific_journal-4814	44	54	)	)	PUNCT
american_scientific_journal-4814	44	55	,	,	PUNCT
american_scientific_journal-4814	44	56	(	(	PUNCT
american_scientific_journal-4814	44	57	3	3	X
american_scientific_journal-4814	44	58	)	)	PUNCT
american_scientific_journal-4814	44	59	𝜎𝜎	𝜎𝜎	PROPN
american_scientific_journal-4814	44	60	�	�	PROPN
american_scientific_journal-4814	44	61	�	�	PROPN
american_scientific_journal-4814	44	62	̈	̈	SYM
american_scientific_journal-4814	44	63	�	�	NOUN
american_scientific_journal-4814	44	64	𝛼𝑖𝑖	𝛼𝑖𝑖	VERB
american_scientific_journal-4814	44	65	−	−	PROPN
american_scientific_journal-4814	44	66	2𝑛𝑛0𝑥𝑥	2𝑛𝑛0𝑥𝑥	NUM
american_scientific_journal-4814	44	67	�	�	PROPN
american_scientific_journal-4814	44	68	̇	̇	NOUN
american_scientific_journal-4814	44	69	�	�	PROPN
american_scientific_journal-4814	44	70	𝜃	𝜃	NOUN
american_scientific_journal-4814	44	71	+	+	X
american_scientific_journal-4814	44	72	(	(	PUNCT
american_scientific_journal-4814	44	73	−1)𝑖𝑖(𝑏𝑏	−1)𝑖𝑖(𝑏𝑏	NOUN
american_scientific_journal-4814	44	74	+	+	CCONJ
american_scientific_journal-4814	44	75	𝑠𝑠)	𝑠𝑠)	PROPN
american_scientific_journal-4814	44	76	�	�	NOUN
american_scientific_journal-4814	44	77	�	�	PROPN
american_scientific_journal-4814	44	78	̈	̈	X
american_scientific_journal-4814	44	79	�	�	NOUN
american_scientific_journal-4814	44	80	𝜃	𝜃	NOUN
american_scientific_journal-4814	44	81	+	+	NOUN
american_scientific_journal-4814	45	1	3𝑛𝑛02𝜃𝜃	3𝑛𝑛02𝜃𝜃	NUM
american_scientific_journal-4814	45	2	�	�	PROPN
american_scientific_journal-4814	45	3	�	�	PROPN
american_scientific_journal-4814	45	4	−	−	PROPN
american_scientific_journal-4814	45	5	�	�	PROPN
american_scientific_journal-4814	45	6	�	�	PROPN
american_scientific_journal-4814	45	7	𝐺𝐺	𝐺𝐺	PROPN
american_scientific_journal-4814	45	8	�	�	PROPN
american_scientific_journal-4814	45	9	+	+	CCONJ
american_scientific_journal-4814	45	10	𝑇𝑇	𝑇𝑇	PROPN
american_scientific_journal-4814	45	11	�	�	PROPN
american_scientific_journal-4814	45	12	(𝑠𝑠)	(𝑠𝑠)	NOUN
american_scientific_journal-4814	45	13	�	�	PROPN
american_scientific_journal-4814	45	14	𝛼𝛼𝑖𝑖′	𝛼𝛼𝑖𝑖′	NUM
american_scientific_journal-4814	45	15	�	�	PROPN
american_scientific_journal-4814	45	16	′	′	NUM
american_scientific_journal-4814	45	17	=	=	NOUN
american_scientific_journal-4814	45	18	0	0	PUNCT
american_scientific_journal-4814	45	19	into	into	ADP
american_scientific_journal-4814	45	20	(	(	PUNCT
american_scientific_journal-4814	45	21	𝐵𝐵𝐵𝐵𝑖𝑖	𝐵𝐵𝐵𝐵𝑖𝑖	PROPN
american_scientific_journal-4814	45	22	)	)	PUNCT
american_scientific_journal-4814	45	23	,	,	PUNCT
american_scientific_journal-4814	45	24	(	(	PUNCT
american_scientific_journal-4814	45	25	4	4	X
american_scientific_journal-4814	45	26	)	)	PUNCT
american_scientific_journal-4814	45	27	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-4814	45	28	�	�	PROPN
american_scientific_journal-4814	45	29	�	�	PROPN
american_scientific_journal-4814	45	30	�	�	PROPN
american_scientific_journal-4814	45	31	̈	̈	SYM
american_scientific_journal-4814	45	32	�	�	NOUN
american_scientific_journal-4814	45	33	𝑢𝑖𝑖(𝑙𝑙	𝑢𝑖𝑖(𝑙𝑙	NOUN
american_scientific_journal-4814	45	34	,	,	PUNCT
american_scientific_journal-4814	45	35	𝑡𝑡	𝑡𝑡	ADJ
american_scientific_journal-4814	45	36	)	)	PUNCT
american_scientific_journal-4814	45	37	+	+	CCONJ
american_scientific_journal-4814	45	38	(	(	PUNCT
american_scientific_journal-4814	45	39	−1)𝑖𝑖(𝑏𝑏	−1)𝑖𝑖(𝑏𝑏	PROPN
american_scientific_journal-4814	45	40	+	+	SYM
american_scientific_journal-4814	45	41	𝑙𝑙)	𝑙𝑙)	PROPN
american_scientific_journal-4814	45	42	�	�	PROPN
american_scientific_journal-4814	45	43	�	�	PROPN
american_scientific_journal-4814	45	44	̈	̈	X
american_scientific_journal-4814	45	45	�	�	NOUN
american_scientific_journal-4814	45	46	𝜃	𝜃	NOUN
american_scientific_journal-4814	45	47	+	+	NOUN
american_scientific_journal-4814	45	48	3𝑛𝑛02𝜃𝜃	3𝑛𝑛02𝜃𝜃	NUM
american_scientific_journal-4814	45	49	�	�	NOUN
american_scientific_journal-4814	45	50	�	�	PROPN
american_scientific_journal-4814	45	51	−	−	PROPN
american_scientific_journal-4814	45	52	𝐸𝐸𝐸𝐸𝑢𝑢𝑖𝑖	𝐸𝐸𝐸𝐸𝑢𝑢𝑖𝑖	PROPN
american_scientific_journal-4814	45	53	(	(	PUNCT
american_scientific_journal-4814	45	54	3)(𝑙𝑙	3)(𝑙𝑙	NUM
american_scientific_journal-4814	45	55	,	,	PUNCT
american_scientific_journal-4814	45	56	𝑡𝑡	𝑡𝑡	ADJ
american_scientific_journal-4814	45	57	)	)	PUNCT
american_scientific_journal-4814	45	58	−	−	ADP
american_scientific_journal-4814	45	59	𝑆𝑆𝑢𝑢𝑖𝑖′(𝑙𝑙	𝑆𝑆𝑢𝑢𝑖𝑖′(𝑙𝑙	PROPN
american_scientific_journal-4814	45	60	,	,	PUNCT
american_scientific_journal-4814	45	61	𝑡𝑡	𝑡𝑡	ADJ
american_scientific_journal-4814	45	62	)	)	PUNCT
american_scientific_journal-4814	45	63	+	+	CCONJ
american_scientific_journal-4814	45	64	�	�	PROPN
american_scientific_journal-4814	45	65	𝐺𝐺	𝐺𝐺	NOUN
american_scientific_journal-4814	45	66	�	�	NOUN
american_scientific_journal-4814	45	67	𝑒𝑒	𝑒𝑒	ADP
american_scientific_journal-4814	45	68	+	+	PROPN
american_scientific_journal-4814	45	69	𝑆𝑆	𝑆𝑆	PROPN
american_scientific_journal-4814	45	70	+	+	CCONJ
american_scientific_journal-4814	45	71	3𝑛𝑛02𝑚𝑚	3𝑛𝑛02𝑚𝑚	NUM
american_scientific_journal-4814	45	72	�	�	NOUN
american_scientific_journal-4814	45	73	(𝑏𝑏	(𝑏𝑏	SYM
american_scientific_journal-4814	45	74	+	+	NUM
american_scientific_journal-4814	45	75	𝑙𝑙)	𝑙𝑙)	PROPN
american_scientific_journal-4814	45	76	�	�	NOUN
american_scientific_journal-4814	45	77	𝛼𝛼𝑖𝑖′(𝑙𝑙	𝛼𝛼𝑖𝑖′(𝑙𝑙	NOUN
american_scientific_journal-4814	45	78	,	,	PUNCT
american_scientific_journal-4814	45	79	𝑡𝑡	𝑡𝑡	ADJ
american_scientific_journal-4814	45	80	)	)	PUNCT
american_scientific_journal-4814	45	81	=	=	SYM
american_scientific_journal-4814	45	82	0	0	NUM
american_scientific_journal-4814	45	83	on	on	ADP
american_scientific_journal-4814	45	84	(	(	PUNCT
american_scientific_journal-4814	45	85	𝑇𝑇𝑆𝑆𝑖𝑖	𝑇𝑇𝑆𝑆𝑖𝑖	PROPN
american_scientific_journal-4814	45	86	)	)	PUNCT
american_scientific_journal-4814	45	87	.	.	PUNCT
american_scientific_journal-4814	46	1	(	(	PUNCT
american_scientific_journal-4814	46	2	5	5	X
american_scientific_journal-4814	46	3	)	)	PUNCT
american_scientific_journal-4814	46	4	here	here	ADV
american_scientific_journal-4814	46	5	:	:	PUNCT
american_scientific_journal-4814	46	6	𝑆𝑆	𝑆𝑆	PROPN
american_scientific_journal-4814	46	7	�	�	PROPN
american_scientific_journal-4814	46	8	(𝑠𝑠	(𝑠𝑠	NOUN
american_scientific_journal-4814	46	9	)	)	PUNCT
american_scientific_journal-4814	46	10	is	be	AUX
american_scientific_journal-4814	46	11	the	the	DET
american_scientific_journal-4814	46	12	dynamic	dynamic	ADJ
american_scientific_journal-4814	46	13	stiffness	stiffness	NOUN
american_scientific_journal-4814	46	14	exerted	exert	VERB
american_scientific_journal-4814	46	15	at	at	ADP
american_scientific_journal-4814	46	16	any	any	DET
american_scientific_journal-4814	46	17	material	material	NOUN
american_scientific_journal-4814	46	18	point	point	NOUN
american_scientific_journal-4814	46	19	𝑀𝑀(𝑠𝑠	𝑀𝑀(𝑠𝑠	NOUN
american_scientific_journal-4814	46	20	)	)	PUNCT
american_scientific_journal-4814	46	21	of	of	ADP
american_scientific_journal-4814	46	22	(	(	PUNCT
american_scientific_journal-4814	46	23	𝑆𝑆𝑆𝑆𝑖𝑖	𝑆𝑆𝑆𝑆𝑖𝑖	PROPN
american_scientific_journal-4814	46	24	):	):	PUNCT
american_scientific_journal-4814	46	25	𝑆𝑆	𝑆𝑆	PROPN
american_scientific_journal-4814	46	26	�	�	PROPN
american_scientific_journal-4814	46	27	(𝑠𝑠	(𝑠𝑠	NOUN
american_scientific_journal-4814	46	28	)	)	PUNCT
american_scientific_journal-4814	46	29	=	=	SYM
american_scientific_journal-4814	46	30	𝑆𝑆	𝑆𝑆	PROPN
american_scientific_journal-4814	46	31	−	−	PROPN
american_scientific_journal-4814	46	32	3𝜌𝜌	3𝜌𝜌	NOUN
american_scientific_journal-4814	46	33	𝑛𝑛0	𝑛𝑛0	VERB
american_scientific_journal-4814	46	34	2	2	NUM
american_scientific_journal-4814	46	35	2	2	NUM
american_scientific_journal-4814	46	36	[	[	X
american_scientific_journal-4814	46	37	(	(	PUNCT
american_scientific_journal-4814	46	38	𝑏𝑏	𝑏𝑏	NOUN
american_scientific_journal-4814	46	39	+	+	NUM
american_scientific_journal-4814	46	40	𝑙𝑙)2	𝑙𝑙)2	PROPN
american_scientific_journal-4814	47	1	−	−	PROPN
american_scientific_journal-4814	47	2	(	(	PUNCT
american_scientific_journal-4814	47	3	𝑏𝑏	𝑏𝑏	NOUN
american_scientific_journal-4814	47	4	+	+	NUM
american_scientific_journal-4814	47	5	𝑠𝑠)2	𝑠𝑠)2	PROPN
american_scientific_journal-4814	47	6	]	]	PUNCT
american_scientific_journal-4814	47	7	.	.	PUNCT
american_scientific_journal-4814	48	1	(	(	PUNCT
american_scientific_journal-4814	48	2	6	6	X
american_scientific_journal-4814	48	3	)	)	PUNCT
american_scientific_journal-4814	48	4	p	p	NOUN
american_scientific_journal-4814	48	5	is	be	AUX
american_scientific_journal-4814	48	6	the	the	DET
american_scientific_journal-4814	48	7	constant	constant	ADJ
american_scientific_journal-4814	48	8	compression	compression	NOUN
american_scientific_journal-4814	48	9	applied	apply	VERB
american_scientific_journal-4814	48	10	to	to	ADP
american_scientific_journal-4814	48	11	the	the	DET
american_scientific_journal-4814	48	12	supporting	support	VERB
american_scientific_journal-4814	48	13	piece	piece	NOUN
american_scientific_journal-4814	48	14	(	(	PUNCT
american_scientific_journal-4814	48	15	𝑆𝑆𝑆𝑆𝑖𝑖	𝑆𝑆𝑆𝑆𝑖𝑖	PROPN
american_scientific_journal-4814	48	16	)	)	PUNCT
american_scientific_journal-4814	48	17	.	.	PUNCT
american_scientific_journal-4814	49	1	american	american	PROPN
american_scientific_journal-4814	49	2	scientific	scientific	ADJ
american_scientific_journal-4814	49	3	research	research	PROPN
american_scientific_journal-4814	49	4	journal	journal	NOUN
american_scientific_journal-4814	49	5	for	for	ADP
american_scientific_journal-4814	49	6	engineering	engineering	NOUN
american_scientific_journal-4814	49	7	,	,	PUNCT
american_scientific_journal-4814	49	8	technology	technology	NOUN
american_scientific_journal-4814	49	9	,	,	PUNCT
american_scientific_journal-4814	49	10	and	and	CCONJ
american_scientific_journal-4814	49	11	sciences	science	NOUN
american_scientific_journal-4814	49	12	(	(	PUNCT
american_scientific_journal-4814	49	13	asrjets	asrjet	NOUN
american_scientific_journal-4814	49	14	)	)	PUNCT
american_scientific_journal-4814	49	15	(	(	PUNCT
american_scientific_journal-4814	49	16	2019	2019	NUM
american_scientific_journal-4814	49	17	)	)	PUNCT
american_scientific_journal-4814	49	18	volume	volume	NOUN
american_scientific_journal-4814	49	19	55	55	NUM
american_scientific_journal-4814	49	20	,	,	PUNCT
american_scientific_journal-4814	49	21	no	no	DET
american_scientific_journal-4814	49	22	1	1	NUM
american_scientific_journal-4814	49	23	,	,	PUNCT
american_scientific_journal-4814	49	24	pp	pp	ADP
american_scientific_journal-4814	49	25	50	50	NUM
american_scientific_journal-4814	49	26	-	-	SYM
american_scientific_journal-4814	49	27	68	68	NUM
american_scientific_journal-4814	49	28	53	53	NUM
american_scientific_journal-4814	49	29	𝑇𝑇	𝑇𝑇	PROPN
american_scientific_journal-4814	49	30	�	�	NOUN
american_scientific_journal-4814	49	31	(𝑠𝑠	(𝑠𝑠	NOUN
american_scientific_journal-4814	49	32	)	)	PUNCT
american_scientific_journal-4814	49	33	is	be	AUX
american_scientific_journal-4814	49	34	the	the	DET
american_scientific_journal-4814	49	35	dynamic	dynamic	ADJ
american_scientific_journal-4814	49	36	stiffness	stiffness	NOUN
american_scientific_journal-4814	49	37	exerted	exert	VERB
american_scientific_journal-4814	49	38	to	to	ADP
american_scientific_journal-4814	49	39	any	any	DET
american_scientific_journal-4814	49	40	material	material	NOUN
american_scientific_journal-4814	49	41	point	point	NOUN
american_scientific_journal-4814	49	42	𝑀𝑀	𝑀𝑀	PROPN
american_scientific_journal-4814	49	43	of	of	ADP
american_scientific_journal-4814	49	44	(	(	PUNCT
american_scientific_journal-4814	49	45	𝐵𝐵𝐵𝐵𝑖𝑖	𝐵𝐵𝐵𝐵𝑖𝑖	PROPN
american_scientific_journal-4814	49	46	):	):	PUNCT
american_scientific_journal-4814	49	47	𝑇𝑇	𝑇𝑇	PROPN
american_scientific_journal-4814	49	48	�	�	NOUN
american_scientific_journal-4814	49	49	(𝑠𝑠	(𝑠𝑠	NUM
american_scientific_journal-4814	49	50	)	)	PUNCT
american_scientific_journal-4814	49	51	=	=	SYM
american_scientific_journal-4814	50	1	𝑃𝑃	𝑃𝑃	ADV
american_scientific_journal-4814	50	2	𝑒𝑒	𝑒𝑒	ADP
american_scientific_journal-4814	50	3	+	+	NOUN
american_scientific_journal-4814	50	4	3	3	NUM
american_scientific_journal-4814	50	5	𝑛𝑛0	𝑛𝑛0	NOUN
american_scientific_journal-4814	50	6	2	2	NUM
american_scientific_journal-4814	50	7	2	2	NUM
american_scientific_journal-4814	50	8	�	�	NOUN
american_scientific_journal-4814	50	9	𝜎𝜎(𝑏𝑏	𝜎𝜎(𝑏𝑏	PROPN
american_scientific_journal-4814	50	10	+	+	CCONJ
american_scientific_journal-4814	50	11	𝑙𝑙)2	𝑙𝑙)2	PROPN
american_scientific_journal-4814	50	12	−	−	PROPN
american_scientific_journal-4814	50	13	𝜎𝜎(𝑏𝑏	𝜎𝜎(𝑏𝑏	PROPN
american_scientific_journal-4814	50	14	+	+	NUM
american_scientific_journal-4814	50	15	𝑠𝑠)2	𝑠𝑠)2	PROPN
american_scientific_journal-4814	50	16	+	+	CCONJ
american_scientific_journal-4814	50	17	2	2	NUM
american_scientific_journal-4814	50	18	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-4814	50	19	�	�	PROPN
american_scientific_journal-4814	50	20	𝑒𝑒	𝑒𝑒	ADP
american_scientific_journal-4814	50	21	(	(	PUNCT
american_scientific_journal-4814	50	22	𝑏𝑏	𝑏𝑏	NOUN
american_scientific_journal-4814	50	23	+	+	NUM
american_scientific_journal-4814	50	24	𝑙𝑙)	𝑙𝑙)	PROPN
american_scientific_journal-4814	50	25	�	�	PROPN
american_scientific_journal-4814	50	26	.	.	PUNCT
american_scientific_journal-4814	51	1	(	(	PUNCT
american_scientific_journal-4814	51	2	7	7	X
american_scientific_journal-4814	51	3	)	)	PUNCT
american_scientific_journal-4814	51	4	𝐺𝐺	𝐺𝐺	PROPN
american_scientific_journal-4814	51	5	�	�	NOUN
american_scientific_journal-4814	51	6	=	=	SYM
american_scientific_journal-4814	51	7	𝐸𝐸ℎ	𝐸𝐸ℎ	ADJ
american_scientific_journal-4814	51	8	4(1	4(1	NUM
american_scientific_journal-4814	51	9	+	+	CCONJ
american_scientific_journal-4814	51	10	𝜈𝜈	𝜈𝜈	NOUN
american_scientific_journal-4814	51	11	)	)	PUNCT
american_scientific_journal-4814	51	12	.	.	PUNCT
american_scientific_journal-4814	52	1	e	e	NOUN
american_scientific_journal-4814	52	2	is	be	AUX
american_scientific_journal-4814	52	3	the	the	DET
american_scientific_journal-4814	52	4	young	young	ADJ
american_scientific_journal-4814	52	5	modulus	modulus	NOUN
american_scientific_journal-4814	52	6	,	,	PUNCT
american_scientific_journal-4814	52	7	𝜈𝜈	𝜈𝜈	PRON
american_scientific_journal-4814	52	8	is	be	AUX
american_scientific_journal-4814	52	9	the	the	DET
american_scientific_journal-4814	52	10	poisson	poisson	PROPN
american_scientific_journal-4814	52	11	ratio	ratio	NOUN
american_scientific_journal-4814	52	12	of	of	ADP
american_scientific_journal-4814	52	13	the	the	DET
american_scientific_journal-4814	52	14	membranes	membrane	NOUN
american_scientific_journal-4814	52	15	,	,	PUNCT
american_scientific_journal-4814	52	16	h	h	NOUN
american_scientific_journal-4814	52	17	is	be	AUX
american_scientific_journal-4814	52	18	the	the	DET
american_scientific_journal-4814	52	19	thickness	thickness	NOUN
american_scientific_journal-4814	52	20	of	of	ADP
american_scientific_journal-4814	52	21	the	the	DET
american_scientific_journal-4814	52	22	blanket	blanket	NOUN
american_scientific_journal-4814	52	23	(	(	PUNCT
american_scientific_journal-4814	52	24	𝐵𝐵𝐵𝐵𝑖𝑖	𝐵𝐵𝐵𝐵𝑖𝑖	PROPN
american_scientific_journal-4814	52	25	)	)	PUNCT
american_scientific_journal-4814	52	26	.	.	PUNCT
american_scientific_journal-4814	53	1	•	•	NUM
american_scientific_journal-4814	53	2	boundary	boundary	ADJ
american_scientific_journal-4814	53	3	conditions	condition	NOUN
american_scientific_journal-4814	53	4	of	of	ADP
american_scientific_journal-4814	53	5	the	the	DET
american_scientific_journal-4814	53	6	problem	problem	NOUN
american_scientific_journal-4814	53	7	the	the	DET
american_scientific_journal-4814	53	8	geometrical	geometrical	ADJ
american_scientific_journal-4814	53	9	conditions	condition	NOUN
american_scientific_journal-4814	53	10	on	on	ADP
american_scientific_journal-4814	53	11	the	the	DET
american_scientific_journal-4814	53	12	boundary	boundary	NOUN
american_scientific_journal-4814	53	13	between	between	ADP
american_scientific_journal-4814	53	14	the	the	DET
american_scientific_journal-4814	53	15	rigid	rigid	ADJ
american_scientific_journal-4814	53	16	interface	interface	NOUN
american_scientific_journal-4814	53	17	(	(	PUNCT
american_scientific_journal-4814	53	18	𝛾𝛾𝑖𝑖	𝛾𝛾𝑖𝑖	PROPN
american_scientific_journal-4814	53	19	)	)	PUNCT
american_scientific_journal-4814	53	20	and	and	CCONJ
american_scientific_journal-4814	53	21	the	the	DET
american_scientific_journal-4814	53	22	solar	solar	ADJ
american_scientific_journal-4814	53	23	array	array	NOUN
american_scientific_journal-4814	53	24	(	(	PUNCT
american_scientific_journal-4814	53	25	𝐵𝐵𝑖𝑖	𝐵𝐵𝑖𝑖	PROPN
american_scientific_journal-4814	53	26	)	)	PUNCT
american_scientific_journal-4814	53	27	,	,	PUNCT
american_scientific_journal-4814	53	28	relative	relative	ADJ
american_scientific_journal-4814	53	29	to	to	ADP
american_scientific_journal-4814	53	30	the	the	DET
american_scientific_journal-4814	53	31	displacement	displacement	NOUN
american_scientific_journal-4814	53	32	fields	field	NOUN
american_scientific_journal-4814	53	33	𝑢𝑢𝑖𝑖(𝑠𝑠	𝑢𝑢𝑖𝑖(𝑠𝑠	NOUN
american_scientific_journal-4814	53	34	,	,	PUNCT
american_scientific_journal-4814	53	35	𝑡𝑡	𝑡𝑡	ADJ
american_scientific_journal-4814	53	36	)	)	PUNCT
american_scientific_journal-4814	53	37	and	and	CCONJ
american_scientific_journal-4814	53	38	𝛼𝛼𝑖𝑖(𝑥𝑥	𝛼𝛼𝑖𝑖(𝑥𝑥	PROPN
american_scientific_journal-4814	53	39	,	,	PUNCT
american_scientific_journal-4814	53	40	𝑠𝑠	𝑠𝑠	ADP
american_scientific_journal-4814	53	41	,	,	PUNCT
american_scientific_journal-4814	53	42	𝑡𝑡	𝑡𝑡	ADJ
american_scientific_journal-4814	53	43	)	)	PUNCT
american_scientific_journal-4814	53	44	of	of	ADP
american_scientific_journal-4814	53	45	(	(	PUNCT
american_scientific_journal-4814	53	46	𝑆𝑆𝑆𝑆𝑖𝑖	𝑆𝑆𝑆𝑆𝑖𝑖	PROPN
american_scientific_journal-4814	53	47	)	)	PUNCT
american_scientific_journal-4814	53	48	and	and	CCONJ
american_scientific_journal-4814	53	49	(	(	PUNCT
american_scientific_journal-4814	53	50	𝐵𝐵𝐵𝐵𝑖𝑖	𝐵𝐵𝐵𝐵𝑖𝑖	PROPN
american_scientific_journal-4814	53	51	)	)	PUNCT
american_scientific_journal-4814	53	52	respectively	respectively	ADV
american_scientific_journal-4814	53	53	,	,	PUNCT
american_scientific_journal-4814	53	54	are	be	AUX
american_scientific_journal-4814	53	55	defined	define	VERB
american_scientific_journal-4814	53	56	by	by	ADP
american_scientific_journal-4814	53	57	:	:	PUNCT
american_scientific_journal-4814	53	58	�	�	PROPN
american_scientific_journal-4814	53	59	𝑢𝑢𝑖𝑖(0	𝑢𝑢𝑖𝑖(0	PROPN
american_scientific_journal-4814	53	60	,	,	PUNCT
american_scientific_journal-4814	53	61	𝑡𝑡	𝑡𝑡	NOUN
american_scientific_journal-4814	53	62	)	)	PUNCT
american_scientific_journal-4814	53	63	=	=	SYM
american_scientific_journal-4814	53	64	0	0	NUM
american_scientific_journal-4814	53	65	𝛼𝛼𝑖𝑖(𝑥𝑥	𝛼𝛼𝑖𝑖(𝑥𝑥	NOUN
american_scientific_journal-4814	53	66	,	,	PUNCT
american_scientific_journal-4814	53	67	0	0	NUM
american_scientific_journal-4814	53	68	,	,	PUNCT
american_scientific_journal-4814	53	69	𝑡𝑡	𝑡𝑡	ADJ
american_scientific_journal-4814	53	70	)	)	PUNCT
american_scientific_journal-4814	53	71	=	=	SYM
american_scientific_journal-4814	53	72	0	0	NUM
american_scientific_journal-4814	53	73	𝑢𝑢𝑖𝑖′(0	𝑢𝑢𝑖𝑖′(0	NOUN
american_scientific_journal-4814	53	74	,	,	PUNCT
american_scientific_journal-4814	53	75	𝑡𝑡	𝑡𝑡	ADJ
american_scientific_journal-4814	53	76	)	)	PUNCT
american_scientific_journal-4814	53	77	=	=	SYM
american_scientific_journal-4814	53	78	0	0	PUNCT
american_scientific_journal-4814	53	79	.	.	PUNCT
american_scientific_journal-4814	54	1	(	(	PUNCT
american_scientific_journal-4814	54	2	8)	8)	NUM
american_scientific_journal-4814	54	3	the	the	DET
american_scientific_journal-4814	54	4	continuity	continuity	NOUN
american_scientific_journal-4814	54	5	of	of	ADP
american_scientific_journal-4814	54	6	the	the	DET
american_scientific_journal-4814	54	7	displacement	displacement	ADJ
american_scientific_journal-4814	54	8	fields	field	NOUN
american_scientific_journal-4814	54	9	on	on	ADP
american_scientific_journal-4814	54	10	the	the	DET
american_scientific_journal-4814	54	11	boundary	boundary	NOUN
american_scientific_journal-4814	54	12	between	between	ADP
american_scientific_journal-4814	54	13	(	(	PUNCT
american_scientific_journal-4814	54	14	𝐵𝐵𝐵𝐵𝑖𝑖	𝐵𝐵𝐵𝐵𝑖𝑖	PROPN
american_scientific_journal-4814	54	15	)	)	PUNCT
american_scientific_journal-4814	54	16	and	and	CCONJ
american_scientific_journal-4814	54	17	(	(	PUNCT
american_scientific_journal-4814	54	18	𝑆𝑆𝑆𝑆𝑖𝑖	𝑆𝑆𝑆𝑆𝑖𝑖	PROPN
american_scientific_journal-4814	54	19	)	)	PUNCT
american_scientific_journal-4814	54	20	,	,	PUNCT
american_scientific_journal-4814	54	21	is	be	AUX
american_scientific_journal-4814	54	22	expressed	express	VERB
american_scientific_journal-4814	54	23	by	by	ADP
american_scientific_journal-4814	54	24	:	:	PUNCT
american_scientific_journal-4814	54	25	𝛼𝛼𝑖𝑖(𝑥𝑥	𝛼𝛼𝑖𝑖(𝑥𝑥	PROPN
american_scientific_journal-4814	54	26	,	,	PUNCT
american_scientific_journal-4814	54	27	𝑙𝑙	𝑙𝑙	X
american_scientific_journal-4814	54	28	,	,	PUNCT
american_scientific_journal-4814	54	29	𝑡𝑡	𝑡𝑡	ADJ
american_scientific_journal-4814	54	30	)	)	PUNCT
american_scientific_journal-4814	54	31	=	=	SYM
american_scientific_journal-4814	54	32	𝑢𝑢𝑖𝑖(𝑙𝑙	𝑢𝑢𝑖𝑖(𝑙𝑙	NOUN
american_scientific_journal-4814	54	33	,	,	PUNCT
american_scientific_journal-4814	54	34	𝑡𝑡	𝑡𝑡	NOUN
american_scientific_journal-4814	54	35	)	)	PUNCT
american_scientific_journal-4814	54	36	.	.	PUNCT
american_scientific_journal-4814	55	1	(	(	PUNCT
american_scientific_journal-4814	55	2	9	9	X
american_scientific_journal-4814	55	3	)	)	PUNCT
american_scientific_journal-4814	55	4	consequently	consequently	ADV
american_scientific_journal-4814	55	5	,	,	PUNCT
american_scientific_journal-4814	55	6	one	one	PRON
american_scientific_journal-4814	55	7	has	have	VERB
american_scientific_journal-4814	55	8	:	:	PUNCT
american_scientific_journal-4814	55	9	𝜕𝜕𝛼𝛼𝑖𝑖(𝑥𝑥	𝜕𝜕𝛼𝛼𝑖𝑖(𝑥𝑥	PROPN
american_scientific_journal-4814	55	10	,	,	PUNCT
american_scientific_journal-4814	55	11	𝑙𝑙	𝑙𝑙	X
american_scientific_journal-4814	55	12	,	,	PUNCT
american_scientific_journal-4814	55	13	𝑡𝑡	𝑡𝑡	ADJ
american_scientific_journal-4814	55	14	)	)	PUNCT
american_scientific_journal-4814	55	15	𝜕𝜕𝑥𝑥	𝜕𝜕𝑥𝑥	PUNCT
american_scientific_journal-4814	56	1	=	=	SYM
american_scientific_journal-4814	56	2	𝜕𝜕𝑢𝑢𝑖𝑖(𝑙𝑙	𝜕𝜕𝑢𝑢𝑖𝑖(𝑙𝑙	PROPN
american_scientific_journal-4814	56	3	,	,	PUNCT
american_scientific_journal-4814	56	4	𝑡𝑡	𝑡𝑡	NOUN
american_scientific_journal-4814	56	5	)	)	PUNCT
american_scientific_journal-4814	56	6	𝜕𝜕𝑥𝑥	𝜕𝜕𝑥𝑥	PUNCT
american_scientific_journal-4814	57	1	=	=	SYM
american_scientific_journal-4814	57	2	0	0	X
american_scientific_journal-4814	57	3	.	.	PUNCT
american_scientific_journal-4814	57	4	from	from	ADP
american_scientific_journal-4814	57	5	(	(	PUNCT
american_scientific_journal-4814	57	6	9	9	NUM
american_scientific_journal-4814	57	7	)	)	PUNCT
american_scientific_journal-4814	57	8	,	,	PUNCT
american_scientific_journal-4814	57	9	one	one	PRON
american_scientific_journal-4814	57	10	considers	consider	VERB
american_scientific_journal-4814	57	11	an	an	DET
american_scientific_journal-4814	57	12	admissible	admissible	ADJ
american_scientific_journal-4814	57	13	function	function	NOUN
american_scientific_journal-4814	57	14	𝛼𝛼𝑖𝑖	𝛼𝛼𝑖𝑖	ADJ
american_scientific_journal-4814	57	15	independent	independent	ADJ
american_scientific_journal-4814	57	16	of	of	ADP
american_scientific_journal-4814	57	17	the	the	DET
american_scientific_journal-4814	57	18	variable	variable	NOUN
american_scientific_journal-4814	57	19	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-4814	57	20	,	,	PUNCT
american_scientific_journal-4814	57	21	of	of	ADP
american_scientific_journal-4814	57	22	the	the	DET
american_scientific_journal-4814	57	23	form	form	NOUN
american_scientific_journal-4814	57	24	:	:	PUNCT
american_scientific_journal-4814	57	25	𝛼𝛼𝑖𝑖	𝛼𝛼𝑖𝑖	ADJ
american_scientific_journal-4814	57	26	=	=	NOUN
american_scientific_journal-4814	57	27	𝛼𝛼𝑖𝑖(𝑠𝑠	𝛼𝛼𝑖𝑖(𝑠𝑠	NOUN
american_scientific_journal-4814	57	28	,	,	PUNCT
american_scientific_journal-4814	57	29	𝑡𝑡	𝑡𝑡	NOUN
american_scientific_journal-4814	57	30	)	)	PUNCT
american_scientific_journal-4814	57	31	.	.	PUNCT
american_scientific_journal-4814	58	1	the	the	DET
american_scientific_journal-4814	58	2	natural	natural	ADJ
american_scientific_journal-4814	58	3	condition	condition	NOUN
american_scientific_journal-4814	58	4	in	in	ADP
american_scientific_journal-4814	58	5	absence	absence	NOUN
american_scientific_journal-4814	58	6	of	of	ADP
american_scientific_journal-4814	58	7	external	external	ADJ
american_scientific_journal-4814	58	8	torques	torque	NOUN
american_scientific_journal-4814	58	9	exerted	exert	VERB
american_scientific_journal-4814	58	10	on	on	ADP
american_scientific_journal-4814	58	11	(	(	PUNCT
american_scientific_journal-4814	58	12	𝑆𝑆𝑆𝑆𝑖𝑖	𝑆𝑆𝑆𝑆𝑖𝑖	ADJ
american_scientific_journal-4814	58	13	)	)	PUNCT
american_scientific_journal-4814	58	14	tip	tip	NOUN
american_scientific_journal-4814	58	15	,	,	PUNCT
american_scientific_journal-4814	58	16	is	be	AUX
american_scientific_journal-4814	58	17	determined	determine	VERB
american_scientific_journal-4814	58	18	by	by	ADP
american_scientific_journal-4814	58	19	:	:	PUNCT
american_scientific_journal-4814	58	20	𝑢𝑢𝑖𝑖′′(𝑙𝑙	𝑢𝑢𝑖𝑖′′(𝑙𝑙	NOUN
american_scientific_journal-4814	58	21	,	,	PUNCT
american_scientific_journal-4814	58	22	𝑡𝑡	𝑡𝑡	ADJ
american_scientific_journal-4814	58	23	)	)	PUNCT
american_scientific_journal-4814	58	24	=	=	SYM
american_scientific_journal-4814	59	1	0	0	X
american_scientific_journal-4814	59	2	.	.	PUNCT
american_scientific_journal-4814	60	1	(	(	PUNCT
american_scientific_journal-4814	60	2	10	10	NUM
american_scientific_journal-4814	60	3	)	)	PUNCT
american_scientific_journal-4814	60	4	3	3	NUM
american_scientific_journal-4814	60	5	.	.	X
american_scientific_journal-4814	61	1	resolution	resolution	NOUN
american_scientific_journal-4814	61	2	of	of	ADP
american_scientific_journal-4814	61	3	the	the	DET
american_scientific_journal-4814	61	4	global	global	ADJ
american_scientific_journal-4814	61	5	modes	mode	NOUN
american_scientific_journal-4814	61	6	equations	equation	NOUN
american_scientific_journal-4814	61	7	3.1	3.1	NUM
american_scientific_journal-4814	61	8	.	.	PUNCT
american_scientific_journal-4814	62	1	analytical	analytical	ADJ
american_scientific_journal-4814	62	2	forms	form	NOUN
american_scientific_journal-4814	62	3	of	of	ADP
american_scientific_journal-4814	62	4	the	the	DET
american_scientific_journal-4814	62	5	shape	shape	NOUN
american_scientific_journal-4814	62	6	functions	function	NOUN
american_scientific_journal-4814	62	7	the	the	DET
american_scientific_journal-4814	62	8	global	global	ADJ
american_scientific_journal-4814	62	9	modes	mode	NOUN
american_scientific_journal-4814	62	10	are	be	AUX
american_scientific_journal-4814	62	11	the	the	DET
american_scientific_journal-4814	62	12	solutions	solution	NOUN
american_scientific_journal-4814	62	13	obtained	obtain	VERB
american_scientific_journal-4814	62	14	by	by	ADP
american_scientific_journal-4814	62	15	setting	set	VERB
american_scientific_journal-4814	62	16	the	the	DET
american_scientific_journal-4814	62	17	following	follow	VERB
american_scientific_journal-4814	62	18	conditions	condition	NOUN
american_scientific_journal-4814	62	19	in	in	ADP
american_scientific_journal-4814	62	20	the	the	DET
american_scientific_journal-4814	62	21	equations	equation	NOUN
american_scientific_journal-4814	62	22	(	(	PUNCT
american_scientific_journal-4814	62	23	1	1	NUM
american_scientific_journal-4814	62	24	)	)	PUNCT
american_scientific_journal-4814	62	25	,	,	PUNCT
american_scientific_journal-4814	62	26	(	(	PUNCT
american_scientific_journal-4814	62	27	3	3	NUM
american_scientific_journal-4814	62	28	)	)	PUNCT
american_scientific_journal-4814	62	29	,	,	PUNCT
american_scientific_journal-4814	62	30	(	(	PUNCT
american_scientific_journal-4814	62	31	4	4	NUM
american_scientific_journal-4814	62	32	)	)	PUNCT
american_scientific_journal-4814	62	33	and	and	CCONJ
american_scientific_journal-4814	62	34	(	(	PUNCT
american_scientific_journal-4814	62	35	5	5	NUM
american_scientific_journal-4814	62	36	):	):	PUNCT
american_scientific_journal-4814	62	37	american	american	ADJ
american_scientific_journal-4814	62	38	scientific	scientific	ADJ
american_scientific_journal-4814	62	39	research	research	PROPN
american_scientific_journal-4814	62	40	journal	journal	NOUN
american_scientific_journal-4814	62	41	for	for	ADP
american_scientific_journal-4814	62	42	engineering	engineering	NOUN
american_scientific_journal-4814	62	43	,	,	PUNCT
american_scientific_journal-4814	62	44	technology	technology	NOUN
american_scientific_journal-4814	62	45	,	,	PUNCT
american_scientific_journal-4814	62	46	and	and	CCONJ
american_scientific_journal-4814	62	47	sciences	science	NOUN
american_scientific_journal-4814	62	48	(	(	PUNCT
american_scientific_journal-4814	62	49	asrjets	asrjet	NOUN
american_scientific_journal-4814	62	50	)	)	PUNCT
american_scientific_journal-4814	62	51	(	(	PUNCT
american_scientific_journal-4814	62	52	2019	2019	NUM
american_scientific_journal-4814	62	53	)	)	PUNCT
american_scientific_journal-4814	62	54	volume	volume	NOUN
american_scientific_journal-4814	62	55	55	55	NUM
american_scientific_journal-4814	62	56	,	,	PUNCT
american_scientific_journal-4814	62	57	no	no	DET
american_scientific_journal-4814	62	58	1	1	NUM
american_scientific_journal-4814	62	59	,	,	PUNCT
american_scientific_journal-4814	62	60	pp	pp	ADP
american_scientific_journal-4814	62	61	50	50	NUM
american_scientific_journal-4814	62	62	-	-	SYM
american_scientific_journal-4814	62	63	68	68	NUM
american_scientific_journal-4814	62	64	54	54	NUM
american_scientific_journal-4814	62	65	υ	υ	NOUN
american_scientific_journal-4814	62	66	=	=	NOUN
american_scientific_journal-4814	62	67	0	0	NUM
american_scientific_journal-4814	62	68	,	,	PUNCT
american_scientific_journal-4814	62	69	𝑛𝑛0	𝑛𝑛0	X
american_scientific_journal-4814	62	70	=	=	SYM
american_scientific_journal-4814	62	71	0	0	X
american_scientific_journal-4814	62	72	.	.	PUNCT
american_scientific_journal-4814	63	1	(	(	PUNCT
american_scientific_journal-4814	63	2	11	11	NUM
american_scientific_journal-4814	63	3	)	)	PUNCT
american_scientific_journal-4814	63	4	in	in	ADP
american_scientific_journal-4814	63	5	this	this	DET
american_scientific_journal-4814	63	6	case	case	NOUN
american_scientific_journal-4814	63	7	,	,	PUNCT
american_scientific_journal-4814	63	8	the	the	DET
american_scientific_journal-4814	63	9	space	space	NOUN
american_scientific_journal-4814	63	10	vehicle	vehicle	NOUN
american_scientific_journal-4814	63	11	attitudes	attitude	NOUN
american_scientific_journal-4814	63	12	motion	motion	NOUN
american_scientific_journal-4814	63	13	are	be	AUX
american_scientific_journal-4814	63	14	decoupled	decouple	VERB
american_scientific_journal-4814	63	15	.	.	PUNCT
american_scientific_journal-4814	64	1	here	here	ADV
american_scientific_journal-4814	64	2	,	,	PUNCT
american_scientific_journal-4814	64	3	one	one	PRON
american_scientific_journal-4814	64	4	recalls	recall	VERB
american_scientific_journal-4814	64	5	that	that	SCONJ
american_scientific_journal-4814	64	6	the	the	DET
american_scientific_journal-4814	64	7	interest	interest	NOUN
american_scientific_journal-4814	64	8	is	be	AUX
american_scientific_journal-4814	64	9	put	put	VERB
american_scientific_journal-4814	64	10	on	on	ADP
american_scientific_journal-4814	64	11	the	the	DET
american_scientific_journal-4814	64	12	lace	lace	NOUN
american_scientific_journal-4814	64	13	attitude	attitude	NOUN
american_scientific_journal-4814	64	14	motion	motion	NOUN
american_scientific_journal-4814	64	15	of	of	ADP
american_scientific_journal-4814	64	16	the	the	DET
american_scientific_journal-4814	64	17	space	space	NOUN
american_scientific_journal-4814	64	18	vehicle	vehicle	NOUN
american_scientific_journal-4814	64	19	interacting	interact	VERB
american_scientific_journal-4814	64	20	with	with	ADP
american_scientific_journal-4814	64	21	the	the	DET
american_scientific_journal-4814	64	22	solar	solar	ADJ
american_scientific_journal-4814	64	23	arrays	array	NOUN
american_scientific_journal-4814	64	24	bending	bend	VERB
american_scientific_journal-4814	64	25	in	in	ADP
american_scientific_journal-4814	64	26	plane	plane	NOUN
american_scientific_journal-4814	64	27	.	.	PUNCT
american_scientific_journal-4814	65	1	the	the	DET
american_scientific_journal-4814	65	2	global	global	ADJ
american_scientific_journal-4814	65	3	modes	mode	NOUN
american_scientific_journal-4814	65	4	solutions	solution	NOUN
american_scientific_journal-4814	65	5	proposed	propose	VERB
american_scientific_journal-4814	65	6	are	be	AUX
american_scientific_journal-4814	65	7	of	of	ADP
american_scientific_journal-4814	65	8	the	the	DET
american_scientific_journal-4814	65	9	forms	form	NOUN
american_scientific_journal-4814	65	10	:	:	PUNCT
american_scientific_journal-4814	65	11	�	�	PROPN
american_scientific_journal-4814	65	12	𝜃𝜃(𝑡𝑡	𝜃𝜃(𝑡𝑡	PROPN
american_scientific_journal-4814	65	13	)	)	PUNCT
american_scientific_journal-4814	66	1	=	=	PRON
american_scientific_journal-4814	66	2	𝜃𝜃𝑛𝑛	𝜃𝜃𝑛𝑛	X
american_scientific_journal-4814	66	3	𝑐𝑐𝑐𝑐𝑠𝑠(𝜑𝜑𝑛𝑛𝑡𝑡	𝑐𝑐𝑐𝑐𝑠𝑠(𝜑𝜑𝑛𝑛𝑡𝑡	NOUN
american_scientific_journal-4814	66	4	)	)	PUNCT
american_scientific_journal-4814	66	5	𝑢𝑢𝑖𝑖(𝑠𝑠	𝑢𝑢𝑖𝑖(𝑠𝑠	NOUN
american_scientific_journal-4814	66	6	,	,	PUNCT
american_scientific_journal-4814	66	7	𝑡𝑡	𝑡𝑡	ADJ
american_scientific_journal-4814	66	8	)	)	PUNCT
american_scientific_journal-4814	66	9	=	=	SYM
american_scientific_journal-4814	66	10	𝑈𝑈𝑛𝑛𝑖𝑖(𝑠𝑠	𝑈𝑈𝑛𝑛𝑖𝑖(𝑠𝑠	PROPN
american_scientific_journal-4814	66	11	)	)	PUNCT
american_scientific_journal-4814	66	12	𝑐𝑐𝑐𝑐𝑠𝑠(𝜑𝜑𝑛𝑛𝑡𝑡	𝑐𝑐𝑐𝑐𝑠𝑠(𝜑𝜑𝑛𝑛𝑡𝑡	NOUN
american_scientific_journal-4814	66	13	)	)	PUNCT
american_scientific_journal-4814	66	14	𝛼𝛼𝑖𝑖(𝑠𝑠	𝛼𝛼𝑖𝑖(𝑠𝑠	NOUN
american_scientific_journal-4814	66	15	,	,	PUNCT
american_scientific_journal-4814	66	16	𝑡𝑡	𝑡𝑡	ADJ
american_scientific_journal-4814	66	17	)	)	PUNCT
american_scientific_journal-4814	66	18	=	=	SYM
american_scientific_journal-4814	66	19	𝛼𝛼𝑛𝑛𝑖𝑖(𝑠𝑠	𝛼𝛼𝑛𝑛𝑖𝑖(𝑠𝑠	NOUN
american_scientific_journal-4814	66	20	)	)	PUNCT
american_scientific_journal-4814	66	21	𝑐𝑐𝑐𝑐𝑠𝑠(𝜑𝜑𝑛𝑛𝑡𝑡	𝑐𝑐𝑐𝑐𝑠𝑠(𝜑𝜑𝑛𝑛𝑡𝑡	NOUN
american_scientific_journal-4814	66	22	)	)	PUNCT
american_scientific_journal-4814	66	23	.	.	PUNCT
american_scientific_journal-4814	67	1	(	(	PUNCT
american_scientific_journal-4814	67	2	12	12	NUM
american_scientific_journal-4814	67	3	)	)	PUNCT
american_scientific_journal-4814	67	4	with	with	ADP
american_scientific_journal-4814	67	5	:	:	PUNCT
american_scientific_journal-4814	67	6	�	�	PROPN
american_scientific_journal-4814	67	7	𝑈𝑈𝑛𝑛𝑖𝑖(𝑠𝑠	𝑈𝑈𝑛𝑛𝑖𝑖(𝑠𝑠	NOUN
american_scientific_journal-4814	67	8	)	)	PUNCT
american_scientific_journal-4814	67	9	=	=	SYM
american_scientific_journal-4814	67	10	(	(	PUNCT
american_scientific_journal-4814	67	11	−1)𝑖𝑖𝜃𝜃𝑛𝑛𝑈𝑈𝑛𝑛∗(𝑠𝑠	−1)𝑖𝑖𝜃𝜃𝑛𝑛𝑈𝑈𝑛𝑛∗(𝑠𝑠	NOUN
american_scientific_journal-4814	67	12	)	)	PUNCT
american_scientific_journal-4814	67	13	𝛼𝛼𝑛𝑛𝑖𝑖(𝑠𝑠	𝛼𝛼𝑛𝑛𝑖𝑖(𝑠𝑠	NOUN
american_scientific_journal-4814	67	14	)	)	PUNCT
american_scientific_journal-4814	67	15	=	=	SYM
american_scientific_journal-4814	67	16	(	(	PUNCT
american_scientific_journal-4814	67	17	−1)𝑖𝑖𝜃𝜃𝑛𝑛𝛼𝛼𝑛𝑛∗(𝑠𝑠	−1)𝑖𝑖𝜃𝜃𝑛𝑛𝛼𝛼𝑛𝑛∗(𝑠𝑠	NOUN
american_scientific_journal-4814	67	18	)	)	PUNCT
american_scientific_journal-4814	67	19	;	;	PUNCT
american_scientific_journal-4814	68	1	𝑛𝑛	𝑛𝑛	NOUN
american_scientific_journal-4814	68	2	=	=	SYM
american_scientific_journal-4814	68	3	1	1	NUM
american_scientific_journal-4814	68	4	,	,	PUNCT
american_scientific_journal-4814	68	5	…	…	PUNCT
american_scientific_journal-4814	68	6	…	…	PUNCT
american_scientific_journal-4814	68	7	,	,	PUNCT
american_scientific_journal-4814	68	8	∞.	∞.	PROPN
american_scientific_journal-4814	68	9	(	(	PUNCT
american_scientific_journal-4814	68	10	13	13	NUM
american_scientific_journal-4814	68	11	)	)	PUNCT
american_scientific_journal-4814	68	12	one	one	NOUN
american_scientific_journal-4814	68	13	gets	get	VERB
american_scientific_journal-4814	68	14	,	,	PUNCT
american_scientific_journal-4814	68	15	from	from	ADP
american_scientific_journal-4814	68	16	the	the	DET
american_scientific_journal-4814	68	17	resolution	resolution	NOUN
american_scientific_journal-4814	68	18	of	of	ADP
american_scientific_journal-4814	68	19	the	the	DET
american_scientific_journal-4814	68	20	equations	equation	NOUN
american_scientific_journal-4814	68	21	(	(	PUNCT
american_scientific_journal-4814	68	22	3	3	NUM
american_scientific_journal-4814	68	23	)	)	PUNCT
american_scientific_journal-4814	68	24	and	and	CCONJ
american_scientific_journal-4814	68	25	(	(	PUNCT
american_scientific_journal-4814	68	26	4	4	NUM
american_scientific_journal-4814	68	27	)	)	PUNCT
american_scientific_journal-4814	68	28	,	,	PUNCT
american_scientific_journal-4814	68	29	the	the	DET
american_scientific_journal-4814	68	30	following	follow	VERB
american_scientific_journal-4814	68	31	solutions	solution	NOUN
american_scientific_journal-4814	68	32	:	:	PUNCT
american_scientific_journal-4814	68	33	⎩	⎩	NUM
american_scientific_journal-4814	68	34	⎪	⎪	NOUN
american_scientific_journal-4814	68	35	⎨	⎨	ADJ
american_scientific_journal-4814	68	36	⎪	⎪	NOUN
american_scientific_journal-4814	69	1	⎧𝑈𝑈𝑛𝑛	⎧𝑈𝑈𝑛𝑛	ADJ
american_scientific_journal-4814	69	2	∗(𝑠𝑠	∗(𝑠𝑠	NOUN
american_scientific_journal-4814	69	3	)	)	PUNCT
american_scientific_journal-4814	69	4	=	=	NOUN
american_scientific_journal-4814	69	5	𝑎𝑎𝑛𝑛	𝑎𝑎𝑛𝑛	NOUN
american_scientific_journal-4814	69	6	𝑐𝑐𝑐𝑐𝑠𝑠ℎ(𝜓𝜓𝑛𝑛𝑠𝑠	𝑐𝑐𝑐𝑐𝑠𝑠ℎ(𝜓𝜓𝑛𝑛𝑠𝑠	NOUN
american_scientific_journal-4814	69	7	)	)	PUNCT
american_scientific_journal-4814	69	8	+	+	NUM
american_scientific_journal-4814	69	9	𝑏𝑏𝑛𝑛	𝑏𝑏𝑛𝑛	PROPN
american_scientific_journal-4814	69	10	𝑠𝑠𝑖𝑖𝑛𝑛ℎ(𝜓𝜓𝑛𝑛𝑠𝑠	𝑠𝑠𝑖𝑖𝑛𝑛ℎ(𝜓𝜓𝑛𝑛𝑠𝑠	PROPN
american_scientific_journal-4814	69	11	)	)	PUNCT
american_scientific_journal-4814	69	12	+	+	CCONJ
american_scientific_journal-4814	69	13	(	(	PUNCT
american_scientific_journal-4814	69	14	𝑏𝑏	𝑏𝑏	NUM
american_scientific_journal-4814	69	15	−	−	PROPN
american_scientific_journal-4814	69	16	𝑎𝑎𝑛𝑛	𝑎𝑎𝑛𝑛	NOUN
american_scientific_journal-4814	69	17	)	)	PUNCT
american_scientific_journal-4814	69	18	𝑐𝑐𝑐𝑐𝑠𝑠(𝜙𝜙𝑛𝑛𝑠𝑠	𝑐𝑐𝑐𝑐𝑠𝑠(𝜙𝜙𝑛𝑛𝑠𝑠	PROPN
american_scientific_journal-4814	69	19	)	)	PUNCT
american_scientific_journal-4814	70	1	+	+	CCONJ
american_scientific_journal-4814	70	2	1	1	NUM
american_scientific_journal-4814	70	3	−	−	NOUN
american_scientific_journal-4814	70	4	𝑏𝑏𝑛𝑛𝜓𝜓𝑛𝑛	𝑏𝑏𝑛𝑛𝜓𝜓𝑛𝑛	PROPN
american_scientific_journal-4814	70	5	𝜙𝜙𝑛𝑛	𝜙𝜙𝑛𝑛	NOUN
american_scientific_journal-4814	70	6	𝑠𝑠𝑖𝑖𝑛𝑛(𝜙𝜙𝑛𝑛𝑠𝑠	𝑠𝑠𝑖𝑖𝑛𝑛(𝜙𝜙𝑛𝑛𝑠𝑠	NOUN
american_scientific_journal-4814	70	7	)	)	PUNCT
american_scientific_journal-4814	70	8	−	−	PROPN
american_scientific_journal-4814	70	9	𝑏𝑏	𝑏𝑏	NOUN
american_scientific_journal-4814	70	10	−	−	NOUN
american_scientific_journal-4814	70	11	𝑠𝑠	𝑠𝑠	ADV
american_scientific_journal-4814	70	12	𝛼𝛼𝑛𝑛∗(𝑠𝑠	𝛼𝛼𝑛𝑛∗(𝑠𝑠	NOUN
american_scientific_journal-4814	70	13	)	)	PUNCT
american_scientific_journal-4814	70	14	=	=	SYM
american_scientific_journal-4814	70	15	𝑐𝑐𝑛𝑛	𝑐𝑐𝑛𝑛	NOUN
american_scientific_journal-4814	70	16	𝑠𝑠𝑖𝑖𝑛𝑛(𝜉𝜉𝑛𝑛𝑠𝑠	𝑠𝑠𝑖𝑖𝑛𝑛(𝜉𝜉𝑛𝑛𝑠𝑠	NOUN
american_scientific_journal-4814	70	17	)	)	PUNCT
american_scientific_journal-4814	71	1	+	+	NUM
american_scientific_journal-4814	71	2	𝑏𝑏	𝑏𝑏	NOUN
american_scientific_journal-4814	71	3	𝑐𝑐𝑐𝑐𝑠𝑠(𝜉𝜉𝑛𝑛𝑠𝑠	𝑐𝑐𝑐𝑐𝑠𝑠(𝜉𝜉𝑛𝑛𝑠𝑠	NOUN
american_scientific_journal-4814	71	4	)	)	PUNCT
american_scientific_journal-4814	72	1	−	−	NOUN
american_scientific_journal-4814	72	2	𝑏𝑏	𝑏𝑏	NOUN
american_scientific_journal-4814	72	3	−	−	NOUN
american_scientific_journal-4814	73	1	𝑠𝑠	𝑠𝑠	ADP
american_scientific_journal-4814	73	2	,	,	PUNCT
american_scientific_journal-4814	73	3	where	where	SCONJ
american_scientific_journal-4814	73	4	:	:	PUNCT
american_scientific_journal-4814	73	5	𝜓𝜓𝑛𝑛	𝜓𝜓𝑛𝑛	PROPN
american_scientific_journal-4814	73	6	=	=	SYM
american_scientific_journal-4814	73	7	�	�	PROPN
american_scientific_journal-4814	73	8	−	−	PROPN
american_scientific_journal-4814	73	9	𝑆𝑆	𝑆𝑆	PROPN
american_scientific_journal-4814	73	10	2𝐸𝐸𝐸𝐸	2𝐸𝐸𝐸𝐸	PROPN
american_scientific_journal-4814	73	11	+	+	CCONJ
american_scientific_journal-4814	73	12	�	�	PROPN
american_scientific_journal-4814	73	13	�	�	PROPN
american_scientific_journal-4814	73	14	𝑆𝑆	𝑆𝑆	PROPN
american_scientific_journal-4814	73	15	2𝐸𝐸𝐸𝐸	2𝐸𝐸𝐸𝐸	PROPN
american_scientific_journal-4814	73	16	�	�	PROPN
american_scientific_journal-4814	73	17	2	2	NUM
american_scientific_journal-4814	73	18	+	+	CCONJ
american_scientific_journal-4814	73	19	𝜌𝜌𝜏𝜏𝑛𝑛2	𝜌𝜌𝜏𝜏𝑛𝑛2	ADJ
american_scientific_journal-4814	73	20	𝐸𝐸𝐸𝐸	𝐸𝐸𝐸𝐸	PROPN
american_scientific_journal-4814	73	21	;	;	PUNCT
american_scientific_journal-4814	73	22	𝜙𝜙𝑛𝑛	𝜙𝜙𝑛𝑛	NOUN
american_scientific_journal-4814	73	23	=	=	SYM
american_scientific_journal-4814	73	24	�	�	PROPN
american_scientific_journal-4814	73	25	𝑆𝑆	𝑆𝑆	PROPN
american_scientific_journal-4814	73	26	2𝐸𝐸𝐸𝐸	2𝐸𝐸𝐸𝐸	PROPN
american_scientific_journal-4814	73	27	+	+	CCONJ
american_scientific_journal-4814	73	28	�	�	PROPN
american_scientific_journal-4814	73	29	�	�	PROPN
american_scientific_journal-4814	73	30	𝑆𝑆	𝑆𝑆	PROPN
american_scientific_journal-4814	73	31	2𝐸𝐸𝐸𝐸	2𝐸𝐸𝐸𝐸	PROPN
american_scientific_journal-4814	73	32	�	�	PROPN
american_scientific_journal-4814	73	33	2	2	NUM
american_scientific_journal-4814	73	34	+	+	CCONJ
american_scientific_journal-4814	73	35	𝜌𝜌𝜏𝜏𝑛𝑛2	𝜌𝜌𝜏𝜏𝑛𝑛2	ADJ
american_scientific_journal-4814	73	36	𝐸𝐸𝐸𝐸	𝐸𝐸𝐸𝐸	PROPN
american_scientific_journal-4814	73	37	;	;	PUNCT
american_scientific_journal-4814	73	38	and	and	CCONJ
american_scientific_journal-4814	73	39	𝜉𝜉𝑛𝑛	𝜉𝜉𝑛𝑛	ADJ
american_scientific_journal-4814	73	40	=	=	SYM
american_scientific_journal-4814	73	41	𝜑𝜑𝑛𝑛	𝜑𝜑𝑛𝑛	PROPN
american_scientific_journal-4814	73	42	�	�	PROPN
american_scientific_journal-4814	73	43	𝜎𝜎𝑒𝑒	𝜎𝜎𝑒𝑒	PROPN
american_scientific_journal-4814	73	44	�	�	PROPN
american_scientific_journal-4814	73	45	𝑒𝑒𝐺𝐺	𝑒𝑒𝐺𝐺	NOUN
american_scientific_journal-4814	73	46	�	�	PROPN
american_scientific_journal-4814	73	47	+	+	CCONJ
american_scientific_journal-4814	73	48	𝑆𝑆	𝑆𝑆	PROPN
american_scientific_journal-4814	73	49	�	�	PROPN
american_scientific_journal-4814	73	50	.	.	PUNCT
american_scientific_journal-4814	74	1	𝜑𝜑𝑛𝑛	𝜑𝜑𝑛𝑛	PROPN
american_scientific_journal-4814	74	2	is	be	AUX
american_scientific_journal-4814	74	3	the	the	DET
american_scientific_journal-4814	74	4	global	global	ADJ
american_scientific_journal-4814	74	5	eigenfrequency	eigenfrequency	NOUN
american_scientific_journal-4814	74	6	associated	associate	VERB
american_scientific_journal-4814	74	7	with	with	ADP
american_scientific_journal-4814	74	8	the	the	DET
american_scientific_journal-4814	74	9	global	global	ADJ
american_scientific_journal-4814	74	10	eigenmodes	eigenmode	NOUN
american_scientific_journal-4814	74	11	𝜃𝜃𝑛𝑛	𝜃𝜃𝑛𝑛	PROPN
american_scientific_journal-4814	74	12	,	,	PUNCT
american_scientific_journal-4814	74	13	𝑈𝑈𝑛𝑛𝑖𝑖(𝑠𝑠	𝑈𝑈𝑛𝑛𝑖𝑖(𝑠𝑠	NOUN
american_scientific_journal-4814	74	14	)	)	PUNCT
american_scientific_journal-4814	74	15	and	and	CCONJ
american_scientific_journal-4814	74	16	𝛼𝛼𝑛𝑛𝑖𝑖(𝑠𝑠	𝛼𝛼𝑛𝑛𝑖𝑖(𝑠𝑠	NOUN
american_scientific_journal-4814	74	17	)	)	PUNCT
american_scientific_journal-4814	74	18	.	.	PUNCT
american_scientific_journal-4814	75	1	3.2	3.2	NUM
american_scientific_journal-4814	75	2	.	.	PUNCT
american_scientific_journal-4814	75	3	equation	equation	NOUN
american_scientific_journal-4814	75	4	of	of	ADP
american_scientific_journal-4814	75	5	the	the	DET
american_scientific_journal-4814	75	6	eigenfrequencies	eigenfrequencie	NOUN
american_scientific_journal-4814	75	7	the	the	DET
american_scientific_journal-4814	75	8	solutions	solution	NOUN
american_scientific_journal-4814	75	9	of	of	ADP
american_scientific_journal-4814	75	10	formula	formula	NOUN
american_scientific_journal-4814	75	11	(	(	PUNCT
american_scientific_journal-4814	75	12	12	12	NUM
american_scientific_journal-4814	75	13	)	)	PUNCT
american_scientific_journal-4814	75	14	are	be	AUX
american_scientific_journal-4814	75	15	introduced	introduce	VERB
american_scientific_journal-4814	75	16	into	into	ADP
american_scientific_journal-4814	75	17	the	the	DET
american_scientific_journal-4814	75	18	equations	equation	NOUN
american_scientific_journal-4814	75	19	of	of	ADP
american_scientific_journal-4814	75	20	the	the	DET
american_scientific_journal-4814	75	21	global	global	ADJ
american_scientific_journal-4814	75	22	motion	motion	NOUN
american_scientific_journal-4814	75	23	(	(	PUNCT
american_scientific_journal-4814	75	24	1	1	NUM
american_scientific_journal-4814	75	25	)	)	PUNCT
american_scientific_journal-4814	75	26	,	,	PUNCT
american_scientific_journal-4814	75	27	and	and	CCONJ
american_scientific_journal-4814	75	28	taking	take	VERB
american_scientific_journal-4814	75	29	into	into	ADP
american_scientific_journal-4814	75	30	account	account	NOUN
american_scientific_journal-4814	75	31	the	the	DET
american_scientific_journal-4814	75	32	conditions	condition	NOUN
american_scientific_journal-4814	75	33	(	(	PUNCT
american_scientific_journal-4814	75	34	11	11	NUM
american_scientific_journal-4814	75	35	)	)	PUNCT
american_scientific_journal-4814	75	36	,	,	PUNCT
american_scientific_journal-4814	75	37	one	one	PRON
american_scientific_journal-4814	75	38	obtains	obtain	VERB
american_scientific_journal-4814	75	39	from	from	ADP
american_scientific_journal-4814	75	40	laborious	laborious	ADJ
american_scientific_journal-4814	75	41	calculations	calculation	NOUN
american_scientific_journal-4814	75	42	the	the	DET
american_scientific_journal-4814	75	43	following	follow	VERB
american_scientific_journal-4814	75	44	equation	equation	NOUN
american_scientific_journal-4814	75	45	of	of	ADP
american_scientific_journal-4814	75	46	the	the	DET
american_scientific_journal-4814	75	47	eigenfrequencies	eigenfrequencie	NOUN
american_scientific_journal-4814	75	48	:	:	PUNCT
american_scientific_journal-4814	75	49	american	american	PROPN
american_scientific_journal-4814	75	50	scientific	scientific	ADJ
american_scientific_journal-4814	75	51	research	research	PROPN
american_scientific_journal-4814	75	52	journal	journal	NOUN
american_scientific_journal-4814	75	53	for	for	ADP
american_scientific_journal-4814	75	54	engineering	engineering	NOUN
american_scientific_journal-4814	75	55	,	,	PUNCT
american_scientific_journal-4814	75	56	technology	technology	NOUN
american_scientific_journal-4814	75	57	,	,	PUNCT
american_scientific_journal-4814	75	58	and	and	CCONJ
american_scientific_journal-4814	75	59	sciences	science	NOUN
american_scientific_journal-4814	75	60	(	(	PUNCT
american_scientific_journal-4814	75	61	asrjets	asrjet	NOUN
american_scientific_journal-4814	75	62	)	)	PUNCT
american_scientific_journal-4814	75	63	(	(	PUNCT
american_scientific_journal-4814	75	64	2019	2019	NUM
american_scientific_journal-4814	75	65	)	)	PUNCT
american_scientific_journal-4814	75	66	volume	volume	NOUN
american_scientific_journal-4814	75	67	55	55	NUM
american_scientific_journal-4814	75	68	,	,	PUNCT
american_scientific_journal-4814	75	69	no	no	DET
american_scientific_journal-4814	75	70	1	1	NUM
american_scientific_journal-4814	75	71	,	,	PUNCT
american_scientific_journal-4814	75	72	pp	pp	ADP
american_scientific_journal-4814	75	73	50	50	NUM
american_scientific_journal-4814	75	74	-	-	SYM
american_scientific_journal-4814	75	75	68	68	NUM
american_scientific_journal-4814	75	76	55	55	NUM
american_scientific_journal-4814	75	77	∫	∫	NOUN
american_scientific_journal-4814	75	78	𝜌𝜌(𝑏𝑏	𝜌𝜌(𝑏𝑏	PROPN
american_scientific_journal-4814	76	1	+	+	CCONJ
american_scientific_journal-4814	77	1	𝑠𝑠)𝑈𝑈𝑛𝑛∗(𝑠𝑠)𝑑𝑑𝑠𝑠𝑙𝑙	𝑠𝑠)𝑈𝑈𝑛𝑛∗(𝑠𝑠)𝑑𝑑𝑠𝑠𝑙𝑙	PROPN
american_scientific_journal-4814	77	2	0	0	NUM
american_scientific_journal-4814	78	1	+	+	NUM
american_scientific_journal-4814	78	2	𝜎𝜎𝑒𝑒	𝜎𝜎𝑒𝑒	NOUN
american_scientific_journal-4814	78	3	∫	∫	PROPN
american_scientific_journal-4814	78	4	(	(	PUNCT
american_scientific_journal-4814	78	5	𝑏𝑏	𝑏𝑏	NOUN
american_scientific_journal-4814	78	6	+	+	CCONJ
american_scientific_journal-4814	78	7	𝑠𝑠)𝛼𝛼𝑛𝑛∗(𝑠𝑠)𝑑𝑑𝑠𝑠𝑙𝑙	𝑠𝑠)𝛼𝛼𝑛𝑛∗(𝑠𝑠)𝑑𝑑𝑠𝑠𝑙𝑙	NUM
american_scientific_journal-4814	78	8	0	0	NUM
american_scientific_journal-4814	79	1	+	+	CCONJ
american_scientific_journal-4814	79	2	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-4814	79	3	�	�	PROPN
american_scientific_journal-4814	79	4	(𝑏𝑏	(𝑏𝑏	SYM
american_scientific_journal-4814	79	5	+	+	NUM
american_scientific_journal-4814	79	6	𝑙𝑙)𝑈𝑈𝑛𝑛∗(𝑙𝑙	𝑙𝑙)𝑈𝑈𝑛𝑛∗(𝑙𝑙	X
american_scientific_journal-4814	79	7	)	)	PUNCT
american_scientific_journal-4814	79	8	=	=	PUNCT
american_scientific_journal-4814	80	1	−𝐶𝐶	−𝐶𝐶	ADJ
american_scientific_journal-4814	80	2	2	2	NUM
american_scientific_journal-4814	80	3	.	.	PUNCT
american_scientific_journal-4814	81	1	(	(	PUNCT
american_scientific_journal-4814	81	2	14	14	NUM
american_scientific_journal-4814	81	3	)	)	PUNCT
american_scientific_journal-4814	81	4	the	the	DET
american_scientific_journal-4814	81	5	global	global	ADJ
american_scientific_journal-4814	81	6	eigenfrequencies	eigenfrequencie	NOUN
american_scientific_journal-4814	81	7	𝜑𝜑𝑛𝑛	𝜑𝜑𝑛𝑛	PROPN
american_scientific_journal-4814	81	8	corresponding	correspond	VERB
american_scientific_journal-4814	81	9	to	to	ADP
american_scientific_journal-4814	81	10	bending	bend	VERB
american_scientific_journal-4814	81	11	in	in	ADP
american_scientific_journal-4814	81	12	plane	plane	NOUN
american_scientific_journal-4814	81	13	,	,	PUNCT
american_scientific_journal-4814	81	14	are	be	AUX
american_scientific_journal-4814	81	15	computed	compute	VERB
american_scientific_journal-4814	81	16	by	by	ADP
american_scientific_journal-4814	81	17	means	mean	NOUN
american_scientific_journal-4814	81	18	of	of	ADP
american_scientific_journal-4814	81	19	the	the	DET
american_scientific_journal-4814	81	20	equation	equation	NOUN
american_scientific_journal-4814	81	21	(	(	PUNCT
american_scientific_journal-4814	81	22	14	14	NUM
american_scientific_journal-4814	81	23	)	)	PUNCT
american_scientific_journal-4814	81	24	.	.	PUNCT
american_scientific_journal-4814	82	1	3.3	3.3	NUM
american_scientific_journal-4814	82	2	.	.	PUNCT
american_scientific_journal-4814	83	1	calculation	calculation	NOUN
american_scientific_journal-4814	83	2	of	of	ADP
american_scientific_journal-4814	83	3	the	the	DET
american_scientific_journal-4814	83	4	lace	lace	NOUN
american_scientific_journal-4814	83	5	attitude	attitude	NOUN
american_scientific_journal-4814	83	6	𝜽𝜽𝒏𝒏	𝜽𝜽𝒏𝒏	PROPN
american_scientific_journal-4814	83	7	one	one	PRON
american_scientific_journal-4814	83	8	considers	consider	VERB
american_scientific_journal-4814	83	9	a	a	DET
american_scientific_journal-4814	83	10	set	set	NOUN
american_scientific_journal-4814	83	11	of	of	ADP
american_scientific_journal-4814	83	12	global	global	ADJ
american_scientific_journal-4814	83	13	eigenmodes	eigenmode	NOUN
american_scientific_journal-4814	83	14	denoted	denote	VERB
american_scientific_journal-4814	83	15	by	by	ADP
american_scientific_journal-4814	83	16	(	(	PUNCT
american_scientific_journal-4814	83	17	𝑈𝑈𝑛𝑛𝑖𝑖	𝑈𝑈𝑛𝑛𝑖𝑖	PROPN
american_scientific_journal-4814	83	18	,	,	PUNCT
american_scientific_journal-4814	83	19	𝑈𝑈𝑝𝑝𝑖𝑖	𝑈𝑈𝑝𝑝𝑖𝑖	PROPN
american_scientific_journal-4814	83	20	)	)	PUNCT
american_scientific_journal-4814	83	21	,	,	PUNCT
american_scientific_journal-4814	83	22	and	and	CCONJ
american_scientific_journal-4814	83	23	(	(	PUNCT
american_scientific_journal-4814	83	24	𝛼𝛼𝑛𝑛𝑖𝑖,𝛼𝛼𝑝𝑝𝑖𝑖	𝛼𝛼𝑛𝑛𝑖𝑖,𝛼𝛼𝑝𝑝𝑖𝑖	NUM
american_scientific_journal-4814	83	25	)	)	PUNCT
american_scientific_journal-4814	83	26	,	,	PUNCT
american_scientific_journal-4814	83	27	satisfying	satisfy	VERB
american_scientific_journal-4814	83	28	the	the	DET
american_scientific_journal-4814	83	29	following	following	NOUN
american_scientific_journal-4814	83	30	normalized	normalize	VERB
american_scientific_journal-4814	83	31	orthogonality	orthogonality	NOUN
american_scientific_journal-4814	83	32	property	property	NOUN
american_scientific_journal-4814	83	33	(	(	PUNCT
american_scientific_journal-4814	83	34	see	see	VERB
american_scientific_journal-4814	83	35	appendix	appendix	NOUN
american_scientific_journal-4814	83	36	3	3	NUM
american_scientific_journal-4814	83	37	):	):	PUNCT
american_scientific_journal-4814	83	38	𝜃𝜃𝑛𝑛𝜃𝜃𝑝𝑝	𝜃𝜃𝑛𝑛𝜃𝜃𝑝𝑝	PROPN
american_scientific_journal-4814	83	39	�	�	PROPN
american_scientific_journal-4814	83	40	2	2	NUM
american_scientific_journal-4814	83	41	�	�	PROPN
american_scientific_journal-4814	83	42	𝜌𝜌	𝜌𝜌	PROPN
american_scientific_journal-4814	83	43	∫	∫	PROPN
american_scientific_journal-4814	83	44	𝑈𝑈𝑛𝑛∗(𝑠𝑠)𝑈𝑈𝑝𝑝∗(𝑠𝑠)𝑑𝑑𝑠𝑠𝑙𝑙	𝑈𝑈𝑛𝑛∗(𝑠𝑠)𝑈𝑈𝑝𝑝∗(𝑠𝑠)𝑑𝑑𝑠𝑠𝑙𝑙	PROPN
american_scientific_journal-4814	83	45	0	0	NUM
american_scientific_journal-4814	84	1	+	+	NUM
american_scientific_journal-4814	84	2	𝜎𝜎𝑒𝑒	𝜎𝜎𝑒𝑒	NOUN
american_scientific_journal-4814	84	3	∫	∫	PROPN
american_scientific_journal-4814	84	4	𝛼𝛼𝑛𝑛∗(𝑠𝑠)𝛼𝛼𝑝𝑝∗(𝑠𝑠)𝑑𝑑𝑠𝑠𝑙𝑙	𝛼𝛼𝑛𝑛∗(𝑠𝑠)𝛼𝛼𝑝𝑝∗(𝑠𝑠)𝑑𝑑𝑠𝑠𝑙𝑙	PROPN
american_scientific_journal-4814	84	5	0	0	NUM
american_scientific_journal-4814	85	1	+	+	CCONJ
american_scientific_journal-4814	85	2	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-4814	85	3	�	�	NOUN
american_scientific_journal-4814	85	4	𝑈𝑈𝑛𝑛∗(𝑙𝑙)𝑈𝑈𝑝𝑝∗(𝑙𝑙	𝑈𝑈𝑛𝑛∗(𝑙𝑙)𝑈𝑈𝑝𝑝∗(𝑙𝑙	NOUN
american_scientific_journal-4814	85	5	)	)	PUNCT
american_scientific_journal-4814	85	6	�	�	PROPN
american_scientific_journal-4814	85	7	−	−	PROPN
american_scientific_journal-4814	85	8	𝐶𝐶	𝐶𝐶	PROPN
american_scientific_journal-4814	85	9	�	�	PROPN
american_scientific_journal-4814	85	10	=	=	SYM
american_scientific_journal-4814	85	11	𝛿𝛿𝑛𝑛𝑝𝑝.	𝛿𝛿𝑛𝑛𝑝𝑝.	PROPN
american_scientific_journal-4814	85	12	(	(	PUNCT
american_scientific_journal-4814	85	13	15	15	NUM
american_scientific_journal-4814	85	14	)	)	PUNCT
american_scientific_journal-4814	85	15	𝛿𝛿𝑛𝑛𝑝𝑝	𝛿𝛿𝑛𝑛𝑝𝑝	NOUN
american_scientific_journal-4814	85	16	=	=	SYM
american_scientific_journal-4814	85	17	�	�	PROPN
american_scientific_journal-4814	85	18	1	1	NUM
american_scientific_journal-4814	85	19	𝑖𝑖𝑖𝑖	𝑖𝑖𝑖𝑖	NOUN
american_scientific_journal-4814	85	20	𝑛𝑛	𝑛𝑛	NOUN
american_scientific_journal-4814	85	21	=	=	PUNCT
american_scientific_journal-4814	85	22	𝑝𝑝	𝑝𝑝	NOUN
american_scientific_journal-4814	85	23	0	0	NUM
american_scientific_journal-4814	85	24	𝑖𝑖𝑖𝑖	𝑖𝑖𝑖𝑖	ADV
american_scientific_journal-4814	85	25	𝑛𝑛	𝑛𝑛	NOUN
american_scientific_journal-4814	85	26	≠	≠	PROPN
american_scientific_journal-4814	85	27	𝑝𝑝	𝑝𝑝	NOUN
american_scientific_journal-4814	85	28	;	;	PUNCT
american_scientific_journal-4814	85	29	𝑛𝑛	𝑛𝑛	NOUN
american_scientific_journal-4814	85	30	=	=	SYM
american_scientific_journal-4814	85	31	1	1	NUM
american_scientific_journal-4814	85	32	,	,	PUNCT
american_scientific_journal-4814	85	33	…	…	PUNCT
american_scientific_journal-4814	85	34	…	…	PUNCT
american_scientific_journal-4814	85	35	,	,	PUNCT
american_scientific_journal-4814	85	36	∞	∞	PROPN
american_scientific_journal-4814	85	37	;	;	PUNCT
american_scientific_journal-4814	85	38	𝑝𝑝	𝑝𝑝	NOUN
american_scientific_journal-4814	85	39	=	=	SYM
american_scientific_journal-4814	85	40	1	1	NUM
american_scientific_journal-4814	85	41	,	,	PUNCT
american_scientific_journal-4814	85	42	…	…	PUNCT
american_scientific_journal-4814	85	43	…	…	PUNCT
american_scientific_journal-4814	85	44	,	,	PUNCT
american_scientific_journal-4814	85	45	∞	∞	PROPN
american_scientific_journal-4814	85	46	,	,	PUNCT
american_scientific_journal-4814	85	47	𝛿𝛿𝑛𝑛𝑝𝑝	𝛿𝛿𝑛𝑛𝑝𝑝	PROPN
american_scientific_journal-4814	85	48	designates	designate	VERB
american_scientific_journal-4814	85	49	kronecker	kronecker	NOUN
american_scientific_journal-4814	85	50	symbol	symbol	NOUN
american_scientific_journal-4814	85	51	.	.	PUNCT
american_scientific_journal-4814	86	1	using	use	VERB
american_scientific_journal-4814	86	2	the	the	DET
american_scientific_journal-4814	86	3	formula	formula	NOUN
american_scientific_journal-4814	86	4	(	(	PUNCT
american_scientific_journal-4814	86	5	15	15	NUM
american_scientific_journal-4814	86	6	)	)	PUNCT
american_scientific_journal-4814	86	7	,	,	PUNCT
american_scientific_journal-4814	86	8	one	one	PRON
american_scientific_journal-4814	86	9	gets	get	VERB
american_scientific_journal-4814	86	10	the	the	DET
american_scientific_journal-4814	86	11	following	follow	VERB
american_scientific_journal-4814	86	12	expression	expression	NOUN
american_scientific_journal-4814	86	13	of	of	ADP
american_scientific_journal-4814	86	14	the	the	DET
american_scientific_journal-4814	86	15	lace	lace	NOUN
american_scientific_journal-4814	86	16	attitude	attitude	NOUN
american_scientific_journal-4814	86	17	𝜃𝜃𝑛𝑛	𝜃𝜃𝑛𝑛	PROPN
american_scientific_journal-4814	86	18	:	:	PUNCT
american_scientific_journal-4814	86	19	𝜃𝜃𝑛𝑛	𝜃𝜃𝑛𝑛	PROPN
american_scientific_journal-4814	86	20	=	=	SYM
american_scientific_journal-4814	86	21	�	�	PROPN
american_scientific_journal-4814	86	22	2	2	NUM
american_scientific_journal-4814	86	23	�	�	PROPN
american_scientific_journal-4814	86	24	𝜌𝜌	𝜌𝜌	VERB
american_scientific_journal-4814	86	25	∫	∫	PROPN
american_scientific_journal-4814	86	26	𝑈𝑈𝑛𝑛∗2(𝑠𝑠)𝑑𝑑𝑠𝑠𝑙𝑙	𝑈𝑈𝑛𝑛∗2(𝑠𝑠)𝑑𝑑𝑠𝑠𝑙𝑙	PROPN
american_scientific_journal-4814	86	27	0	0	NUM
american_scientific_journal-4814	87	1	+	+	NUM
american_scientific_journal-4814	87	2	𝜎𝜎𝑒𝑒	𝜎𝜎𝑒𝑒	NOUN
american_scientific_journal-4814	87	3	∫	∫	PROPN
american_scientific_journal-4814	87	4	𝛼𝛼𝑛𝑛∗2(𝑠𝑠)𝑑𝑑𝑠𝑠𝑙𝑙	𝛼𝛼𝑛𝑛∗2(𝑠𝑠)𝑑𝑑𝑠𝑠𝑙𝑙	VERB
american_scientific_journal-4814	87	5	0	0	NUM
american_scientific_journal-4814	88	1	+	+	CCONJ
american_scientific_journal-4814	88	2	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-4814	88	3	�	�	NOUN
american_scientific_journal-4814	88	4	𝑈𝑈𝑛𝑛∗2(𝑙𝑙	𝑈𝑈𝑛𝑛∗2(𝑙𝑙	NOUN
american_scientific_journal-4814	88	5	)	)	PUNCT
american_scientific_journal-4814	88	6	�	�	PROPN
american_scientific_journal-4814	88	7	−	−	PROPN
american_scientific_journal-4814	88	8	𝐶𝐶	𝐶𝐶	PROPN
american_scientific_journal-4814	88	9	�	�	PROPN
american_scientific_journal-4814	88	10	−12	−12	PROPN
american_scientific_journal-4814	88	11	.	.	PUNCT
american_scientific_journal-4814	89	1	(	(	PUNCT
american_scientific_journal-4814	89	2	16	16	NUM
american_scientific_journal-4814	89	3	)	)	PUNCT
american_scientific_journal-4814	89	4	4	4	NUM
american_scientific_journal-4814	89	5	.	.	PUNCT
american_scientific_journal-4814	89	6	general	general	ADJ
american_scientific_journal-4814	89	7	motion	motion	NOUN
american_scientific_journal-4814	89	8	of	of	ADP
american_scientific_journal-4814	89	9	the	the	DET
american_scientific_journal-4814	89	10	space	space	NOUN
american_scientific_journal-4814	89	11	vehicle	vehicle	NOUN
american_scientific_journal-4814	89	12	in	in	ADP
american_scientific_journal-4814	89	13	term	term	NOUN
american_scientific_journal-4814	89	14	of	of	ADP
american_scientific_journal-4814	89	15	the	the	DET
american_scientific_journal-4814	89	16	global	global	ADJ
american_scientific_journal-4814	89	17	modes	mode	NOUN
american_scientific_journal-4814	89	18	superposition	superposition	VERB
american_scientific_journal-4814	89	19	the	the	DET
american_scientific_journal-4814	89	20	general	general	ADJ
american_scientific_journal-4814	89	21	motion	motion	NOUN
american_scientific_journal-4814	89	22	of	of	ADP
american_scientific_journal-4814	89	23	the	the	DET
american_scientific_journal-4814	89	24	space	space	NOUN
american_scientific_journal-4814	89	25	vehicle	vehicle	NOUN
american_scientific_journal-4814	89	26	is	be	AUX
american_scientific_journal-4814	89	27	governed	govern	VERB
american_scientific_journal-4814	89	28	by	by	ADP
american_scientific_journal-4814	89	29	the	the	DET
american_scientific_journal-4814	89	30	global	global	ADJ
american_scientific_journal-4814	89	31	equation	equation	NOUN
american_scientific_journal-4814	89	32	(	(	PUNCT
american_scientific_journal-4814	89	33	1	1	NUM
american_scientific_journal-4814	89	34	)	)	PUNCT
american_scientific_journal-4814	89	35	and	and	CCONJ
american_scientific_journal-4814	89	36	the	the	DET
american_scientific_journal-4814	89	37	local	local	ADJ
american_scientific_journal-4814	89	38	equation	equation	NOUN
american_scientific_journal-4814	89	39	(	(	PUNCT
american_scientific_journal-4814	89	40	3	3	NUM
american_scientific_journal-4814	89	41	)	)	PUNCT
american_scientific_journal-4814	89	42	and	and	CCONJ
american_scientific_journal-4814	89	43	(	(	PUNCT
american_scientific_journal-4814	89	44	4	4	X
american_scientific_journal-4814	89	45	)	)	PUNCT
american_scientific_journal-4814	89	46	under	under	ADP
american_scientific_journal-4814	89	47	the	the	DET
american_scientific_journal-4814	89	48	following	following	ADJ
american_scientific_journal-4814	89	49	conditions	condition	NOUN
american_scientific_journal-4814	89	50	:	:	PUNCT
american_scientific_journal-4814	89	51	υ	υ	PROPN
american_scientific_journal-4814	89	52	≠	≠	PROPN
american_scientific_journal-4814	89	53	0	0	NUM
american_scientific_journal-4814	89	54	;	;	PUNCT
american_scientific_journal-4814	89	55	𝑛𝑛0	𝑛𝑛0	X
american_scientific_journal-4814	89	56	≠	≠	PROPN
american_scientific_journal-4814	89	57	0	0	NUM
american_scientific_journal-4814	89	58	;	;	PUNCT
american_scientific_journal-4814	89	59	𝜃𝜃(𝑡𝑡	𝜃𝜃(𝑡𝑡	NOUN
american_scientific_journal-4814	89	60	)	)	PUNCT
american_scientific_journal-4814	89	61	≠	≠	PROPN
american_scientific_journal-4814	89	62	0	0	NUM
american_scientific_journal-4814	89	63	;	;	PUNCT
american_scientific_journal-4814	89	64	𝛼𝛼𝑖𝑖(𝑠𝑠	𝛼𝛼𝑖𝑖(𝑠𝑠	NOUN
american_scientific_journal-4814	89	65	,	,	PUNCT
american_scientific_journal-4814	89	66	𝑡𝑡	𝑡𝑡	ADJ
american_scientific_journal-4814	89	67	)	)	PUNCT
american_scientific_journal-4814	89	68	≠	≠	PROPN
american_scientific_journal-4814	89	69	0	0	NUM
american_scientific_journal-4814	89	70	;	;	PUNCT
american_scientific_journal-4814	89	71	𝑢𝑢𝑖𝑖(𝑠𝑠	𝑢𝑢𝑖𝑖(𝑠𝑠	NOUN
american_scientific_journal-4814	89	72	,	,	PUNCT
american_scientific_journal-4814	89	73	𝑡𝑡	𝑡𝑡	ADJ
american_scientific_journal-4814	89	74	)	)	PUNCT
american_scientific_journal-4814	89	75	≠	≠	PROPN
american_scientific_journal-4814	89	76	0	0	NUM
american_scientific_journal-4814	89	77	.	.	PUNCT
american_scientific_journal-4814	90	1	according	accord	VERB
american_scientific_journal-4814	90	2	to	to	ADP
american_scientific_journal-4814	90	3	the	the	DET
american_scientific_journal-4814	90	4	rayleigh	rayleigh	PROPN
american_scientific_journal-4814	90	5	-	-	PUNCT
american_scientific_journal-4814	90	6	ritz	ritz	PROPN
american_scientific_journal-4814	90	7	superposition	superposition	NOUN
american_scientific_journal-4814	90	8	method	method	NOUN
american_scientific_journal-4814	90	9	[	[	X
american_scientific_journal-4814	90	10	1	1	NUM
american_scientific_journal-4814	90	11	-	-	SYM
american_scientific_journal-4814	90	12	12	12	NUM
american_scientific_journal-4814	90	13	]	]	PUNCT
american_scientific_journal-4814	90	14	,	,	PUNCT
american_scientific_journal-4814	90	15	the	the	DET
american_scientific_journal-4814	90	16	deformations	deformation	NOUN
american_scientific_journal-4814	90	17	of	of	ADP
american_scientific_journal-4814	90	18	the	the	DET
american_scientific_journal-4814	90	19	flexible	flexible	ADJ
american_scientific_journal-4814	90	20	bodies	body	NOUN
american_scientific_journal-4814	90	21	and	and	CCONJ
american_scientific_journal-4814	90	22	the	the	DET
american_scientific_journal-4814	90	23	lace	lace	NOUN
american_scientific_journal-4814	90	24	attitudes	attitude	NOUN
american_scientific_journal-4814	90	25	of	of	ADP
american_scientific_journal-4814	90	26	the	the	DET
american_scientific_journal-4814	90	27	space	space	NOUN
american_scientific_journal-4814	90	28	vehicle	vehicle	NOUN
american_scientific_journal-4814	90	29	,	,	PUNCT
american_scientific_journal-4814	90	30	solutions	solution	NOUN
american_scientific_journal-4814	90	31	of	of	ADP
american_scientific_journal-4814	90	32	these	these	DET
american_scientific_journal-4814	90	33	equations	equation	NOUN
american_scientific_journal-4814	90	34	are	be	AUX
american_scientific_journal-4814	90	35	represented	represent	VERB
american_scientific_journal-4814	90	36	by	by	ADP
american_scientific_journal-4814	90	37	a	a	DET
american_scientific_journal-4814	90	38	linear	linear	ADJ
american_scientific_journal-4814	90	39	combination	combination	NOUN
american_scientific_journal-4814	90	40	of	of	ADP
american_scientific_journal-4814	90	41	the	the	DET
american_scientific_journal-4814	90	42	global	global	ADJ
american_scientific_journal-4814	90	43	eigenmodes	eigenmode	NOUN
american_scientific_journal-4814	90	44	known	know	VERB
american_scientific_journal-4814	90	45	associated	associate	VERB
american_scientific_journal-4814	90	46	with	with	ADP
american_scientific_journal-4814	90	47	functions	function	NOUN
american_scientific_journal-4814	90	48	called	call	VERB
american_scientific_journal-4814	90	49	generalized	generalized	ADJ
american_scientific_journal-4814	90	50	coordinates	coordinate	NOUN
american_scientific_journal-4814	90	51	.	.	PUNCT
american_scientific_journal-4814	91	1	it	it	PRON
american_scientific_journal-4814	91	2	follows	follow	VERB
american_scientific_journal-4814	91	3	:	:	PUNCT
american_scientific_journal-4814	92	1	⎩	⎩	NUM
american_scientific_journal-4814	92	2	⎪	⎪	NOUN
american_scientific_journal-4814	92	3	⎨	⎨	VERB
american_scientific_journal-4814	92	4	⎪	⎪	NOUN
american_scientific_journal-4814	92	5	⎧𝑢𝑢𝑖𝑖(𝑠𝑠	⎧𝑢𝑢𝑖𝑖(𝑠𝑠	NOUN
american_scientific_journal-4814	92	6	,	,	PUNCT
american_scientific_journal-4814	92	7	𝑡𝑡	𝑡𝑡	ADJ
american_scientific_journal-4814	92	8	)	)	PUNCT
american_scientific_journal-4814	92	9	=	=	SYM
american_scientific_journal-4814	92	10	∑	∑	PUNCT
american_scientific_journal-4814	92	11	(	(	PUNCT
american_scientific_journal-4814	92	12	−1)𝑖𝑖𝜃𝜃𝑛𝑛𝑈𝑈𝑛𝑛∗(𝑠𝑠)𝑔𝑔𝑛𝑛(𝑡𝑡)∞	−1)𝑖𝑖𝜃𝜃𝑛𝑛𝑈𝑈𝑛𝑛∗(𝑠𝑠)𝑔𝑔𝑛𝑛(𝑡𝑡)∞	NUM
american_scientific_journal-4814	92	13	𝑛𝑛=1	𝑛𝑛=1	VERB
american_scientific_journal-4814	92	14	𝛼𝛼𝑖𝑖(𝑠𝑠	𝛼𝛼𝑖𝑖(𝑠𝑠	NOUN
american_scientific_journal-4814	92	15	,	,	PUNCT
american_scientific_journal-4814	92	16	𝑡𝑡	𝑡𝑡	ADJ
american_scientific_journal-4814	92	17	)	)	PUNCT
american_scientific_journal-4814	92	18	=	=	SYM
american_scientific_journal-4814	92	19	∑	∑	PUNCT
american_scientific_journal-4814	92	20	(	(	PUNCT
american_scientific_journal-4814	92	21	−1)𝑖𝑖𝜃𝜃𝑛𝑛𝛼𝛼𝑛𝑛∗(𝑠𝑠)𝑔𝑔𝑛𝑛(𝑡𝑡)∞	−1)𝑖𝑖𝜃𝜃𝑛𝑛𝛼𝛼𝑛𝑛∗(𝑠𝑠)𝑔𝑔𝑛𝑛(𝑡𝑡)∞	ADV
american_scientific_journal-4814	92	22	𝑛𝑛=1	𝑛𝑛=1	NOUN
american_scientific_journal-4814	92	23	𝜃𝜃(𝑡𝑡	𝜃𝜃(𝑡𝑡	NOUN
american_scientific_journal-4814	92	24	)	)	PUNCT
american_scientific_journal-4814	92	25	=	=	SYM
american_scientific_journal-4814	92	26	𝜆𝜆(𝑡𝑡	𝜆𝜆(𝑡𝑡	PROPN
american_scientific_journal-4814	92	27	)	)	PUNCT
american_scientific_journal-4814	93	1	+	+	CCONJ
american_scientific_journal-4814	93	2	∑	∑	PART
american_scientific_journal-4814	93	3	𝜃𝜃𝑛𝑛𝑔𝑔𝑛𝑛(𝑡𝑡)∞	𝜃𝜃𝑛𝑛𝑔𝑔𝑛𝑛(𝑡𝑡)∞	NUM
american_scientific_journal-4814	93	4	𝑛𝑛=1	𝑛𝑛=1	NOUN
american_scientific_journal-4814	93	5	,	,	PUNCT
american_scientific_journal-4814	93	6	(	(	PUNCT
american_scientific_journal-4814	93	7	17	17	NUM
american_scientific_journal-4814	93	8	)	)	PUNCT
american_scientific_journal-4814	93	9	𝑔𝑔𝑛𝑛(𝑡𝑡	𝑔𝑔𝑛𝑛(𝑡𝑡	PROPN
american_scientific_journal-4814	93	10	)	)	PUNCT
american_scientific_journal-4814	93	11	is	be	AUX
american_scientific_journal-4814	93	12	the	the	DET
american_scientific_journal-4814	93	13	generalized	generalize	VERB
american_scientific_journal-4814	93	14	coordinates	coordinate	NOUN
american_scientific_journal-4814	93	15	to	to	PART
american_scientific_journal-4814	93	16	be	be	AUX
american_scientific_journal-4814	93	17	determined	determine	VERB
american_scientific_journal-4814	93	18	by	by	ADP
american_scientific_journal-4814	93	19	the	the	DET
american_scientific_journal-4814	93	20	modal	modal	ADJ
american_scientific_journal-4814	93	21	analysis	analysis	NOUN
american_scientific_journal-4814	93	22	.	.	PUNCT
american_scientific_journal-4814	94	1	here	here	ADV
american_scientific_journal-4814	94	2	,	,	PUNCT
american_scientific_journal-4814	94	3	𝜆𝜆(𝑡𝑡	𝜆𝜆(𝑡𝑡	PROPN
american_scientific_journal-4814	94	4	)	)	PUNCT
american_scientific_journal-4814	94	5	represents	represent	VERB
american_scientific_journal-4814	94	6	the	the	DET
american_scientific_journal-4814	94	7	rigid	rigid	ADJ
american_scientific_journal-4814	94	8	american	american	ADJ
american_scientific_journal-4814	94	9	scientific	scientific	ADJ
american_scientific_journal-4814	94	10	research	research	NOUN
american_scientific_journal-4814	94	11	journal	journal	NOUN
american_scientific_journal-4814	94	12	for	for	ADP
american_scientific_journal-4814	94	13	engineering	engineering	NOUN
american_scientific_journal-4814	94	14	,	,	PUNCT
american_scientific_journal-4814	94	15	technology	technology	NOUN
american_scientific_journal-4814	94	16	,	,	PUNCT
american_scientific_journal-4814	94	17	and	and	CCONJ
american_scientific_journal-4814	94	18	sciences	science	NOUN
american_scientific_journal-4814	94	19	(	(	PUNCT
american_scientific_journal-4814	94	20	asrjets	asrjet	NOUN
american_scientific_journal-4814	94	21	)	)	PUNCT
american_scientific_journal-4814	94	22	(	(	PUNCT
american_scientific_journal-4814	94	23	2019	2019	NUM
american_scientific_journal-4814	94	24	)	)	PUNCT
american_scientific_journal-4814	94	25	volume	volume	NOUN
american_scientific_journal-4814	94	26	55	55	NUM
american_scientific_journal-4814	94	27	,	,	PUNCT
american_scientific_journal-4814	94	28	no	no	DET
american_scientific_journal-4814	94	29	1	1	NUM
american_scientific_journal-4814	94	30	,	,	PUNCT
american_scientific_journal-4814	94	31	pp	pp	ADP
american_scientific_journal-4814	94	32	50	50	NUM
american_scientific_journal-4814	94	33	-	-	SYM
american_scientific_journal-4814	94	34	68	68	NUM
american_scientific_journal-4814	94	35	56	56	NUM
american_scientific_journal-4814	94	36	response	response	NOUN
american_scientific_journal-4814	94	37	of	of	ADP
american_scientific_journal-4814	94	38	the	the	DET
american_scientific_journal-4814	94	39	whole	whole	ADJ
american_scientific_journal-4814	94	40	spacecraft	spacecraft	NOUN
american_scientific_journal-4814	94	41	if	if	SCONJ
american_scientific_journal-4814	94	42	it	it	PRON
american_scientific_journal-4814	94	43	were	be	AUX
american_scientific_journal-4814	94	44	rigid	rigid	ADJ
american_scientific_journal-4814	94	45	.	.	PUNCT
american_scientific_journal-4814	95	1	4.1	4.1	NUM
american_scientific_journal-4814	95	2	.	.	PUNCT
american_scientific_journal-4814	95	3	determination	determination	NOUN
american_scientific_journal-4814	95	4	of	of	ADP
american_scientific_journal-4814	95	5	generalized	generalized	ADJ
american_scientific_journal-4814	95	6	coordinates	coordinate	NOUN
american_scientific_journal-4814	95	7	injecting	inject	VERB
american_scientific_journal-4814	95	8	the	the	DET
american_scientific_journal-4814	95	9	expansions	expansion	NOUN
american_scientific_journal-4814	95	10	(	(	PUNCT
american_scientific_journal-4814	95	11	17	17	NUM
american_scientific_journal-4814	95	12	)	)	PUNCT
american_scientific_journal-4814	95	13	of	of	ADP
american_scientific_journal-4814	95	14	the	the	DET
american_scientific_journal-4814	95	15	elastic	elastic	ADJ
american_scientific_journal-4814	95	16	deformations	deformation	NOUN
american_scientific_journal-4814	95	17	and	and	CCONJ
american_scientific_journal-4814	95	18	the	the	DET
american_scientific_journal-4814	95	19	lace	lace	NOUN
american_scientific_journal-4814	95	20	attitudes	attitude	NOUN
american_scientific_journal-4814	95	21	into	into	ADP
american_scientific_journal-4814	95	22	the	the	DET
american_scientific_journal-4814	95	23	local	local	ADJ
american_scientific_journal-4814	95	24	equations	equation	NOUN
american_scientific_journal-4814	95	25	(	(	PUNCT
american_scientific_journal-4814	95	26	3	3	NUM
american_scientific_journal-4814	95	27	)	)	PUNCT
american_scientific_journal-4814	95	28	,	,	PUNCT
american_scientific_journal-4814	95	29	(	(	PUNCT
american_scientific_journal-4814	95	30	4	4	NUM
american_scientific_journal-4814	95	31	)	)	PUNCT
american_scientific_journal-4814	95	32	and	and	CCONJ
american_scientific_journal-4814	95	33	(	(	PUNCT
american_scientific_journal-4814	95	34	5	5	NUM
american_scientific_journal-4814	95	35	)	)	PUNCT
american_scientific_journal-4814	95	36	and	and	CCONJ
american_scientific_journal-4814	95	37	taking	take	VERB
american_scientific_journal-4814	95	38	into	into	ADP
american_scientific_journal-4814	95	39	account	account	NOUN
american_scientific_journal-4814	95	40	the	the	DET
american_scientific_journal-4814	95	41	boundary	boundary	ADJ
american_scientific_journal-4814	95	42	conditions	condition	NOUN
american_scientific_journal-4814	95	43	(	(	PUNCT
american_scientific_journal-4814	95	44	8)	8)	NUM
american_scientific_journal-4814	95	45	,	,	PUNCT
american_scientific_journal-4814	95	46	(	(	PUNCT
american_scientific_journal-4814	95	47	9	9	NUM
american_scientific_journal-4814	95	48	)	)	PUNCT
american_scientific_journal-4814	95	49	and	and	CCONJ
american_scientific_journal-4814	95	50	(	(	PUNCT
american_scientific_journal-4814	95	51	10	10	NUM
american_scientific_journal-4814	95	52	)	)	PUNCT
american_scientific_journal-4814	95	53	the	the	DET
american_scientific_journal-4814	95	54	normalized	normalize	VERB
american_scientific_journal-4814	95	55	orthogonality	orthogonality	NOUN
american_scientific_journal-4814	95	56	property	property	NOUN
american_scientific_journal-4814	95	57	(	(	PUNCT
american_scientific_journal-4814	95	58	15	15	NUM
american_scientific_journal-4814	95	59	)	)	PUNCT
american_scientific_journal-4814	95	60	and	and	CCONJ
american_scientific_journal-4814	95	61	the	the	DET
american_scientific_journal-4814	95	62	natural	natural	ADJ
american_scientific_journal-4814	95	63	frequencies	frequency	NOUN
american_scientific_journal-4814	95	64	equation	equation	NOUN
american_scientific_journal-4814	95	65	(	(	PUNCT
american_scientific_journal-4814	95	66	14	14	NUM
american_scientific_journal-4814	95	67	)	)	PUNCT
american_scientific_journal-4814	95	68	,	,	PUNCT
american_scientific_journal-4814	95	69	one	one	PRON
american_scientific_journal-4814	95	70	gets	get	VERB
american_scientific_journal-4814	95	71	the	the	DET
american_scientific_journal-4814	95	72	following	follow	VERB
american_scientific_journal-4814	95	73	differential	differential	ADJ
american_scientific_journal-4814	95	74	equation	equation	NOUN
american_scientific_journal-4814	95	75	of	of	ADP
american_scientific_journal-4814	95	76	the	the	DET
american_scientific_journal-4814	95	77	generalized	generalized	ADJ
american_scientific_journal-4814	95	78	coordinates	coordinate	NOUN
american_scientific_journal-4814	95	79	:	:	PUNCT
american_scientific_journal-4814	95	80	�	�	PROPN
american_scientific_journal-4814	95	81	̈	̈	NOUN
american_scientific_journal-4814	95	82	�	�	NOUN
american_scientific_journal-4814	95	83	𝑔𝑘𝑘(𝑡𝑡	𝑔𝑘𝑘(𝑡𝑡	PROPN
american_scientific_journal-4814	95	84	)	)	PUNCT
american_scientific_journal-4814	96	1	+	+	CCONJ
american_scientific_journal-4814	96	2	𝜑𝜑𝑘𝑘2𝑔𝑔𝑘𝑘(𝑡𝑡	𝜑𝜑𝑘𝑘2𝑔𝑔𝑘𝑘(𝑡𝑡	NOUN
american_scientific_journal-4814	96	3	)	)	PUNCT
american_scientific_journal-4814	96	4	+	+	CCONJ
american_scientific_journal-4814	96	5	3𝑛𝑛02	3𝑛𝑛02	NUM
american_scientific_journal-4814	96	6	∑	∑	PUNCT
american_scientific_journal-4814	96	7	𝑚𝑚𝑛𝑛𝑘𝑘𝑔𝑔𝑛𝑛(𝑡𝑡)∞	𝑚𝑚𝑛𝑛𝑘𝑘𝑔𝑔𝑛𝑛(𝑡𝑡)∞	NUM
american_scientific_journal-4814	96	8	𝑛𝑛=1	𝑛𝑛=1	NOUN
american_scientific_journal-4814	96	9	=	=	SYM
american_scientific_journal-4814	96	10	𝐶𝐶𝜃𝜃𝑘𝑘	𝐶𝐶𝜃𝜃𝑘𝑘	PROPN
american_scientific_journal-4814	96	11	�	�	PROPN
american_scientific_journal-4814	96	12	�	�	PROPN
american_scientific_journal-4814	96	13	̈	̈	X
american_scientific_journal-4814	96	14	�	�	NOUN
american_scientific_journal-4814	96	15	𝜆(𝑡𝑡	𝜆(𝑡𝑡	NOUN
american_scientific_journal-4814	96	16	)	)	PUNCT
american_scientific_journal-4814	97	1	+	+	NUM
american_scientific_journal-4814	97	2	3𝑛𝑛02𝜆𝜆(𝑡𝑡	3𝑛𝑛02𝜆𝜆(𝑡𝑡	NUM
american_scientific_journal-4814	97	3	)	)	PUNCT
american_scientific_journal-4814	97	4	�	�	PROPN
american_scientific_journal-4814	97	5	,	,	PUNCT
american_scientific_journal-4814	97	6	𝑘𝑘	𝑘𝑘	NOUN
american_scientific_journal-4814	97	7	=	=	SYM
american_scientific_journal-4814	97	8	1,2	1,2	NUM
american_scientific_journal-4814	97	9	,	,	PUNCT
american_scientific_journal-4814	97	10	…	…	PUNCT
american_scientific_journal-4814	97	11	.	.	PUNCT
american_scientific_journal-4814	98	1	(	(	PUNCT
american_scientific_journal-4814	98	2	18	18	NUM
american_scientific_journal-4814	98	3	)	)	PUNCT
american_scientific_journal-4814	98	4	here	here	ADV
american_scientific_journal-4814	98	5	:	:	PUNCT
american_scientific_journal-4814	98	6	𝑚𝑚𝑛𝑛𝑘𝑘	𝑚𝑚𝑛𝑛𝑘𝑘	NOUN
american_scientific_journal-4814	98	7	=	=	PUNCT
american_scientific_journal-4814	98	8	𝜃𝜃𝑛𝑛𝜃𝜃𝑘𝑘	𝜃𝜃𝑛𝑛𝜃𝜃𝑘𝑘	NOUN
american_scientific_journal-4814	98	9	�	�	PROPN
american_scientific_journal-4814	98	10	∫	∫	PROPN
american_scientific_journal-4814	98	11	𝑒𝑒𝑇𝑇	𝑒𝑒𝑇𝑇	PROPN
american_scientific_journal-4814	98	12	�	�	PROPN
american_scientific_journal-4814	98	13	1∗(𝑠𝑠)𝛼𝛼𝑛𝑛∗	1∗(𝑠𝑠)𝛼𝛼𝑛𝑛∗	NUM
american_scientific_journal-4814	98	14	′(𝑠𝑠)𝛼𝛼𝑘𝑘∗	′(𝑠𝑠)𝛼𝛼𝑘𝑘∗	PROPN
american_scientific_journal-4814	98	15	′(𝑠𝑠)𝑑𝑑𝑠𝑠𝑙𝑙	′(𝑠𝑠)𝑑𝑑𝑠𝑠𝑙𝑙	PROPN
american_scientific_journal-4814	98	16	0	0	NUM
american_scientific_journal-4814	98	17	+	+	NUM
american_scientific_journal-4814	98	18	∫	∫	PROPN
american_scientific_journal-4814	98	19	𝑆𝑆	𝑆𝑆	PROPN
american_scientific_journal-4814	98	20	�	�	PROPN
american_scientific_journal-4814	98	21	1∗(𝑠𝑠)𝑈𝑈𝑛𝑛∗	1∗(𝑠𝑠)𝑈𝑈𝑛𝑛∗	NUM
american_scientific_journal-4814	98	22	′(𝑠𝑠)𝑈𝑈𝑘𝑘∗	′(𝑠𝑠)𝑈𝑈𝑘𝑘∗	PROPN
american_scientific_journal-4814	98	23	′(𝑠𝑠)𝑑𝑑𝑠𝑠𝑙𝑙	′(𝑠𝑠)𝑑𝑑𝑠𝑠𝑙𝑙	PROPN
american_scientific_journal-4814	98	24	0	0	NUM
american_scientific_journal-4814	99	1	−	−	PROPN
american_scientific_journal-4814	99	2	𝐶𝐶	𝐶𝐶	PROPN
american_scientific_journal-4814	99	3	�	�	PROPN
american_scientific_journal-4814	99	4	,	,	PUNCT
american_scientific_journal-4814	99	5	(	(	PUNCT
american_scientific_journal-4814	99	6	19	19	NUM
american_scientific_journal-4814	99	7	)	)	PUNCT
american_scientific_journal-4814	99	8	with	with	ADP
american_scientific_journal-4814	99	9	𝑇𝑇	𝑇𝑇	PROPN
american_scientific_journal-4814	99	10	�	�	NOUN
american_scientific_journal-4814	99	11	1∗(𝑠𝑠	1∗(𝑠𝑠	NUM
american_scientific_journal-4814	99	12	)	)	PUNCT
american_scientific_journal-4814	99	13	=	=	SYM
american_scientific_journal-4814	99	14	𝜎𝜎(𝑏𝑏	𝜎𝜎(𝑏𝑏	PROPN
american_scientific_journal-4814	99	15	+	+	NUM
american_scientific_journal-4814	99	16	𝑙𝑙)2	𝑙𝑙)2	PROPN
american_scientific_journal-4814	99	17	−	−	PROPN
american_scientific_journal-4814	99	18	𝜎𝜎(𝑏𝑏	𝜎𝜎(𝑏𝑏	PROPN
american_scientific_journal-4814	99	19	+	+	NUM
american_scientific_journal-4814	99	20	𝑠𝑠)2	𝑠𝑠)2	PROPN
american_scientific_journal-4814	99	21	+	+	CCONJ
american_scientific_journal-4814	99	22	2	2	NUM
american_scientific_journal-4814	99	23	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-4814	99	24	�	�	PROPN
american_scientific_journal-4814	99	25	𝑒𝑒	𝑒𝑒	ADP
american_scientific_journal-4814	99	26	(	(	PUNCT
american_scientific_journal-4814	99	27	𝑏𝑏	𝑏𝑏	NOUN
american_scientific_journal-4814	99	28	+	+	CCONJ
american_scientific_journal-4814	99	29	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-4814	99	30	)	)	PUNCT
american_scientific_journal-4814	99	31	;	;	PUNCT
american_scientific_journal-4814	99	32	𝑆𝑆	𝑆𝑆	PROPN
american_scientific_journal-4814	99	33	�	�	PROPN
american_scientific_journal-4814	99	34	1∗(𝑠𝑠	1∗(𝑠𝑠	NUM
american_scientific_journal-4814	99	35	)	)	PUNCT
american_scientific_journal-4814	99	36	=	=	PUNCT
american_scientific_journal-4814	99	37	𝜌𝜌[(𝑏𝑏	𝜌𝜌[(𝑏𝑏	PUNCT
american_scientific_journal-4814	99	38	+	+	NUM
american_scientific_journal-4814	99	39	𝑙𝑙)2	𝑙𝑙)2	PROPN
american_scientific_journal-4814	99	40	−	−	PROPN
american_scientific_journal-4814	99	41	(	(	PUNCT
american_scientific_journal-4814	99	42	𝑏𝑏	𝑏𝑏	NOUN
american_scientific_journal-4814	99	43	+	+	NUM
american_scientific_journal-4814	99	44	𝑠𝑠)2	𝑠𝑠)2	PROPN
american_scientific_journal-4814	99	45	]	]	PUNCT
american_scientific_journal-4814	99	46	.	.	PUNCT
american_scientific_journal-4814	100	1	one	one	NUM
american_scientific_journal-4814	100	2	supposes	suppose	VERB
american_scientific_journal-4814	100	3	that	that	SCONJ
american_scientific_journal-4814	100	4	the	the	DET
american_scientific_journal-4814	100	5	generalized	generalized	ADJ
american_scientific_journal-4814	100	6	coordinates	coordinate	NOUN
american_scientific_journal-4814	100	7	and	and	CCONJ
american_scientific_journal-4814	100	8	the	the	DET
american_scientific_journal-4814	100	9	rigid	rigid	ADJ
american_scientific_journal-4814	100	10	response	response	NOUN
american_scientific_journal-4814	100	11	are	be	AUX
american_scientific_journal-4814	100	12	harmonic	harmonic	ADJ
american_scientific_journal-4814	100	13	of	of	ADP
american_scientific_journal-4814	100	14	the	the	DET
american_scientific_journal-4814	100	15	form	form	NOUN
american_scientific_journal-4814	100	16	:	:	PUNCT
american_scientific_journal-4814	100	17	𝑔𝑔𝑛𝑛(𝑡𝑡	𝑔𝑔𝑛𝑛(𝑡𝑡	NOUN
american_scientific_journal-4814	100	18	)	)	PUNCT
american_scientific_journal-4814	100	19	=	=	SYM
american_scientific_journal-4814	100	20	𝑔𝑔	𝑔𝑔	PROPN
american_scientific_journal-4814	100	21	�	�	PROPN
american_scientific_journal-4814	100	22	𝑛𝑛𝑒𝑒𝑗𝑗𝑗𝑗𝑗𝑗	𝑛𝑛𝑒𝑒𝑗𝑗𝑗𝑗𝑗𝑗	NOUN
american_scientific_journal-4814	100	23	,	,	PUNCT
american_scientific_journal-4814	100	24	𝜆𝜆(𝑡𝑡	𝜆𝜆(𝑡𝑡	PROPN
american_scientific_journal-4814	100	25	)	)	PUNCT
american_scientific_journal-4814	100	26	=	=	SYM
american_scientific_journal-4814	100	27	�	�	PROPN
american_scientific_journal-4814	100	28	̂	̂	NOUN
american_scientific_journal-4814	100	29	�	�	NOUN
american_scientific_journal-4814	100	30	𝜆𝑒𝑒𝑗𝑗𝑗𝑗𝑗𝑗	𝜆𝑒𝑒𝑗𝑗𝑗𝑗𝑗𝑗	NOUN
american_scientific_journal-4814	100	31	,	,	PUNCT
american_scientific_journal-4814	100	32	(	(	PUNCT
american_scientific_journal-4814	100	33	20	20	NUM
american_scientific_journal-4814	100	34	)	)	PUNCT
american_scientific_journal-4814	100	35	here	here	ADV
american_scientific_journal-4814	100	36	:	:	PUNCT
american_scientific_journal-4814	100	37	𝛺𝛺	𝛺𝛺	PROPN
american_scientific_journal-4814	100	38	is	be	AUX
american_scientific_journal-4814	100	39	a	a	DET
american_scientific_journal-4814	100	40	real	real	ADJ
american_scientific_journal-4814	100	41	parameter	parameter	NOUN
american_scientific_journal-4814	100	42	to	to	PART
american_scientific_journal-4814	100	43	be	be	AUX
american_scientific_journal-4814	100	44	determined	determine	VERB
american_scientific_journal-4814	100	45	and	and	CCONJ
american_scientific_journal-4814	100	46	𝑗𝑗2	𝑗𝑗2	NOUN
american_scientific_journal-4814	100	47	=	=	SYM
american_scientific_journal-4814	100	48	−1	−1	NOUN
american_scientific_journal-4814	100	49	.	.	PUNCT
american_scientific_journal-4814	101	1	one	one	NUM
american_scientific_journal-4814	101	2	defines	define	VERB
american_scientific_journal-4814	101	3	the	the	DET
american_scientific_journal-4814	101	4	following	follow	VERB
american_scientific_journal-4814	101	5	column	column	NOUN
american_scientific_journal-4814	101	6	vectors	vector	NOUN
american_scientific_journal-4814	101	7	:	:	PUNCT
american_scientific_journal-4814	101	8	𝐺𝐺	𝐺𝐺	PROPN
american_scientific_journal-4814	101	9	�	�	NOUN
american_scientific_journal-4814	101	10	𝑇𝑇𝑁𝑁	𝑇𝑇𝑁𝑁	NOUN
american_scientific_journal-4814	101	11	=	=	SYM
american_scientific_journal-4814	101	12	(	(	PUNCT
american_scientific_journal-4814	101	13	𝑔𝑔	𝑔𝑔	PROPN
american_scientific_journal-4814	101	14	�	�	PROPN
american_scientific_journal-4814	101	15	1,⋯⋯	1,⋯⋯	NUM
american_scientific_journal-4814	101	16	,	,	PUNCT
american_scientific_journal-4814	101	17	𝑔𝑔	𝑔𝑔	PROPN
american_scientific_journal-4814	101	18	�	�	PROPN
american_scientific_journal-4814	101	19	𝑁𝑁	𝑁𝑁	PROPN
american_scientific_journal-4814	101	20	)	)	PUNCT
american_scientific_journal-4814	101	21	,	,	PUNCT
american_scientific_journal-4814	101	22	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-4814	101	23	𝑁𝑁	𝑁𝑁	PROPN
american_scientific_journal-4814	101	24	𝑇𝑇	𝑇𝑇	PROPN
american_scientific_journal-4814	101	25	=	=	SYM
american_scientific_journal-4814	101	26	(	(	PUNCT
american_scientific_journal-4814	101	27	𝜃𝜃1,⋯⋯	𝜃𝜃1,⋯⋯	NOUN
american_scientific_journal-4814	101	28	,	,	PUNCT
american_scientific_journal-4814	101	29	𝜃𝜃𝑁𝑁	𝜃𝜃𝑁𝑁	NOUN
american_scientific_journal-4814	101	30	)	)	PUNCT
american_scientific_journal-4814	101	31	,	,	PUNCT
american_scientific_journal-4814	101	32	and	and	CCONJ
american_scientific_journal-4814	101	33	the	the	DET
american_scientific_journal-4814	101	34	following	follow	VERB
american_scientific_journal-4814	101	35	matrix	matrix	NOUN
american_scientific_journal-4814	101	36	:	:	PUNCT
american_scientific_journal-4814	101	37	𝑀𝑀	𝑀𝑀	PROPN
american_scientific_journal-4814	101	38	𝑁𝑁	𝑁𝑁	PROPN
american_scientific_journal-4814	101	39	=	=	SYM
american_scientific_journal-4814	101	40	⎝	⎝	PROPN
american_scientific_journal-4814	101	41	⎜	⎜	PROPN
american_scientific_journal-4814	101	42	⎜	⎜	PROPN
american_scientific_journal-4814	101	43	⎛	⎛	NOUN
american_scientific_journal-4814	101	44	𝜑𝜑12	𝜑𝜑12	PROPN
american_scientific_journal-4814	101	45	+	+	NUM
american_scientific_journal-4814	101	46	3𝑛𝑛02𝑚𝑚11	3𝑛𝑛02𝑚𝑚11	NUM
american_scientific_journal-4814	101	47	3𝑛𝑛02𝑚𝑚21	3𝑛𝑛02𝑚𝑚21	NUM
american_scientific_journal-4814	101	48	⋮	⋮	NOUN
american_scientific_journal-4814	101	49	3𝑛𝑛02𝑚𝑚𝑘𝑘1	3𝑛𝑛02𝑚𝑚𝑘𝑘1	NUM
american_scientific_journal-4814	101	50	⋮	⋮	NOUN
american_scientific_journal-4814	101	51	3𝑛𝑛02𝑚𝑚𝑁𝑁1	3𝑛𝑛02𝑚𝑚𝑁𝑁1	NUM
american_scientific_journal-4814	101	52	3𝑛𝑛02𝑚𝑚12	3𝑛𝑛02𝑚𝑚12	NUM
american_scientific_journal-4814	101	53	𝜑𝜑22	𝜑𝜑22	PROPN
american_scientific_journal-4814	101	54	+	+	CCONJ
american_scientific_journal-4814	102	1	3𝑛𝑛02𝑚𝑚22	3𝑛𝑛02𝑚𝑚22	NUM
american_scientific_journal-4814	102	2	⋯	⋯	NOUN
american_scientific_journal-4814	102	3	⋯	⋯	NOUN
american_scientific_journal-4814	102	4	⋯	⋯	NOUN
american_scientific_journal-4814	102	5	⋯	⋯	NOUN
american_scientific_journal-4814	102	6	⋱	⋱	X
american_scientific_journal-4814	102	7	…	…	PUNCT
american_scientific_journal-4814	102	8	…	…	PUNCT
american_scientific_journal-4814	102	9	3𝑛𝑛02𝑚𝑚1𝑘𝑘	3𝑛𝑛02𝑚𝑚1𝑘𝑘	NUM
american_scientific_journal-4814	102	10	3𝑛𝑛02𝑚𝑚2𝑘𝑘	3𝑛𝑛02𝑚𝑚2𝑘𝑘	NUM
american_scientific_journal-4814	102	11	⋮	⋮	NOUN
american_scientific_journal-4814	102	12	𝜑𝜑𝑘𝑘2	𝜑𝜑𝑘𝑘2	NOUN
american_scientific_journal-4814	102	13	+	+	CCONJ
american_scientific_journal-4814	102	14	3𝑛𝑛02𝑚𝑚𝑘𝑘𝑘𝑘	3𝑛𝑛02𝑚𝑚𝑘𝑘𝑘𝑘	NUM
american_scientific_journal-4814	102	15	⋮	⋮	NOUN
american_scientific_journal-4814	102	16	3𝑛𝑛02𝑚𝑚𝑁𝑁𝑘𝑘	3𝑛𝑛02𝑚𝑚𝑁𝑁𝑘𝑘	PROPN
american_scientific_journal-4814	102	17	⋯	⋯	NOUN
american_scientific_journal-4814	102	18	…	…	PUNCT
american_scientific_journal-4814	102	19	⋱	⋱	X
american_scientific_journal-4814	102	20	…	…	PUNCT
american_scientific_journal-4814	102	21	3𝑛𝑛02𝑚𝑚1𝑁𝑁	3𝑛𝑛02𝑚𝑚1𝑁𝑁	NOUN
american_scientific_journal-4814	102	22	3𝑛𝑛02𝑚𝑚2𝑁𝑁	3𝑛𝑛02𝑚𝑚2𝑁𝑁	NUM
american_scientific_journal-4814	102	23	⋮	⋮	NOUN
american_scientific_journal-4814	102	24	3𝑛𝑛02𝑚𝑚𝑘𝑘𝑁𝑁	3𝑛𝑛02𝑚𝑚𝑘𝑘𝑁𝑁	NOUN
american_scientific_journal-4814	102	25	⋮	⋮	NOUN
american_scientific_journal-4814	102	26	𝜑𝜑𝑁𝑁2	𝜑𝜑𝑁𝑁2	ADV
american_scientific_journal-4814	102	27	+	+	NUM
american_scientific_journal-4814	102	28	3𝑛𝑛02𝑚𝑚𝑁𝑁𝑁𝑁⎠	3𝑛𝑛02𝑚𝑚𝑁𝑁𝑁𝑁⎠	NUM
american_scientific_journal-4814	102	29	⎟	⎟	X
american_scientific_journal-4814	102	30	⎟	⎟	PROPN
american_scientific_journal-4814	102	31	⎞	⎞	PROPN
american_scientific_journal-4814	102	32	,	,	PUNCT
american_scientific_journal-4814	102	33	�	�	PROPN
american_scientific_journal-4814	102	34	𝑀𝑀	𝑀𝑀	PROPN
american_scientific_journal-4814	102	35	𝑁𝑁	𝑁𝑁	PROPN
american_scientific_journal-4814	102	36	�	�	PROPN
american_scientific_journal-4814	102	37	𝑛𝑛𝑘𝑘	𝑛𝑛𝑘𝑘	ADV
american_scientific_journal-4814	102	38	=	=	PUNCT
american_scientific_journal-4814	102	39	𝜑𝜑𝑛𝑛2𝛿𝛿𝑛𝑛𝑘𝑘	𝜑𝜑𝑛𝑛2𝛿𝛿𝑛𝑛𝑘𝑘	X
american_scientific_journal-4814	102	40	+	+	SYM
american_scientific_journal-4814	102	41	3𝑛𝑛02𝑚𝑚𝑛𝑛𝑘𝑘.	3𝑛𝑛02𝑚𝑚𝑛𝑛𝑘𝑘.	NUM
american_scientific_journal-4814	102	42	american	american	ADJ
american_scientific_journal-4814	102	43	scientific	scientific	ADJ
american_scientific_journal-4814	102	44	research	research	NOUN
american_scientific_journal-4814	102	45	journal	journal	NOUN
american_scientific_journal-4814	102	46	for	for	ADP
american_scientific_journal-4814	102	47	engineering	engineering	NOUN
american_scientific_journal-4814	102	48	,	,	PUNCT
american_scientific_journal-4814	102	49	technology	technology	NOUN
american_scientific_journal-4814	102	50	,	,	PUNCT
american_scientific_journal-4814	102	51	and	and	CCONJ
american_scientific_journal-4814	102	52	sciences	science	NOUN
american_scientific_journal-4814	102	53	(	(	PUNCT
american_scientific_journal-4814	102	54	asrjets	asrjet	NOUN
american_scientific_journal-4814	102	55	)	)	PUNCT
american_scientific_journal-4814	102	56	(	(	PUNCT
american_scientific_journal-4814	102	57	2019	2019	NUM
american_scientific_journal-4814	102	58	)	)	PUNCT
american_scientific_journal-4814	102	59	volume	volume	NOUN
american_scientific_journal-4814	102	60	55	55	NUM
american_scientific_journal-4814	102	61	,	,	PUNCT
american_scientific_journal-4814	102	62	no	no	DET
american_scientific_journal-4814	102	63	1	1	NUM
american_scientific_journal-4814	102	64	,	,	PUNCT
american_scientific_journal-4814	102	65	pp	pp	ADP
american_scientific_journal-4814	102	66	50	50	NUM
american_scientific_journal-4814	102	67	-	-	SYM
american_scientific_journal-4814	102	68	68	68	NUM
american_scientific_journal-4814	102	69	57	57	NUM
american_scientific_journal-4814	102	70	equations	equation	NOUN
american_scientific_journal-4814	102	71	(	(	PUNCT
american_scientific_journal-4814	102	72	18	18	NUM
american_scientific_journal-4814	102	73	)	)	PUNCT
american_scientific_journal-4814	102	74	are	be	AUX
american_scientific_journal-4814	102	75	written	write	VERB
american_scientific_journal-4814	102	76	in	in	ADP
american_scientific_journal-4814	102	77	the	the	DET
american_scientific_journal-4814	102	78	following	follow	VERB
american_scientific_journal-4814	102	79	matrix	matrix	NOUN
american_scientific_journal-4814	102	80	forms	form	NOUN
american_scientific_journal-4814	102	81	:	:	PUNCT
american_scientific_journal-4814	102	82	�	�	PROPN
american_scientific_journal-4814	102	83	𝑀𝑀	𝑀𝑀	PROPN
american_scientific_journal-4814	102	84	𝑁𝑁	𝑁𝑁	PROPN
american_scientific_journal-4814	102	85	−	−	PROPN
american_scientific_journal-4814	102	86	𝛺𝛺2𝐸𝐸	𝛺𝛺2𝐸𝐸	PUNCT
american_scientific_journal-4814	102	87	𝑁𝑁	𝑁𝑁	PROPN
american_scientific_journal-4814	102	88	�	�	PROPN
american_scientific_journal-4814	102	89	𝐺𝐺	𝐺𝐺	PROPN
american_scientific_journal-4814	102	90	�	�	PROPN
american_scientific_journal-4814	102	91	𝑁𝑁	𝑁𝑁	PROPN
american_scientific_journal-4814	102	92	=	=	PUNCT
american_scientific_journal-4814	102	93	𝐶𝐶(3𝑛𝑛02	𝐶𝐶(3𝑛𝑛02	NOUN
american_scientific_journal-4814	102	94	−	−	PROPN
american_scientific_journal-4814	102	95	𝛺𝛺2)𝜃𝜃	𝛺𝛺2)𝜃𝜃	PROPN
american_scientific_journal-4814	102	96	𝑁𝑁	𝑁𝑁	PROPN
american_scientific_journal-4814	102	97	�	�	PROPN
american_scientific_journal-4814	102	98	̂	̂	PROPN
american_scientific_journal-4814	102	99	�	�	NOUN
american_scientific_journal-4814	102	100	𝜆.	𝜆.	NOUN
american_scientific_journal-4814	102	101	(	(	PUNCT
american_scientific_journal-4814	102	102	21	21	NUM
american_scientific_journal-4814	102	103	)	)	PUNCT
american_scientific_journal-4814	102	104	𝐸𝐸	𝐸𝐸	PROPN
american_scientific_journal-4814	102	105	𝑁𝑁	𝑁𝑁	PROPN
american_scientific_journal-4814	102	106	is	be	AUX
american_scientific_journal-4814	102	107	the	the	DET
american_scientific_journal-4814	102	108	unit	unit	NOUN
american_scientific_journal-4814	102	109	matrix	matrix	NOUN
american_scientific_journal-4814	102	110	𝑁𝑁	𝑁𝑁	PROPN
american_scientific_journal-4814	102	111	×	×	NOUN
american_scientific_journal-4814	102	112	𝑁𝑁.	𝑁𝑁.	PUNCT
american_scientific_journal-4814	102	113	the	the	DET
american_scientific_journal-4814	102	114	symmetrical	symmetrical	ADJ
american_scientific_journal-4814	102	115	matrix	matrix	NOUN
american_scientific_journal-4814	102	116	𝑀𝑀	𝑀𝑀	PROPN
american_scientific_journal-4814	102	117	𝑁𝑁	𝑁𝑁	PROPN
american_scientific_journal-4814	102	118	with	with	ADP
american_scientific_journal-4814	102	119	respective	respective	ADJ
american_scientific_journal-4814	102	120	eigenvalues	eigenvalue	NOUN
american_scientific_journal-4814	102	121	denoted	denote	VERB
american_scientific_journal-4814	102	122	ℎ𝑘𝑘	ℎ𝑘𝑘	X
american_scientific_journal-4814	102	123	(	(	PUNCT
american_scientific_journal-4814	102	124	𝑘𝑘	𝑘𝑘	NOUN
american_scientific_journal-4814	102	125	=	=	SYM
american_scientific_journal-4814	102	126	1,⋯	1,⋯	NUM
american_scientific_journal-4814	102	127	,	,	PUNCT
american_scientific_journal-4814	102	128	𝑁𝑁	𝑁𝑁	PROPN
american_scientific_journal-4814	102	129	)	)	PUNCT
american_scientific_journal-4814	102	130	can	can	AUX
american_scientific_journal-4814	102	131	be	be	AUX
american_scientific_journal-4814	102	132	diagonalized	diagonalize	VERB
american_scientific_journal-4814	102	133	as	as	ADP
american_scientific_journal-4814	102	134	:	:	PUNCT
american_scientific_journal-4814	102	135	𝑀𝑀	𝑀𝑀	PROPN
american_scientific_journal-4814	102	136	𝑁𝑁	𝑁𝑁	PROPN
american_scientific_journal-4814	102	137	=	=	SYM
american_scientific_journal-4814	102	138	𝐵𝐵	𝐵𝐵	PROPN
american_scientific_journal-4814	102	139	𝑁𝑁	𝑁𝑁	PROPN
american_scientific_journal-4814	102	140	𝐻𝐻	𝐻𝐻	PROPN
american_scientific_journal-4814	102	141	𝑁𝑁	𝑁𝑁	PROPN
american_scientific_journal-4814	102	142	𝐵𝐵𝑇𝑇	𝐵𝐵𝑇𝑇	PROPN
american_scientific_journal-4814	102	143	𝑁𝑁	𝑁𝑁	PROPN
american_scientific_journal-4814	102	144	,	,	PUNCT
american_scientific_journal-4814	102	145	(	(	PUNCT
american_scientific_journal-4814	102	146	22	22	NUM
american_scientific_journal-4814	102	147	)	)	PUNCT
american_scientific_journal-4814	102	148	here	here	ADV
american_scientific_journal-4814	102	149	:	:	PUNCT
american_scientific_journal-4814	102	150	�	�	PROPN
american_scientific_journal-4814	102	151	𝐵𝐵	𝐵𝐵	PROPN
american_scientific_journal-4814	102	152	𝑁𝑁	𝑁𝑁	PROPN
american_scientific_journal-4814	102	153	�	�	PROPN
american_scientific_journal-4814	102	154	𝑛𝑛𝑘𝑘	𝑛𝑛𝑘𝑘	ADV
american_scientific_journal-4814	102	155	=	=	SYM
american_scientific_journal-4814	102	156	𝑏𝑏𝑛𝑛𝑘𝑘	𝑏𝑏𝑛𝑛𝑘𝑘	PROPN
american_scientific_journal-4814	102	157	,	,	PUNCT
american_scientific_journal-4814	102	158	𝐻𝐻	𝐻𝐻	PROPN
american_scientific_journal-4814	102	159	𝑁𝑁	𝑁𝑁	PROPN
american_scientific_journal-4814	102	160	=	=	SYM
american_scientific_journal-4814	102	161	�	�	PROPN
american_scientific_journal-4814	102	162	ℎ1	ℎ1	PROPN
american_scientific_journal-4814	102	163	⋯	⋯	PROPN
american_scientific_journal-4814	102	164	0	0	NUM
american_scientific_journal-4814	102	165	⋮	⋮	NOUN
american_scientific_journal-4814	102	166	⋱	⋱	PUNCT
american_scientific_journal-4814	102	167	⋮	⋮	NOUN
american_scientific_journal-4814	102	168	0	0	PUNCT
american_scientific_journal-4814	103	1	⋯	⋯	VERB
american_scientific_journal-4814	103	2	ℎ𝑁𝑁	ℎ𝑁𝑁	NOUN
american_scientific_journal-4814	103	3	�	�	NOUN
american_scientific_journal-4814	103	4	.	.	PUNCT
american_scientific_journal-4814	104	1	the	the	DET
american_scientific_journal-4814	104	2	matrix	matrix	NOUN
american_scientific_journal-4814	104	3	𝐵𝐵	𝐵𝐵	PROPN
american_scientific_journal-4814	104	4	𝑁𝑁	𝑁𝑁	PROPN
american_scientific_journal-4814	104	5	is	be	AUX
american_scientific_journal-4814	104	6	orthogonal	orthogonal	ADJ
american_scientific_journal-4814	104	7	matrix	matrix	NOUN
american_scientific_journal-4814	104	8	.	.	PUNCT
american_scientific_journal-4814	105	1	substituting	substitute	VERB
american_scientific_journal-4814	105	2	the	the	DET
american_scientific_journal-4814	105	3	factorizations	factorization	NOUN
american_scientific_journal-4814	105	4	(	(	PUNCT
american_scientific_journal-4814	105	5	22	22	NUM
american_scientific_journal-4814	105	6	)	)	PUNCT
american_scientific_journal-4814	105	7	into	into	ADP
american_scientific_journal-4814	105	8	the	the	DET
american_scientific_journal-4814	105	9	equation	equation	NOUN
american_scientific_journal-4814	105	10	(	(	PUNCT
american_scientific_journal-4814	105	11	21	21	NUM
american_scientific_journal-4814	105	12	)	)	PUNCT
american_scientific_journal-4814	105	13	and	and	CCONJ
american_scientific_journal-4814	105	14	assuming	assume	VERB
american_scientific_journal-4814	105	15	that	that	PRON
american_scientific_journal-4814	105	16	:	:	PUNCT
american_scientific_journal-4814	105	17	ℎ𝑘𝑘	ℎ𝑘𝑘	PROPN
american_scientific_journal-4814	105	18	≠	≠	PROPN
american_scientific_journal-4814	105	19	𝛺𝛺2	𝛺𝛺2	PROPN
american_scientific_journal-4814	105	20	.	.	PUNCT
american_scientific_journal-4814	106	1	one	one	PRON
american_scientific_journal-4814	106	2	gets	get	VERB
american_scientific_journal-4814	106	3	finally	finally	ADV
american_scientific_journal-4814	106	4	the	the	DET
american_scientific_journal-4814	106	5	generalized	generalized	ADJ
american_scientific_journal-4814	106	6	coordinates	coordinate	NOUN
american_scientific_journal-4814	106	7	:	:	PUNCT
american_scientific_journal-4814	106	8	𝑔𝑔	𝑔𝑔	X
american_scientific_journal-4814	106	9	�	�	PROPN
american_scientific_journal-4814	106	10	𝑛𝑛	𝑛𝑛	NOUN
american_scientific_journal-4814	106	11	=	=	SYM
american_scientific_journal-4814	106	12	𝑔𝑔	𝑔𝑔	PROPN
american_scientific_journal-4814	106	13	�	�	PROPN
american_scientific_journal-4814	106	14	𝑛𝑛∗	𝑛𝑛∗	ADJ
american_scientific_journal-4814	106	15	�	�	PROPN
american_scientific_journal-4814	106	16	̂	̂	VERB
american_scientific_journal-4814	106	17	�	�	NOUN
american_scientific_journal-4814	106	18	𝜆	𝜆	NOUN
american_scientific_journal-4814	106	19	,	,	PUNCT
american_scientific_journal-4814	106	20	(	(	PUNCT
american_scientific_journal-4814	106	21	23	23	NUM
american_scientific_journal-4814	106	22	)	)	PUNCT
american_scientific_journal-4814	106	23	here	here	ADV
american_scientific_journal-4814	106	24	𝑔𝑔	𝑔𝑔	ADP
american_scientific_journal-4814	106	25	�	�	PROPN
american_scientific_journal-4814	106	26	𝑛𝑛∗	𝑛𝑛∗	ADV
american_scientific_journal-4814	106	27	=	=	NOUN
american_scientific_journal-4814	106	28	𝐶𝐶(3𝑛𝑛02	𝐶𝐶(3𝑛𝑛02	NOUN
american_scientific_journal-4814	106	29	−	−	PROPN
american_scientific_journal-4814	106	30	𝛺𝛺2	𝛺𝛺2	PROPN
american_scientific_journal-4814	106	31	)	)	PUNCT
american_scientific_journal-4814	106	32	�	�	PROPN
american_scientific_journal-4814	106	33	�	�	PROPN
american_scientific_journal-4814	106	34	𝑏𝑏𝑛𝑛𝑘𝑘	𝑏𝑏𝑛𝑛𝑘𝑘	PROPN
american_scientific_journal-4814	106	35	ℎ𝑘𝑘	ℎ𝑘𝑘	VERB
american_scientific_journal-4814	106	36	−	−	PROPN
american_scientific_journal-4814	106	37	𝛺𝛺2	𝛺𝛺2	PROPN
american_scientific_journal-4814	106	38	�	�	PROPN
american_scientific_journal-4814	106	39	𝑏𝑏𝑘𝑘𝑘𝑘𝜃𝜃𝑘𝑘	𝑏𝑏𝑘𝑘𝑘𝑘𝜃𝜃𝑘𝑘	PROPN
american_scientific_journal-4814	106	40	𝑁𝑁	𝑁𝑁	PROPN
american_scientific_journal-4814	106	41	𝑘𝑘=1	𝑘𝑘=1	PROPN
american_scientific_journal-4814	106	42	�	�	PROPN
american_scientific_journal-4814	106	43	𝑁𝑁	𝑁𝑁	PROPN
american_scientific_journal-4814	106	44	𝑘𝑘=1	𝑘𝑘=1	PROPN
american_scientific_journal-4814	106	45	,	,	PUNCT
american_scientific_journal-4814	106	46	𝑛𝑛	𝑛𝑛	NOUN
american_scientific_journal-4814	106	47	=	=	SYM
american_scientific_journal-4814	106	48	1,2	1,2	NUM
american_scientific_journal-4814	106	49	,	,	PUNCT
american_scientific_journal-4814	106	50	…	…	PUNCT
american_scientific_journal-4814	106	51	..	..	PUNCT
american_scientific_journal-4814	106	52	4.2	4.2	NUM
american_scientific_journal-4814	106	53	.	.	PUNCT
american_scientific_journal-4814	107	1	determination	determination	NOUN
american_scientific_journal-4814	107	2	of	of	ADP
american_scientific_journal-4814	107	3	the	the	DET
american_scientific_journal-4814	107	4	impedance	impedance	NOUN
american_scientific_journal-4814	107	5	function	function	NOUN
american_scientific_journal-4814	107	6	of	of	ADP
american_scientific_journal-4814	107	7	the	the	DET
american_scientific_journal-4814	107	8	system	system	NOUN
american_scientific_journal-4814	107	9	by	by	ADP
american_scientific_journal-4814	107	10	using	use	VERB
american_scientific_journal-4814	107	11	the	the	DET
american_scientific_journal-4814	107	12	expressions	expression	NOUN
american_scientific_journal-4814	107	13	(	(	PUNCT
american_scientific_journal-4814	107	14	2	2	NUM
american_scientific_journal-4814	107	15	)	)	PUNCT
american_scientific_journal-4814	107	16	,	,	PUNCT
american_scientific_journal-4814	107	17	the	the	DET
american_scientific_journal-4814	107	18	solutions	solution	NOUN
american_scientific_journal-4814	107	19	(	(	PUNCT
american_scientific_journal-4814	107	20	17	17	NUM
american_scientific_journal-4814	107	21	)	)	PUNCT
american_scientific_journal-4814	107	22	,	,	PUNCT
american_scientific_journal-4814	107	23	the	the	DET
american_scientific_journal-4814	107	24	equations	equation	NOUN
american_scientific_journal-4814	107	25	of	of	ADP
american_scientific_journal-4814	107	26	eigenfrequencies	eigenfrequencie	NOUN
american_scientific_journal-4814	107	27	(	(	PUNCT
american_scientific_journal-4814	107	28	14	14	NUM
american_scientific_journal-4814	107	29	)	)	PUNCT
american_scientific_journal-4814	107	30	,	,	PUNCT
american_scientific_journal-4814	107	31	and	and	CCONJ
american_scientific_journal-4814	107	32	the	the	DET
american_scientific_journal-4814	107	33	fourier	fourier	NOUN
american_scientific_journal-4814	107	34	transformation	transformation	NOUN
american_scientific_journal-4814	107	35	,	,	PUNCT
american_scientific_journal-4814	107	36	the	the	DET
american_scientific_journal-4814	107	37	equations	equation	NOUN
american_scientific_journal-4814	107	38	(	(	PUNCT
american_scientific_journal-4814	107	39	1	1	NUM
american_scientific_journal-4814	107	40	)	)	PUNCT
american_scientific_journal-4814	107	41	of	of	ADP
american_scientific_journal-4814	107	42	the	the	DET
american_scientific_journal-4814	107	43	global	global	ADJ
american_scientific_journal-4814	107	44	motion	motion	NOUN
american_scientific_journal-4814	107	45	becomes	become	VERB
american_scientific_journal-4814	107	46	:	:	PUNCT
american_scientific_journal-4814	107	47	american	american	ADJ
american_scientific_journal-4814	107	48	scientific	scientific	ADJ
american_scientific_journal-4814	107	49	research	research	PROPN
american_scientific_journal-4814	107	50	journal	journal	NOUN
american_scientific_journal-4814	107	51	for	for	ADP
american_scientific_journal-4814	107	52	engineering	engineering	NOUN
american_scientific_journal-4814	107	53	,	,	PUNCT
american_scientific_journal-4814	107	54	technology	technology	NOUN
american_scientific_journal-4814	107	55	,	,	PUNCT
american_scientific_journal-4814	107	56	and	and	CCONJ
american_scientific_journal-4814	107	57	sciences	science	NOUN
american_scientific_journal-4814	107	58	(	(	PUNCT
american_scientific_journal-4814	107	59	asrjets	asrjet	NOUN
american_scientific_journal-4814	107	60	)	)	PUNCT
american_scientific_journal-4814	107	61	(	(	PUNCT
american_scientific_journal-4814	107	62	2019	2019	NUM
american_scientific_journal-4814	107	63	)	)	PUNCT
american_scientific_journal-4814	107	64	volume	volume	NOUN
american_scientific_journal-4814	107	65	55	55	NUM
american_scientific_journal-4814	107	66	,	,	PUNCT
american_scientific_journal-4814	107	67	no	no	DET
american_scientific_journal-4814	107	68	1	1	NUM
american_scientific_journal-4814	107	69	,	,	PUNCT
american_scientific_journal-4814	107	70	pp	pp	ADP
american_scientific_journal-4814	107	71	50	50	NUM
american_scientific_journal-4814	107	72	-	-	SYM
american_scientific_journal-4814	107	73	68	68	NUM
american_scientific_journal-4814	107	74	58	58	NUM
american_scientific_journal-4814	107	75	{	{	PUNCT
american_scientific_journal-4814	107	76	3𝑛𝑛02[𝐵𝐵	3𝑛𝑛02[𝐵𝐵	NUM
american_scientific_journal-4814	107	77	−	−	NOUN
american_scientific_journal-4814	108	1	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-4814	109	1	+	+	CCONJ
american_scientific_journal-4814	110	1	(	(	PUNCT
american_scientific_journal-4814	110	2	𝐵𝐵	𝐵𝐵	PROPN
american_scientific_journal-4814	110	3	−	−	PROPN
american_scientific_journal-4814	110	4	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-4814	110	5	−	−	PROPN
american_scientific_journal-4814	110	6	𝐶𝐶)∑	𝐶𝐶)∑	PROPN
american_scientific_journal-4814	110	7	𝜃𝜃𝑛𝑛𝑔𝑔	𝜃𝜃𝑛𝑛𝑔𝑔	PROPN
american_scientific_journal-4814	110	8	�	�	PROPN
american_scientific_journal-4814	110	9	𝑛𝑛∗	𝑛𝑛∗	ADJ
american_scientific_journal-4814	110	10	𝑁𝑁	𝑁𝑁	PROPN
american_scientific_journal-4814	110	11	𝑛𝑛=1	𝑛𝑛=1	NOUN
american_scientific_journal-4814	110	12	]	]	PUNCT
american_scientific_journal-4814	110	13	−	−	PUNCT
american_scientific_journal-4814	110	14	𝛺𝛺2𝐶𝐶}	𝛺𝛺2𝐶𝐶}	VERB
american_scientific_journal-4814	110	15	�	�	PROPN
american_scientific_journal-4814	110	16	̂	̂	NOUN
american_scientific_journal-4814	110	17	�	�	PROPN
american_scientific_journal-4814	110	18	𝜆	𝜆	NOUN
american_scientific_journal-4814	110	19	=	=	X
american_scientific_journal-4814	110	20	υ	υ	PROPN
american_scientific_journal-4814	110	21	�	�	PROPN
american_scientific_journal-4814	110	22	.	.	PUNCT
american_scientific_journal-4814	111	1	(	(	PUNCT
american_scientific_journal-4814	111	2	24	24	NUM
american_scientific_journal-4814	111	3	)	)	PUNCT
american_scientific_journal-4814	111	4	one	one	NOUN
american_scientific_journal-4814	111	5	defines	define	VERB
american_scientific_journal-4814	111	6	the	the	DET
american_scientific_journal-4814	111	7	following	following	ADJ
american_scientific_journal-4814	111	8	terms	term	NOUN
american_scientific_journal-4814	111	9	:	:	PUNCT
american_scientific_journal-4814	111	10	𝑍𝑍0(𝛺𝛺	𝑍𝑍0(𝛺𝛺	PROPN
american_scientific_journal-4814	111	11	)	)	PUNCT
american_scientific_journal-4814	111	12	=	=	SYM
american_scientific_journal-4814	111	13	3𝑛𝑛02(𝐵𝐵	3𝑛𝑛02(𝐵𝐵	NUM
american_scientific_journal-4814	111	14	−	−	PROPN
american_scientific_journal-4814	111	15	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-4814	111	16	)	)	PUNCT
american_scientific_journal-4814	111	17	−	−	PROPN
american_scientific_journal-4814	112	1	𝛺𝛺2𝐶𝐶	𝛺𝛺2𝐶𝐶	PROPN
american_scientific_journal-4814	112	2	,	,	PUNCT
american_scientific_journal-4814	112	3	𝑍𝑍𝑛𝑛(𝛺𝛺	𝑍𝑍𝑛𝑛(𝛺𝛺	PUNCT
american_scientific_journal-4814	112	4	)	)	PUNCT
american_scientific_journal-4814	112	5	=	=	SYM
american_scientific_journal-4814	112	6	3𝑛𝑛02(𝐵𝐵	3𝑛𝑛02(𝐵𝐵	NUM
american_scientific_journal-4814	112	7	−	−	NOUN
american_scientific_journal-4814	112	8	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-4814	112	9	−	−	PROPN
american_scientific_journal-4814	112	10	𝐶𝐶)𝜃𝜃𝑛𝑛𝑔𝑔	𝐶𝐶)𝜃𝜃𝑛𝑛𝑔𝑔	PROPN
american_scientific_journal-4814	112	11	�	�	PROPN
american_scientific_journal-4814	112	12	𝑛𝑛∗	𝑛𝑛∗	ADV
american_scientific_journal-4814	112	13	,	,	PUNCT
american_scientific_journal-4814	112	14	(	(	PUNCT
american_scientific_journal-4814	112	15	25	25	NUM
american_scientific_journal-4814	112	16	)	)	PUNCT
american_scientific_journal-4814	112	17	𝑍𝑍(𝛺𝛺	𝑍𝑍(𝛺𝛺	PROPN
american_scientific_journal-4814	112	18	)	)	PUNCT
american_scientific_journal-4814	112	19	=	=	PUNCT
american_scientific_journal-4814	112	20	𝑍𝑍0(𝛺𝛺	𝑍𝑍0(𝛺𝛺	PROPN
american_scientific_journal-4814	112	21	)	)	PUNCT
american_scientific_journal-4814	113	1	+	+	CCONJ
american_scientific_journal-4814	113	2	∑	∑	PUNCT
american_scientific_journal-4814	113	3	𝑍𝑍𝑛𝑛𝑁𝑁	𝑍𝑍𝑛𝑛𝑁𝑁	ADJ
american_scientific_journal-4814	113	4	𝑛𝑛=1	𝑛𝑛=1	NOUN
american_scientific_journal-4814	113	5	(	(	PUNCT
american_scientific_journal-4814	113	6	𝛺𝛺	𝛺𝛺	PROPN
american_scientific_journal-4814	113	7	)	)	PUNCT
american_scientific_journal-4814	113	8	.	.	PUNCT
american_scientific_journal-4814	114	1	(	(	PUNCT
american_scientific_journal-4814	114	2	26	26	NUM
american_scientific_journal-4814	114	3	)	)	PUNCT
american_scientific_journal-4814	114	4	one	one	NOUN
american_scientific_journal-4814	114	5	can	can	AUX
american_scientific_journal-4814	114	6	rewrite	rewrite	VERB
american_scientific_journal-4814	114	7	the	the	DET
american_scientific_journal-4814	114	8	equation	equation	NOUN
american_scientific_journal-4814	114	9	(	(	PUNCT
american_scientific_journal-4814	114	10	24	24	NUM
american_scientific_journal-4814	114	11	)	)	PUNCT
american_scientific_journal-4814	114	12	in	in	ADP
american_scientific_journal-4814	114	13	the	the	DET
american_scientific_journal-4814	114	14	form	form	NOUN
american_scientific_journal-4814	114	15	:	:	PUNCT
american_scientific_journal-4814	114	16	𝑍𝑍(𝛺𝛺)	𝑍𝑍(𝛺𝛺)	PROPN
american_scientific_journal-4814	114	17	�	�	PROPN
american_scientific_journal-4814	114	18	̂	̂	NUM
american_scientific_journal-4814	114	19	�	�	PROPN
american_scientific_journal-4814	114	20	𝜆	𝜆	NOUN
american_scientific_journal-4814	114	21	=	=	X
american_scientific_journal-4814	114	22	υ	υ	PROPN
american_scientific_journal-4814	114	23	�	�	PROPN
american_scientific_journal-4814	114	24	.	.	PUNCT
american_scientific_journal-4814	115	1	(	(	PUNCT
american_scientific_journal-4814	115	2	27	27	NUM
american_scientific_journal-4814	115	3	)	)	PUNCT
american_scientific_journal-4814	115	4	here	here	ADV
american_scientific_journal-4814	115	5	:	:	PUNCT
american_scientific_journal-4814	115	6	𝑍𝑍(𝛺𝛺	𝑍𝑍(𝛺𝛺	NOUN
american_scientific_journal-4814	115	7	)	)	PUNCT
american_scientific_journal-4814	115	8	is	be	AUX
american_scientific_journal-4814	115	9	the	the	DET
american_scientific_journal-4814	115	10	impedance	impedance	NOUN
american_scientific_journal-4814	115	11	function	function	NOUN
american_scientific_journal-4814	115	12	connecting	connect	VERB
american_scientific_journal-4814	115	13	the	the	DET
american_scientific_journal-4814	115	14	external	external	ADJ
american_scientific_journal-4814	115	15	forces	force	NOUN
american_scientific_journal-4814	115	16	υ	υ	PROPN
american_scientific_journal-4814	115	17	�	�	PROPN
american_scientific_journal-4814	115	18	and	and	CCONJ
american_scientific_journal-4814	115	19	the	the	DET
american_scientific_journal-4814	115	20	response	response	NOUN
american_scientific_journal-4814	115	21	�	�	PROPN
american_scientific_journal-4814	115	22	̂	̂	VERB
american_scientific_journal-4814	115	23	�	�	PROPN
american_scientific_journal-4814	115	24	𝜆	𝜆	NOUN
american_scientific_journal-4814	115	25	of	of	ADP
american_scientific_journal-4814	115	26	the	the	DET
american_scientific_journal-4814	115	27	space	space	NOUN
american_scientific_journal-4814	115	28	vehicle	vehicle	NOUN
american_scientific_journal-4814	115	29	.	.	PUNCT
american_scientific_journal-4814	116	1	formula	formula	NOUN
american_scientific_journal-4814	116	2	(	(	PUNCT
american_scientific_journal-4814	116	3	26	26	NUM
american_scientific_journal-4814	116	4	)	)	PUNCT
american_scientific_journal-4814	116	5	is	be	AUX
american_scientific_journal-4814	116	6	the	the	DET
american_scientific_journal-4814	116	7	spectral	spectral	ADJ
american_scientific_journal-4814	116	8	expansion	expansion	NOUN
american_scientific_journal-4814	116	9	of	of	ADP
american_scientific_journal-4814	116	10	the	the	DET
american_scientific_journal-4814	116	11	impedance	impedance	NOUN
american_scientific_journal-4814	116	12	function	function	NOUN
american_scientific_journal-4814	116	13	𝑍𝑍(𝛺𝛺	𝑍𝑍(𝛺𝛺	PROPN
american_scientific_journal-4814	116	14	)	)	PUNCT
american_scientific_journal-4814	116	15	.	.	PUNCT
american_scientific_journal-4814	117	1	4.3	4.3	NUM
american_scientific_journal-4814	117	2	.	.	PUNCT
american_scientific_journal-4814	117	3	equation	equation	NOUN
american_scientific_journal-4814	117	4	of	of	ADP
american_scientific_journal-4814	117	5	global	global	ADJ
american_scientific_journal-4814	117	6	frequencies	frequency	NOUN
american_scientific_journal-4814	117	7	in	in	ADP
american_scientific_journal-4814	117	8	the	the	DET
american_scientific_journal-4814	117	9	absence	absence	NOUN
american_scientific_journal-4814	117	10	of	of	ADP
american_scientific_journal-4814	117	11	external	external	ADJ
american_scientific_journal-4814	117	12	forces	force	NOUN
american_scientific_journal-4814	117	13	,	,	PUNCT
american_scientific_journal-4814	117	14	the	the	DET
american_scientific_journal-4814	117	15	global	global	ADJ
american_scientific_journal-4814	117	16	motion	motion	NOUN
american_scientific_journal-4814	117	17	of	of	ADP
american_scientific_journal-4814	117	18	the	the	DET
american_scientific_journal-4814	117	19	space	space	NOUN
american_scientific_journal-4814	117	20	vehicle	vehicle	NOUN
american_scientific_journal-4814	117	21	is	be	AUX
american_scientific_journal-4814	117	22	governed	govern	VERB
american_scientific_journal-4814	117	23	by	by	ADP
american_scientific_journal-4814	117	24	the	the	DET
american_scientific_journal-4814	117	25	following	follow	VERB
american_scientific_journal-4814	117	26	equation	equation	NOUN
american_scientific_journal-4814	117	27	:	:	PUNCT
american_scientific_journal-4814	117	28	𝑍𝑍(𝛺𝛺)	𝑍𝑍(𝛺𝛺)	PROPN
american_scientific_journal-4814	117	29	�	�	PROPN
american_scientific_journal-4814	117	30	̂	̂	NUM
american_scientific_journal-4814	117	31	�	�	PROPN
american_scientific_journal-4814	117	32	𝜆	𝜆	NOUN
american_scientific_journal-4814	117	33	=	=	NOUN
american_scientific_journal-4814	117	34	0	0	PROPN
american_scientific_journal-4814	117	35	.	.	PUNCT
american_scientific_journal-4814	118	1	(	(	PUNCT
american_scientific_journal-4814	118	2	28	28	NUM
american_scientific_journal-4814	118	3	)	)	PUNCT
american_scientific_journal-4814	118	4	one	one	PRON
american_scientific_journal-4814	118	5	assumes	assume	VERB
american_scientific_journal-4814	118	6	non	non	ADJ
american_scientific_journal-4814	118	7	trivial	trivial	ADJ
american_scientific_journal-4814	118	8	solution	solution	NOUN
american_scientific_journal-4814	118	9	�	�	NOUN
american_scientific_journal-4814	118	10	̂	̂	NOUN
american_scientific_journal-4814	118	11	�	�	PROPN
american_scientific_journal-4814	118	12	𝜆	𝜆	NOUN
american_scientific_journal-4814	118	13	of	of	ADP
american_scientific_journal-4814	118	14	equation	equation	NOUN
american_scientific_journal-4814	118	15	(	(	PUNCT
american_scientific_journal-4814	118	16	28	28	NUM
american_scientific_journal-4814	118	17	)	)	PUNCT
american_scientific_journal-4814	118	18	.	.	PUNCT
american_scientific_journal-4814	119	1	hence	hence	ADV
american_scientific_journal-4814	119	2	the	the	DET
american_scientific_journal-4814	119	3	function	function	NOUN
american_scientific_journal-4814	119	4	𝑍𝑍(𝛺𝛺	𝑍𝑍(𝛺𝛺	NOUN
american_scientific_journal-4814	119	5	)	)	PUNCT
american_scientific_journal-4814	119	6	must	must	AUX
american_scientific_journal-4814	119	7	necessarily	necessarily	ADV
american_scientific_journal-4814	119	8	verifies	verifie	NOUN
american_scientific_journal-4814	119	9	:	:	PUNCT
american_scientific_journal-4814	119	10	𝑍𝑍(𝛺𝛺	𝑍𝑍(𝛺𝛺	X
american_scientific_journal-4814	119	11	)	)	PUNCT
american_scientific_journal-4814	119	12	=	=	SYM
american_scientific_journal-4814	119	13	0	0	X
american_scientific_journal-4814	119	14	.	.	PUNCT
american_scientific_journal-4814	120	1	(	(	PUNCT
american_scientific_journal-4814	120	2	29	29	NUM
american_scientific_journal-4814	120	3	)	)	PUNCT
american_scientific_journal-4814	120	4	equation	equation	NOUN
american_scientific_journal-4814	120	5	(	(	PUNCT
american_scientific_journal-4814	120	6	29	29	NUM
american_scientific_journal-4814	120	7	)	)	PUNCT
american_scientific_journal-4814	120	8	is	be	AUX
american_scientific_journal-4814	120	9	the	the	DET
american_scientific_journal-4814	120	10	equation	equation	NOUN
american_scientific_journal-4814	120	11	of	of	ADP
american_scientific_journal-4814	120	12	the	the	DET
american_scientific_journal-4814	120	13	global	global	ADJ
american_scientific_journal-4814	120	14	eigenfrequencies	eigenfrequencie	NOUN
american_scientific_journal-4814	120	15	𝛺𝛺	𝛺𝛺	PROPN
american_scientific_journal-4814	120	16	when	when	SCONJ
american_scientific_journal-4814	120	17	the	the	DET
american_scientific_journal-4814	120	18	space	space	NOUN
american_scientific_journal-4814	120	19	vehicle	vehicle	NOUN
american_scientific_journal-4814	120	20	undergoes	undergo	VERB
american_scientific_journal-4814	120	21	natural	natural	ADJ
american_scientific_journal-4814	120	22	lace	lace	NOUN
american_scientific_journal-4814	120	23	attitude	attitude	NOUN
american_scientific_journal-4814	120	24	motion	motion	NOUN
american_scientific_journal-4814	120	25	interacting	interact	VERB
american_scientific_journal-4814	120	26	with	with	ADP
american_scientific_journal-4814	120	27	elastic	elastic	ADJ
american_scientific_journal-4814	120	28	deformations	deformation	NOUN
american_scientific_journal-4814	120	29	.	.	PUNCT
american_scientific_journal-4814	121	1	4.4	4.4	NUM
american_scientific_journal-4814	121	2	.	.	PUNCT
american_scientific_journal-4814	122	1	convergence	convergence	NOUN
american_scientific_journal-4814	122	2	of	of	ADP
american_scientific_journal-4814	122	3	the	the	DET
american_scientific_journal-4814	122	4	global	global	ADJ
american_scientific_journal-4814	122	5	modes	mode	NOUN
american_scientific_journal-4814	122	6	gain	gain	VERB
american_scientific_journal-4814	122	7	one	one	NUM
american_scientific_journal-4814	122	8	defines	define	VERB
american_scientific_journal-4814	122	9	the	the	DET
american_scientific_journal-4814	122	10	global	global	ADJ
american_scientific_journal-4814	122	11	modes	mode	NOUN
american_scientific_journal-4814	122	12	gain	gain	VERB
american_scientific_journal-4814	122	13	as	as	ADP
american_scientific_journal-4814	122	14	the	the	DET
american_scientific_journal-4814	122	15	following	follow	VERB
american_scientific_journal-4814	122	16	series	series	NOUN
american_scientific_journal-4814	122	17	:	:	PUNCT
american_scientific_journal-4814	122	18	�	�	PROPN
american_scientific_journal-4814	122	19	𝜃𝜃𝑛𝑛2	𝜃𝜃𝑛𝑛2	NUM
american_scientific_journal-4814	122	20	∞	∞	NUM
american_scientific_journal-4814	122	21	𝑛𝑛=1	𝑛𝑛=1	PROPN
american_scientific_journal-4814	122	22	.	.	PUNCT
american_scientific_journal-4814	123	1	the	the	DET
american_scientific_journal-4814	123	2	modal	modal	ADJ
american_scientific_journal-4814	123	3	analysis	analysis	NOUN
american_scientific_journal-4814	123	4	of	of	ADP
american_scientific_journal-4814	123	5	the	the	DET
american_scientific_journal-4814	123	6	space	space	NOUN
american_scientific_journal-4814	123	7	vehicle	vehicle	NOUN
american_scientific_journal-4814	123	8	equations	equation	NOUN
american_scientific_journal-4814	123	9	motion	motion	NOUN
american_scientific_journal-4814	123	10	performed	perform	VERB
american_scientific_journal-4814	123	11	using	use	VERB
american_scientific_journal-4814	123	12	the	the	DET
american_scientific_journal-4814	123	13	superposition	superposition	NOUN
american_scientific_journal-4814	123	14	method	method	NOUN
american_scientific_journal-4814	123	15	of	of	ADP
american_scientific_journal-4814	123	16	american	american	ADJ
american_scientific_journal-4814	123	17	scientific	scientific	ADJ
american_scientific_journal-4814	123	18	research	research	NOUN
american_scientific_journal-4814	123	19	journal	journal	NOUN
american_scientific_journal-4814	123	20	for	for	ADP
american_scientific_journal-4814	123	21	engineering	engineering	NOUN
american_scientific_journal-4814	123	22	,	,	PUNCT
american_scientific_journal-4814	123	23	technology	technology	NOUN
american_scientific_journal-4814	123	24	,	,	PUNCT
american_scientific_journal-4814	123	25	and	and	CCONJ
american_scientific_journal-4814	123	26	sciences	science	NOUN
american_scientific_journal-4814	123	27	(	(	PUNCT
american_scientific_journal-4814	123	28	asrjets	asrjet	NOUN
american_scientific_journal-4814	123	29	)	)	PUNCT
american_scientific_journal-4814	123	30	(	(	PUNCT
american_scientific_journal-4814	123	31	2019	2019	NUM
american_scientific_journal-4814	123	32	)	)	PUNCT
american_scientific_journal-4814	123	33	volume	volume	NOUN
american_scientific_journal-4814	123	34	55	55	NUM
american_scientific_journal-4814	123	35	,	,	PUNCT
american_scientific_journal-4814	123	36	no	no	DET
american_scientific_journal-4814	123	37	1	1	NUM
american_scientific_journal-4814	123	38	,	,	PUNCT
american_scientific_journal-4814	123	39	pp	pp	ADP
american_scientific_journal-4814	123	40	50	50	NUM
american_scientific_journal-4814	123	41	-	-	SYM
american_scientific_journal-4814	123	42	68	68	NUM
american_scientific_journal-4814	123	43	59	59	NUM
american_scientific_journal-4814	123	44	rayleigh	rayleigh	PROPN
american_scientific_journal-4814	123	45	-	-	PUNCT
american_scientific_journal-4814	123	46	ritz	ritz	PROPN
american_scientific_journal-4814	123	47	,	,	PUNCT
american_scientific_journal-4814	123	48	establishes	establish	VERB
american_scientific_journal-4814	123	49	the	the	DET
american_scientific_journal-4814	123	50	convergence	convergence	NOUN
american_scientific_journal-4814	123	51	of	of	ADP
american_scientific_journal-4814	123	52	the	the	DET
american_scientific_journal-4814	123	53	global	global	ADJ
american_scientific_journal-4814	123	54	modes	mode	NOUN
american_scientific_journal-4814	123	55	gain	gain	VERB
american_scientific_journal-4814	123	56	above	above	ADV
american_scientific_journal-4814	123	57	(	(	PUNCT
american_scientific_journal-4814	123	58	see	see	VERB
american_scientific_journal-4814	123	59	appendix	appendix	NOUN
american_scientific_journal-4814	123	60	4	4	NUM
american_scientific_journal-4814	123	61	):	):	PUNCT
american_scientific_journal-4814	123	62	∑	∑	PUNCT
american_scientific_journal-4814	123	63	𝜃𝜃𝑛𝑛2∞	𝜃𝜃𝑛𝑛2∞	ADP
american_scientific_journal-4814	123	64	𝑛𝑛=1	𝑛𝑛=1	NOUN
american_scientific_journal-4814	123	65	=	=	SYM
american_scientific_journal-4814	123	66	2ℒ	2ℒ	PROPN
american_scientific_journal-4814	123	67	𝐶𝐶(𝐶𝐶−2ℒ	𝐶𝐶(𝐶𝐶−2ℒ	PROPN
american_scientific_journal-4814	123	68	)	)	PUNCT
american_scientific_journal-4814	123	69	,	,	PUNCT
american_scientific_journal-4814	123	70	(	(	PUNCT
american_scientific_journal-4814	123	71	30	30	NUM
american_scientific_journal-4814	123	72	)	)	PUNCT
american_scientific_journal-4814	123	73	here	here	ADV
american_scientific_journal-4814	123	74	:	:	PUNCT
american_scientific_journal-4814	123	75	ℒ	ℒ	PROPN
american_scientific_journal-4814	123	76	=	=	PUNCT
american_scientific_journal-4814	123	77	𝑚𝑚	𝑚𝑚	NOUN
american_scientific_journal-4814	123	78	�	�	PROPN
american_scientific_journal-4814	123	79	(𝑏𝑏	(𝑏𝑏	PUNCT
american_scientific_journal-4814	123	80	+	+	NUM
american_scientific_journal-4814	123	81	𝑙𝑙)2	𝑙𝑙)2	PROPN
american_scientific_journal-4814	123	82	+	+	CCONJ
american_scientific_journal-4814	123	83	(	(	PUNCT
american_scientific_journal-4814	123	84	𝜎𝜎𝑒𝑒	𝜎𝜎𝑒𝑒	NOUN
american_scientific_journal-4814	123	85	+	+	CCONJ
american_scientific_journal-4814	123	86	𝜌𝜌	𝜌𝜌	ADJ
american_scientific_journal-4814	123	87	)	)	PUNCT
american_scientific_journal-4814	123	88	�	�	PROPN
american_scientific_journal-4814	123	89	𝑏𝑏2𝑙𝑙	𝑏𝑏2𝑙𝑙	NOUN
american_scientific_journal-4814	123	90	+	+	CCONJ
american_scientific_journal-4814	123	91	𝑏𝑏𝑙𝑙2	𝑏𝑏𝑙𝑙2	ADJ
american_scientific_journal-4814	123	92	+	+	CCONJ
american_scientific_journal-4814	123	93	𝑙𝑙3	𝑙𝑙3	ADJ
american_scientific_journal-4814	123	94	3	3	NUM
american_scientific_journal-4814	123	95	�	�	PROPN
american_scientific_journal-4814	123	96	.	.	PUNCT
american_scientific_journal-4814	124	1	this	this	DET
american_scientific_journal-4814	124	2	convergence	convergence	NOUN
american_scientific_journal-4814	124	3	property	property	NOUN
american_scientific_journal-4814	124	4	gives	give	VERB
american_scientific_journal-4814	124	5	an	an	DET
american_scientific_journal-4814	124	6	approximation	approximation	NOUN
american_scientific_journal-4814	124	7	of	of	ADP
american_scientific_journal-4814	124	8	the	the	DET
american_scientific_journal-4814	124	9	modal	modal	ADJ
american_scientific_journal-4814	124	10	gain	gain	NOUN
american_scientific_journal-4814	124	11	with	with	ADP
american_scientific_journal-4814	124	12	a	a	DET
american_scientific_journal-4814	124	13	finite	finite	ADJ
american_scientific_journal-4814	124	14	number	number	NOUN
american_scientific_journal-4814	124	15	n	n	NUM
american_scientific_journal-4814	124	16	of	of	ADP
american_scientific_journal-4814	124	17	the	the	DET
american_scientific_journal-4814	124	18	global	global	ADJ
american_scientific_journal-4814	124	19	modes	mode	NOUN
american_scientific_journal-4814	124	20	selected	select	VERB
american_scientific_journal-4814	124	21	in	in	ADP
american_scientific_journal-4814	124	22	order	order	NOUN
american_scientific_journal-4814	124	23	to	to	PART
american_scientific_journal-4814	124	24	perform	perform	VERB
american_scientific_journal-4814	124	25	the	the	DET
american_scientific_journal-4814	124	26	dynamical	dynamical	ADJ
american_scientific_journal-4814	124	27	model	model	NOUN
american_scientific_journal-4814	124	28	of	of	ADP
american_scientific_journal-4814	124	29	the	the	DET
american_scientific_journal-4814	124	30	space	space	NOUN
american_scientific_journal-4814	124	31	vehicle	vehicle	NOUN
american_scientific_journal-4814	124	32	.	.	PUNCT
american_scientific_journal-4814	125	1	5	5	X
american_scientific_journal-4814	125	2	.	.	X
american_scientific_journal-4814	125	3	digital	digital	ADJ
american_scientific_journal-4814	125	4	simulations	simulation	NOUN
american_scientific_journal-4814	125	5	the	the	DET
american_scientific_journal-4814	125	6	simulations	simulation	NOUN
american_scientific_journal-4814	125	7	are	be	AUX
american_scientific_journal-4814	125	8	performed	perform	VERB
american_scientific_journal-4814	125	9	with	with	ADP
american_scientific_journal-4814	125	10	the	the	DET
american_scientific_journal-4814	125	11	following	follow	VERB
american_scientific_journal-4814	125	12	data	datum	NOUN
american_scientific_journal-4814	125	13	:	:	PUNCT
american_scientific_journal-4814	125	14	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-4814	125	15	=	=	NUM
american_scientific_journal-4814	125	16	9.5	9.5	NUM
american_scientific_journal-4814	125	17	×	×	NOUN
american_scientific_journal-4814	125	18	106	106	NUM
american_scientific_journal-4814	125	19	𝑘𝑘𝑔𝑔.𝑚𝑚2	𝑘𝑘𝑔𝑔.𝑚𝑚2	PROPN
american_scientific_journal-4814	125	20	;	;	PUNCT
american_scientific_journal-4814	125	21	𝐵𝐵	𝐵𝐵	PROPN
american_scientific_journal-4814	125	22	=	=	SYM
american_scientific_journal-4814	125	23	106	106	NUM
american_scientific_journal-4814	125	24	𝑘𝑘𝑔𝑔.𝑚𝑚2	𝑘𝑘𝑔𝑔.𝑚𝑚2	PROPN
american_scientific_journal-4814	125	25	;	;	PUNCT
american_scientific_journal-4814	125	26	𝐶𝐶	𝐶𝐶	NOUN
american_scientific_journal-4814	125	27	=	=	SYM
american_scientific_journal-4814	125	28	4	4	NUM
american_scientific_journal-4814	125	29	×	×	NOUN
american_scientific_journal-4814	125	30	106	106	NUM
american_scientific_journal-4814	125	31	𝑘𝑘𝑔𝑔.𝑚𝑚2	𝑘𝑘𝑔𝑔.𝑚𝑚2	PROPN
american_scientific_journal-4814	125	32	;	;	PUNCT
american_scientific_journal-4814	125	33	𝐸𝐸	𝐸𝐸	PROPN
american_scientific_journal-4814	125	34	=	=	SYM
american_scientific_journal-4814	125	35	103	103	NUM
american_scientific_journal-4814	125	36	𝑁𝑁.𝑚𝑚2	𝑁𝑁.𝑚𝑚2	NOUN
american_scientific_journal-4814	125	37	;	;	PUNCT
american_scientific_journal-4814	125	38	𝐸𝐸	𝐸𝐸	PROPN
american_scientific_journal-4814	125	39	=	=	SYM
american_scientific_journal-4814	125	40	103	103	NUM
american_scientific_journal-4814	125	41	𝑁𝑁.𝑚𝑚−2	𝑁𝑁.𝑚𝑚−2	NOUN
american_scientific_journal-4814	125	42	;	;	PUNCT
american_scientific_journal-4814	126	1	ℎ	ℎ	X
american_scientific_journal-4814	126	2	=	=	NOUN
american_scientific_journal-4814	126	3	0,01	0,01	PROPN
american_scientific_journal-4814	126	4	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-4814	126	5	;	;	PUNCT
american_scientific_journal-4814	126	6	𝑒𝑒	𝑒𝑒	ADP
american_scientific_journal-4814	126	7	=	=	PUNCT
american_scientific_journal-4814	126	8	3,2	3,2	NUM
american_scientific_journal-4814	126	9	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-4814	126	10	;	;	PUNCT
american_scientific_journal-4814	126	11	𝑙𝑙	𝑙𝑙	X
american_scientific_journal-4814	126	12	=	=	SYM
american_scientific_journal-4814	126	13	28,8	28,8	NUM
american_scientific_journal-4814	126	14	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-4814	126	15	;	;	PUNCT
american_scientific_journal-4814	126	16	𝑏𝑏	𝑏𝑏	NOUN
american_scientific_journal-4814	126	17	=	=	SYM
american_scientific_journal-4814	126	18	1,8	1,8	NUM
american_scientific_journal-4814	126	19	𝑚𝑚	𝑚𝑚	NOUN
american_scientific_journal-4814	126	20	;	;	PUNCT
american_scientific_journal-4814	126	21	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-4814	126	22	�	�	PROPN
american_scientific_journal-4814	126	23	=	=	SYM
american_scientific_journal-4814	126	24	6	6	NUM
american_scientific_journal-4814	126	25	𝑘𝑘𝑔𝑔	𝑘𝑘𝑔𝑔	NOUN
american_scientific_journal-4814	126	26	;	;	PUNCT
american_scientific_journal-4814	126	27	𝑆𝑆	𝑆𝑆	PROPN
american_scientific_journal-4814	126	28	=	=	PROPN
american_scientific_journal-4814	126	29	140	140	NUM
american_scientific_journal-4814	126	30	𝑁𝑁	𝑁𝑁	PROPN
american_scientific_journal-4814	126	31	;	;	PUNCT
american_scientific_journal-4814	126	32	𝜎𝜎	𝜎𝜎	X
american_scientific_journal-4814	126	33	=	=	SYM
american_scientific_journal-4814	126	34	1,4	1,4	NUM
american_scientific_journal-4814	126	35	𝑘𝑘𝑔𝑔.𝑚𝑚−2	𝑘𝑘𝑔𝑔.𝑚𝑚−2	NOUN
american_scientific_journal-4814	126	36	;	;	PUNCT
american_scientific_journal-4814	126	37	𝜌𝜌	𝜌𝜌	ADP
american_scientific_journal-4814	126	38	=	=	SYM
american_scientific_journal-4814	126	39	204	204	NUM
american_scientific_journal-4814	126	40	𝑁𝑁.𝑚𝑚−3	𝑁𝑁.𝑚𝑚−3	PROPN
american_scientific_journal-4814	126	41	;	;	PUNCT
american_scientific_journal-4814	126	42	𝜈𝜈	𝜈𝜈	NOUN
american_scientific_journal-4814	126	43	=	=	NOUN
american_scientific_journal-4814	126	44	0,3	0,3	NOUN
american_scientific_journal-4814	126	45	𝐸𝐸	𝐸𝐸	PROPN
american_scientific_journal-4814	126	46	is	be	AUX
american_scientific_journal-4814	126	47	the	the	DET
american_scientific_journal-4814	126	48	moment	moment	NOUN
american_scientific_journal-4814	126	49	of	of	ADP
american_scientific_journal-4814	126	50	inertia	inertia	NOUN
american_scientific_journal-4814	126	51	𝑁𝑁	𝑁𝑁	PROPN
american_scientific_journal-4814	126	52	:	:	PUNCT
american_scientific_journal-4814	126	53	newton	newton	PROPN
american_scientific_journal-4814	126	54	;	;	PUNCT
american_scientific_journal-4814	126	55	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-4814	126	56	:	:	PUNCT
american_scientific_journal-4814	126	57	meter	meter	NOUN
american_scientific_journal-4814	126	58	;	;	PUNCT
american_scientific_journal-4814	126	59	𝑘𝑘𝑔𝑔	𝑘𝑘𝑔𝑔	NUM
american_scientific_journal-4814	126	60	:	:	PUNCT
american_scientific_journal-4814	127	1	kilogram	kilogram	PROPN
american_scientific_journal-4814	127	2	;	;	PUNCT
american_scientific_journal-4814	127	3	5.1	5.1	NUM
american_scientific_journal-4814	127	4	.	.	PUNCT
american_scientific_journal-4814	128	1	global	global	ADJ
american_scientific_journal-4814	128	2	modes	mode	NOUN
american_scientific_journal-4814	128	3	gain	gain	VERB
american_scientific_journal-4814	128	4	the	the	DET
american_scientific_journal-4814	128	5	convergence	convergence	NOUN
american_scientific_journal-4814	128	6	of	of	ADP
american_scientific_journal-4814	128	7	the	the	DET
american_scientific_journal-4814	128	8	global	global	ADJ
american_scientific_journal-4814	128	9	modes	mode	NOUN
american_scientific_journal-4814	128	10	gain	gain	NOUN
american_scientific_journal-4814	128	11	is	be	AUX
american_scientific_journal-4814	128	12	given	give	VERB
american_scientific_journal-4814	128	13	by	by	ADP
american_scientific_journal-4814	128	14	the	the	DET
american_scientific_journal-4814	128	15	equation	equation	NOUN
american_scientific_journal-4814	128	16	(	(	PUNCT
american_scientific_journal-4814	128	17	30	30	NUM
american_scientific_journal-4814	128	18	)	)	PUNCT
american_scientific_journal-4814	128	19	.	.	PUNCT
american_scientific_journal-4814	129	1	one	one	NUM
american_scientific_journal-4814	129	2	defines	define	VERB
american_scientific_journal-4814	129	3	the	the	DET
american_scientific_journal-4814	129	4	numerical	numerical	ADJ
american_scientific_journal-4814	129	5	sequence	sequence	NOUN
american_scientific_journal-4814	129	6	𝑖𝑖𝑁𝑁	𝑖𝑖𝑁𝑁	NOUN
american_scientific_journal-4814	129	7	:	:	PUNCT
american_scientific_journal-4814	129	8	𝑖𝑖𝑁𝑁	𝑖𝑖𝑁𝑁	PROPN
american_scientific_journal-4814	129	9	=	=	SYM
american_scientific_journal-4814	129	10	�	�	PROPN
american_scientific_journal-4814	129	11	𝜃𝜃𝑛𝑛2	𝜃𝜃𝑛𝑛2	SYM
american_scientific_journal-4814	129	12	𝑁𝑁	𝑁𝑁	PROPN
american_scientific_journal-4814	129	13	𝑛𝑛=1	𝑛𝑛=1	NOUN
american_scientific_journal-4814	129	14	.	.	PUNCT
american_scientific_journal-4814	130	1	as	as	SCONJ
american_scientific_journal-4814	130	2	the	the	DET
american_scientific_journal-4814	130	3	global	global	ADJ
american_scientific_journal-4814	130	4	modes	mode	NOUN
american_scientific_journal-4814	130	5	gain	gain	VERB
american_scientific_journal-4814	130	6	is	be	AUX
american_scientific_journal-4814	130	7	convergent	convergent	NOUN
american_scientific_journal-4814	130	8	,	,	PUNCT
american_scientific_journal-4814	130	9	the	the	DET
american_scientific_journal-4814	130	10	number	number	NOUN
american_scientific_journal-4814	130	11	n	n	PRON
american_scientific_journal-4814	130	12	selected	select	VERB
american_scientific_journal-4814	130	13	achieves	achieve	VERB
american_scientific_journal-4814	130	14	a	a	DET
american_scientific_journal-4814	130	15	good	good	ADJ
american_scientific_journal-4814	130	16	approximation	approximation	NOUN
american_scientific_journal-4814	130	17	of	of	ADP
american_scientific_journal-4814	130	18	formula	formula	NOUN
american_scientific_journal-4814	130	19	(	(	PUNCT
american_scientific_journal-4814	130	20	30	30	NUM
american_scientific_journal-4814	130	21	)	)	PUNCT
american_scientific_journal-4814	130	22	.	.	PUNCT
american_scientific_journal-4814	131	1	𝑁𝑁	𝑁𝑁	PROPN
american_scientific_journal-4814	131	2	=	=	SYM
american_scientific_journal-4814	131	3	35	35	NUM
american_scientific_journal-4814	131	4	is	be	AUX
american_scientific_journal-4814	131	5	suitable	suitable	ADJ
american_scientific_journal-4814	131	6	to	to	PART
american_scientific_journal-4814	131	7	perform	perform	VERB
american_scientific_journal-4814	131	8	the	the	DET
american_scientific_journal-4814	131	9	numerical	numerical	ADJ
american_scientific_journal-4814	131	10	simulations	simulation	NOUN
american_scientific_journal-4814	131	11	in	in	ADP
american_scientific_journal-4814	131	12	the	the	DET
american_scientific_journal-4814	131	13	following	following	NOUN
american_scientific_journal-4814	131	14	.	.	PUNCT
american_scientific_journal-4814	132	1	the	the	DET
american_scientific_journal-4814	132	2	figure	figure	NOUN
american_scientific_journal-4814	132	3	5	5	NUM
american_scientific_journal-4814	132	4	represents	represent	VERB
american_scientific_journal-4814	132	5	the	the	DET
american_scientific_journal-4814	132	6	simulation	simulation	NOUN
american_scientific_journal-4814	132	7	of	of	ADP
american_scientific_journal-4814	132	8	the	the	DET
american_scientific_journal-4814	132	9	numerical	numerical	ADJ
american_scientific_journal-4814	132	10	sequence	sequence	NOUN
american_scientific_journal-4814	132	11	𝑖𝑖𝑁𝑁.	𝑖𝑖𝑁𝑁.	PROPN
american_scientific_journal-4814	132	12	5.2	5.2	NUM
american_scientific_journal-4814	132	13	.	.	PUNCT
american_scientific_journal-4814	133	1	computation	computation	NOUN
american_scientific_journal-4814	133	2	of	of	ADP
american_scientific_journal-4814	133	3	the	the	DET
american_scientific_journal-4814	133	4	global	global	ADJ
american_scientific_journal-4814	133	5	eigenfrequencies	eigenfrequencie	NOUN
american_scientific_journal-4814	133	6	in	in	ADP
american_scientific_journal-4814	133	7	the	the	DET
american_scientific_journal-4814	133	8	absence	absence	NOUN
american_scientific_journal-4814	133	9	of	of	ADP
american_scientific_journal-4814	133	10	external	external	ADJ
american_scientific_journal-4814	133	11	forces	force	NOUN
american_scientific_journal-4814	133	12	and	and	CCONJ
american_scientific_journal-4814	133	13	orbital	orbital	ADJ
american_scientific_journal-4814	133	14	motion	motion	NOUN
american_scientific_journal-4814	133	15	,	,	PUNCT
american_scientific_journal-4814	133	16	the	the	DET
american_scientific_journal-4814	133	17	space	space	NOUN
american_scientific_journal-4814	133	18	vehicle	vehicle	NOUN
american_scientific_journal-4814	133	19	lace	lace	NOUN
american_scientific_journal-4814	133	20	attitude	attitude	NOUN
american_scientific_journal-4814	133	21	motion	motion	NOUN
american_scientific_journal-4814	133	22	𝜃𝜃(𝑡𝑡	𝜃𝜃(𝑡𝑡	NOUN
american_scientific_journal-4814	133	23	)	)	PUNCT
american_scientific_journal-4814	133	24	is	be	AUX
american_scientific_journal-4814	133	25	interacting	interact	VERB
american_scientific_journal-4814	133	26	with	with	ADP
american_scientific_journal-4814	133	27	array	array	NOUN
american_scientific_journal-4814	133	28	bending	bend	VERB
american_scientific_journal-4814	133	29	in	in	ADP
american_scientific_journal-4814	133	30	plane	plane	NOUN
american_scientific_journal-4814	133	31	.	.	PUNCT
american_scientific_journal-4814	134	1	from	from	ADP
american_scientific_journal-4814	134	2	equations	equation	NOUN
american_scientific_journal-4814	134	3	(	(	PUNCT
american_scientific_journal-4814	134	4	14	14	NUM
american_scientific_journal-4814	134	5	)	)	PUNCT
american_scientific_journal-4814	134	6	,	,	PUNCT
american_scientific_journal-4814	134	7	one	one	PRON
american_scientific_journal-4814	134	8	computes	compute	VERB
american_scientific_journal-4814	134	9	the	the	DET
american_scientific_journal-4814	134	10	global	global	ADJ
american_scientific_journal-4814	134	11	modes	mode	NOUN
american_scientific_journal-4814	134	12	eigenfrequencies	eigenfrequencie	NOUN
american_scientific_journal-4814	134	13	𝜑𝜑𝑛𝑛	𝜑𝜑𝑛𝑛	PROPN
american_scientific_journal-4814	134	14	corresponding	correspond	VERB
american_scientific_journal-4814	134	15	to	to	AUX
american_scientific_journal-4814	134	16	arrays	array	NOUN
american_scientific_journal-4814	134	17	bending	bend	VERB
american_scientific_journal-4814	134	18	in	in	ADP
american_scientific_journal-4814	134	19	plane	plane	NOUN
american_scientific_journal-4814	134	20	and	and	CCONJ
american_scientific_journal-4814	134	21	the	the	DET
american_scientific_journal-4814	134	22	lace	lace	NOUN
american_scientific_journal-4814	134	23	attitude	attitude	NOUN
american_scientific_journal-4814	134	24	of	of	ADP
american_scientific_journal-4814	134	25	the	the	DET
american_scientific_journal-4814	134	26	space	space	NOUN
american_scientific_journal-4814	134	27	vehicle	vehicle	NOUN
american_scientific_journal-4814	134	28	.	.	PUNCT
american_scientific_journal-4814	135	1	in	in	ADP
american_scientific_journal-4814	135	2	accordance	accordance	NOUN
american_scientific_journal-4814	135	3	with	with	ADP
american_scientific_journal-4814	135	4	the	the	DET
american_scientific_journal-4814	135	5	modal	modal	ADJ
american_scientific_journal-4814	135	6	gain	gain	NOUN
american_scientific_journal-4814	135	7	approximation	approximation	NOUN
american_scientific_journal-4814	135	8	(	(	PUNCT
american_scientific_journal-4814	135	9	30	30	NUM
american_scientific_journal-4814	135	10	)	)	PUNCT
american_scientific_journal-4814	135	11	,	,	PUNCT
american_scientific_journal-4814	135	12	35	35	NUM
american_scientific_journal-4814	135	13	american	american	ADJ
american_scientific_journal-4814	135	14	scientific	scientific	ADJ
american_scientific_journal-4814	135	15	research	research	NOUN
american_scientific_journal-4814	135	16	journal	journal	NOUN
american_scientific_journal-4814	135	17	for	for	ADP
american_scientific_journal-4814	135	18	engineering	engineering	NOUN
american_scientific_journal-4814	135	19	,	,	PUNCT
american_scientific_journal-4814	135	20	technology	technology	NOUN
american_scientific_journal-4814	135	21	,	,	PUNCT
american_scientific_journal-4814	135	22	and	and	CCONJ
american_scientific_journal-4814	135	23	sciences	science	NOUN
american_scientific_journal-4814	135	24	(	(	PUNCT
american_scientific_journal-4814	135	25	asrjets	asrjet	NOUN
american_scientific_journal-4814	135	26	)	)	PUNCT
american_scientific_journal-4814	135	27	(	(	PUNCT
american_scientific_journal-4814	135	28	2019	2019	NUM
american_scientific_journal-4814	135	29	)	)	PUNCT
american_scientific_journal-4814	135	30	volume	volume	NOUN
american_scientific_journal-4814	135	31	55	55	NUM
american_scientific_journal-4814	135	32	,	,	PUNCT
american_scientific_journal-4814	135	33	no	no	DET
american_scientific_journal-4814	135	34	1	1	NUM
american_scientific_journal-4814	135	35	,	,	PUNCT
american_scientific_journal-4814	135	36	pp	pp	ADP
american_scientific_journal-4814	135	37	50	50	NUM
american_scientific_journal-4814	135	38	-	-	SYM
american_scientific_journal-4814	135	39	68	68	NUM
american_scientific_journal-4814	135	40	60	60	NUM
american_scientific_journal-4814	135	41	eigenfrequencies	eigenfrequencie	NOUN
american_scientific_journal-4814	135	42	are	be	AUX
american_scientific_journal-4814	135	43	selected	select	VERB
american_scientific_journal-4814	135	44	in	in	ADP
american_scientific_journal-4814	135	45	each	each	DET
american_scientific_journal-4814	135	46	case	case	NOUN
american_scientific_journal-4814	135	47	of	of	ADP
american_scientific_journal-4814	135	48	global	global	ADJ
american_scientific_journal-4814	135	49	modes	mode	NOUN
american_scientific_journal-4814	135	50	(	(	PUNCT
american_scientific_journal-4814	135	51	see	see	VERB
american_scientific_journal-4814	135	52	table	table	NOUN
american_scientific_journal-4814	135	53	1	1	NUM
american_scientific_journal-4814	135	54	)	)	PUNCT
american_scientific_journal-4814	135	55	.	.	PUNCT
american_scientific_journal-4814	136	1	table	table	NOUN
american_scientific_journal-4814	136	2	1	1	NUM
american_scientific_journal-4814	136	3	:	:	PUNCT
american_scientific_journal-4814	136	4	global	global	ADJ
american_scientific_journal-4814	136	5	eigenfrequencies	eigenfrequencie	NOUN
american_scientific_journal-4814	136	6	bending	bend	VERB
american_scientific_journal-4814	136	7	in	in	ADP
american_scientific_journal-4814	136	8	plane	plane	NOUN
american_scientific_journal-4814	136	9	in	in	ADP
american_scientific_journal-4814	136	10	the	the	DET
american_scientific_journal-4814	136	11	bandwidth	bandwidth	NOUN
american_scientific_journal-4814	136	12	[	[	X
american_scientific_journal-4814	136	13	0	0	NUM
american_scientific_journal-4814	136	14	–	–	PUNCT
american_scientific_journal-4814	136	15	4	4	NUM
american_scientific_journal-4814	136	16	hz	hz	VERB
american_scientific_journal-4814	136	17	]	]	X
american_scientific_journal-4814	136	18	𝜑𝜑𝑛𝑛/2𝜋𝜋(𝐻𝐻𝐻𝐻	𝜑𝜑𝑛𝑛/2𝜋𝜋(𝐻𝐻𝐻𝐻	NOUN
american_scientific_journal-4814	136	19	)	)	PUNCT
american_scientific_journal-4814	136	20	0.100	0.100	NUM
american_scientific_journal-4814	136	21	0.179	0.179	NUM
american_scientific_journal-4814	136	22	0.201	0.201	NUM
american_scientific_journal-4814	136	23	0.397	0.397	NUM
american_scientific_journal-4814	136	24	0.495	0.495	NUM
american_scientific_journal-4814	136	25	0.579	0.579	NUM
american_scientific_journal-4814	136	26	0.597	0.597	NUM
american_scientific_journal-4814	136	27	0.695	0.695	NUM
american_scientific_journal-4814	136	28	0.298	0.298	NUM
american_scientific_journal-4814	136	29	0.793	0.793	NUM
american_scientific_journal-4814	136	30	0.893	0.893	NUM
american_scientific_journal-4814	136	31	0.992	0.992	NUM
american_scientific_journal-4814	136	32	1.091	1.091	NUM
american_scientific_journal-4814	136	33	1.184	1.184	NUM
american_scientific_journal-4814	136	34	1.199	1.199	NUM
american_scientific_journal-4814	136	35	1.289	1.289	NUM
american_scientific_journal-4814	136	36	1.389	1.389	NUM
american_scientific_journal-4814	136	37	1.487	1.487	NUM
american_scientific_journal-4814	136	38	1.686	1.686	NUM
american_scientific_journal-4814	136	39	1.785	1.785	NUM
american_scientific_journal-4814	136	40	1.884	1.884	NUM
american_scientific_journal-4814	136	41	1.587	1.587	NUM
american_scientific_journal-4814	136	42	1.983	1.983	NUM
american_scientific_journal-4814	136	43	2.017	2.017	NUM
american_scientific_journal-4814	136	44	2.084	2.084	NUM
american_scientific_journal-4814	136	45	2.182	2.182	NUM
american_scientific_journal-4814	136	46	2.281	2.281	NUM
american_scientific_journal-4814	136	47	2.380	2.380	NUM
american_scientific_journal-4814	136	48	2.479	2.479	NUM
american_scientific_journal-4814	136	49	2.578	2.578	NUM
american_scientific_journal-4814	136	50	2.678	2.678	NUM
american_scientific_journal-4814	136	51	2.776	2.776	NUM
american_scientific_journal-4814	136	52	2.876	2.876	NUM
american_scientific_journal-4814	136	53	2.974	2.974	NUM
american_scientific_journal-4814	136	54	3.068	3.068	NUM
american_scientific_journal-4814	136	55	5.3	5.3	NUM
american_scientific_journal-4814	136	56	.	.	PUNCT
american_scientific_journal-4814	137	1	calculation	calculation	NOUN
american_scientific_journal-4814	137	2	of	of	ADP
american_scientific_journal-4814	137	3	the	the	DET
american_scientific_journal-4814	137	4	space	space	NOUN
american_scientific_journal-4814	137	5	vehicle	vehicle	NOUN
american_scientific_journal-4814	137	6	global	global	ADJ
american_scientific_journal-4814	137	7	frequencies	frequency	NOUN
american_scientific_journal-4814	137	8	table	table	VERB
american_scientific_journal-4814	137	9	2	2	NUM
american_scientific_journal-4814	137	10	:	:	PUNCT
american_scientific_journal-4814	137	11	global	global	ADJ
american_scientific_journal-4814	137	12	frequencies	frequency	NOUN
american_scientific_journal-4814	137	13	in	in	ADP
american_scientific_journal-4814	137	14	band	band	NOUN
american_scientific_journal-4814	137	15	width	width	NOUN
american_scientific_journal-4814	138	1	[	[	X
american_scientific_journal-4814	138	2	0	0	NUM
american_scientific_journal-4814	138	3	–	–	PUNCT
american_scientific_journal-4814	138	4	2	2	NUM
american_scientific_journal-4814	138	5	hz	hz	VERB
american_scientific_journal-4814	138	6	]	]	X
american_scientific_journal-4814	138	7	𝑛𝑛0	𝑛𝑛0	X
american_scientific_journal-4814	138	8	(	(	PUNCT
american_scientific_journal-4814	138	9	𝑟𝑟𝑎𝑎𝑑𝑑/𝑠𝑠	𝑟𝑟𝑎𝑎𝑑𝑑/𝑠𝑠	NOUN
american_scientific_journal-4814	138	10	)	)	PUNCT
american_scientific_journal-4814	138	11	10−8	10−8	NUM
american_scientific_journal-4814	138	12	10−7	10−7	NUM
american_scientific_journal-4814	138	13	10	10	NUM
american_scientific_journal-4814	138	14	-	-	SYM
american_scientific_journal-4814	138	15	6	6	NUM
american_scientific_journal-4814	138	16	10	10	NUM
american_scientific_journal-4814	138	17	-	-	SYM
american_scientific_journal-4814	138	18	5	5	NUM
american_scientific_journal-4814	138	19	10	10	NUM
american_scientific_journal-4814	138	20	-	-	SYM
american_scientific_journal-4814	138	21	4	4	NUM
american_scientific_journal-4814	138	22	10	10	NUM
american_scientific_journal-4814	138	23	-	-	SYM
american_scientific_journal-4814	138	24	3	3	NUM
american_scientific_journal-4814	138	25	ω/2π	ω/2π	NUM
american_scientific_journal-4814	138	26	(	(	PUNCT
american_scientific_journal-4814	138	27	𝐻𝐻𝐻𝐻	𝐻𝐻𝐻𝐻	PROPN
american_scientific_journal-4814	138	28	)	)	PUNCT
american_scientific_journal-4814	138	29	5.436×10	5.436×10	NOUN
american_scientific_journal-4814	138	30	-	-	SYM
american_scientific_journal-4814	138	31	9	9	NUM
american_scientific_journal-4814	138	32	5.43×10	5.43×10	NUM
american_scientific_journal-4814	138	33	-	-	SYM
american_scientific_journal-4814	138	34	8	8	NUM
american_scientific_journal-4814	138	35	5.436×10	5.436×10	NUM
american_scientific_journal-4814	138	36	-	-	SYM
american_scientific_journal-4814	138	37	7	7	NUM
american_scientific_journal-4814	138	38	5.436×10	5.436×10	NUM
american_scientific_journal-4814	138	39	-	-	SYM
american_scientific_journal-4814	138	40	6	6	NUM
american_scientific_journal-4814	138	41	5.456×10	5.456×10	NUM
american_scientific_journal-4814	138	42	-	-	SYM
american_scientific_journal-4814	138	43	5	5	NUM
american_scientific_journal-4814	138	44	2.777×10	2.777×10	NOUN
american_scientific_journal-4814	138	45	-	-	SYM
american_scientific_journal-4814	138	46	4	4	NUM
american_scientific_journal-4814	138	47	1.412×10	1.412×10	NOUN
american_scientific_journal-4814	138	48	-	-	SYM
american_scientific_journal-4814	138	49	8	8	NUM
american_scientific_journal-4814	138	50	1.412×10	1.412×10	NOUN
american_scientific_journal-4814	138	51	-	-	SYM
american_scientific_journal-4814	138	52	7	7	NUM
american_scientific_journal-4814	138	53	1.412×10	1.412×10	NOUN
american_scientific_journal-4814	138	54	-	-	SYM
american_scientific_journal-4814	138	55	6	6	NUM
american_scientific_journal-4814	138	56	1.412×10	1.412×10	NOUN
american_scientific_journal-4814	138	57	-	-	SYM
american_scientific_journal-4814	138	58	5	5	NUM
american_scientific_journal-4814	138	59	1.419×10	1.419×10	NOUN
american_scientific_journal-4814	138	60	-	-	SYM
american_scientific_journal-4814	138	61	4	4	NUM
american_scientific_journal-4814	138	62	4.667×10	4.667×10	NOUN
american_scientific_journal-4814	138	63	-	-	SYM
american_scientific_journal-4814	138	64	4	4	NUM
american_scientific_journal-4814	138	65	2.311×10	2.311×10	NUM
american_scientific_journal-4814	138	66	-	-	SYM
american_scientific_journal-4814	138	67	8	8	NUM
american_scientific_journal-4814	138	68	1.875×10	1.875×10	NUM
american_scientific_journal-4814	138	69	-	-	SYM
american_scientific_journal-4814	138	70	7	7	NUM
american_scientific_journal-4814	138	71	1.875×10	1.875×10	NUM
american_scientific_journal-4814	138	72	-	-	SYM
american_scientific_journal-4814	138	73	6	6	NUM
american_scientific_journal-4814	138	74	1.875×10	1.875×10	NUM
american_scientific_journal-4814	138	75	-	-	SYM
american_scientific_journal-4814	138	76	5	5	NUM
american_scientific_journal-4814	138	77	1.879×10	1.879×10	NUM
american_scientific_journal-4814	138	78	-	-	SYM
american_scientific_journal-4814	138	79	4	4	NUM
american_scientific_journal-4814	138	80	8.938×10	8.938×10	NUM
american_scientific_journal-4814	138	81	-	-	SYM
american_scientific_journal-4814	138	82	4	4	NUM
american_scientific_journal-4814	138	83	2.602×10	2.602×10	NUM
american_scientific_journal-4814	138	84	-	-	SYM
american_scientific_journal-4814	138	85	8	8	NUM
american_scientific_journal-4814	138	86	2.311×10	2.311×10	NUM
american_scientific_journal-4814	138	87	-	-	SYM
american_scientific_journal-4814	138	88	7	7	NUM
american_scientific_journal-4814	138	89	2.311×10	2.311×10	NUM
american_scientific_journal-4814	138	90	-	-	SYM
american_scientific_journal-4814	138	91	6	6	NUM
american_scientific_journal-4814	138	92	2.311×10	2.311×10	NUM
american_scientific_journal-4814	138	93	-	-	SYM
american_scientific_journal-4814	138	94	5	5	NUM
american_scientific_journal-4814	138	95	2.331×10	2.331×10	NOUN
american_scientific_journal-4814	138	96	-	-	SYM
american_scientific_journal-4814	138	97	4	4	NUM
american_scientific_journal-4814	138	98	3.051×10	3.051×10	NOUN
american_scientific_journal-4814	138	99	-	-	SYM
american_scientific_journal-4814	138	100	8	8	NUM
american_scientific_journal-4814	138	101	2.602×10	2.602×10	NUM
american_scientific_journal-4814	138	102	-	-	SYM
american_scientific_journal-4814	138	103	7	7	NUM
american_scientific_journal-4814	138	104	2.602×10	2.602×10	NUM
american_scientific_journal-4814	138	105	-	-	SYM
american_scientific_journal-4814	138	106	6	6	NUM
american_scientific_journal-4814	138	107	2.605×10	2.605×10	NUM
american_scientific_journal-4814	138	108	-	-	SYM
american_scientific_journal-4814	138	109	5	5	NUM
american_scientific_journal-4814	138	110	2.808×10	2.808×10	NUM
american_scientific_journal-4814	138	111	-	-	SYM
american_scientific_journal-4814	138	112	4	4	NUM
american_scientific_journal-4814	138	113	3.473×10	3.473×10	NUM
american_scientific_journal-4814	138	114	-	-	SYM
american_scientific_journal-4814	138	115	8	8	NUM
american_scientific_journal-4814	138	116	3.051×10	3.051×10	NUM
american_scientific_journal-4814	138	117	-	-	SYM
american_scientific_journal-4814	138	118	7	7	NUM
american_scientific_journal-4814	138	119	3.051×10	3.051×10	NOUN
american_scientific_journal-4814	138	120	-	-	SYM
american_scientific_journal-4814	138	121	6	6	NUM
american_scientific_journal-4814	138	122	3.052×10	3.052×10	NUM
american_scientific_journal-4814	138	123	-	-	SYM
american_scientific_journal-4814	138	124	5	5	NUM
american_scientific_journal-4814	138	125	3.120×10	3.120×10	NUM
american_scientific_journal-4814	138	126	-	-	SYM
american_scientific_journal-4814	138	127	4	4	NUM
american_scientific_journal-4814	138	128	3.950×10	3.950×10	NUM
american_scientific_journal-4814	138	129	-	-	SYM
american_scientific_journal-4814	138	130	8	8	NUM
american_scientific_journal-4814	138	131	3.473×10	3.473×10	NUM
american_scientific_journal-4814	138	132	-	-	SYM
american_scientific_journal-4814	138	133	7	7	NUM
american_scientific_journal-4814	138	134	3.473×10	3.473×10	NUM
american_scientific_journal-4814	138	135	-	-	SYM
american_scientific_journal-4814	138	136	6	6	NUM
american_scientific_journal-4814	138	137	3.476×10	3.476×10	NUM
american_scientific_journal-4814	138	138	-	-	SYM
american_scientific_journal-4814	138	139	5	5	NUM
american_scientific_journal-4814	138	140	3.553×10	3.553×10	NUM
american_scientific_journal-4814	138	141	-	-	SYM
american_scientific_journal-4814	138	142	4	4	NUM
american_scientific_journal-4814	138	143	4.359×10	4.359×10	NUM
american_scientific_journal-4814	138	144	-	-	SYM
american_scientific_journal-4814	138	145	8	8	NUM
american_scientific_journal-4814	138	146	3.950×10	3.950×10	NUM
american_scientific_journal-4814	138	147	-	-	SYM
american_scientific_journal-4814	138	148	7	7	NUM
american_scientific_journal-4814	138	149	3.950×10	3.950×10	NUM
american_scientific_journal-4814	138	150	-	-	SYM
american_scientific_journal-4814	138	151	6	6	NUM
american_scientific_journal-4814	138	152	3.962×10	3.962×10	NOUN
american_scientific_journal-4814	138	153	-	-	SYM
american_scientific_journal-4814	138	154	5	5	NUM
american_scientific_journal-4814	138	155	4.098×10	4.098×10	NOUN
american_scientific_journal-4814	138	156	-	-	SYM
american_scientific_journal-4814	138	157	4	4	NUM
american_scientific_journal-4814	138	158	5.071×10	5.071×10	NUM
american_scientific_journal-4814	138	159	-	-	SYM
american_scientific_journal-4814	138	160	8	8	NUM
american_scientific_journal-4814	138	161	4.359×10	4.359×10	NUM
american_scientific_journal-4814	138	162	-	-	SYM
american_scientific_journal-4814	138	163	7	7	NUM
american_scientific_journal-4814	138	164	4.359×10	4.359×10	NUM
american_scientific_journal-4814	138	165	-	-	SYM
american_scientific_journal-4814	138	166	6	6	NUM
american_scientific_journal-4814	138	167	4.369×10	4.369×10	NUM
american_scientific_journal-4814	138	168	-	-	SYM
american_scientific_journal-4814	138	169	5	5	NUM
american_scientific_journal-4814	138	170	4.465×10	4.465×10	NOUN
american_scientific_journal-4814	138	171	-	-	SYM
american_scientific_journal-4814	138	172	4	4	NUM
american_scientific_journal-4814	138	173	5.276×10	5.276×10	NUM
american_scientific_journal-4814	138	174	-	-	SYM
american_scientific_journal-4814	138	175	8	8	NUM
american_scientific_journal-4814	138	176	5.071×10	5.071×10	NUM
american_scientific_journal-4814	138	177	-	-	SYM
american_scientific_journal-4814	138	178	7	7	NUM
american_scientific_journal-4814	138	179	5.071×10	5.071×10	NUM
american_scientific_journal-4814	138	180	-	-	SYM
american_scientific_journal-4814	138	181	6	6	NUM
american_scientific_journal-4814	138	182	5.101×10	5.101×10	NUM
american_scientific_journal-4814	138	183	-	-	SYM
american_scientific_journal-4814	138	184	5	5	NUM
american_scientific_journal-4814	138	185	5.155×10	5.155×10	NUM
american_scientific_journal-4814	138	186	-	-	SYM
american_scientific_journal-4814	138	187	4	4	NUM
american_scientific_journal-4814	138	188	5.996×10	5.996×10	NUM
american_scientific_journal-4814	138	189	-	-	SYM
american_scientific_journal-4814	138	190	8	8	NUM
american_scientific_journal-4814	138	191	5.276×10	5.276×10	NUM
american_scientific_journal-4814	138	192	-	-	SYM
american_scientific_journal-4814	138	193	7	7	NUM
american_scientific_journal-4814	138	194	5.276×10	5.276×10	NUM
american_scientific_journal-4814	138	195	-	-	SYM
american_scientific_journal-4814	138	196	6	6	NUM
american_scientific_journal-4814	138	197	5.313×10	5.313×10	NUM
american_scientific_journal-4814	138	198	-	-	SYM
american_scientific_journal-4814	138	199	5	5	NUM
american_scientific_journal-4814	138	200	5.454×10	5.454×10	NUM
american_scientific_journal-4814	138	201	-	-	SYM
american_scientific_journal-4814	138	202	4	4	NUM
american_scientific_journal-4814	138	203	6.722×10	6.722×10	NOUN
american_scientific_journal-4814	138	204	-	-	SYM
american_scientific_journal-4814	138	205	8	8	NUM
american_scientific_journal-4814	138	206	5.996×10	5.996×10	NUM
american_scientific_journal-4814	138	207	-	-	SYM
american_scientific_journal-4814	138	208	7	7	NUM
american_scientific_journal-4814	138	209	5.996×10	5.996×10	NOUN
american_scientific_journal-4814	138	210	-	-	SYM
american_scientific_journal-4814	138	211	6	6	NUM
american_scientific_journal-4814	138	212	6.040×10	6.040×10	NOUN
american_scientific_journal-4814	138	213	-	-	SYM
american_scientific_journal-4814	138	214	5	5	NUM
american_scientific_journal-4814	138	215	6.110×10	6.110×10	NOUN
american_scientific_journal-4814	138	216	-	-	SYM
american_scientific_journal-4814	138	217	4	4	NUM
american_scientific_journal-4814	138	218	7.428×10	7.428×10	NUM
american_scientific_journal-4814	138	219	-	-	SYM
american_scientific_journal-4814	138	220	8	8	NUM
american_scientific_journal-4814	138	221	6.722×10	6.722×10	NOUN
american_scientific_journal-4814	138	222	-	-	SYM
american_scientific_journal-4814	138	223	7	7	NUM
american_scientific_journal-4814	138	224	6.722×10	6.722×10	NOUN
american_scientific_journal-4814	138	225	-	-	SYM
american_scientific_journal-4814	138	226	6	6	NUM
american_scientific_journal-4814	138	227	6.779×10	6.779×10	NOUN
american_scientific_journal-4814	138	228	-	-	SYM
american_scientific_journal-4814	138	229	5	5	NUM
american_scientific_journal-4814	138	230	8.136×10	8.136×10	NUM
american_scientific_journal-4814	138	231	-	-	SYM
american_scientific_journal-4814	138	232	8	8	NUM
american_scientific_journal-4814	138	233	7.134×10	7.134×10	NUM
american_scientific_journal-4814	138	234	-	-	SYM
american_scientific_journal-4814	138	235	7	7	NUM
american_scientific_journal-4814	138	236	7.134×10	7.134×10	NUM
american_scientific_journal-4814	138	237	-	-	SYM
american_scientific_journal-4814	138	238	6	6	NUM
american_scientific_journal-4814	138	239	7.143×10	7.143×10	NUM
american_scientific_journal-4814	138	240	-	-	SYM
american_scientific_journal-4814	138	241	5	5	NUM
american_scientific_journal-4814	138	242	8.592×10	8.592×10	NOUN
american_scientific_journal-4814	138	243	-	-	SYM
american_scientific_journal-4814	138	244	8	8	NUM
american_scientific_journal-4814	138	245	7.428×10	7.428×10	NUM
american_scientific_journal-4814	138	246	-	-	SYM
american_scientific_journal-4814	138	247	7	7	NUM
american_scientific_journal-4814	138	248	7.428×10	7.428×10	NUM
american_scientific_journal-4814	138	249	-	-	SYM
american_scientific_journal-4814	138	250	6	6	NUM
american_scientific_journal-4814	138	251	7.458×10	7.458×10	NOUN
american_scientific_journal-4814	138	252	-	-	SYM
american_scientific_journal-4814	138	253	5	5	NUM
american_scientific_journal-4814	138	254	9.445×10	9.445×10	NUM
american_scientific_journal-4814	138	255	-	-	SYM
american_scientific_journal-4814	138	256	8	8	NUM
american_scientific_journal-4814	138	257	8.136×10	8.136×10	NUM
american_scientific_journal-4814	138	258	-	-	SYM
american_scientific_journal-4814	138	259	7	7	NUM
american_scientific_journal-4814	138	260	8.136×10	8.136×10	NUM
american_scientific_journal-4814	138	261	-	-	SYM
american_scientific_journal-4814	138	262	6	6	NUM
american_scientific_journal-4814	138	263	8.174×10	8.174×10	NUM
american_scientific_journal-4814	138	264	-	-	SYM
american_scientific_journal-4814	138	265	5	5	NUM
american_scientific_journal-4814	138	266	9.910×10	9.910×10	NOUN
american_scientific_journal-4814	138	267	-	-	SYM
american_scientific_journal-4814	138	268	8	8	NUM
american_scientific_journal-4814	138	269	8.592×10	8.592×10	NUM
american_scientific_journal-4814	138	270	-	-	SYM
american_scientific_journal-4814	138	271	7	7	NUM
american_scientific_journal-4814	138	272	8.592×10	8.592×10	NUM
american_scientific_journal-4814	138	273	-	-	SYM
american_scientific_journal-4814	138	274	6	6	NUM
american_scientific_journal-4814	138	275	8.621×10	8.621×10	NOUN
american_scientific_journal-4814	138	276	-	-	SYM
american_scientific_journal-4814	138	277	5	5	NUM
american_scientific_journal-4814	138	278	1.080×10	1.080×10	NUM
american_scientific_journal-4814	138	279	-	-	SYM
american_scientific_journal-4814	138	280	8	8	NUM
american_scientific_journal-4814	138	281	9.445×10	9.445×10	NUM
american_scientific_journal-4814	138	282	-	-	SYM
american_scientific_journal-4814	138	283	7	7	NUM
american_scientific_journal-4814	138	284	9.445×10	9.445×10	NUM
american_scientific_journal-4814	138	285	-	-	SYM
american_scientific_journal-4814	138	286	6	6	NUM
american_scientific_journal-4814	138	287	9.475×10	9.475×10	NOUN
american_scientific_journal-4814	138	288	-	-	SYM
american_scientific_journal-4814	138	289	5	5	NUM
american_scientific_journal-4814	138	290	1.142×10	1.142×10	NUM
american_scientific_journal-4814	138	291	-	-	SYM
american_scientific_journal-4814	138	292	7	7	NUM
american_scientific_journal-4814	138	293	9.910×10	9.910×10	NOUN
american_scientific_journal-4814	138	294	-	-	SYM
american_scientific_journal-4814	138	295	7	7	NUM
american_scientific_journal-4814	138	296	9.910×10	9.910×10	NOUN
american_scientific_journal-4814	138	297	-	-	SYM
american_scientific_journal-4814	138	298	6	6	NUM
american_scientific_journal-4814	138	299	9.938×10	9.938×10	NOUN
american_scientific_journal-4814	138	300	-	-	SYM
american_scientific_journal-4814	138	301	5	5	NUM
american_scientific_journal-4814	138	302	1.331×10	1.331×10	NUM
american_scientific_journal-4814	138	303	-	-	SYM
american_scientific_journal-4814	138	304	7	7	NUM
american_scientific_journal-4814	138	305	1.080×10	1.080×10	NUM
american_scientific_journal-4814	138	306	-	-	SYM
american_scientific_journal-4814	138	307	6	6	NUM
american_scientific_journal-4814	138	308	1.080×10	1.080×10	NUM
american_scientific_journal-4814	138	309	-	-	SYM
american_scientific_journal-4814	138	310	6	6	NUM
american_scientific_journal-4814	138	311	1.081×10	1.081×10	NUM
american_scientific_journal-4814	138	312	-	-	SYM
american_scientific_journal-4814	138	313	4	4	NUM
american_scientific_journal-4814	138	314	5.503×10	5.503×10	NUM
american_scientific_journal-4814	138	315	-	-	SYM
american_scientific_journal-4814	138	316	7	7	NUM
american_scientific_journal-4814	138	317	1.142×10	1.142×10	NUM
american_scientific_journal-4814	138	318	-	-	SYM
american_scientific_journal-4814	138	319	6	6	NUM
american_scientific_journal-4814	138	320	1.142×10	1.142×10	NUM
american_scientific_journal-4814	138	321	-	-	SYM
american_scientific_journal-4814	138	322	6	6	NUM
american_scientific_journal-4814	138	323	1.145×10	1.145×10	NUM
american_scientific_journal-4814	138	324	-	-	SYM
american_scientific_journal-4814	138	325	4	4	NUM
american_scientific_journal-4814	138	326	1.114×10	1.114×10	NUM
american_scientific_journal-4814	138	327	-	-	SYM
american_scientific_journal-4814	138	328	5	5	NUM
american_scientific_journal-4814	138	329	1.331×10	1.331×10	NOUN
american_scientific_journal-4814	138	330	-	-	SYM
american_scientific_journal-4814	138	331	6	6	NUM
american_scientific_journal-4814	138	332	1.331×10	1.331×10	NUM
american_scientific_journal-4814	138	333	-	-	SYM
american_scientific_journal-4814	138	334	5	5	NUM
american_scientific_journal-4814	138	335	1.334×10	1.334×10	NUM
american_scientific_journal-4814	138	336	-	-	SYM
american_scientific_journal-4814	138	337	4	4	NUM
american_scientific_journal-4814	138	338	american	american	ADJ
american_scientific_journal-4814	138	339	scientific	scientific	ADJ
american_scientific_journal-4814	138	340	research	research	NOUN
american_scientific_journal-4814	138	341	journal	journal	NOUN
american_scientific_journal-4814	138	342	for	for	ADP
american_scientific_journal-4814	138	343	engineering	engineering	NOUN
american_scientific_journal-4814	138	344	,	,	PUNCT
american_scientific_journal-4814	138	345	technology	technology	NOUN
american_scientific_journal-4814	138	346	,	,	PUNCT
american_scientific_journal-4814	138	347	and	and	CCONJ
american_scientific_journal-4814	138	348	sciences	science	NOUN
american_scientific_journal-4814	138	349	(	(	PUNCT
american_scientific_journal-4814	138	350	asrjets	asrjet	NOUN
american_scientific_journal-4814	138	351	)	)	PUNCT
american_scientific_journal-4814	138	352	(	(	PUNCT
american_scientific_journal-4814	138	353	2019	2019	NUM
american_scientific_journal-4814	138	354	)	)	PUNCT
american_scientific_journal-4814	138	355	volume	volume	NOUN
american_scientific_journal-4814	138	356	55	55	NUM
american_scientific_journal-4814	138	357	,	,	PUNCT
american_scientific_journal-4814	138	358	no	no	DET
american_scientific_journal-4814	138	359	1	1	NUM
american_scientific_journal-4814	138	360	,	,	PUNCT
american_scientific_journal-4814	138	361	pp	pp	ADP
american_scientific_journal-4814	138	362	50	50	NUM
american_scientific_journal-4814	138	363	-	-	SYM
american_scientific_journal-4814	138	364	68	68	NUM
american_scientific_journal-4814	138	365	61	61	NUM
american_scientific_journal-4814	138	366	one	one	NUM
american_scientific_journal-4814	138	367	considers	consider	VERB
american_scientific_journal-4814	138	368	that	that	SCONJ
american_scientific_journal-4814	138	369	the	the	DET
american_scientific_journal-4814	138	370	space	space	NOUN
american_scientific_journal-4814	138	371	vehicle	vehicle	NOUN
american_scientific_journal-4814	138	372	undergoes	undergo	VERB
american_scientific_journal-4814	138	373	orbital	orbital	ADJ
american_scientific_journal-4814	138	374	motion	motion	NOUN
american_scientific_journal-4814	138	375	interacting	interact	VERB
american_scientific_journal-4814	138	376	with	with	ADP
american_scientific_journal-4814	138	377	the	the	DET
american_scientific_journal-4814	138	378	lace	lace	NOUN
american_scientific_journal-4814	138	379	attitude	attitude	NOUN
american_scientific_journal-4814	138	380	motion	motion	NOUN
american_scientific_journal-4814	138	381	and	and	CCONJ
american_scientific_journal-4814	138	382	the	the	DET
american_scientific_journal-4814	138	383	arrays	arrays	ADJ
american_scientific_journal-4814	138	384	deformations	deformation	NOUN
american_scientific_journal-4814	138	385	.	.	PUNCT
american_scientific_journal-4814	139	1	in	in	ADP
american_scientific_journal-4814	139	2	this	this	DET
american_scientific_journal-4814	139	3	case	case	NOUN
american_scientific_journal-4814	139	4	,	,	PUNCT
american_scientific_journal-4814	139	5	one	one	PRON
american_scientific_journal-4814	139	6	uses	use	VERB
american_scientific_journal-4814	139	7	the	the	DET
american_scientific_journal-4814	139	8	spectral	spectral	ADJ
american_scientific_journal-4814	139	9	expansion	expansion	NOUN
american_scientific_journal-4814	139	10	(	(	PUNCT
american_scientific_journal-4814	139	11	26	26	NUM
american_scientific_journal-4814	139	12	)	)	PUNCT
american_scientific_journal-4814	139	13	of	of	ADP
american_scientific_journal-4814	139	14	the	the	DET
american_scientific_journal-4814	139	15	truncated	truncated	ADJ
american_scientific_journal-4814	139	16	impedance	impedance	NOUN
american_scientific_journal-4814	139	17	function	function	NOUN
american_scientific_journal-4814	139	18	𝑍𝑍(𝛺𝛺	𝑍𝑍(𝛺𝛺	PROPN
american_scientific_journal-4814	139	19	)	)	PUNCT
american_scientific_journal-4814	139	20	(	(	PUNCT
american_scientific_journal-4814	139	21	𝑁𝑁	𝑁𝑁	PROPN
american_scientific_journal-4814	139	22	=	=	SYM
american_scientific_journal-4814	139	23	35	35	NUM
american_scientific_journal-4814	139	24	)	)	PUNCT
american_scientific_journal-4814	139	25	in	in	ADP
american_scientific_journal-4814	139	26	accordance	accordance	NOUN
american_scientific_journal-4814	139	27	with	with	ADP
american_scientific_journal-4814	139	28	the	the	DET
american_scientific_journal-4814	139	29	modal	modal	ADJ
american_scientific_journal-4814	139	30	gain	gain	NOUN
american_scientific_journal-4814	139	31	approximation	approximation	NOUN
american_scientific_journal-4814	139	32	(	(	PUNCT
american_scientific_journal-4814	139	33	30	30	NUM
american_scientific_journal-4814	139	34	)	)	PUNCT
american_scientific_journal-4814	139	35	.	.	PUNCT
american_scientific_journal-4814	140	1	the	the	DET
american_scientific_journal-4814	140	2	natural	natural	ADJ
american_scientific_journal-4814	140	3	global	global	ADJ
american_scientific_journal-4814	140	4	frequencies	frequency	NOUN
american_scientific_journal-4814	140	5	𝛺𝛺	𝛺𝛺	PROPN
american_scientific_journal-4814	140	6	of	of	ADP
american_scientific_journal-4814	140	7	the	the	DET
american_scientific_journal-4814	140	8	whole	whole	ADJ
american_scientific_journal-4814	140	9	space	space	NOUN
american_scientific_journal-4814	140	10	vehicle	vehicle	NOUN
american_scientific_journal-4814	140	11	in	in	ADP
american_scientific_journal-4814	140	12	absence	absence	NOUN
american_scientific_journal-4814	140	13	of	of	ADP
american_scientific_journal-4814	140	14	external	external	ADJ
american_scientific_journal-4814	140	15	torques	torque	NOUN
american_scientific_journal-4814	140	16	,	,	PUNCT
american_scientific_journal-4814	140	17	are	be	AUX
american_scientific_journal-4814	140	18	computed	compute	VERB
american_scientific_journal-4814	140	19	from	from	ADP
american_scientific_journal-4814	140	20	equation	equation	NOUN
american_scientific_journal-4814	140	21	(	(	PUNCT
american_scientific_journal-4814	140	22	29	29	NUM
american_scientific_journal-4814	140	23	)	)	PUNCT
american_scientific_journal-4814	140	24	.	.	PUNCT
american_scientific_journal-4814	141	1	different	different	ADJ
american_scientific_journal-4814	141	2	values	value	NOUN
american_scientific_journal-4814	141	3	of	of	ADP
american_scientific_journal-4814	141	4	the	the	DET
american_scientific_journal-4814	141	5	orbital	orbital	ADJ
american_scientific_journal-4814	141	6	parameter	parameter	NOUN
american_scientific_journal-4814	141	7	𝑛𝑛0	𝑛𝑛0	X
american_scientific_journal-4814	141	8	are	be	AUX
american_scientific_journal-4814	141	9	considered	consider	VERB
american_scientific_journal-4814	141	10	to	to	PART
american_scientific_journal-4814	141	11	simulate	simulate	VERB
american_scientific_journal-4814	141	12	the	the	DET
american_scientific_journal-4814	141	13	global	global	ADJ
american_scientific_journal-4814	141	14	frequencies	frequency	NOUN
american_scientific_journal-4814	141	15	of	of	ADP
american_scientific_journal-4814	141	16	the	the	DET
american_scientific_journal-4814	141	17	whole	whole	ADJ
american_scientific_journal-4814	141	18	space	space	NOUN
american_scientific_journal-4814	141	19	vehicle	vehicle	NOUN
american_scientific_journal-4814	141	20	(	(	PUNCT
american_scientific_journal-4814	141	21	see	see	VERB
american_scientific_journal-4814	141	22	table	table	NOUN
american_scientific_journal-4814	141	23	2	2	NUM
american_scientific_journal-4814	141	24	)	)	PUNCT
american_scientific_journal-4814	141	25	.	.	PUNCT
american_scientific_journal-4814	142	1	in	in	ADP
american_scientific_journal-4814	142	2	the	the	DET
american_scientific_journal-4814	142	3	case	case	NOUN
american_scientific_journal-4814	142	4	of	of	ADP
american_scientific_journal-4814	142	5	small	small	ADJ
american_scientific_journal-4814	142	6	angular	angular	ADJ
american_scientific_journal-4814	142	7	speed	speed	NOUN
american_scientific_journal-4814	142	8	𝑛𝑛0	𝑛𝑛0	NOUN
american_scientific_journal-4814	142	9	of	of	ADP
american_scientific_journal-4814	142	10	orders	order	NOUN
american_scientific_journal-4814	142	11	10−8	10−8	NUM
american_scientific_journal-4814	142	12	,	,	PUNCT
american_scientific_journal-4814	142	13	10−7	10−7	NUM
american_scientific_journal-4814	142	14	,	,	PUNCT
american_scientific_journal-4814	142	15	10−6	10−6	NUM
american_scientific_journal-4814	142	16	and	and	CCONJ
american_scientific_journal-4814	142	17	10−5	10−5	NUM
american_scientific_journal-4814	142	18	in	in	ADP
american_scientific_journal-4814	142	19	the	the	DET
american_scientific_journal-4814	142	20	bandwidth	bandwidth	NOUN
american_scientific_journal-4814	142	21	considered	consider	VERB
american_scientific_journal-4814	142	22	,	,	PUNCT
american_scientific_journal-4814	142	23	one	one	PRON
american_scientific_journal-4814	142	24	obtains	obtain	VERB
american_scientific_journal-4814	142	25	for	for	ADP
american_scientific_journal-4814	142	26	each	each	DET
american_scientific_journal-4814	142	27	order	order	NOUN
american_scientific_journal-4814	142	28	a	a	DET
american_scientific_journal-4814	142	29	spectrum	spectrum	NOUN
american_scientific_journal-4814	142	30	of	of	ADP
american_scientific_journal-4814	142	31	22	22	NUM
american_scientific_journal-4814	142	32	eigenfrequencies	eigenfrequencie	NOUN
american_scientific_journal-4814	142	33	𝛺𝛺	𝛺𝛺	PROPN
american_scientific_journal-4814	142	34	computed	compute	VERB
american_scientific_journal-4814	142	35	.	.	PUNCT
american_scientific_journal-4814	143	1	on	on	ADP
american_scientific_journal-4814	143	2	the	the	DET
american_scientific_journal-4814	143	3	other	other	ADJ
american_scientific_journal-4814	143	4	hand	hand	NOUN
american_scientific_journal-4814	143	5	,	,	PUNCT
american_scientific_journal-4814	143	6	the	the	DET
american_scientific_journal-4814	143	7	spectrum	spectrum	NOUN
american_scientific_journal-4814	143	8	of	of	ADP
american_scientific_journal-4814	143	9	eigenfrequencies	eigenfrequencie	NOUN
american_scientific_journal-4814	143	10	obtained	obtain	VERB
american_scientific_journal-4814	143	11	in	in	ADP
american_scientific_journal-4814	143	12	work	work	NOUN
american_scientific_journal-4814	143	13	[	[	X
american_scientific_journal-4814	143	14	12	12	NUM
american_scientific_journal-4814	143	15	]	]	PUNCT
american_scientific_journal-4814	143	16	where	where	SCONJ
american_scientific_journal-4814	143	17	the	the	DET
american_scientific_journal-4814	143	18	attitudes	attitude	NOUN
american_scientific_journal-4814	143	19	motion	motion	NOUN
american_scientific_journal-4814	143	20	are	be	AUX
american_scientific_journal-4814	143	21	coupled	couple	VERB
american_scientific_journal-4814	143	22	,	,	PUNCT
american_scientific_journal-4814	143	23	is	be	AUX
american_scientific_journal-4814	143	24	very	very	ADV
american_scientific_journal-4814	143	25	reduced	reduce	VERB
american_scientific_journal-4814	143	26	.	.	PUNCT
american_scientific_journal-4814	144	1	since	since	SCONJ
american_scientific_journal-4814	144	2	then	then	ADV
american_scientific_journal-4814	144	3	,	,	PUNCT
american_scientific_journal-4814	144	4	one	one	NUM
american_scientific_journal-4814	144	5	notes	note	VERB
american_scientific_journal-4814	144	6	a	a	DET
american_scientific_journal-4814	144	7	great	great	ADJ
american_scientific_journal-4814	144	8	interaction	interaction	NOUN
american_scientific_journal-4814	144	9	between	between	ADP
american_scientific_journal-4814	144	10	the	the	DET
american_scientific_journal-4814	144	11	lace	lace	NOUN
american_scientific_journal-4814	144	12	attitude	attitude	NOUN
american_scientific_journal-4814	144	13	motion	motion	NOUN
american_scientific_journal-4814	144	14	and	and	CCONJ
american_scientific_journal-4814	144	15	the	the	DET
american_scientific_journal-4814	144	16	vibrations	vibration	NOUN
american_scientific_journal-4814	144	17	of	of	ADP
american_scientific_journal-4814	144	18	the	the	DET
american_scientific_journal-4814	144	19	space	space	NOUN
american_scientific_journal-4814	144	20	vehicle	vehicle	NOUN
american_scientific_journal-4814	144	21	.	.	PUNCT
american_scientific_journal-4814	145	1	consequently	consequently	ADV
american_scientific_journal-4814	145	2	,	,	PUNCT
american_scientific_journal-4814	145	3	the	the	DET
american_scientific_journal-4814	145	4	model	model	NOUN
american_scientific_journal-4814	145	5	of	of	ADP
american_scientific_journal-4814	145	6	attitude	attitude	NOUN
american_scientific_journal-4814	145	7	control	control	NOUN
american_scientific_journal-4814	145	8	suitable	suitable	ADJ
american_scientific_journal-4814	145	9	of	of	ADP
american_scientific_journal-4814	145	10	the	the	DET
american_scientific_journal-4814	145	11	space	space	NOUN
american_scientific_journal-4814	145	12	vehicle	vehicle	NOUN
american_scientific_journal-4814	145	13	should	should	AUX
american_scientific_journal-4814	145	14	take	take	VERB
american_scientific_journal-4814	145	15	into	into	ADP
american_scientific_journal-4814	145	16	account	account	NOUN
american_scientific_journal-4814	145	17	the	the	DET
american_scientific_journal-4814	145	18	spectrum	spectrum	NOUN
american_scientific_journal-4814	145	19	of	of	ADP
american_scientific_journal-4814	145	20	lace	lace	NOUN
american_scientific_journal-4814	145	21	attitude	attitude	NOUN
american_scientific_journal-4814	145	22	eigenfrequencies	eigenfrequencie	NOUN
american_scientific_journal-4814	145	23	to	to	PART
american_scientific_journal-4814	145	24	avoid	avoid	VERB
american_scientific_journal-4814	145	25	the	the	DET
american_scientific_journal-4814	145	26	resonance	resonance	NOUN
american_scientific_journal-4814	145	27	phenomena	phenomenon	NOUN
american_scientific_journal-4814	145	28	.	.	PUNCT
american_scientific_journal-4814	146	1	5.4	5.4	NUM
american_scientific_journal-4814	146	2	.	.	PUNCT
american_scientific_journal-4814	146	3	graphical	graphical	ADJ
american_scientific_journal-4814	146	4	simulation	simulation	NOUN
american_scientific_journal-4814	146	5	of	of	ADP
american_scientific_journal-4814	146	6	the	the	DET
american_scientific_journal-4814	146	7	array	array	NOUN
american_scientific_journal-4814	146	8	membrane	membrane	NOUN
american_scientific_journal-4814	146	9	deformations	deformation	NOUN
american_scientific_journal-4814	146	10	using	use	VERB
american_scientific_journal-4814	146	11	the	the	DET
american_scientific_journal-4814	146	12	eigenfrequencies	eigenfrequencie	NOUN
american_scientific_journal-4814	146	13	bending	bend	VERB
american_scientific_journal-4814	146	14	in	in	ADP
american_scientific_journal-4814	146	15	plane	plane	NOUN
american_scientific_journal-4814	146	16	𝜑𝜑𝑛𝑛	𝜑𝜑𝑛𝑛	PROPN
american_scientific_journal-4814	146	17	,	,	PUNCT
american_scientific_journal-4814	146	18	one	one	NUM
american_scientific_journal-4814	146	19	simulates	simulate	VERB
american_scientific_journal-4814	146	20	the	the	DET
american_scientific_journal-4814	146	21	different	different	ADJ
american_scientific_journal-4814	146	22	deformations	deformation	NOUN
american_scientific_journal-4814	146	23	of	of	ADP
american_scientific_journal-4814	146	24	the	the	DET
american_scientific_journal-4814	146	25	array	array	NOUN
american_scientific_journal-4814	146	26	membrane	membrane	NOUN
american_scientific_journal-4814	146	27	.	.	PUNCT
american_scientific_journal-4814	147	1	this	this	DET
american_scientific_journal-4814	147	2	simulations	simulation	NOUN
american_scientific_journal-4814	147	3	are	be	AUX
american_scientific_journal-4814	147	4	represented	represent	VERB
american_scientific_journal-4814	147	5	in	in	ADP
american_scientific_journal-4814	147	6	the	the	DET
american_scientific_journal-4814	147	7	figure	figure	NOUN
american_scientific_journal-4814	147	8	6	6	NUM
american_scientific_journal-4814	147	9	,	,	PUNCT
american_scientific_journal-4814	147	10	7	7	NUM
american_scientific_journal-4814	147	11	and	and	CCONJ
american_scientific_journal-4814	147	12	8	8	NUM
american_scientific_journal-4814	147	13	.	.	NOUN
american_scientific_journal-4814	147	14	6	6	NUM
american_scientific_journal-4814	147	15	.	.	X
american_scientific_journal-4814	147	16	conclusion	conclusion	NOUN
american_scientific_journal-4814	147	17	a	a	DET
american_scientific_journal-4814	147	18	previous	previous	ADJ
american_scientific_journal-4814	147	19	work	work	NOUN
american_scientific_journal-4814	147	20	[	[	X
american_scientific_journal-4814	147	21	12	12	NUM
american_scientific_journal-4814	147	22	]	]	PUNCT
american_scientific_journal-4814	147	23	has	have	AUX
american_scientific_journal-4814	147	24	investigated	investigate	VERB
american_scientific_journal-4814	147	25	the	the	DET
american_scientific_journal-4814	147	26	space	space	NOUN
american_scientific_journal-4814	147	27	vehicle	vehicle	NOUN
american_scientific_journal-4814	147	28	using	use	VERB
american_scientific_journal-4814	147	29	the	the	DET
american_scientific_journal-4814	147	30	spectral	spectral	ADJ
american_scientific_journal-4814	147	31	decompositions	decomposition	NOUN
american_scientific_journal-4814	147	32	method	method	NOUN
american_scientific_journal-4814	147	33	.	.	PUNCT
american_scientific_journal-4814	148	1	the	the	DET
american_scientific_journal-4814	148	2	global	global	ADJ
american_scientific_journal-4814	148	3	modes	mode	NOUN
american_scientific_journal-4814	148	4	of	of	ADP
american_scientific_journal-4814	148	5	the	the	DET
american_scientific_journal-4814	148	6	investigated	investigate	VERB
american_scientific_journal-4814	148	7	space	space	NOUN
american_scientific_journal-4814	148	8	vehicle	vehicle	NOUN
american_scientific_journal-4814	148	9	considering	consider	VERB
american_scientific_journal-4814	148	10	its	its	PRON
american_scientific_journal-4814	148	11	attitudes	attitude	NOUN
american_scientific_journal-4814	148	12	motions	motion	NOUN
american_scientific_journal-4814	148	13	coupled	couple	VERB
american_scientific_journal-4814	148	14	,	,	PUNCT
american_scientific_journal-4814	148	15	are	be	AUX
american_scientific_journal-4814	148	16	performed	perform	VERB
american_scientific_journal-4814	148	17	[	[	X
american_scientific_journal-4814	148	18	12	12	NUM
american_scientific_journal-4814	148	19	]	]	PUNCT
american_scientific_journal-4814	148	20	.	.	PUNCT
american_scientific_journal-4814	149	1	a	a	DET
american_scientific_journal-4814	149	2	reduced	reduced	ADJ
american_scientific_journal-4814	149	3	spectrum	spectrum	NOUN
american_scientific_journal-4814	149	4	of	of	ADP
american_scientific_journal-4814	149	5	the	the	DET
american_scientific_journal-4814	149	6	eigenfrequencies	eigenfrequencie	NOUN
american_scientific_journal-4814	149	7	is	be	AUX
american_scientific_journal-4814	149	8	obtained	obtain	VERB
american_scientific_journal-4814	149	9	in	in	ADP
american_scientific_journal-4814	149	10	this	this	DET
american_scientific_journal-4814	149	11	case	case	NOUN
american_scientific_journal-4814	149	12	.	.	PUNCT
american_scientific_journal-4814	150	1	this	this	DET
american_scientific_journal-4814	150	2	fact	fact	NOUN
american_scientific_journal-4814	150	3	is	be	AUX
american_scientific_journal-4814	150	4	characterized	characterize	VERB
american_scientific_journal-4814	150	5	by	by	ADP
american_scientific_journal-4814	150	6	a	a	DET
american_scientific_journal-4814	150	7	small	small	ADJ
american_scientific_journal-4814	150	8	interaction	interaction	NOUN
american_scientific_journal-4814	150	9	between	between	ADP
american_scientific_journal-4814	150	10	the	the	DET
american_scientific_journal-4814	150	11	coupled	couple	VERB
american_scientific_journal-4814	150	12	attitudes	attitude	NOUN
american_scientific_journal-4814	150	13	motions	motion	NOUN
american_scientific_journal-4814	150	14	and	and	CCONJ
american_scientific_journal-4814	150	15	the	the	DET
american_scientific_journal-4814	150	16	elastic	elastic	ADJ
american_scientific_journal-4814	150	17	deformations	deformation	NOUN
american_scientific_journal-4814	150	18	.	.	PUNCT
american_scientific_journal-4814	151	1	therefore	therefore	ADV
american_scientific_journal-4814	151	2	,	,	PUNCT
american_scientific_journal-4814	151	3	it	it	PRON
american_scientific_journal-4814	151	4	is	be	AUX
american_scientific_journal-4814	151	5	necessary	necessary	ADJ
american_scientific_journal-4814	151	6	to	to	PART
american_scientific_journal-4814	151	7	simulate	simulate	VERB
american_scientific_journal-4814	151	8	a	a	DET
american_scientific_journal-4814	151	9	decoupling	decoupling	NOUN
american_scientific_journal-4814	151	10	of	of	ADP
american_scientific_journal-4814	151	11	the	the	DET
american_scientific_journal-4814	151	12	space	space	NOUN
american_scientific_journal-4814	151	13	vehicle	vehicle	NOUN
american_scientific_journal-4814	151	14	attitudes	attitude	NOUN
american_scientific_journal-4814	151	15	motions	motion	NOUN
american_scientific_journal-4814	151	16	in	in	ADP
american_scientific_journal-4814	151	17	order	order	NOUN
american_scientific_journal-4814	151	18	to	to	PART
american_scientific_journal-4814	151	19	get	get	VERB
american_scientific_journal-4814	151	20	a	a	DET
american_scientific_journal-4814	151	21	great	great	ADJ
american_scientific_journal-4814	151	22	interaction	interaction	NOUN
american_scientific_journal-4814	151	23	with	with	ADP
american_scientific_journal-4814	151	24	the	the	DET
american_scientific_journal-4814	151	25	elastic	elastic	ADJ
american_scientific_journal-4814	151	26	deformations	deformation	NOUN
american_scientific_journal-4814	151	27	.	.	PUNCT
american_scientific_journal-4814	152	1	here	here	ADV
american_scientific_journal-4814	152	2	,	,	PUNCT
american_scientific_journal-4814	152	3	the	the	DET
american_scientific_journal-4814	152	4	decoupling	decoupling	NOUN
american_scientific_journal-4814	152	5	of	of	ADP
american_scientific_journal-4814	152	6	the	the	DET
american_scientific_journal-4814	152	7	space	space	NOUN
american_scientific_journal-4814	152	8	vehicle	vehicle	NOUN
american_scientific_journal-4814	152	9	attitudes	attitude	NOUN
american_scientific_journal-4814	152	10	motion	motion	NOUN
american_scientific_journal-4814	152	11	brings	bring	VERB
american_scientific_journal-4814	152	12	out	out	ADP
american_scientific_journal-4814	152	13	the	the	DET
american_scientific_journal-4814	152	14	interaction	interaction	NOUN
american_scientific_journal-4814	152	15	between	between	ADP
american_scientific_journal-4814	152	16	the	the	DET
american_scientific_journal-4814	152	17	lace	lace	NOUN
american_scientific_journal-4814	152	18	attitude	attitude	NOUN
american_scientific_journal-4814	152	19	motions	motion	NOUN
american_scientific_journal-4814	152	20	and	and	CCONJ
american_scientific_journal-4814	152	21	the	the	DET
american_scientific_journal-4814	152	22	elastic	elastic	ADJ
american_scientific_journal-4814	152	23	deformations	deformation	NOUN
american_scientific_journal-4814	152	24	of	of	ADP
american_scientific_journal-4814	152	25	the	the	DET
american_scientific_journal-4814	152	26	space	space	NOUN
american_scientific_journal-4814	152	27	vehicle	vehicle	NOUN
american_scientific_journal-4814	152	28	.	.	PUNCT
american_scientific_journal-4814	153	1	consequently	consequently	ADV
american_scientific_journal-4814	153	2	,	,	PUNCT
american_scientific_journal-4814	153	3	one	one	PRON
american_scientific_journal-4814	153	4	gets	get	VERB
american_scientific_journal-4814	153	5	in	in	ADP
american_scientific_journal-4814	153	6	this	this	DET
american_scientific_journal-4814	153	7	present	present	ADJ
american_scientific_journal-4814	153	8	study	study	NOUN
american_scientific_journal-4814	153	9	a	a	DET
american_scientific_journal-4814	153	10	great	great	ADJ
american_scientific_journal-4814	153	11	spectrum	spectrum	NOUN
american_scientific_journal-4814	153	12	of	of	ADP
american_scientific_journal-4814	153	13	the	the	DET
american_scientific_journal-4814	153	14	eigenfrequencies	eigenfrequencie	NOUN
american_scientific_journal-4814	153	15	contrary	contrary	ADJ
american_scientific_journal-4814	153	16	to	to	PART
american_scientific_journal-4814	153	17	work	work	VERB
american_scientific_journal-4814	153	18	[	[	X
american_scientific_journal-4814	153	19	12	12	NUM
american_scientific_journal-4814	153	20	]	]	PUNCT
american_scientific_journal-4814	153	21	.	.	PUNCT
american_scientific_journal-4814	154	1	this	this	DET
american_scientific_journal-4814	154	2	wide	wide	ADJ
american_scientific_journal-4814	154	3	spectrum	spectrum	NOUN
american_scientific_journal-4814	154	4	of	of	ADP
american_scientific_journal-4814	154	5	the	the	DET
american_scientific_journal-4814	154	6	eigenfrequencies	eigenfrequencie	NOUN
american_scientific_journal-4814	154	7	obtained	obtain	VERB
american_scientific_journal-4814	154	8	here	here	ADV
american_scientific_journal-4814	154	9	is	be	AUX
american_scientific_journal-4814	154	10	necessary	necessary	ADJ
american_scientific_journal-4814	154	11	to	to	PART
american_scientific_journal-4814	154	12	perform	perform	VERB
american_scientific_journal-4814	154	13	a	a	DET
american_scientific_journal-4814	154	14	suitable	suitable	ADJ
american_scientific_journal-4814	154	15	model	model	NOUN
american_scientific_journal-4814	154	16	attitude	attitude	NOUN
american_scientific_journal-4814	154	17	control	control	NOUN
american_scientific_journal-4814	154	18	of	of	ADP
american_scientific_journal-4814	154	19	the	the	DET
american_scientific_journal-4814	154	20	space	space	NOUN
american_scientific_journal-4814	154	21	vehicle	vehicle	NOUN
american_scientific_journal-4814	154	22	in	in	ADP
american_scientific_journal-4814	154	23	the	the	DET
american_scientific_journal-4814	154	24	practice	practice	NOUN
american_scientific_journal-4814	154	25	.	.	PUNCT
american_scientific_journal-4814	155	1	references	reference	NOUN
american_scientific_journal-4814	155	2	[	[	X
american_scientific_journal-4814	155	3	1	1	NUM
american_scientific_journal-4814	155	4	]	]	PUNCT
american_scientific_journal-4814	155	5	h.	h.	PROPN
american_scientific_journal-4814	155	6	b.	b.	PROPN
american_scientific_journal-4814	155	7	hablani	hablani	PROPN
american_scientific_journal-4814	155	8	.	.	PUNCT
american_scientific_journal-4814	156	1	"	"	PUNCT
american_scientific_journal-4814	156	2	modal	modal	ADJ
american_scientific_journal-4814	156	3	analysis	analysis	NOUN
american_scientific_journal-4814	156	4	of	of	ADP
american_scientific_journal-4814	156	5	gyroscopic	gyroscopic	ADJ
american_scientific_journal-4814	156	6	flexible	flexible	ADJ
american_scientific_journal-4814	156	7	spacecraft	spacecraft	NOUN
american_scientific_journal-4814	156	8	,	,	PUNCT
american_scientific_journal-4814	156	9	a	a	DET
american_scientific_journal-4814	156	10	continuum	continuum	ADJ
american_scientific_journal-4814	156	11	approach	approach	NOUN
american_scientific_journal-4814	156	12	.	.	PUNCT
american_scientific_journal-4814	156	13	"	"	PUNCT
american_scientific_journal-4814	157	1	j.	j.	PROPN
american_scientific_journal-4814	157	2	guid	guid	PROPN
american_scientific_journal-4814	157	3	5	5	NUM
american_scientific_journal-4814	157	4	(	(	PUNCT
american_scientific_journal-4814	157	5	5	5	NUM
american_scientific_journal-4814	157	6	)	)	PUNCT
american_scientific_journal-4814	157	7	,	,	PUNCT
american_scientific_journal-4814	157	8	pp	pp	ADP
american_scientific_journal-4814	157	9	.	.	PUNCT
american_scientific_journal-4814	158	1	448	448	NUM
american_scientific_journal-4814	158	2	–	–	PUNCT
american_scientific_journal-4814	158	3	457	457	NUM
american_scientific_journal-4814	158	4	,	,	PUNCT
american_scientific_journal-4814	158	5	1982	1982	NUM
american_scientific_journal-4814	158	6	.	.	PUNCT
american_scientific_journal-4814	159	1	[	[	X
american_scientific_journal-4814	159	2	2	2	NUM
american_scientific_journal-4814	159	3	]	]	PUNCT
american_scientific_journal-4814	159	4	p.	p.	NOUN
american_scientific_journal-4814	159	5	c.	c.	PROPN
american_scientific_journal-4814	159	6	hughes	hughes	PROPN
american_scientific_journal-4814	159	7	.	.	PUNCT
american_scientific_journal-4814	160	1	"	"	PUNCT
american_scientific_journal-4814	160	2	dynamics	dynamic	NOUN
american_scientific_journal-4814	160	3	of	of	ADP
american_scientific_journal-4814	160	4	flexible	flexible	ADJ
american_scientific_journal-4814	160	5	space	space	NOUN
american_scientific_journal-4814	160	6	vehicles	vehicle	NOUN
american_scientific_journal-4814	160	7	with	with	ADP
american_scientific_journal-4814	160	8	active	active	ADJ
american_scientific_journal-4814	160	9	attitudes	attitude	NOUN
american_scientific_journal-4814	160	10	control	control	NOUN
american_scientific_journal-4814	160	11	.	.	PUNCT
american_scientific_journal-4814	160	12	"	"	PUNCT
american_scientific_journal-4814	161	1	celest	celest	PROPN
american_scientific_journal-4814	161	2	.	.	PUNCT
american_scientific_journal-4814	162	1	mech	mech	PROPN
american_scientific_journal-4814	162	2	.	.	PUNCT
american_scientific_journal-4814	163	1	9	9	NUM
american_scientific_journal-4814	163	2	,	,	PUNCT
american_scientific_journal-4814	163	3	pp	pp	ADJ
american_scientific_journal-4814	163	4	.	.	PUNCT
american_scientific_journal-4814	164	1	21	21	NUM
american_scientific_journal-4814	164	2	-	-	SYM
american_scientific_journal-4814	164	3	39	39	NUM
american_scientific_journal-4814	164	4	,	,	PUNCT
american_scientific_journal-4814	164	5	1974	1974	NUM
american_scientific_journal-4814	164	6	.	.	PUNCT
american_scientific_journal-4814	165	1	[	[	X
american_scientific_journal-4814	165	2	3	3	X
american_scientific_journal-4814	165	3	]	]	X
american_scientific_journal-4814	165	4	l.	l.	PROPN
american_scientific_journal-4814	165	5	meirovitch	meirovitch	PROPN
american_scientific_journal-4814	165	6	.	.	PUNCT
american_scientific_journal-4814	166	1	"	"	PUNCT
american_scientific_journal-4814	166	2	a	a	DET
american_scientific_journal-4814	166	3	stationary	stationary	ADJ
american_scientific_journal-4814	166	4	principle	principle	NOUN
american_scientific_journal-4814	166	5	for	for	ADP
american_scientific_journal-4814	166	6	the	the	DET
american_scientific_journal-4814	166	7	eigenvalue	eigenvalue	PROPN
american_scientific_journal-4814	166	8	problem	problem	NOUN
american_scientific_journal-4814	166	9	for	for	ADP
american_scientific_journal-4814	166	10	rotating	rotate	VERB
american_scientific_journal-4814	166	11	structures	structure	NOUN
american_scientific_journal-4814	166	12	.	.	PUNCT
american_scientific_journal-4814	166	13	"	"	PUNCT
american_scientific_journal-4814	167	1	aiaaj	aiaaj	ADJ
american_scientific_journal-4814	167	2	.	.	PUNCT
american_scientific_journal-4814	168	1	14	14	NUM
american_scientific_journal-4814	168	2	(	(	PUNCT
american_scientific_journal-4814	168	3	10	10	NUM
american_scientific_journal-4814	168	4	)	)	PUNCT
american_scientific_journal-4814	168	5	,	,	PUNCT
american_scientific_journal-4814	169	1	pp	pp	ADJ
american_scientific_journal-4814	169	2	.	.	PUNCT
american_scientific_journal-4814	170	1	1387	1387	NUM
american_scientific_journal-4814	170	2	–	–	PUNCT
american_scientific_journal-4814	170	3	1394	1394	NUM
american_scientific_journal-4814	170	4	,	,	PUNCT
american_scientific_journal-4814	170	5	1976	1976	NUM
american_scientific_journal-4814	170	6	.	.	PUNCT
american_scientific_journal-4814	171	1	[	[	X
american_scientific_journal-4814	171	2	4	4	NUM
american_scientific_journal-4814	171	3	]	]	PUNCT
american_scientific_journal-4814	171	4	m.	m.	NOUN
american_scientific_journal-4814	171	5	pascal	pascal	NOUN
american_scientific_journal-4814	171	6	.	.	PUNCT
american_scientific_journal-4814	172	1	"	"	PUNCT
american_scientific_journal-4814	172	2	modal	modal	ADJ
american_scientific_journal-4814	172	3	analysis	analysis	NOUN
american_scientific_journal-4814	172	4	of	of	ADP
american_scientific_journal-4814	172	5	a	a	DET
american_scientific_journal-4814	172	6	rotating	rotate	VERB
american_scientific_journal-4814	172	7	flexible	flexible	ADJ
american_scientific_journal-4814	172	8	space	space	NOUN
american_scientific_journal-4814	172	9	by	by	ADP
american_scientific_journal-4814	172	10	a	a	DET
american_scientific_journal-4814	172	11	continuum	continuum	ADJ
american_scientific_journal-4814	172	12	approach	approach	NOUN
american_scientific_journal-4814	172	13	.	.	PUNCT
american_scientific_journal-4814	172	14	"	"	PUNCT
american_scientific_journal-4814	173	1	z.	z.	PROPN
american_scientific_journal-4814	173	2	flug	flug	PROPN
american_scientific_journal-4814	173	3	–	–	PUNCT
american_scientific_journal-4814	173	4	wiss	wiss	PROPN
american_scientific_journal-4814	173	5	.	.	PUNCT
american_scientific_journal-4814	174	1	weltraumforsch	weltraumforsch	PROPN
american_scientific_journal-4814	174	2	.	.	PUNCT
american_scientific_journal-4814	175	1	18	18	NUM
american_scientific_journal-4814	175	2	,	,	PUNCT
american_scientific_journal-4814	175	3	pp	pp	ADJ
american_scientific_journal-4814	175	4	.	.	PUNCT
american_scientific_journal-4814	176	1	395	395	NUM
american_scientific_journal-4814	176	2	–	–	SYM
american_scientific_journal-4814	176	3	401	401	NUM
american_scientific_journal-4814	176	4	,	,	PUNCT
american_scientific_journal-4814	176	5	1994	1994	NUM
american_scientific_journal-4814	176	6	.	.	PUNCT
american_scientific_journal-4814	177	1	[	[	X
american_scientific_journal-4814	177	2	5	5	NUM
american_scientific_journal-4814	177	3	]	]	PUNCT
american_scientific_journal-4814	177	4	m.	m.	NOUN
american_scientific_journal-4814	177	5	pascal	pascal	PROPN
american_scientific_journal-4814	177	6	,	,	PUNCT
american_scientific_journal-4814	177	7	m.	m.	NOUN
american_scientific_journal-4814	177	8	sylla	sylla	PROPN
american_scientific_journal-4814	177	9	.	.	PUNCT
american_scientific_journal-4814	178	1	"	"	PUNCT
american_scientific_journal-4814	178	2	dynamic	dynamic	ADJ
american_scientific_journal-4814	178	3	model	model	NOUN
american_scientific_journal-4814	178	4	of	of	ADP
american_scientific_journal-4814	178	5	a	a	DET
american_scientific_journal-4814	178	6	large	large	ADJ
american_scientific_journal-4814	178	7	space	space	NOUN
american_scientific_journal-4814	178	8	structure	structure	NOUN
american_scientific_journal-4814	178	9	by	by	ADP
american_scientific_journal-4814	178	10	a	a	DET
american_scientific_journal-4814	178	11	continuous	continuous	ADJ
american_scientific_journal-4814	178	12	approach	approach	NOUN
american_scientific_journal-4814	178	13	.	.	PUNCT
american_scientific_journal-4814	178	14	"	"	PUNCT
american_scientific_journal-4814	179	1	american	american	ADJ
american_scientific_journal-4814	179	2	scientific	scientific	ADJ
american_scientific_journal-4814	179	3	research	research	NOUN
american_scientific_journal-4814	179	4	journal	journal	NOUN
american_scientific_journal-4814	179	5	for	for	ADP
american_scientific_journal-4814	179	6	engineering	engineering	NOUN
american_scientific_journal-4814	179	7	,	,	PUNCT
american_scientific_journal-4814	179	8	technology	technology	NOUN
american_scientific_journal-4814	179	9	,	,	PUNCT
american_scientific_journal-4814	179	10	and	and	CCONJ
american_scientific_journal-4814	179	11	sciences	science	NOUN
american_scientific_journal-4814	179	12	(	(	PUNCT
american_scientific_journal-4814	179	13	asrjets	asrjet	NOUN
american_scientific_journal-4814	179	14	)	)	PUNCT
american_scientific_journal-4814	179	15	(	(	PUNCT
american_scientific_journal-4814	179	16	2019	2019	NUM
american_scientific_journal-4814	179	17	)	)	PUNCT
american_scientific_journal-4814	179	18	volume	volume	NOUN
american_scientific_journal-4814	179	19	55	55	NUM
american_scientific_journal-4814	179	20	,	,	PUNCT
american_scientific_journal-4814	179	21	no	no	DET
american_scientific_journal-4814	179	22	1	1	NUM
american_scientific_journal-4814	179	23	,	,	PUNCT
american_scientific_journal-4814	179	24	pp	pp	ADP
american_scientific_journal-4814	179	25	50	50	NUM
american_scientific_journal-4814	179	26	-	-	SYM
american_scientific_journal-4814	179	27	68	68	NUM
american_scientific_journal-4814	179	28	62	62	NUM
american_scientific_journal-4814	179	29	recherche	recherche	X
american_scientific_journal-4814	179	30	aerospatiale	aerospatiale	PROPN
american_scientific_journal-4814	179	31	n	n	CCONJ
american_scientific_journal-4814	179	32	°	°	NUM
american_scientific_journal-4814	179	33	2	2	NUM
american_scientific_journal-4814	179	34	,	,	PUNCT
american_scientific_journal-4814	179	35	pp	pp	ADJ
american_scientific_journal-4814	179	36	.	.	PUNCT
american_scientific_journal-4814	180	1	67	67	NUM
american_scientific_journal-4814	180	2	–	–	PUNCT
american_scientific_journal-4814	180	3	77	77	NUM
american_scientific_journal-4814	180	4	,	,	PUNCT
american_scientific_journal-4814	180	5	1993	1993	NUM
american_scientific_journal-4814	180	6	.	.	PUNCT
american_scientific_journal-4814	181	1	[	[	X
american_scientific_journal-4814	181	2	6	6	NUM
american_scientific_journal-4814	181	3	]	]	PUNCT
american_scientific_journal-4814	181	4	a.	a.	NOUN
american_scientific_journal-4814	181	5	sandu	sandu	PROPN
american_scientific_journal-4814	181	6	,	,	PUNCT
american_scientific_journal-4814	181	7	d.	d.	PROPN
american_scientific_journal-4814	181	8	negrut	negrut	PROPN
american_scientific_journal-4814	181	9	,	,	PUNCT
american_scientific_journal-4814	181	10	e.	e.	PROPN
american_scientific_journal-4814	181	11	j.	j.	PROPN
american_scientific_journal-4814	181	12	haug	haug	PROPN
american_scientific_journal-4814	181	13	,	,	PUNCT
american_scientific_journal-4814	181	14	f.a	f.a	PROPN
american_scientific_journal-4814	181	15	.	.	PROPN
american_scientific_journal-4814	181	16	potra	potra	PROPN
american_scientific_journal-4814	181	17	,	,	PUNCT
american_scientific_journal-4814	181	18	c.	c.	PROPN
american_scientific_journal-4814	181	19	sandu	sandu	NOUN
american_scientific_journal-4814	181	20	.	.	PUNCT
american_scientific_journal-4814	182	1	"	"	PUNCT
american_scientific_journal-4814	182	2	a	a	DET
american_scientific_journal-4814	182	3	rosenbrock	rosenbrock	NOUN
american_scientific_journal-4814	182	4	-	-	PUNCT
american_scientific_journal-4814	182	5	nystrom	nystrom	NOUN
american_scientific_journal-4814	182	6	state	state	NOUN
american_scientific_journal-4814	182	7	space	space	NOUN
american_scientific_journal-4814	182	8	implicit	implicit	ADJ
american_scientific_journal-4814	182	9	approach	approach	NOUN
american_scientific_journal-4814	182	10	for	for	ADP
american_scientific_journal-4814	182	11	the	the	DET
american_scientific_journal-4814	182	12	dynamic	dynamic	ADJ
american_scientific_journal-4814	182	13	analysis	analysis	NOUN
american_scientific_journal-4814	182	14	of	of	ADP
american_scientific_journal-4814	182	15	mechanical	mechanical	ADJ
american_scientific_journal-4814	182	16	system	system	NOUN
american_scientific_journal-4814	182	17	.	.	PUNCT
american_scientific_journal-4814	182	18	"	"	PUNCT
american_scientific_journal-4814	183	1	theoretical	theoretical	ADJ
american_scientific_journal-4814	183	2	formulation	formulation	NOUN
american_scientific_journal-4814	183	3	,	,	PUNCT
american_scientific_journal-4814	183	4	j.	j.	PROPN
american_scientific_journal-4814	183	5	multibody	multibody	PROPN
american_scientific_journal-4814	183	6	dyn	dyn	PROPN
american_scientific_journal-4814	183	7	.	.	PUNCT
american_scientific_journal-4814	184	1	217(4	217(4	NUM
american_scientific_journal-4814	184	2	)	)	PUNCT
american_scientific_journal-4814	184	3	,	,	PUNCT
american_scientific_journal-4814	184	4	263	263	NUM
american_scientific_journal-4814	184	5	–	–	PUNCT
american_scientific_journal-4814	184	6	271	271	NUM
american_scientific_journal-4814	184	7	,	,	PUNCT
american_scientific_journal-4814	184	8	2003	2003	NUM
american_scientific_journal-4814	184	9	.	.	PUNCT
american_scientific_journal-4814	185	1	[	[	X
american_scientific_journal-4814	185	2	7	7	X
american_scientific_journal-4814	185	3	]	]	PUNCT
american_scientific_journal-4814	185	4	m.	m.	NOUN
american_scientific_journal-4814	185	5	sylla	sylla	PROPN
american_scientific_journal-4814	185	6	.	.	PUNCT
american_scientific_journal-4814	186	1	"	"	PUNCT
american_scientific_journal-4814	186	2	spectral	spectral	ADJ
american_scientific_journal-4814	186	3	decomposition	decomposition	NOUN
american_scientific_journal-4814	186	4	analysis	analysis	NOUN
american_scientific_journal-4814	186	5	using	use	VERB
american_scientific_journal-4814	186	6	the	the	DET
american_scientific_journal-4814	186	7	global	global	ADJ
american_scientific_journal-4814	186	8	modes	mode	NOUN
american_scientific_journal-4814	186	9	of	of	ADP
american_scientific_journal-4814	186	10	a	a	DET
american_scientific_journal-4814	186	11	rotating	rotate	VERB
american_scientific_journal-4814	186	12	elastic	elastic	ADJ
american_scientific_journal-4814	186	13	space	space	NOUN
american_scientific_journal-4814	186	14	vehicle	vehicle	NOUN
american_scientific_journal-4814	186	15	.	.	PUNCT
american_scientific_journal-4814	186	16	"	"	PUNCT
american_scientific_journal-4814	187	1	far	far	ADV
american_scientific_journal-4814	187	2	east	east	PROPN
american_scientific_journal-4814	187	3	journal	journal	NOUN
american_scientific_journal-4814	187	4	of	of	ADP
american_scientific_journal-4814	187	5	applied	apply	VERB
american_scientific_journal-4814	187	6	mathematics	mathematic	NOUN
american_scientific_journal-4814	187	7	37(1	37(1	NUM
american_scientific_journal-4814	187	8	)	)	PUNCT
american_scientific_journal-4814	187	9	,	,	PUNCT
american_scientific_journal-4814	187	10	pp	pp	PROPN
american_scientific_journal-4814	187	11	.	.	PUNCT
american_scientific_journal-4814	188	1	69	69	NUM
american_scientific_journal-4814	188	2	–	–	SYM
american_scientific_journal-4814	188	3	89	89	NUM
american_scientific_journal-4814	188	4	,	,	PUNCT
american_scientific_journal-4814	188	5	2009	2009	NUM
american_scientific_journal-4814	188	6	.	.	PUNCT
american_scientific_journal-4814	189	1	[	[	X
american_scientific_journal-4814	189	2	8	8	NUM
american_scientific_journal-4814	189	3	]	]	PUNCT
american_scientific_journal-4814	189	4	m.	m.	NOUN
american_scientific_journal-4814	189	5	sylla	sylla	PROPN
american_scientific_journal-4814	189	6	and	and	CCONJ
american_scientific_journal-4814	189	7	b.	b.	PROPN
american_scientific_journal-4814	189	8	asseke	asseke	PROPN
american_scientific_journal-4814	189	9	.	.	PUNCT
american_scientific_journal-4814	190	1	"	"	PUNCT
american_scientific_journal-4814	190	2	dynamics	dynamic	NOUN
american_scientific_journal-4814	190	3	of	of	ADP
american_scientific_journal-4814	190	4	a	a	DET
american_scientific_journal-4814	190	5	rotating	rotate	VERB
american_scientific_journal-4814	190	6	flexible	flexible	ADJ
american_scientific_journal-4814	190	7	and	and	CCONJ
american_scientific_journal-4814	190	8	symmetric	symmetric	ADJ
american_scientific_journal-4814	190	9	spacecraft	spacecraft	NOUN
american_scientific_journal-4814	190	10	using	use	VERB
american_scientific_journal-4814	190	11	impedance	impedance	NOUN
american_scientific_journal-4814	190	12	matrix	matrix	NOUN
american_scientific_journal-4814	190	13	in	in	ADP
american_scientific_journal-4814	190	14	terms	term	NOUN
american_scientific_journal-4814	190	15	of	of	ADP
american_scientific_journal-4814	190	16	the	the	DET
american_scientific_journal-4814	190	17	flexible	flexible	ADJ
american_scientific_journal-4814	190	18	appendages	appendage	NOUN
american_scientific_journal-4814	190	19	cantilever	cantilever	NOUN
american_scientific_journal-4814	190	20	modes	mode	NOUN
american_scientific_journal-4814	190	21	.	.	PUNCT
american_scientific_journal-4814	190	22	"	"	PUNCT
american_scientific_journal-4814	190	23	multibody	multibody	ADJ
american_scientific_journal-4814	190	24	system	system	NOUN
american_scientific_journal-4814	190	25	dynamics	dynamic	NOUN
american_scientific_journal-4814	190	26	.	.	PUNCT
american_scientific_journal-4814	191	1	19	19	NUM
american_scientific_journal-4814	191	2	,	,	PUNCT
american_scientific_journal-4814	191	3	pp	pp	ADJ
american_scientific_journal-4814	191	4	.	.	PUNCT
american_scientific_journal-4814	192	1	345	345	NUM
american_scientific_journal-4814	192	2	–	–	PUNCT
american_scientific_journal-4814	192	3	364	364	NUM
american_scientific_journal-4814	192	4	,	,	PUNCT
american_scientific_journal-4814	192	5	2008	2008	NUM
american_scientific_journal-4814	192	6	.	.	PUNCT
american_scientific_journal-4814	193	1	[	[	X
american_scientific_journal-4814	193	2	9	9	NUM
american_scientific_journal-4814	193	3	]	]	PUNCT
american_scientific_journal-4814	193	4	m.	m.	NOUN
american_scientific_journal-4814	193	5	sylla	sylla	PROPN
american_scientific_journal-4814	193	6	and	and	CCONJ
american_scientific_journal-4814	193	7	r.	r.	PROPN
american_scientific_journal-4814	193	8	a.	a.	PROPN
american_scientific_journal-4814	193	9	p.	p.	PROPN
american_scientific_journal-4814	193	10	barou	barou	PROPN
american_scientific_journal-4814	193	11	.	.	PUNCT
american_scientific_journal-4814	194	1	"	"	PUNCT
american_scientific_journal-4814	194	2	a	a	DET
american_scientific_journal-4814	194	3	mathematical	mathematical	ADJ
american_scientific_journal-4814	194	4	model	model	NOUN
american_scientific_journal-4814	194	5	of	of	ADP
american_scientific_journal-4814	194	6	a	a	DET
american_scientific_journal-4814	194	7	helicopter	helicopter	NOUN
american_scientific_journal-4814	194	8	standing	stand	VERB
american_scientific_journal-4814	194	9	and	and	CCONJ
american_scientific_journal-4814	194	10	rotating	rotate	VERB
american_scientific_journal-4814	194	11	rotor	rotor	NOUN
american_scientific_journal-4814	194	12	blade	blade	NOUN
american_scientific_journal-4814	194	13	.	.	PUNCT
american_scientific_journal-4814	194	14	"	"	PUNCT
american_scientific_journal-4814	195	1	far	far	ADV
american_scientific_journal-4814	195	2	east	east	PROPN
american_scientific_journal-4814	195	3	journal	journal	NOUN
american_scientific_journal-4814	195	4	of	of	ADP
american_scientific_journal-4814	195	5	applied	apply	VERB
american_scientific_journal-4814	195	6	mathematics	mathematic	NOUN
american_scientific_journal-4814	195	7	.	.	PUNCT
american_scientific_journal-4814	196	1	31(1	31(1	NUM
american_scientific_journal-4814	196	2	)	)	PUNCT
american_scientific_journal-4814	196	3	,	,	PUNCT
american_scientific_journal-4814	197	1	pp	pp	ADP
american_scientific_journal-4814	197	2	.	.	NOUN
american_scientific_journal-4814	197	3	1	1	NUM
american_scientific_journal-4814	197	4	–	–	PUNCT
american_scientific_journal-4814	197	5	25	25	NUM
american_scientific_journal-4814	197	6	,	,	PUNCT
american_scientific_journal-4814	197	7	2008	2008	NUM
american_scientific_journal-4814	197	8	.	.	PUNCT
american_scientific_journal-4814	198	1	[	[	X
american_scientific_journal-4814	198	2	10	10	NUM
american_scientific_journal-4814	198	3	]	]	PUNCT
american_scientific_journal-4814	198	4	m.	m.	NOUN
american_scientific_journal-4814	198	5	sylla	sylla	PROPN
american_scientific_journal-4814	198	6	,	,	PUNCT
american_scientific_journal-4814	198	7	m.	m.	NOUN
american_scientific_journal-4814	198	8	dosso	dosso	NOUN
american_scientific_journal-4814	198	9	and	and	CCONJ
american_scientific_journal-4814	198	10	r.	r.	PROPN
american_scientific_journal-4814	198	11	a.	a.	PROPN
american_scientific_journal-4814	198	12	p.	p.	PROPN
american_scientific_journal-4814	198	13	barou	barou	PROPN
american_scientific_journal-4814	198	14	.	.	PUNCT
american_scientific_journal-4814	199	1	"	"	PUNCT
american_scientific_journal-4814	199	2	dynamical	dynamical	ADJ
american_scientific_journal-4814	199	3	analysis	analysis	NOUN
american_scientific_journal-4814	199	4	of	of	ADP
american_scientific_journal-4814	199	5	a	a	DET
american_scientific_journal-4814	199	6	flexible	flexible	ADJ
american_scientific_journal-4814	199	7	mechanism	mechanism	NOUN
american_scientific_journal-4814	199	8	by	by	ADP
american_scientific_journal-4814	199	9	a	a	DET
american_scientific_journal-4814	199	10	continuum	continuum	ADJ
american_scientific_journal-4814	199	11	approach	approach	NOUN
american_scientific_journal-4814	199	12	using	use	VERB
american_scientific_journal-4814	199	13	the	the	DET
american_scientific_journal-4814	199	14	rotating	rotate	VERB
american_scientific_journal-4814	199	15	base	base	NOUN
american_scientific_journal-4814	199	16	cantilever	cantilever	NOUN
american_scientific_journal-4814	199	17	modes	mode	NOUN
american_scientific_journal-4814	199	18	.	.	PUNCT
american_scientific_journal-4814	199	19	"	"	PUNCT
american_scientific_journal-4814	200	1	far	far	ADV
american_scientific_journal-4814	200	2	fast	fast	ADJ
american_scientific_journal-4814	200	3	journal	journal	NOUN
american_scientific_journal-4814	200	4	of	of	ADP
american_scientific_journal-4814	200	5	applied	apply	VERB
american_scientific_journal-4814	200	6	mathematics	mathematic	NOUN
american_scientific_journal-4814	200	7	.	.	PUNCT
american_scientific_journal-4814	201	1	33(2	33(2	NUM
american_scientific_journal-4814	201	2	)	)	PUNCT
american_scientific_journal-4814	201	3	,	,	PUNCT
american_scientific_journal-4814	202	1	pp	pp	ADP
american_scientific_journal-4814	202	2	.	.	PUNCT
american_scientific_journal-4814	203	1	187	187	NUM
american_scientific_journal-4814	203	2	–	–	SYM
american_scientific_journal-4814	203	3	204	204	NUM
american_scientific_journal-4814	203	4	,	,	PUNCT
american_scientific_journal-4814	203	5	2008	2008	NUM
american_scientific_journal-4814	203	6	.	.	PUNCT
american_scientific_journal-4814	204	1	[	[	X
american_scientific_journal-4814	204	2	11	11	NUM
american_scientific_journal-4814	204	3	]	]	PUNCT
american_scientific_journal-4814	204	4	m.	m.	NOUN
american_scientific_journal-4814	204	5	sylla	sylla	PROPN
american_scientific_journal-4814	204	6	and	and	CCONJ
american_scientific_journal-4814	204	7	l.	l.	PROPN
american_scientific_journal-4814	204	8	gomat	gomat	PROPN
american_scientific_journal-4814	204	9	.	.	PUNCT
american_scientific_journal-4814	205	1	"	"	PUNCT
american_scientific_journal-4814	205	2	modal	modal	ADJ
american_scientific_journal-4814	205	3	analysis	analysis	NOUN
american_scientific_journal-4814	205	4	of	of	ADP
american_scientific_journal-4814	205	5	a	a	DET
american_scientific_journal-4814	205	6	rotation	rotation	NOUN
american_scientific_journal-4814	205	7	flexible	flexible	ADJ
american_scientific_journal-4814	205	8	manipulator	manipulator	NOUN
american_scientific_journal-4814	205	9	arm	arm	NOUN
american_scientific_journal-4814	205	10	.	.	PUNCT
american_scientific_journal-4814	205	11	"	"	PUNCT
american_scientific_journal-4814	206	1	afrika	afrika	PROPN
american_scientific_journal-4814	206	2	matematika	matematika	PROPN
american_scientific_journal-4814	206	3	.	.	PUNCT
american_scientific_journal-4814	206	4	serie	serie	PROPN
american_scientific_journal-4814	206	5	3(19	3(19	NUM
american_scientific_journal-4814	206	6	)	)	PUNCT
american_scientific_journal-4814	206	7	,	,	PUNCT
american_scientific_journal-4814	206	8	7	7	NUM
american_scientific_journal-4814	206	9	–	–	SYM
american_scientific_journal-4814	206	10	28	28	NUM
american_scientific_journal-4814	206	11	,	,	PUNCT
american_scientific_journal-4814	206	12	2008	2008	NUM
american_scientific_journal-4814	206	13	.	.	PUNCT
american_scientific_journal-4814	207	1	[	[	X
american_scientific_journal-4814	207	2	12	12	NUM
american_scientific_journal-4814	207	3	]	]	PUNCT
american_scientific_journal-4814	207	4	m.	m.	NOUN
american_scientific_journal-4814	207	5	sylla	sylla	PROPN
american_scientific_journal-4814	207	6	and	and	CCONJ
american_scientific_journal-4814	207	7	s.	s.	PROPN
american_scientific_journal-4814	207	8	j.	j.	PROPN
american_scientific_journal-4814	207	9	m.	m.	PROPN
american_scientific_journal-4814	207	10	kouassi	kouassi	PROPN
american_scientific_journal-4814	207	11	.	.	PUNCT
american_scientific_journal-4814	208	1	"	"	PUNCT
american_scientific_journal-4814	208	2	method	method	NOUN
american_scientific_journal-4814	208	3	of	of	ADP
american_scientific_journal-4814	208	4	modal	modal	ADJ
american_scientific_journal-4814	208	5	synthesis	synthesis	NOUN
american_scientific_journal-4814	208	6	in	in	ADP
american_scientific_journal-4814	208	7	the	the	DET
american_scientific_journal-4814	208	8	dynamics	dynamic	NOUN
american_scientific_journal-4814	208	9	of	of	ADP
american_scientific_journal-4814	208	10	a	a	DET
american_scientific_journal-4814	208	11	deformable	deformable	ADJ
american_scientific_journal-4814	208	12	spatial	spatial	ADJ
american_scientific_journal-4814	208	13	structure	structure	NOUN
american_scientific_journal-4814	208	14	.	.	PUNCT
american_scientific_journal-4814	208	15	"	"	PUNCT
american_scientific_journal-4814	209	1	far	far	ADV
american_scientific_journal-4814	209	2	east	east	PROPN
american_scientific_journal-4814	209	3	journal	journal	PROPN
american_scientific_journal-4814	209	4	of	of	ADP
american_scientific_journal-4814	209	5	dynamical	dynamical	ADJ
american_scientific_journal-4814	209	6	systems	system	NOUN
american_scientific_journal-4814	209	7	volume	volume	NOUN
american_scientific_journal-4814	209	8	30(3	30(3	NOUN
american_scientific_journal-4814	209	9	)	)	PUNCT
american_scientific_journal-4814	209	10	,	,	PUNCT
american_scientific_journal-4814	209	11	103	103	NUM
american_scientific_journal-4814	209	12	-	-	SYM
american_scientific_journal-4814	209	13	133	133	NUM
american_scientific_journal-4814	209	14	,	,	PUNCT
american_scientific_journal-4814	209	15	2018	2018	NUM
american_scientific_journal-4814	209	16	.	.	PUNCT
american_scientific_journal-4814	210	1	[	[	X
american_scientific_journal-4814	210	2	13	13	NUM
american_scientific_journal-4814	210	3	]	]	PUNCT
american_scientific_journal-4814	210	4	m.	m.	NOUN
american_scientific_journal-4814	210	5	pascal	pascal	NOUN
american_scientific_journal-4814	210	6	.	.	PUNCT
american_scientific_journal-4814	211	1	"	"	PUNCT
american_scientific_journal-4814	211	2	la	la	DET
american_scientific_journal-4814	211	3	stabilité	stabilité	PROPN
american_scientific_journal-4814	211	4	d'attitude	d'attitude	PROPN
american_scientific_journal-4814	211	5	d'un	d'un	PROPN
american_scientific_journal-4814	211	6	satellite	satellite	PROPN
american_scientific_journal-4814	211	7	muni	muni	PROPN
american_scientific_journal-4814	211	8	de	de	PROPN
american_scientific_journal-4814	211	9	panneaux	panneaux	PROPN
american_scientific_journal-4814	211	10	solaires	solaires	PROPN
american_scientific_journal-4814	211	11	.	.	PUNCT
american_scientific_journal-4814	211	12	"	"	PUNCT
american_scientific_journal-4814	212	1	acta	acta	PROPN
american_scientific_journal-4814	212	2	astronaut	astronaut	PROPN
american_scientific_journal-4814	212	3	.	.	PUNCT
american_scientific_journal-4814	213	1	5	5	NUM
american_scientific_journal-4814	213	2	,	,	PUNCT
american_scientific_journal-4814	213	3	pp	pp	ADJ
american_scientific_journal-4814	213	4	.	.	PUNCT
american_scientific_journal-4814	214	1	817	817	NUM
american_scientific_journal-4814	214	2	–	–	PUNCT
american_scientific_journal-4814	214	3	844	844	NUM
american_scientific_journal-4814	214	4	,	,	PUNCT
american_scientific_journal-4814	214	5	1978	1978	NUM
american_scientific_journal-4814	214	6	.	.	PUNCT
american_scientific_journal-4814	215	1	•	•	NOUN
american_scientific_journal-4814	215	2	appendix	appendix	NOUN
american_scientific_journal-4814	215	3	1	1	NUM
american_scientific_journal-4814	215	4	model	model	NOUN
american_scientific_journal-4814	215	5	description	description	NOUN
american_scientific_journal-4814	215	6	figure	figure	NOUN
american_scientific_journal-4814	215	7	1	1	NUM
american_scientific_journal-4814	215	8	:	:	PUNCT
american_scientific_journal-4814	215	9	satellite	satellite	NOUN
american_scientific_journal-4814	215	10	and	and	CCONJ
american_scientific_journal-4814	215	11	solar	solar	ADJ
american_scientific_journal-4814	215	12	arrays	array	VERB
american_scientific_journal-4814	215	13	.	.	PUNCT
american_scientific_journal-4814	216	1	american	american	ADJ
american_scientific_journal-4814	216	2	scientific	scientific	ADJ
american_scientific_journal-4814	216	3	research	research	PROPN
american_scientific_journal-4814	216	4	journal	journal	NOUN
american_scientific_journal-4814	216	5	for	for	ADP
american_scientific_journal-4814	216	6	engineering	engineering	NOUN
american_scientific_journal-4814	216	7	,	,	PUNCT
american_scientific_journal-4814	216	8	technology	technology	NOUN
american_scientific_journal-4814	216	9	,	,	PUNCT
american_scientific_journal-4814	216	10	and	and	CCONJ
american_scientific_journal-4814	216	11	sciences	science	NOUN
american_scientific_journal-4814	216	12	(	(	PUNCT
american_scientific_journal-4814	216	13	asrjets	asrjet	NOUN
american_scientific_journal-4814	216	14	)	)	PUNCT
american_scientific_journal-4814	216	15	(	(	PUNCT
american_scientific_journal-4814	216	16	2019	2019	NUM
american_scientific_journal-4814	216	17	)	)	PUNCT
american_scientific_journal-4814	216	18	volume	volume	NOUN
american_scientific_journal-4814	216	19	55	55	NUM
american_scientific_journal-4814	216	20	,	,	PUNCT
american_scientific_journal-4814	216	21	no	no	DET
american_scientific_journal-4814	216	22	1	1	NUM
american_scientific_journal-4814	216	23	,	,	PUNCT
american_scientific_journal-4814	216	24	pp	pp	ADP
american_scientific_journal-4814	216	25	50	50	NUM
american_scientific_journal-4814	216	26	-	-	SYM
american_scientific_journal-4814	216	27	68	68	NUM
american_scientific_journal-4814	216	28	63	63	NUM
american_scientific_journal-4814	216	29	figure	figure	NOUN
american_scientific_journal-4814	216	30	2	2	NUM
american_scientific_journal-4814	216	31	:	:	PUNCT
american_scientific_journal-4814	216	32	satellite	satellite	NOUN
american_scientific_journal-4814	216	33	orbiting	orbit	VERB
american_scientific_journal-4814	216	34	the	the	DET
american_scientific_journal-4814	216	35	earth	earth	NOUN
american_scientific_journal-4814	216	36	.	.	PUNCT
american_scientific_journal-4814	217	1	figure	figure	VERB
american_scientific_journal-4814	217	2	3	3	NUM
american_scientific_journal-4814	217	3	:	:	PUNCT
american_scientific_journal-4814	217	4	attitude	attitude	NOUN
american_scientific_journal-4814	217	5	𝜃𝜃	𝜃𝜃	PRON
american_scientific_journal-4814	217	6	motion	motion	NOUN
american_scientific_journal-4814	217	7	.	.	PUNCT
american_scientific_journal-4814	218	1	the	the	DET
american_scientific_journal-4814	218	2	angular	angular	ADJ
american_scientific_journal-4814	218	3	velocity	velocity	NOUN
american_scientific_journal-4814	218	4	vector	vector	PROPN
american_scientific_journal-4814	218	5	λ	λ	PROPN
american_scientific_journal-4814	218	6	�	�	PROPN
american_scientific_journal-4814	218	7	�	�	NOUN
american_scientific_journal-4814	218	8	⃗	⃗	PROPN
american_scientific_journal-4814	218	9	of	of	ADP
american_scientific_journal-4814	218	10	the	the	DET
american_scientific_journal-4814	218	11	reference	reference	NOUN
american_scientific_journal-4814	218	12	frame	frame	NOUN
american_scientific_journal-4814	218	13	ℜ	ℜ	PROPN
american_scientific_journal-4814	218	14	with	with	ADP
american_scientific_journal-4814	218	15	respect	respect	NOUN
american_scientific_journal-4814	218	16	to	to	ADP
american_scientific_journal-4814	218	17	the	the	DET
american_scientific_journal-4814	218	18	reference	reference	NOUN
american_scientific_journal-4814	218	19	frame	frame	NOUN
american_scientific_journal-4814	218	20	ℜ𝑇𝑇	ℜ𝑇𝑇	PROPN
american_scientific_journal-4814	218	21	in	in	ADP
american_scientific_journal-4814	218	22	�	�	PROPN
american_scientific_journal-4814	218	23	𝐺𝐺	𝐺𝐺	PROPN
american_scientific_journal-4814	218	24	;	;	PUNCT
american_scientific_journal-4814	218	25	�	�	PROPN
american_scientific_journal-4814	218	26	⃗	⃗	PROPN
american_scientific_journal-4814	218	27	�	�	PROPN
american_scientific_journal-4814	218	28	𝑋0,𝑌𝑌	𝑋0,𝑌𝑌	NOUN
american_scientific_journal-4814	218	29	�	�	PROPN
american_scientific_journal-4814	218	30	⃗0,𝑍𝑍0	⃗0,𝑍𝑍0	NOUN
american_scientific_journal-4814	218	31	�	�	PROPN
american_scientific_journal-4814	218	32	components	component	NOUN
american_scientific_journal-4814	218	33	is	be	AUX
american_scientific_journal-4814	218	34	(	(	PUNCT
american_scientific_journal-4814	218	35	figure	figure	NOUN
american_scientific_journal-4814	218	36	3	3	NUM
american_scientific_journal-4814	218	37	):	):	PUNCT
american_scientific_journal-4814	218	38	λ	λ	PROPN
american_scientific_journal-4814	218	39	�	�	PROPN
american_scientific_journal-4814	218	40	�	�	NOUN
american_scientific_journal-4814	218	41	⃗	⃗	PROPN
american_scientific_journal-4814	218	42	=	=	SYM
american_scientific_journal-4814	218	43	�	�	PROPN
american_scientific_journal-4814	218	44	0	0	NUM
american_scientific_journal-4814	218	45	0	0	NUM
american_scientific_journal-4814	218	46	𝑛𝑛0	𝑛𝑛0	X
american_scientific_journal-4814	218	47	+	+	CCONJ
american_scientific_journal-4814	218	48	�	�	PROPN
american_scientific_journal-4814	218	49	̇	̇	PROPN
american_scientific_journal-4814	218	50	�	�	PROPN
american_scientific_journal-4814	218	51	𝜃	𝜃	NUM
american_scientific_journal-4814	218	52	�	�	PROPN
american_scientific_journal-4814	218	53	�	�	PROPN
american_scientific_journal-4814	218	54	𝑋𝑋	𝑋𝑋	PROPN
american_scientific_journal-4814	218	55	�	�	PROPN
american_scientific_journal-4814	218	56	⃗	⃗	PROPN
american_scientific_journal-4814	218	57	0,𝑌𝑌	0,𝑌𝑌	NUM
american_scientific_journal-4814	218	58	�	�	PROPN
american_scientific_journal-4814	218	59	⃗0,	⃗0,	NOUN
american_scientific_journal-4814	218	60	�	�	PROPN
american_scientific_journal-4814	218	61	⃗	⃗	PROPN
american_scientific_journal-4814	218	62	�	�	PROPN
american_scientific_journal-4814	218	63	𝑍0	𝑍0	PROPN
american_scientific_journal-4814	218	64	�	�	PROPN
american_scientific_journal-4814	218	65	.	.	PUNCT
american_scientific_journal-4814	219	1	the	the	DET
american_scientific_journal-4814	219	2	elastic	elastic	ADJ
american_scientific_journal-4814	219	3	displacement	displacement	NOUN
american_scientific_journal-4814	219	4	fields	field	NOUN
american_scientific_journal-4814	219	5	modelling	modelling	NOUN
american_scientific_journal-4814	219	6	of	of	ADP
american_scientific_journal-4814	219	7	the	the	DET
american_scientific_journal-4814	219	8	solar	solar	ADJ
american_scientific_journal-4814	219	9	arrays	array	NOUN
american_scientific_journal-4814	219	10	investigated	investigate	VERB
american_scientific_journal-4814	219	11	in	in	ADP
american_scientific_journal-4814	219	12	works	work	NOUN
american_scientific_journal-4814	219	13	[	[	X
american_scientific_journal-4814	219	14	4	4	NUM
american_scientific_journal-4814	219	15	,	,	PUNCT
american_scientific_journal-4814	219	16	5	5	NUM
american_scientific_journal-4814	219	17	,	,	PUNCT
american_scientific_journal-4814	219	18	8	8	NUM
american_scientific_journal-4814	219	19	]	]	PUNCT
american_scientific_journal-4814	219	20	,	,	PUNCT
american_scientific_journal-4814	219	21	is	be	AUX
american_scientific_journal-4814	219	22	used	use	VERB
american_scientific_journal-4814	219	23	here	here	ADV
american_scientific_journal-4814	219	24	.	.	PUNCT
american_scientific_journal-4814	220	1	consequently	consequently	ADV
american_scientific_journal-4814	220	2	,	,	PUNCT
american_scientific_journal-4814	220	3	for	for	ADP
american_scientific_journal-4814	220	4	each	each	DET
american_scientific_journal-4814	220	5	solar	solar	ADJ
american_scientific_journal-4814	220	6	array	array	NOUN
american_scientific_journal-4814	220	7	(	(	PUNCT
american_scientific_journal-4814	220	8	𝔅𝔅𝑖𝑖	𝔅𝔅𝑖𝑖	PROPN
american_scientific_journal-4814	220	9	)	)	PUNCT
american_scientific_journal-4814	220	10	𝑖𝑖	𝑖𝑖	PUNCT
american_scientific_journal-4814	220	11	=	=	SYM
american_scientific_journal-4814	220	12	1	1	NUM
american_scientific_journal-4814	220	13	,	,	PUNCT
american_scientific_journal-4814	220	14	2	2	NUM
american_scientific_journal-4814	220	15	the	the	DET
american_scientific_journal-4814	220	16	elastic	elastic	ADJ
american_scientific_journal-4814	220	17	displacement	displacement	ADJ
american_scientific_journal-4814	220	18	field	field	NOUN
american_scientific_journal-4814	220	19	𝑑𝑑𝑖𝑖	𝑑𝑑𝑖𝑖	NOUN
american_scientific_journal-4814	220	20	is	be	AUX
american_scientific_journal-4814	220	21	:	:	PUNCT
american_scientific_journal-4814	220	22	on	on	ADP
american_scientific_journal-4814	220	23	(	(	PUNCT
american_scientific_journal-4814	220	24	𝑆𝑆𝑆𝑆𝑖𝑖	𝑆𝑆𝑆𝑆𝑖𝑖	PROPN
american_scientific_journal-4814	220	25	)	)	PUNCT
american_scientific_journal-4814	220	26	,	,	PUNCT
american_scientific_journal-4814	220	27	𝑑𝑑𝑖𝑖(𝑀𝑀	𝑑𝑑𝑖𝑖(𝑀𝑀	NOUN
american_scientific_journal-4814	220	28	,	,	PUNCT
american_scientific_journal-4814	220	29	𝑡𝑡	𝑡𝑡	PROPN
american_scientific_journal-4814	220	30	)	)	PUNCT
american_scientific_journal-4814	220	31	=	=	SYM
american_scientific_journal-4814	220	32	(	(	PUNCT
american_scientific_journal-4814	220	33	𝑢𝑢𝑖𝑖(𝑠𝑠	𝑢𝑢𝑖𝑖(𝑠𝑠	NOUN
american_scientific_journal-4814	220	34	,	,	PUNCT
american_scientific_journal-4814	220	35	𝑡𝑡	𝑡𝑡	NOUN
american_scientific_journal-4814	220	36	)	)	PUNCT
american_scientific_journal-4814	220	37	,	,	PUNCT
american_scientific_journal-4814	220	38	0,0)𝑇𝑇	0,0)𝑇𝑇	NUM
american_scientific_journal-4814	221	1	𝑠𝑠	𝑠𝑠	ADV
american_scientific_journal-4814	221	2	∈	∈	PROPN
american_scientific_journal-4814	222	1	[	[	X
american_scientific_journal-4814	222	2	0	0	NUM
american_scientific_journal-4814	222	3	;	;	PUNCT
american_scientific_journal-4814	222	4	𝑙𝑙	𝑙𝑙	X
american_scientific_journal-4814	222	5	]	]	PUNCT
american_scientific_journal-4814	222	6	,	,	PUNCT
american_scientific_journal-4814	222	7	on	on	ADP
american_scientific_journal-4814	222	8	(	(	PUNCT
american_scientific_journal-4814	222	9	𝐵𝐵𝐵𝐵𝑖𝑖	𝐵𝐵𝐵𝐵𝑖𝑖	PROPN
american_scientific_journal-4814	222	10	)	)	PUNCT
american_scientific_journal-4814	222	11	,	,	PUNCT
american_scientific_journal-4814	222	12	𝑑𝑑𝑖𝑖(𝑀𝑀	𝑑𝑑𝑖𝑖(𝑀𝑀	NOUN
american_scientific_journal-4814	222	13	,	,	PUNCT
american_scientific_journal-4814	222	14	𝑡𝑡	𝑡𝑡	PROPN
american_scientific_journal-4814	222	15	)	)	PUNCT
american_scientific_journal-4814	222	16	=	=	SYM
american_scientific_journal-4814	222	17	(	(	PUNCT
american_scientific_journal-4814	222	18	𝛼𝛼𝑖𝑖(𝑥𝑥	𝛼𝛼𝑖𝑖(𝑥𝑥	PROPN
american_scientific_journal-4814	222	19	,	,	PUNCT
american_scientific_journal-4814	222	20	𝑠𝑠	𝑠𝑠	ADP
american_scientific_journal-4814	222	21	,	,	PUNCT
american_scientific_journal-4814	222	22	𝑡𝑡	𝑡𝑡	ADJ
american_scientific_journal-4814	222	23	)	)	PUNCT
american_scientific_journal-4814	222	24	,	,	PUNCT
american_scientific_journal-4814	222	25	0,0)𝑇𝑇	0,0)𝑇𝑇	NUM
american_scientific_journal-4814	222	26	(	(	PUNCT
american_scientific_journal-4814	222	27	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-4814	222	28	,	,	PUNCT
american_scientific_journal-4814	222	29	𝑠𝑠	𝑠𝑠	PRON
american_scientific_journal-4814	222	30	)	)	PUNCT
american_scientific_journal-4814	222	31	∈	∈	NOUN
american_scientific_journal-4814	222	32	𝑅𝑅.	𝑅𝑅.	NOUN
american_scientific_journal-4814	222	33	since	since	SCONJ
american_scientific_journal-4814	222	34	the	the	DET
american_scientific_journal-4814	222	35	solar	solar	ADJ
american_scientific_journal-4814	222	36	arrays	array	NOUN
american_scientific_journal-4814	222	37	are	be	AUX
american_scientific_journal-4814	222	38	inextensible	inextensible	ADJ
american_scientific_journal-4814	222	39	,	,	PUNCT
american_scientific_journal-4814	222	40	the	the	DET
american_scientific_journal-4814	222	41	longitudinal	longitudinal	ADJ
american_scientific_journal-4814	222	42	displacement	displacement	ADJ
american_scientific_journal-4814	222	43	𝑣𝑣𝑖𝑖(𝑠𝑠	𝑣𝑣𝑖𝑖(𝑠𝑠	NOUN
american_scientific_journal-4814	222	44	,	,	PUNCT
american_scientific_journal-4814	222	45	𝑡𝑡	𝑡𝑡	ADJ
american_scientific_journal-4814	222	46	)	)	PUNCT
american_scientific_journal-4814	222	47	and	and	CCONJ
american_scientific_journal-4814	222	48	𝛽𝛽𝑖𝑖(𝑥𝑥	𝛽𝛽𝑖𝑖(𝑥𝑥	PROPN
american_scientific_journal-4814	222	49	,	,	PUNCT
american_scientific_journal-4814	222	50	𝑠𝑠	𝑠𝑠	ADV
american_scientific_journal-4814	222	51	,	,	PUNCT
american_scientific_journal-4814	222	52	𝑡𝑡	𝑡𝑡	ADJ
american_scientific_journal-4814	222	53	)	)	PUNCT
american_scientific_journal-4814	222	54	is	be	AUX
american_scientific_journal-4814	222	55	of	of	ADP
american_scientific_journal-4814	222	56	second	second	ADJ
american_scientific_journal-4814	222	57	order	order	NOUN
american_scientific_journal-4814	222	58	and	and	CCONJ
american_scientific_journal-4814	222	59	neglected	neglect	VERB
american_scientific_journal-4814	222	60	in	in	ADP
american_scientific_journal-4814	222	61	the	the	DET
american_scientific_journal-4814	222	62	linear	linear	ADJ
american_scientific_journal-4814	222	63	theory	theory	NOUN
american_scientific_journal-4814	222	64	[	[	X
american_scientific_journal-4814	222	65	2	2	NUM
american_scientific_journal-4814	222	66	,	,	PUNCT
american_scientific_journal-4814	222	67	3	3	NUM
american_scientific_journal-4814	222	68	,	,	PUNCT
american_scientific_journal-4814	222	69	4	4	NUM
american_scientific_journal-4814	222	70	]	]	NOUN
american_scientific_journal-4814	222	71	:	:	PUNCT
american_scientific_journal-4814	222	72	𝑣𝑣𝑖𝑖(𝑠𝑠	𝑣𝑣𝑖𝑖(𝑠𝑠	NOUN
american_scientific_journal-4814	222	73	,	,	PUNCT
american_scientific_journal-4814	222	74	𝑡𝑡	𝑡𝑡	ADJ
american_scientific_journal-4814	222	75	)	)	PUNCT
american_scientific_journal-4814	222	76	=	=	PUNCT
american_scientific_journal-4814	223	1	−	−	PROPN
american_scientific_journal-4814	223	2	1	1	NUM
american_scientific_journal-4814	223	3	2	2	NUM
american_scientific_journal-4814	223	4	�	�	PROPN
american_scientific_journal-4814	223	5	�	�	PROPN
american_scientific_journal-4814	223	6	�	�	PROPN
american_scientific_journal-4814	223	7	𝜕𝜕𝑢𝑢𝑖𝑖	𝜕𝜕𝑢𝑢𝑖𝑖	PROPN
american_scientific_journal-4814	223	8	𝜕𝜕𝜕𝜕	𝜕𝜕𝜕𝜕	PROPN
american_scientific_journal-4814	223	9	�	�	PROPN
american_scientific_journal-4814	223	10	2	2	NUM
american_scientific_journal-4814	223	11	�	�	PROPN
american_scientific_journal-4814	223	12	𝑑𝑑𝜕𝜕	𝑑𝑑𝜕𝜕	VERB
american_scientific_journal-4814	223	13	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-4814	223	14	0	0	NUM
american_scientific_journal-4814	223	15	;	;	PUNCT
american_scientific_journal-4814	223	16	𝛽𝛽𝑖𝑖(𝑥𝑥	𝛽𝛽𝑖𝑖(𝑥𝑥	NOUN
american_scientific_journal-4814	223	17	,	,	PUNCT
american_scientific_journal-4814	223	18	𝑠𝑠	𝑠𝑠	ADV
american_scientific_journal-4814	223	19	,	,	PUNCT
american_scientific_journal-4814	223	20	𝑡𝑡	𝑡𝑡	ADJ
american_scientific_journal-4814	223	21	)	)	PUNCT
american_scientific_journal-4814	223	22	=	=	PUNCT
american_scientific_journal-4814	224	1	−	−	PROPN
american_scientific_journal-4814	224	2	1	1	NUM
american_scientific_journal-4814	224	3	2	2	NUM
american_scientific_journal-4814	224	4	�	�	PROPN
american_scientific_journal-4814	224	5	�	�	PROPN
american_scientific_journal-4814	224	6	�	�	PROPN
american_scientific_journal-4814	224	7	𝜕𝜕𝛼𝛼𝑖𝑖	𝜕𝜕𝛼𝛼𝑖𝑖	PROPN
american_scientific_journal-4814	224	8	𝜕𝜕𝜕𝜕	𝜕𝜕𝜕𝜕	PROPN
american_scientific_journal-4814	224	9	�	�	PROPN
american_scientific_journal-4814	224	10	2	2	NUM
american_scientific_journal-4814	224	11	�	�	PROPN
american_scientific_journal-4814	224	12	𝑑𝑑𝜕𝜕	𝑑𝑑𝜕𝜕	VERB
american_scientific_journal-4814	224	13	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-4814	224	14	0	0	NUM
american_scientific_journal-4814	224	15	.	.	PUNCT
american_scientific_journal-4814	225	1	american	american	PROPN
american_scientific_journal-4814	225	2	scientific	scientific	PROPN
american_scientific_journal-4814	225	3	research	research	PROPN
american_scientific_journal-4814	225	4	journal	journal	NOUN
american_scientific_journal-4814	225	5	for	for	ADP
american_scientific_journal-4814	225	6	engineering	engineering	NOUN
american_scientific_journal-4814	225	7	,	,	PUNCT
american_scientific_journal-4814	225	8	technology	technology	NOUN
american_scientific_journal-4814	225	9	,	,	PUNCT
american_scientific_journal-4814	225	10	and	and	CCONJ
american_scientific_journal-4814	225	11	sciences	science	NOUN
american_scientific_journal-4814	225	12	(	(	PUNCT
american_scientific_journal-4814	225	13	asrjets	asrjet	NOUN
american_scientific_journal-4814	225	14	)	)	PUNCT
american_scientific_journal-4814	225	15	(	(	PUNCT
american_scientific_journal-4814	225	16	2019	2019	NUM
american_scientific_journal-4814	225	17	)	)	PUNCT
american_scientific_journal-4814	225	18	volume	volume	NOUN
american_scientific_journal-4814	225	19	55	55	NUM
american_scientific_journal-4814	225	20	,	,	PUNCT
american_scientific_journal-4814	225	21	no	no	DET
american_scientific_journal-4814	225	22	1	1	NUM
american_scientific_journal-4814	225	23	,	,	PUNCT
american_scientific_journal-4814	225	24	pp	pp	ADP
american_scientific_journal-4814	225	25	50	50	NUM
american_scientific_journal-4814	225	26	-	-	SYM
american_scientific_journal-4814	225	27	68	68	NUM
american_scientific_journal-4814	225	28	64	64	NUM
american_scientific_journal-4814	225	29	figure	figure	NOUN
american_scientific_journal-4814	225	30	4	4	NUM
american_scientific_journal-4814	225	31	:	:	PUNCT
american_scientific_journal-4814	225	32	bending	bend	VERB
american_scientific_journal-4814	225	33	in	in	ADP
american_scientific_journal-4814	225	34	plane	plane	NOUN
american_scientific_journal-4814	225	35	𝛼𝛼𝑖𝑖	𝛼𝛼𝑖𝑖	NOUN
american_scientific_journal-4814	225	36	,	,	PUNCT
american_scientific_journal-4814	225	37	𝑢𝑢𝑖𝑖	𝑢𝑢𝑖𝑖	NOUN
american_scientific_journal-4814	225	38	of	of	ADP
american_scientific_journal-4814	225	39	the	the	DET
american_scientific_journal-4814	225	40	solar	solar	ADJ
american_scientific_journal-4814	225	41	arrays	array	NOUN
american_scientific_journal-4814	225	42	and	and	CCONJ
american_scientific_journal-4814	225	43	lace	lace	NOUN
american_scientific_journal-4814	225	44	attitude	attitude	NOUN
american_scientific_journal-4814	225	45	motion	motion	NOUN
american_scientific_journal-4814	225	46	of	of	ADP
american_scientific_journal-4814	225	47	the	the	DET
american_scientific_journal-4814	225	48	space	space	NOUN
american_scientific_journal-4814	225	49	vehicle	vehicle	NOUN
american_scientific_journal-4814	225	50	.	.	PUNCT
american_scientific_journal-4814	226	1	•	•	NUM
american_scientific_journal-4814	226	2	appendix	appendix	VERB
american_scientific_journal-4814	226	3	2	2	NUM
american_scientific_journal-4814	226	4	the	the	DET
american_scientific_journal-4814	226	5	following	follow	VERB
american_scientific_journal-4814	226	6	variational	variational	ADJ
american_scientific_journal-4814	226	7	principle	principle	NOUN
american_scientific_journal-4814	226	8	of	of	ADP
american_scientific_journal-4814	226	9	hamilton	hamilton	PROPN
american_scientific_journal-4814	226	10	is	be	AUX
american_scientific_journal-4814	226	11	used	use	VERB
american_scientific_journal-4814	226	12	to	to	PART
american_scientific_journal-4814	226	13	establish	establish	VERB
american_scientific_journal-4814	226	14	the	the	DET
american_scientific_journal-4814	226	15	motion	motion	NOUN
american_scientific_journal-4814	226	16	equations	equation	NOUN
american_scientific_journal-4814	226	17	[	[	X
american_scientific_journal-4814	226	18	4	4	NUM
american_scientific_journal-4814	226	19	,	,	PUNCT
american_scientific_journal-4814	226	20	5	5	NUM
american_scientific_journal-4814	226	21	,	,	PUNCT
american_scientific_journal-4814	226	22	7	7	NUM
american_scientific_journal-4814	226	23	,	,	PUNCT
american_scientific_journal-4814	226	24	8	8	NUM
american_scientific_journal-4814	226	25	,	,	PUNCT
american_scientific_journal-4814	226	26	13	13	NUM
american_scientific_journal-4814	226	27	]	]	PUNCT
american_scientific_journal-4814	226	28	.	.	PUNCT
american_scientific_journal-4814	227	1	𝛿𝛿	𝛿𝛿	PROPN
american_scientific_journal-4814	227	2	�	�	PROPN
american_scientific_journal-4814	227	3	(	(	PUNCT
american_scientific_journal-4814	227	4	𝐾𝐾	𝐾𝐾	PROPN
american_scientific_journal-4814	227	5	−	−	PROPN
american_scientific_journal-4814	227	6	𝑉𝑉)𝑑𝑑𝑡𝑡	𝑉𝑉)𝑑𝑑𝑡𝑡	NUM
american_scientific_journal-4814	227	7	𝑗𝑗2	𝑗𝑗2	NOUN
american_scientific_journal-4814	227	8	𝑗𝑗1	𝑗𝑗1	NOUN
american_scientific_journal-4814	227	9	=	=	SYM
american_scientific_journal-4814	227	10	0	0	PROPN
american_scientific_journal-4814	227	11	,	,	PUNCT
american_scientific_journal-4814	227	12	where	where	SCONJ
american_scientific_journal-4814	227	13	𝐾𝐾	𝐾𝐾	NOUN
american_scientific_journal-4814	227	14	and	and	CCONJ
american_scientific_journal-4814	227	15	𝑉𝑉	𝑉𝑉	PROPN
american_scientific_journal-4814	227	16	are	be	AUX
american_scientific_journal-4814	227	17	,	,	PUNCT
american_scientific_journal-4814	227	18	respectively	respectively	ADV
american_scientific_journal-4814	227	19	,	,	PUNCT
american_scientific_journal-4814	227	20	the	the	DET
american_scientific_journal-4814	227	21	kinetic	kinetic	NOUN
american_scientific_journal-4814	227	22	and	and	CCONJ
american_scientific_journal-4814	227	23	the	the	DET
american_scientific_journal-4814	227	24	total	total	ADJ
american_scientific_journal-4814	227	25	potential	potential	ADJ
american_scientific_journal-4814	227	26	energy	energy	NOUN
american_scientific_journal-4814	227	27	(	(	PUNCT
american_scientific_journal-4814	227	28	including	include	VERB
american_scientific_journal-4814	227	29	gravitational	gravitational	ADJ
american_scientific_journal-4814	227	30	potential	potential	ADJ
american_scientific_journal-4814	227	31	energy	energy	NOUN
american_scientific_journal-4814	227	32	and	and	CCONJ
american_scientific_journal-4814	227	33	the	the	DET
american_scientific_journal-4814	227	34	work	work	NOUN
american_scientific_journal-4814	227	35	of	of	ADP
american_scientific_journal-4814	227	36	external	external	ADJ
american_scientific_journal-4814	227	37	torques	torque	NOUN
american_scientific_journal-4814	227	38	)	)	PUNCT
american_scientific_journal-4814	227	39	of	of	ADP
american_scientific_journal-4814	227	40	the	the	DET
american_scientific_journal-4814	227	41	space	space	NOUN
american_scientific_journal-4814	227	42	vehicle	vehicle	NOUN
american_scientific_journal-4814	227	43	.	.	PUNCT
american_scientific_journal-4814	228	1	𝑉𝑉	𝑉𝑉	NOUN
american_scientific_journal-4814	228	2	=	=	SYM
american_scientific_journal-4814	229	1	𝑛𝑛02	𝑛𝑛02	PROPN
american_scientific_journal-4814	229	2	2	2	NUM
american_scientific_journal-4814	230	1	[	[	X
american_scientific_journal-4814	230	2	3(𝐴𝐴	3(𝐴𝐴	NUM
american_scientific_journal-4814	230	3	−	−	NUM
american_scientific_journal-4814	230	4	𝐵𝐵)𝜃𝜃2	𝐵𝐵)𝜃𝜃2	PROPN
american_scientific_journal-4814	230	5	+	+	CCONJ
american_scientific_journal-4814	230	6	6𝑁𝑁𝑢𝑢∗𝜃𝜃	6𝑁𝑁𝑢𝑢∗𝜃𝜃	NUM
american_scientific_journal-4814	230	7	]	]	X
american_scientific_journal-4814	230	8	+	+	CCONJ
american_scientific_journal-4814	230	9	𝛱𝛱	𝛱𝛱	PROPN
american_scientific_journal-4814	230	10	�	�	PROPN
american_scientific_journal-4814	230	11	𝐷𝐷	𝐷𝐷	PROPN
american_scientific_journal-4814	230	12	+	+	CCONJ
american_scientific_journal-4814	230	13	υ𝜃𝜃	υ𝜃𝜃	PROPN
american_scientific_journal-4814	230	14	,	,	PUNCT
american_scientific_journal-4814	230	15	𝛱𝛱	𝛱𝛱	PROPN
american_scientific_journal-4814	230	16	�	�	PROPN
american_scientific_journal-4814	230	17	𝐷𝐷	𝐷𝐷	PROPN
american_scientific_journal-4814	230	18	=	=	PUNCT
american_scientific_journal-4814	230	19	�	�	PROPN
american_scientific_journal-4814	230	20	�	�	PROPN
american_scientific_journal-4814	230	21	𝐸𝐸𝐸𝐸	𝐸𝐸𝐸𝐸	PROPN
american_scientific_journal-4814	230	22	2	2	NUM
american_scientific_journal-4814	230	23	�	�	PROPN
american_scientific_journal-4814	230	24	𝜕𝜕𝑢𝑢𝑖𝑖	𝜕𝜕𝑢𝑢𝑖𝑖	PROPN
american_scientific_journal-4814	230	25	𝜕𝜕𝑠𝑠	𝜕𝜕𝑠𝑠	PROPN
american_scientific_journal-4814	230	26	�	�	PROPN
american_scientific_journal-4814	230	27	2	2	NUM
american_scientific_journal-4814	230	28	−	−	PROPN
american_scientific_journal-4814	230	29	𝑆𝑆	𝑆𝑆	PROPN
american_scientific_journal-4814	230	30	�	�	PROPN
american_scientific_journal-4814	230	31	2	2	NUM
american_scientific_journal-4814	230	32	�	�	PROPN
american_scientific_journal-4814	230	33	𝜕𝜕𝑢𝑢𝑖𝑖	𝜕𝜕𝑢𝑢𝑖𝑖	PROPN
american_scientific_journal-4814	230	34	𝜕𝜕𝑠𝑠	𝜕𝜕𝑠𝑠	PROPN
american_scientific_journal-4814	230	35	�	�	PROPN
american_scientific_journal-4814	230	36	2	2	NUM
american_scientific_journal-4814	230	37	𝑑𝑑𝑠𝑠	𝑑𝑑𝑠𝑠	NOUN
american_scientific_journal-4814	230	38	𝑙𝑙	𝑙𝑙	VERB
american_scientific_journal-4814	230	39	0	0	NUM
american_scientific_journal-4814	230	40	2	2	NUM
american_scientific_journal-4814	230	41	𝑖𝑖=1	𝑖𝑖=1	PUNCT
american_scientific_journal-4814	230	42	+	+	SYM
american_scientific_journal-4814	230	43	�	�	PROPN
american_scientific_journal-4814	230	44	�	�	PROPN
american_scientific_journal-4814	230	45	γ	γ	PROPN
american_scientific_journal-4814	230	46	2	2	NUM
american_scientific_journal-4814	230	47	�	�	PROPN
american_scientific_journal-4814	230	48	�	�	PROPN
american_scientific_journal-4814	230	49	𝜕𝜕𝛼𝛼𝑖𝑖	𝜕𝜕𝛼𝛼𝑖𝑖	PROPN
american_scientific_journal-4814	230	50	𝜕𝜕𝑥𝑥	𝜕𝜕𝑥𝑥	PROPN
american_scientific_journal-4814	230	51	�	�	PROPN
american_scientific_journal-4814	230	52	2	2	NUM
american_scientific_journal-4814	230	53	+	+	CCONJ
american_scientific_journal-4814	230	54	1	1	NUM
american_scientific_journal-4814	230	55	2	2	NUM
american_scientific_journal-4814	230	56	�	�	NOUN
american_scientific_journal-4814	230	57	𝐺𝐺	𝐺𝐺	NOUN
american_scientific_journal-4814	230	58	�	�	PROPN
american_scientific_journal-4814	230	59	+	+	CCONJ
american_scientific_journal-4814	230	60	𝑇𝑇	𝑇𝑇	PROPN
american_scientific_journal-4814	230	61	�	�	PROPN
american_scientific_journal-4814	230	62	(𝑠𝑠	(𝑠𝑠	NOUN
american_scientific_journal-4814	230	63	)	)	PUNCT
american_scientific_journal-4814	230	64	�	�	PROPN
american_scientific_journal-4814	230	65	�	�	PROPN
american_scientific_journal-4814	230	66	𝜕𝜕𝛼𝛼𝑖𝑖	𝜕𝜕𝛼𝛼𝑖𝑖	PROPN
american_scientific_journal-4814	230	67	𝜕𝜕𝑠𝑠	𝜕𝜕𝑠𝑠	PROPN
american_scientific_journal-4814	230	68	�	�	PROPN
american_scientific_journal-4814	230	69	2	2	NUM
american_scientific_journal-4814	230	70	�	�	PROPN
american_scientific_journal-4814	230	71	𝑑𝑑𝑥𝑥𝑑𝑑𝑠𝑠	𝑑𝑑𝑥𝑥𝑑𝑑𝑠𝑠	VERB
american_scientific_journal-4814	230	72	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-4814	230	73	2	2	NUM
american_scientific_journal-4814	230	74	𝑖𝑖=1	𝑖𝑖=1	NOUN
american_scientific_journal-4814	230	75	,	,	PUNCT
american_scientific_journal-4814	230	76	𝐾𝐾	𝐾𝐾	NOUN
american_scientific_journal-4814	230	77	=	=	NOUN
american_scientific_journal-4814	230	78	1	1	NUM
american_scientific_journal-4814	230	79	2	2	NUM
american_scientific_journal-4814	230	80	�	�	PROPN
american_scientific_journal-4814	230	81	𝑉𝑉	𝑉𝑉	PROPN
american_scientific_journal-4814	230	82	�	�	NOUN
american_scientific_journal-4814	230	83	⃗	⃗	PROPN
american_scientific_journal-4814	230	84	(	(	PUNCT
american_scientific_journal-4814	230	85	𝐺𝐺/ℜ𝑇𝑇	𝐺𝐺/ℜ𝑇𝑇	NOUN
american_scientific_journal-4814	230	86	)	)	PUNCT
american_scientific_journal-4814	230	87	�	�	PROPN
american_scientific_journal-4814	230	88	2	2	NUM
american_scientific_journal-4814	230	89	+	+	CCONJ
american_scientific_journal-4814	230	90	𝜔𝜔	𝜔𝜔	PROPN
american_scientific_journal-4814	230	91	�	�	PROPN
american_scientific_journal-4814	230	92	�	�	NOUN
american_scientific_journal-4814	230	93	⃗	⃗	PROPN
american_scientific_journal-4814	230	94	.	.	PUNCT
american_scientific_journal-4814	231	1	𝐽𝐽𝐺𝐺(𝜔𝜔	𝐽𝐽𝐺𝐺(𝜔𝜔	PROPN
american_scientific_journal-4814	231	2	�	�	PROPN
american_scientific_journal-4814	231	3	�	�	NOUN
american_scientific_journal-4814	231	4	⃗	⃗	PROPN
american_scientific_journal-4814	231	5	)	)	PUNCT
american_scientific_journal-4814	232	1	+	+	CCONJ
american_scientific_journal-4814	232	2	�	�	PROPN
american_scientific_journal-4814	232	3	𝐺𝐺𝑆𝑆	𝐺𝐺𝑆𝑆	PROPN
american_scientific_journal-4814	232	4	�	�	PROPN
american_scientific_journal-4814	232	5	�	�	PROPN
american_scientific_journal-4814	232	6	�	�	PROPN
american_scientific_journal-4814	232	7	�	�	PROPN
american_scientific_journal-4814	232	8	�	�	NOUN
american_scientific_journal-4814	232	9	⃗	⃗	PROPN
american_scientific_journal-4814	232	10	2𝑑𝑑𝑚𝑚	2𝑑𝑑𝑚𝑚	NUM
american_scientific_journal-4814	232	11	𝑃𝑃∈(𝔅𝔅	𝑃𝑃∈(𝔅𝔅	NOUN
american_scientific_journal-4814	232	12	)	)	PUNCT
american_scientific_journal-4814	232	13	+	+	CCONJ
american_scientific_journal-4814	232	14	2𝜔𝜔	2𝜔𝜔	PROPN
american_scientific_journal-4814	232	15	�	�	PROPN
american_scientific_journal-4814	232	16	�	�	PROPN
american_scientific_journal-4814	232	17	⃗	⃗	PROPN
american_scientific_journal-4814	232	18	.	.	PUNCT
american_scientific_journal-4814	232	19	�	�	PROPN
american_scientific_journal-4814	232	20	𝐺𝐺𝑆𝑆	𝐺𝐺𝑆𝑆	PROPN
american_scientific_journal-4814	232	21	�	�	PROPN
american_scientific_journal-4814	232	22	�	�	PROPN
american_scientific_journal-4814	232	23	�	�	PROPN
american_scientific_journal-4814	232	24	�	�	PROPN
american_scientific_journal-4814	232	25	�	�	PROPN
american_scientific_journal-4814	232	26	⃗	⃗	PROPN
american_scientific_journal-4814	232	27	∧	∧	PROPN
american_scientific_journal-4814	232	28	𝐺𝐺𝑆𝑆	𝐺𝐺𝑆𝑆	PROPN
american_scientific_journal-4814	232	29	�	�	PROPN
american_scientific_journal-4814	232	30	�	�	PROPN
american_scientific_journal-4814	232	31	�	�	PROPN
american_scientific_journal-4814	232	32	�	�	PROPN
american_scientific_journal-4814	232	33	�	�	PROPN
american_scientific_journal-4814	232	34	̇⃗	̇⃗	PROPN
american_scientific_journal-4814	232	35	𝑑𝑑𝑚𝑚	𝑑𝑑𝑚𝑚	NOUN
american_scientific_journal-4814	232	36	𝑃𝑃∈(𝔅𝔅	𝑃𝑃∈(𝔅𝔅	NOUN
american_scientific_journal-4814	232	37	)	)	PUNCT
american_scientific_journal-4814	232	38	,	,	PUNCT
american_scientific_journal-4814	232	39	�	�	PROPN
american_scientific_journal-4814	232	40	𝑉𝑉	𝑉𝑉	PROPN
american_scientific_journal-4814	232	41	�	�	NOUN
american_scientific_journal-4814	232	42	⃗	⃗	PROPN
american_scientific_journal-4814	232	43	(	(	PUNCT
american_scientific_journal-4814	232	44	𝐺𝐺/ℜ𝑇𝑇	𝐺𝐺/ℜ𝑇𝑇	NOUN
american_scientific_journal-4814	232	45	)	)	PUNCT
american_scientific_journal-4814	232	46	�	�	PROPN
american_scientific_journal-4814	232	47	2	2	NUM
american_scientific_journal-4814	232	48	=	=	SYM
american_scientific_journal-4814	232	49	(	(	PUNCT
american_scientific_journal-4814	232	50	𝑛𝑛0𝑟𝑟0)2	𝑛𝑛0𝑟𝑟0)2	NOUN
american_scientific_journal-4814	232	51	.	.	PUNCT
american_scientific_journal-4814	233	1	𝑛𝑛0	𝑛𝑛0	X
american_scientific_journal-4814	233	2	is	be	AUX
american_scientific_journal-4814	233	3	constant	constant	ADJ
american_scientific_journal-4814	233	4	orbital	orbital	ADJ
american_scientific_journal-4814	233	5	parameter	parameter	NOUN
american_scientific_journal-4814	233	6	.	.	PUNCT
american_scientific_journal-4814	234	1	here	here	ADV
american_scientific_journal-4814	234	2	𝐽𝐽𝐺𝐺	𝐽𝐽𝐺𝐺	PROPN
american_scientific_journal-4814	234	3	designates	designate	VERB
american_scientific_journal-4814	234	4	the	the	DET
american_scientific_journal-4814	234	5	inertia	inertia	NOUN
american_scientific_journal-4814	234	6	tensor	tensor	NOUN
american_scientific_journal-4814	234	7	in	in	ADP
american_scientific_journal-4814	234	8	𝐺𝐺	𝐺𝐺	PROPN
american_scientific_journal-4814	234	9	𝐽𝐽𝐺𝐺	𝐽𝐽𝐺𝐺	PROPN
american_scientific_journal-4814	234	10	=	=	SYM
american_scientific_journal-4814	234	11	�	�	PROPN
american_scientific_journal-4814	234	12	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-4814	234	13	+	+	CCONJ
american_scientific_journal-4814	234	14	𝑁𝑁1	𝑁𝑁1	PROPN
american_scientific_journal-4814	234	15	𝑁𝑁4	𝑁𝑁4	PROPN
american_scientific_journal-4814	234	16	0	0	PUNCT
american_scientific_journal-4814	235	1	𝑁𝑁4	𝑁𝑁4	ADJ
american_scientific_journal-4814	235	2	𝐵𝐵	𝐵𝐵	PROPN
american_scientific_journal-4814	235	3	+	+	CCONJ
american_scientific_journal-4814	235	4	𝑁𝑁2	𝑁𝑁2	PROPN
american_scientific_journal-4814	235	5	0	0	NUM
american_scientific_journal-4814	235	6	0	0	NUM
american_scientific_journal-4814	235	7	0	0	NUM
american_scientific_journal-4814	235	8	𝐶𝐶	𝐶𝐶	PROPN
american_scientific_journal-4814	235	9	+	+	PROPN
american_scientific_journal-4814	235	10	𝑀𝑀3	𝑀𝑀3	PROPN
american_scientific_journal-4814	235	11	�	�	PROPN
american_scientific_journal-4814	235	12	,	,	PUNCT
american_scientific_journal-4814	235	13	𝑡𝑡𝑟𝑟(𝐽𝐽𝐺𝐺	𝑡𝑡𝑟𝑟(𝐽𝐽𝐺𝐺	PROPN
american_scientific_journal-4814	235	14	)	)	PUNCT
american_scientific_journal-4814	235	15	=	=	SYM
american_scientific_journal-4814	235	16	𝐴𝐴	𝐴𝐴	PROPN
american_scientific_journal-4814	235	17	+	+	CCONJ
american_scientific_journal-4814	235	18	𝐵𝐵	𝐵𝐵	PROPN
american_scientific_journal-4814	235	19	+	+	CCONJ
american_scientific_journal-4814	235	20	𝐶𝐶	𝐶𝐶	NOUN
american_scientific_journal-4814	235	21	+	+	CCONJ
american_scientific_journal-4814	235	22	𝑁𝑁1	𝑁𝑁1	PROPN
american_scientific_journal-4814	235	23	+	+	CCONJ
american_scientific_journal-4814	235	24	𝑁𝑁2	𝑁𝑁2	PROPN
american_scientific_journal-4814	235	25	+	+	PROPN
american_scientific_journal-4814	235	26	𝑁𝑁3	𝑁𝑁3	PROPN
american_scientific_journal-4814	235	27	,	,	PUNCT
american_scientific_journal-4814	235	28	american	american	ADJ
american_scientific_journal-4814	235	29	scientific	scientific	ADJ
american_scientific_journal-4814	235	30	research	research	NOUN
american_scientific_journal-4814	235	31	journal	journal	NOUN
american_scientific_journal-4814	235	32	for	for	ADP
american_scientific_journal-4814	235	33	engineering	engineering	NOUN
american_scientific_journal-4814	235	34	,	,	PUNCT
american_scientific_journal-4814	235	35	technology	technology	NOUN
american_scientific_journal-4814	235	36	,	,	PUNCT
american_scientific_journal-4814	235	37	and	and	CCONJ
american_scientific_journal-4814	235	38	sciences	science	NOUN
american_scientific_journal-4814	235	39	(	(	PUNCT
american_scientific_journal-4814	235	40	asrjets	asrjet	NOUN
american_scientific_journal-4814	235	41	)	)	PUNCT
american_scientific_journal-4814	235	42	(	(	PUNCT
american_scientific_journal-4814	235	43	2019	2019	NUM
american_scientific_journal-4814	235	44	)	)	PUNCT
american_scientific_journal-4814	235	45	volume	volume	NOUN
american_scientific_journal-4814	235	46	55	55	NUM
american_scientific_journal-4814	235	47	,	,	PUNCT
american_scientific_journal-4814	235	48	no	no	DET
american_scientific_journal-4814	235	49	1	1	NUM
american_scientific_journal-4814	235	50	,	,	PUNCT
american_scientific_journal-4814	235	51	pp	pp	ADP
american_scientific_journal-4814	235	52	50	50	NUM
american_scientific_journal-4814	235	53	-	-	SYM
american_scientific_journal-4814	235	54	68	68	NUM
american_scientific_journal-4814	235	55	65	65	NUM
american_scientific_journal-4814	235	56	𝑁𝑁1	𝑁𝑁1	PROPN
american_scientific_journal-4814	235	57	=	=	SYM
american_scientific_journal-4814	235	58	�	�	PROPN
american_scientific_journal-4814	235	59	�	�	PROPN
american_scientific_journal-4814	235	60	−	−	PROPN
american_scientific_journal-4814	235	61	�	�	PROPN
american_scientific_journal-4814	235	62	𝑆𝑆	𝑆𝑆	PROPN
american_scientific_journal-4814	235	63	�	�	PROPN
american_scientific_journal-4814	235	64	1(𝑠𝑠	1(𝑠𝑠	NOUN
american_scientific_journal-4814	235	65	)	)	PUNCT
american_scientific_journal-4814	235	66	3𝑛𝑛02	3𝑛𝑛02	PROPN
american_scientific_journal-4814	235	67	�	�	PROPN
american_scientific_journal-4814	235	68	𝑑𝑑𝑢𝑢𝑖𝑖	𝑑𝑑𝑢𝑢𝑖𝑖	PROPN
american_scientific_journal-4814	235	69	𝑑𝑑𝑠𝑠	𝑑𝑑𝑠𝑠	PROPN
american_scientific_journal-4814	235	70	�	�	PROPN
american_scientific_journal-4814	235	71	2	2	NUM
american_scientific_journal-4814	235	72	𝑑𝑑𝑠𝑠	𝑑𝑑𝑠𝑠	NOUN
american_scientific_journal-4814	235	73	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-4814	235	74	0	0	NUM
american_scientific_journal-4814	236	1	−	−	NUM
american_scientific_journal-4814	236	2	�	�	PROPN
american_scientific_journal-4814	236	3	𝑇𝑇	𝑇𝑇	PROPN
american_scientific_journal-4814	236	4	�	�	NOUN
american_scientific_journal-4814	236	5	1(𝑠𝑠	1(𝑠𝑠	NUM
american_scientific_journal-4814	236	6	)	)	PUNCT
american_scientific_journal-4814	236	7	3𝑛𝑛02	3𝑛𝑛02	PROPN
american_scientific_journal-4814	236	8	�	�	PROPN
american_scientific_journal-4814	236	9	𝜕𝜕𝛼𝛼𝑖𝑖	𝜕𝜕𝛼𝛼𝑖𝑖	PROPN
american_scientific_journal-4814	236	10	𝜕𝜕𝑠𝑠	𝜕𝜕𝑠𝑠	PROPN
american_scientific_journal-4814	236	11	�	�	PROPN
american_scientific_journal-4814	236	12	2	2	NUM
american_scientific_journal-4814	236	13	𝑑𝑑𝑥𝑥𝑑𝑑𝑠𝑠	𝑑𝑑𝑥𝑥𝑑𝑑𝑠𝑠	VERB
american_scientific_journal-4814	236	14	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-4814	236	15	�	�	PROPN
american_scientific_journal-4814	236	16	2	2	NUM
american_scientific_journal-4814	236	17	𝑖𝑖=1	𝑖𝑖=1	NOUN
american_scientific_journal-4814	236	18	,	,	PUNCT
american_scientific_journal-4814	236	19	𝑁𝑁2	𝑁𝑁2	PROPN
american_scientific_journal-4814	236	20	=	=	SYM
american_scientific_journal-4814	236	21	�	�	PROPN
american_scientific_journal-4814	236	22	�	�	PROPN
american_scientific_journal-4814	236	23	�	�	PROPN
american_scientific_journal-4814	236	24	𝜌𝜌𝑢𝑢𝑖𝑖2𝑑𝑑𝑠𝑠	𝜌𝜌𝑢𝑢𝑖𝑖2𝑑𝑑𝑠𝑠	PROPN
american_scientific_journal-4814	236	25	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-4814	236	26	0	0	NUM
american_scientific_journal-4814	236	27	+	+	NUM
american_scientific_journal-4814	236	28	�	�	PROPN
american_scientific_journal-4814	236	29	𝜎𝜎[𝛼𝛼𝑖𝑖2	𝜎𝜎[𝛼𝛼𝑖𝑖2	PROPN
american_scientific_journal-4814	236	30	+	+	NUM
american_scientific_journal-4814	236	31	2𝑥𝑥𝛼𝛼𝑖𝑖]𝑑𝑑𝑠𝑠𝑑𝑑𝑥𝑥	2𝑥𝑥𝛼𝛼𝑖𝑖]𝑑𝑑𝑠𝑠𝑑𝑑𝑥𝑥	PROPN
american_scientific_journal-4814	236	32	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-4814	236	33	+	+	CCONJ
american_scientific_journal-4814	236	34	𝑚𝑚	𝑚𝑚	PROPN
american_scientific_journal-4814	236	35	�	�	PROPN
american_scientific_journal-4814	236	36	𝑢𝑢𝑖𝑖2(𝑙𝑙	𝑢𝑢𝑖𝑖2(𝑙𝑙	PROPN
american_scientific_journal-4814	236	37	)	)	PUNCT
american_scientific_journal-4814	236	38	�	�	PROPN
american_scientific_journal-4814	236	39	2	2	NUM
american_scientific_journal-4814	236	40	𝑖𝑖=1	𝑖𝑖=1	NOUN
american_scientific_journal-4814	236	41	−	−	NOUN
american_scientific_journal-4814	236	42	𝑚𝑚∑𝑋𝑋𝐺𝐺2	𝑚𝑚∑𝑋𝑋𝐺𝐺2	PROPN
american_scientific_journal-4814	236	43	,	,	PUNCT
american_scientific_journal-4814	236	44	𝑁𝑁3	𝑁𝑁3	PROPN
american_scientific_journal-4814	236	45	=	=	SYM
american_scientific_journal-4814	236	46	�	�	PROPN
american_scientific_journal-4814	236	47	�	�	PROPN
american_scientific_journal-4814	236	48	�	�	PROPN
american_scientific_journal-4814	236	49	𝜌𝜌𝑢𝑢𝑖𝑖2𝑑𝑑𝑠𝑠	𝜌𝜌𝑢𝑢𝑖𝑖2𝑑𝑑𝑠𝑠	PROPN
american_scientific_journal-4814	236	50	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-4814	236	51	0	0	NUM
american_scientific_journal-4814	236	52	+	+	NUM
american_scientific_journal-4814	236	53	�	�	PROPN
american_scientific_journal-4814	236	54	𝜎𝜎[𝛼𝛼𝑖𝑖2	𝜎𝜎[𝛼𝛼𝑖𝑖2	PROPN
american_scientific_journal-4814	236	55	+	+	NUM
american_scientific_journal-4814	236	56	2𝑥𝑥𝛼𝛼𝑖𝑖]𝑑𝑑𝑠𝑠𝑑𝑑𝑥𝑥	2𝑥𝑥𝛼𝛼𝑖𝑖]𝑑𝑑𝑠𝑠𝑑𝑑𝑥𝑥	PROPN
american_scientific_journal-4814	236	57	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-4814	236	58	−	−	PROPN
american_scientific_journal-4814	236	59	�	�	PROPN
american_scientific_journal-4814	236	60	𝑆𝑆	𝑆𝑆	PROPN
american_scientific_journal-4814	236	61	�	�	PROPN
american_scientific_journal-4814	236	62	1(𝑠𝑠	1(𝑠𝑠	NOUN
american_scientific_journal-4814	236	63	)	)	PUNCT
american_scientific_journal-4814	236	64	3𝑛𝑛02	3𝑛𝑛02	PROPN
american_scientific_journal-4814	236	65	�	�	PROPN
american_scientific_journal-4814	236	66	𝑑𝑑𝑢𝑢𝑖𝑖	𝑑𝑑𝑢𝑢𝑖𝑖	PROPN
american_scientific_journal-4814	236	67	𝑑𝑑𝑠𝑠	𝑑𝑑𝑠𝑠	PROPN
american_scientific_journal-4814	236	68	�	�	PROPN
american_scientific_journal-4814	236	69	2	2	NUM
american_scientific_journal-4814	236	70	𝑑𝑑𝑠𝑠	𝑑𝑑𝑠𝑠	NOUN
american_scientific_journal-4814	236	71	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-4814	236	72	0	0	NUM
american_scientific_journal-4814	237	1	−	−	NUM
american_scientific_journal-4814	237	2	�	�	PROPN
american_scientific_journal-4814	237	3	𝑇𝑇	𝑇𝑇	PROPN
american_scientific_journal-4814	237	4	�	�	NOUN
american_scientific_journal-4814	237	5	1(𝑠𝑠	1(𝑠𝑠	NUM
american_scientific_journal-4814	237	6	)	)	PUNCT
american_scientific_journal-4814	237	7	3𝑛𝑛02	3𝑛𝑛02	PROPN
american_scientific_journal-4814	237	8	�	�	PROPN
american_scientific_journal-4814	237	9	𝜕𝜕𝛼𝛼𝑖𝑖	𝜕𝜕𝛼𝛼𝑖𝑖	PROPN
american_scientific_journal-4814	237	10	𝜕𝜕𝑠𝑠	𝜕𝜕𝑠𝑠	PROPN
american_scientific_journal-4814	237	11	�	�	PROPN
american_scientific_journal-4814	237	12	2	2	NUM
american_scientific_journal-4814	237	13	𝑑𝑑𝑥𝑥𝑑𝑑𝑠𝑠	𝑑𝑑𝑥𝑥𝑑𝑑𝑠𝑠	VERB
american_scientific_journal-4814	237	14	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-4814	237	15	+	+	CCONJ
american_scientific_journal-4814	237	16	𝑚𝑚	𝑚𝑚	PROPN
american_scientific_journal-4814	237	17	�	�	PROPN
american_scientific_journal-4814	237	18	𝑢𝑢𝑖𝑖2(𝑙𝑙	𝑢𝑢𝑖𝑖2(𝑙𝑙	PROPN
american_scientific_journal-4814	237	19	)	)	PUNCT
american_scientific_journal-4814	237	20	�	�	PROPN
american_scientific_journal-4814	237	21	2	2	NUM
american_scientific_journal-4814	237	22	𝑖𝑖=1	𝑖𝑖=1	NOUN
american_scientific_journal-4814	237	23	−	−	NOUN
american_scientific_journal-4814	237	24	𝑚𝑚∑𝑋𝑋𝐺𝐺2	𝑚𝑚∑𝑋𝑋𝐺𝐺2	NOUN
american_scientific_journal-4814	237	25	,	,	PUNCT
american_scientific_journal-4814	237	26	𝑁𝑁4	𝑁𝑁4	PROPN
american_scientific_journal-4814	237	27	=	=	PUNCT
american_scientific_journal-4814	237	28	∑	∑	PUNCT
american_scientific_journal-4814	237	29	(	(	PUNCT
american_scientific_journal-4814	237	30	−1)𝑖𝑖	−1)𝑖𝑖	PROPN
american_scientific_journal-4814	237	31	�	�	NOUN
american_scientific_journal-4814	237	32	∬	∬	NOUN
american_scientific_journal-4814	237	33	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-4814	237	34	𝑃𝑃1(𝑠𝑠	𝑃𝑃1(𝑠𝑠	NOUN
american_scientific_journal-4814	237	35	)	)	PUNCT
american_scientific_journal-4814	237	36	3𝑛𝑛0	3𝑛𝑛0	NUM
american_scientific_journal-4814	237	37	2	2	NUM
american_scientific_journal-4814	237	38	�	�	PROPN
american_scientific_journal-4814	237	39	𝜕𝜕𝛼𝛼𝑖𝑖	𝜕𝜕𝛼𝛼𝑖𝑖	PROPN
american_scientific_journal-4814	237	40	𝜕𝜕𝑠𝑠	𝜕𝜕𝑠𝑠	PROPN
american_scientific_journal-4814	237	41	�	�	PROPN
american_scientific_journal-4814	237	42	2	2	NUM
american_scientific_journal-4814	237	43	𝑑𝑑𝑥𝑥𝑑𝑑𝑠𝑠	𝑑𝑑𝑥𝑥𝑑𝑑𝑠𝑠	VERB
american_scientific_journal-4814	237	44	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-4814	237	45	+	+	CCONJ
american_scientific_journal-4814	237	46	∫	∫	PROPN
american_scientific_journal-4814	237	47	𝜌𝜌(𝑏𝑏	𝜌𝜌(𝑏𝑏	PROPN
american_scientific_journal-4814	237	48	+	+	CCONJ
american_scientific_journal-4814	237	49	𝑠𝑠)𝑢𝑢𝑖𝑖𝑑𝑑𝑠𝑠	𝑠𝑠)𝑢𝑢𝑖𝑖𝑑𝑑𝑠𝑠	NOUN
american_scientific_journal-4814	237	50	𝑙𝑙	𝑙𝑙	VERB
american_scientific_journal-4814	237	51	0	0	NUM
american_scientific_journal-4814	237	52	+	+	CCONJ
american_scientific_journal-4814	237	53	∬	∬	ADJ
american_scientific_journal-4814	237	54	𝜎𝜎(𝑏𝑏	𝜎𝜎(𝑏𝑏	PROPN
american_scientific_journal-4814	237	55	+	+	NUM
american_scientific_journal-4814	237	56	𝑠𝑠)𝛼𝛼𝑖𝑖𝑑𝑑𝑠𝑠𝑑𝑑𝑥𝑥	𝑠𝑠)𝛼𝛼𝑖𝑖𝑑𝑑𝑠𝑠𝑑𝑑𝑥𝑥	NOUN
american_scientific_journal-4814	237	57	𝑅𝑅	𝑅𝑅	NOUN
american_scientific_journal-4814	237	58	+	+	CCONJ
american_scientific_journal-4814	237	59	𝑚𝑚	𝑚𝑚	PROPN
american_scientific_journal-4814	237	60	�	�	PROPN
american_scientific_journal-4814	237	61	(𝑏𝑏	(𝑏𝑏	SYM
american_scientific_journal-4814	237	62	+	+	ADJ
american_scientific_journal-4814	237	63	𝑠𝑠)𝑢𝑢𝑖𝑖(𝑙𝑙)	𝑠𝑠)𝑢𝑢𝑖𝑖(𝑙𝑙)	NOUN
american_scientific_journal-4814	237	64	�	�	NOUN
american_scientific_journal-4814	237	65	2	2	NUM
american_scientific_journal-4814	237	66	𝑖𝑖=1	𝑖𝑖=1	NUM
american_scientific_journal-4814	237	67	.	.	PUNCT
american_scientific_journal-4814	238	1	here	here	ADV
american_scientific_journal-4814	238	2	:	:	PUNCT
american_scientific_journal-4814	238	3	𝑆𝑆	𝑆𝑆	PROPN
american_scientific_journal-4814	238	4	�	�	PROPN
american_scientific_journal-4814	238	5	1(𝑠𝑠	1(𝑠𝑠	NUM
american_scientific_journal-4814	238	6	)	)	PUNCT
american_scientific_journal-4814	239	1	=	=	SYM
american_scientific_journal-4814	239	2	3𝜌𝜌	3𝜌𝜌	NOUN
american_scientific_journal-4814	239	3	𝑛𝑛02	𝑛𝑛02	PROPN
american_scientific_journal-4814	239	4	2	2	NUM
american_scientific_journal-4814	240	1	[	[	X
american_scientific_journal-4814	240	2	(	(	PUNCT
american_scientific_journal-4814	240	3	𝑏𝑏	𝑏𝑏	NOUN
american_scientific_journal-4814	240	4	+	+	NUM
american_scientific_journal-4814	240	5	𝑙𝑙)2	𝑙𝑙)2	PROPN
american_scientific_journal-4814	240	6	−	−	PROPN
american_scientific_journal-4814	240	7	(	(	PUNCT
american_scientific_journal-4814	240	8	𝑏𝑏	𝑏𝑏	NOUN
american_scientific_journal-4814	240	9	+	+	CCONJ
american_scientific_journal-4814	240	10	𝑠𝑠)2	𝑠𝑠)2	PROPN
american_scientific_journal-4814	240	11	]	]	PUNCT
american_scientific_journal-4814	240	12	,	,	PUNCT
american_scientific_journal-4814	240	13	𝑆𝑆1(𝑠𝑠	𝑆𝑆1(𝑠𝑠	NUM
american_scientific_journal-4814	240	14	)	)	PUNCT
american_scientific_journal-4814	240	15	=	=	SYM
american_scientific_journal-4814	240	16	𝑛𝑛02	𝑛𝑛02	PROPN
american_scientific_journal-4814	240	17	2	2	NUM
american_scientific_journal-4814	240	18	�	�	NOUN
american_scientific_journal-4814	240	19	𝜎𝜎(𝑙𝑙	𝜎𝜎(𝑙𝑙	NOUN
american_scientific_journal-4814	240	20	−	−	NOUN
american_scientific_journal-4814	240	21	𝑠𝑠	𝑠𝑠	NOUN
american_scientific_journal-4814	240	22	)	)	PUNCT
american_scientific_journal-4814	240	23	+	+	CCONJ
american_scientific_journal-4814	240	24	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-4814	240	25	�	�	PROPN
american_scientific_journal-4814	240	26	𝑒𝑒	𝑒𝑒	ADP
american_scientific_journal-4814	240	27	�	�	PROPN
american_scientific_journal-4814	240	28	,	,	PUNCT
american_scientific_journal-4814	240	29	𝑇𝑇	𝑇𝑇	PROPN
american_scientific_journal-4814	240	30	�	�	NOUN
american_scientific_journal-4814	240	31	1(𝑠𝑠	1(𝑠𝑠	NUM
american_scientific_journal-4814	240	32	)	)	PUNCT
american_scientific_journal-4814	240	33	=	=	SYM
american_scientific_journal-4814	240	34	3	3	NUM
american_scientific_journal-4814	240	35	𝑛𝑛02	𝑛𝑛02	PROPN
american_scientific_journal-4814	240	36	2	2	NUM
american_scientific_journal-4814	240	37	�	�	PROPN
american_scientific_journal-4814	240	38	𝜎𝜎(𝑏𝑏	𝜎𝜎(𝑏𝑏	PROPN
american_scientific_journal-4814	240	39	+	+	CCONJ
american_scientific_journal-4814	240	40	𝑙𝑙)2	𝑙𝑙)2	PROPN
american_scientific_journal-4814	240	41	−	−	PROPN
american_scientific_journal-4814	241	1	𝜎𝜎(𝑏𝑏	𝜎𝜎(𝑏𝑏	PROPN
american_scientific_journal-4814	241	2	+	+	NUM
american_scientific_journal-4814	241	3	𝑠𝑠)2	𝑠𝑠)2	PROPN
american_scientific_journal-4814	241	4	+	+	CCONJ
american_scientific_journal-4814	241	5	2	2	NUM
american_scientific_journal-4814	241	6	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-4814	241	7	�	�	PROPN
american_scientific_journal-4814	241	8	𝑒𝑒	𝑒𝑒	ADP
american_scientific_journal-4814	241	9	(	(	PUNCT
american_scientific_journal-4814	241	10	𝑏𝑏	𝑏𝑏	NOUN
american_scientific_journal-4814	241	11	+	+	CCONJ
american_scientific_journal-4814	241	12	𝑙𝑙	𝑙𝑙	X
american_scientific_journal-4814	241	13	)	)	PUNCT
american_scientific_journal-4814	241	14	�	�	PROPN
american_scientific_journal-4814	241	15	,	,	PUNCT
american_scientific_journal-4814	241	16	⎩	⎩	PROPN
american_scientific_journal-4814	241	17	⎪⎪	⎪⎪	PROPN
american_scientific_journal-4814	241	18	⎨	⎨	PROPN
american_scientific_journal-4814	241	19	⎪⎪	⎪⎪	PROPN
american_scientific_journal-4814	241	20	⎧𝑋𝑋𝐺𝐺	⎧𝑋𝑋𝐺𝐺	NOUN
american_scientific_journal-4814	241	21	=	=	NOUN
american_scientific_journal-4814	241	22	1	1	NUM
american_scientific_journal-4814	241	23	𝑚𝑚∑	𝑚𝑚∑	PROPN
american_scientific_journal-4814	241	24	�	�	PROPN
american_scientific_journal-4814	241	25	�	�	PROPN
american_scientific_journal-4814	241	26	�	�	PROPN
american_scientific_journal-4814	241	27	𝜌𝜌𝑢𝑢𝑖𝑖𝑑𝑑𝑠𝑠	𝜌𝜌𝑢𝑢𝑖𝑖𝑑𝑑𝑠𝑠	PROPN
american_scientific_journal-4814	241	28	+	+	CCONJ
american_scientific_journal-4814	241	29	𝜎𝜎	𝜎𝜎	PROPN
american_scientific_journal-4814	241	30	�	�	PROPN
american_scientific_journal-4814	241	31	𝛼𝛼𝑖𝑖𝑑𝑑𝑥𝑥𝑑𝑑𝑠𝑠	𝛼𝛼𝑖𝑖𝑑𝑑𝑥𝑥𝑑𝑑𝑠𝑠	PROPN
american_scientific_journal-4814	241	32	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-4814	241	33	+	+	CCONJ
american_scientific_journal-4814	241	34	𝑚𝑚	𝑚𝑚	NOUN
american_scientific_journal-4814	241	35	�	�	NOUN
american_scientific_journal-4814	241	36	𝑢𝑢𝑖𝑖(𝑙𝑙	𝑢𝑢𝑖𝑖(𝑙𝑙	NOUN
american_scientific_journal-4814	241	37	,	,	PUNCT
american_scientific_journal-4814	241	38	𝑡𝑡	𝑡𝑡	ADJ
american_scientific_journal-4814	241	39	)	)	PUNCT
american_scientific_journal-4814	241	40	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-4814	241	41	0	0	NUM
american_scientific_journal-4814	241	42	�	�	PROPN
american_scientific_journal-4814	241	43	2	2	NUM
american_scientific_journal-4814	241	44	𝑖𝑖=1	𝑖𝑖=1	NOUN
american_scientific_journal-4814	241	45	𝑌𝑌𝐺𝐺	𝑌𝑌𝐺𝐺	NOUN
american_scientific_journal-4814	241	46	=	=	SYM
american_scientific_journal-4814	241	47	1	1	NUM
american_scientific_journal-4814	241	48	𝑚𝑚∑	𝑚𝑚∑	PROPN
american_scientific_journal-4814	241	49	�	�	PROPN
american_scientific_journal-4814	241	50	�	�	PROPN
american_scientific_journal-4814	241	51	�	�	PROPN
american_scientific_journal-4814	241	52	𝜌𝜌𝑣𝑣𝑖𝑖𝑑𝑑𝑠𝑠	𝜌𝜌𝑣𝑣𝑖𝑖𝑑𝑑𝑠𝑠	PROPN
american_scientific_journal-4814	241	53	+	+	CCONJ
american_scientific_journal-4814	241	54	𝜎𝜎	𝜎𝜎	PROPN
american_scientific_journal-4814	241	55	�	�	PROPN
american_scientific_journal-4814	241	56	𝛽𝛽𝑖𝑖𝑑𝑑𝑥𝑥𝑑𝑑𝑠𝑠	𝛽𝛽𝑖𝑖𝑑𝑑𝑥𝑥𝑑𝑑𝑠𝑠	PROPN
american_scientific_journal-4814	241	57	𝑅𝑅	𝑅𝑅	PROPN
american_scientific_journal-4814	241	58	+	+	CCONJ
american_scientific_journal-4814	241	59	𝑚𝑚	𝑚𝑚	PROPN
american_scientific_journal-4814	241	60	�	�	PROPN
american_scientific_journal-4814	241	61	𝑣𝑣𝑖𝑖(𝑙𝑙	𝑣𝑣𝑖𝑖(𝑙𝑙	NOUN
american_scientific_journal-4814	241	62	,	,	PUNCT
american_scientific_journal-4814	241	63	𝑡𝑡	𝑡𝑡	ADJ
american_scientific_journal-4814	241	64	)	)	PUNCT
american_scientific_journal-4814	241	65	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-4814	241	66	0	0	NUM
american_scientific_journal-4814	241	67	�	�	PROPN
american_scientific_journal-4814	241	68	2	2	NUM
american_scientific_journal-4814	241	69	𝑖𝑖=1	𝑖𝑖=1	PROPN
american_scientific_journal-4814	241	70	𝑍𝑍𝐺𝐺	𝑍𝑍𝐺𝐺	PROPN
american_scientific_journal-4814	241	71	=	=	SYM
american_scientific_journal-4814	241	72	0	0	NUM
american_scientific_journal-4814	241	73	,	,	PUNCT
american_scientific_journal-4814	241	74	𝑚𝑚∑	𝑚𝑚∑	PROPN
american_scientific_journal-4814	241	75	is	be	AUX
american_scientific_journal-4814	241	76	the	the	DET
american_scientific_journal-4814	241	77	mass	mass	NOUN
american_scientific_journal-4814	241	78	of	of	ADP
american_scientific_journal-4814	241	79	the	the	DET
american_scientific_journal-4814	241	80	space	space	NOUN
american_scientific_journal-4814	241	81	vehicle	vehicle	NOUN
american_scientific_journal-4814	241	82	.	.	PUNCT
american_scientific_journal-4814	242	1	hence	hence	ADV
american_scientific_journal-4814	242	2	,	,	PUNCT
american_scientific_journal-4814	242	3	the	the	DET
american_scientific_journal-4814	242	4	application	application	NOUN
american_scientific_journal-4814	242	5	of	of	ADP
american_scientific_journal-4814	242	6	hamilton	hamilton	PROPN
american_scientific_journal-4814	242	7	's	's	PART
american_scientific_journal-4814	242	8	variational	variational	ADJ
american_scientific_journal-4814	242	9	principle	principle	NOUN
american_scientific_journal-4814	242	10	above	above	ADV
american_scientific_journal-4814	242	11	,	,	PUNCT
american_scientific_journal-4814	242	12	gives	give	VERB
american_scientific_journal-4814	242	13	the	the	DET
american_scientific_journal-4814	242	14	linearized	linearize	VERB
american_scientific_journal-4814	242	15	equations	equation	NOUN
american_scientific_journal-4814	242	16	(	(	PUNCT
american_scientific_journal-4814	242	17	1	1	NUM
american_scientific_journal-4814	242	18	)	)	PUNCT
american_scientific_journal-4814	242	19	to	to	ADP
american_scientific_journal-4814	242	20	(	(	PUNCT
american_scientific_journal-4814	242	21	10	10	NUM
american_scientific_journal-4814	242	22	)	)	PUNCT
american_scientific_journal-4814	242	23	.	.	PUNCT
american_scientific_journal-4814	243	1	•	•	NUM
american_scientific_journal-4814	243	2	appendix	appendix	VERB
american_scientific_journal-4814	243	3	3	3	NUM
american_scientific_journal-4814	243	4	one	one	NUM
american_scientific_journal-4814	243	5	introduces	introduce	VERB
american_scientific_journal-4814	243	6	the	the	DET
american_scientific_journal-4814	243	7	expression	expression	NOUN
american_scientific_journal-4814	243	8	of	of	ADP
american_scientific_journal-4814	243	9	the	the	DET
american_scientific_journal-4814	243	10	deformations	deformation	NOUN
american_scientific_journal-4814	243	11	𝑢𝑢𝑖𝑖(𝑠𝑠	𝑢𝑢𝑖𝑖(𝑠𝑠	NOUN
american_scientific_journal-4814	243	12	,	,	PUNCT
american_scientific_journal-4814	243	13	𝑡𝑡	𝑡𝑡	ADJ
american_scientific_journal-4814	243	14	)	)	PUNCT
american_scientific_journal-4814	243	15	(	(	PUNCT
american_scientific_journal-4814	243	16	17	17	NUM
american_scientific_journal-4814	243	17	)	)	PUNCT
american_scientific_journal-4814	243	18	in	in	ADP
american_scientific_journal-4814	243	19	the	the	DET
american_scientific_journal-4814	243	20	equation	equation	NOUN
american_scientific_journal-4814	243	21	(	(	PUNCT
american_scientific_journal-4814	243	22	3	3	NUM
american_scientific_journal-4814	243	23	)	)	PUNCT
american_scientific_journal-4814	243	24	of	of	ADP
american_scientific_journal-4814	243	25	local	local	ADJ
american_scientific_journal-4814	243	26	motion	motion	NOUN
american_scientific_journal-4814	243	27	(	(	PUNCT
american_scientific_journal-4814	243	28	𝐵𝐵𝐵𝐵𝑖𝑖	𝐵𝐵𝐵𝐵𝑖𝑖	PROPN
american_scientific_journal-4814	243	29	)	)	PUNCT
american_scientific_journal-4814	243	30	.	.	PUNCT
american_scientific_journal-4814	244	1	taking	take	VERB
american_scientific_journal-4814	244	2	into	into	ADP
american_scientific_journal-4814	244	3	account	account	NOUN
american_scientific_journal-4814	244	4	the	the	DET
american_scientific_journal-4814	244	5	conditions	condition	NOUN
american_scientific_journal-4814	244	6	(	(	PUNCT
american_scientific_journal-4814	244	7	11	11	NUM
american_scientific_journal-4814	244	8	)	)	PUNCT
american_scientific_journal-4814	244	9	,	,	PUNCT
american_scientific_journal-4814	244	10	the	the	DET
american_scientific_journal-4814	244	11	expressions	expression	NOUN
american_scientific_journal-4814	244	12	(	(	PUNCT
american_scientific_journal-4814	244	13	13	13	NUM
american_scientific_journal-4814	244	14	)	)	PUNCT
american_scientific_journal-4814	244	15	and	and	CCONJ
american_scientific_journal-4814	244	16	(	(	PUNCT
american_scientific_journal-4814	244	17	6	6	X
american_scientific_journal-4814	244	18	)	)	PUNCT
american_scientific_journal-4814	244	19	one	one	NOUN
american_scientific_journal-4814	244	20	gets	get	VERB
american_scientific_journal-4814	244	21	:	:	PUNCT
american_scientific_journal-4814	244	22	𝜌𝜌∑	𝜌𝜌∑	NOUN
american_scientific_journal-4814	244	23	(	(	PUNCT
american_scientific_journal-4814	244	24	−1)𝑖𝑖𝜃𝜃𝑛𝑛[𝑈𝑈𝑛𝑛∗(𝑠𝑠	−1)𝑖𝑖𝜃𝜃𝑛𝑛[𝑈𝑈𝑛𝑛∗(𝑠𝑠	NUM
american_scientific_journal-4814	244	25	)	)	PUNCT
american_scientific_journal-4814	245	1	+	+	CCONJ
american_scientific_journal-4814	245	2	(	(	PUNCT
american_scientific_journal-4814	245	3	𝑏𝑏	𝑏𝑏	NUM
american_scientific_journal-4814	245	4	+	+	CCONJ
american_scientific_journal-4814	245	5	𝑠𝑠)][	𝑠𝑠)][	PROPN
american_scientific_journal-4814	245	6	�	�	PROPN
american_scientific_journal-4814	245	7	̈	̈	SYM
american_scientific_journal-4814	245	8	�	�	NOUN
american_scientific_journal-4814	245	9	𝑔𝑛𝑛(𝑡𝑡	𝑔𝑛𝑛(𝑡𝑡	NOUN
american_scientific_journal-4814	245	10	)	)	PUNCT
american_scientific_journal-4814	246	1	+	+	NUM
american_scientific_journal-4814	246	2	𝜑𝜑𝑛𝑛2𝑔𝑔𝑛𝑛(𝑡𝑡)]∞	𝜑𝜑𝑛𝑛2𝑔𝑔𝑛𝑛(𝑡𝑡)]∞	PROPN
american_scientific_journal-4814	246	3	𝑛𝑛=1	𝑛𝑛=1	NOUN
american_scientific_journal-4814	246	4	+	+	CCONJ
american_scientific_journal-4814	246	5	3𝑛𝑛02𝜌𝜌(−1)𝑖𝑖	3𝑛𝑛02𝜌𝜌(−1)𝑖𝑖	NUM
american_scientific_journal-4814	246	6	∑	∑	PUNCT
american_scientific_journal-4814	246	7	�	�	PROPN
american_scientific_journal-4814	246	8	(	(	PUNCT
american_scientific_journal-4814	246	9	𝑏𝑏	𝑏𝑏	NOUN
american_scientific_journal-4814	246	10	+	+	NOUN
american_scientific_journal-4814	246	11	𝑠𝑠	𝑠𝑠	X
american_scientific_journal-4814	246	12	)	)	PUNCT
american_scientific_journal-4814	246	13	−	−	PROPN
american_scientific_journal-4814	246	14	1	1	NUM
american_scientific_journal-4814	246	15	2	2	NUM
american_scientific_journal-4814	246	16	�	�	NOUN
american_scientific_journal-4814	246	17	[	[	X
american_scientific_journal-4814	246	18	(	(	PUNCT
american_scientific_journal-4814	246	19	𝑏𝑏	𝑏𝑏	NOUN
american_scientific_journal-4814	246	20	+	+	CCONJ
american_scientific_journal-4814	246	21	𝑙𝑙)2	𝑙𝑙)2	NOUN
american_scientific_journal-4814	246	22	−∞	−∞	ADP
american_scientific_journal-4814	246	23	𝑛𝑛=1	𝑛𝑛=1	NOUN
american_scientific_journal-4814	246	24	(	(	PUNCT
american_scientific_journal-4814	246	25	𝑏𝑏	𝑏𝑏	NOUN
american_scientific_journal-4814	246	26	+	+	CCONJ
american_scientific_journal-4814	246	27	𝑠𝑠)2]𝑈𝑈𝑛𝑛∗′(𝑠𝑠)	𝑠𝑠)2]𝑈𝑈𝑛𝑛∗′(𝑠𝑠)	NOUN
american_scientific_journal-4814	246	28	�	�	NOUN
american_scientific_journal-4814	246	29	′	′	NUM
american_scientific_journal-4814	246	30	�	�	PROPN
american_scientific_journal-4814	246	31	𝜃𝜃𝑛𝑛𝑔𝑔𝑛𝑛(𝑡𝑡	𝜃𝜃𝑛𝑛𝑔𝑔𝑛𝑛(𝑡𝑡	NOUN
american_scientific_journal-4814	246	32	)	)	PUNCT
american_scientific_journal-4814	246	33	=	=	PUNCT
american_scientific_journal-4814	246	34	−𝜌𝜌(−1)𝑖𝑖(𝑏𝑏	−𝜌𝜌(−1)𝑖𝑖(𝑏𝑏	NOUN
american_scientific_journal-4814	246	35	+	+	CCONJ
american_scientific_journal-4814	246	36	𝑠𝑠)	𝑠𝑠)	PROPN
american_scientific_journal-4814	246	37	�	�	NOUN
american_scientific_journal-4814	246	38	�	�	PROPN
american_scientific_journal-4814	246	39	̈	̈	X
american_scientific_journal-4814	246	40	�	�	NOUN
american_scientific_journal-4814	246	41	𝜆(𝑡𝑡	𝜆(𝑡𝑡	NOUN
american_scientific_journal-4814	246	42	)	)	PUNCT
american_scientific_journal-4814	247	1	+	+	CCONJ
american_scientific_journal-4814	247	2	3𝑛𝑛02𝜆𝜆(𝑡𝑡)	3𝑛𝑛02𝜆𝜆(𝑡𝑡)	NUM
american_scientific_journal-4814	247	3	�	�	NOUN
american_scientific_journal-4814	247	4	.	.	PUNCT
american_scientific_journal-4814	248	1	(	(	PUNCT
american_scientific_journal-4814	248	2	a	a	X
american_scientific_journal-4814	248	3	)	)	PUNCT
american_scientific_journal-4814	248	4	one	one	NUM
american_scientific_journal-4814	248	5	multiplies	multiply	VERB
american_scientific_journal-4814	248	6	the	the	DET
american_scientific_journal-4814	248	7	previous	previous	ADJ
american_scientific_journal-4814	248	8	equation	equation	NOUN
american_scientific_journal-4814	248	9	by	by	ADP
american_scientific_journal-4814	248	10	(	(	PUNCT
american_scientific_journal-4814	248	11	−1)𝑖𝑖𝜃𝜃𝑘𝑘𝑈𝑈𝑘𝑘∗(𝑠𝑠	−1)𝑖𝑖𝜃𝜃𝑘𝑘𝑈𝑈𝑘𝑘∗(𝑠𝑠	NUM
american_scientific_journal-4814	248	12	)	)	PUNCT
american_scientific_journal-4814	248	13	then	then	ADV
american_scientific_journal-4814	248	14	one	one	NUM
american_scientific_journal-4814	248	15	integrates	integrate	NOUN
american_scientific_journal-4814	248	16	along	along	ADP
american_scientific_journal-4814	248	17	(	(	PUNCT
american_scientific_journal-4814	248	18	𝑆𝑆𝑆𝑆𝑖𝑖	𝑆𝑆𝑆𝑆𝑖𝑖	PROPN
american_scientific_journal-4814	248	19	)	)	PUNCT
american_scientific_journal-4814	248	20	.	.	PUNCT
american_scientific_journal-4814	249	1	after	after	ADP
american_scientific_journal-4814	249	2	calculation	calculation	NOUN
american_scientific_journal-4814	249	3	one	one	NOUN
american_scientific_journal-4814	249	4	gets	get	VERB
american_scientific_journal-4814	249	5	:	:	PUNCT
american_scientific_journal-4814	249	6	american	american	ADJ
american_scientific_journal-4814	249	7	scientific	scientific	ADJ
american_scientific_journal-4814	249	8	research	research	PROPN
american_scientific_journal-4814	249	9	journal	journal	NOUN
american_scientific_journal-4814	249	10	for	for	ADP
american_scientific_journal-4814	249	11	engineering	engineering	NOUN
american_scientific_journal-4814	249	12	,	,	PUNCT
american_scientific_journal-4814	249	13	technology	technology	NOUN
american_scientific_journal-4814	249	14	,	,	PUNCT
american_scientific_journal-4814	249	15	and	and	CCONJ
american_scientific_journal-4814	249	16	sciences	science	NOUN
american_scientific_journal-4814	249	17	(	(	PUNCT
american_scientific_journal-4814	249	18	asrjets	asrjet	NOUN
american_scientific_journal-4814	249	19	)	)	PUNCT
american_scientific_journal-4814	249	20	(	(	PUNCT
american_scientific_journal-4814	249	21	2019	2019	NUM
american_scientific_journal-4814	249	22	)	)	PUNCT
american_scientific_journal-4814	249	23	volume	volume	NOUN
american_scientific_journal-4814	249	24	55	55	NUM
american_scientific_journal-4814	249	25	,	,	PUNCT
american_scientific_journal-4814	249	26	no	no	DET
american_scientific_journal-4814	249	27	1	1	NUM
american_scientific_journal-4814	249	28	,	,	PUNCT
american_scientific_journal-4814	249	29	pp	pp	ADP
american_scientific_journal-4814	249	30	50	50	NUM
american_scientific_journal-4814	249	31	-	-	SYM
american_scientific_journal-4814	249	32	68	68	NUM
american_scientific_journal-4814	249	33	66	66	NUM
american_scientific_journal-4814	249	34	�	�	PROPN
american_scientific_journal-4814	249	35	𝜃𝜃𝑛𝑛𝜃𝜃𝑘𝑘	𝜃𝜃𝑛𝑛𝜃𝜃𝑘𝑘	NOUN
american_scientific_journal-4814	249	36	�	�	PROPN
american_scientific_journal-4814	249	37	�	�	PROPN
american_scientific_journal-4814	249	38	�	�	PROPN
american_scientific_journal-4814	249	39	𝜌𝜌𝑈𝑈𝑛𝑛∗(𝑠𝑠)𝑈𝑈𝑘𝑘∗(𝑠𝑠)𝑑𝑑𝑠𝑠	𝜌𝜌𝑈𝑈𝑛𝑛∗(𝑠𝑠)𝑈𝑈𝑘𝑘∗(𝑠𝑠)𝑑𝑑𝑠𝑠	PROPN
american_scientific_journal-4814	249	40	𝑙𝑙	𝑙𝑙	ADP
american_scientific_journal-4814	249	41	0	0	NUM
american_scientific_journal-4814	250	1	+	+	NUM
american_scientific_journal-4814	250	2	�	�	PROPN
american_scientific_journal-4814	250	3	𝜌𝜌(𝑏𝑏	𝜌𝜌(𝑏𝑏	PROPN
american_scientific_journal-4814	250	4	+	+	CCONJ
american_scientific_journal-4814	250	5	𝑠𝑠)𝑈𝑈𝑘𝑘∗(𝑠𝑠)𝑑𝑑𝑠𝑠	𝑠𝑠)𝑈𝑈𝑘𝑘∗(𝑠𝑠)𝑑𝑑𝑠𝑠	PROPN
american_scientific_journal-4814	250	6	𝑙𝑙	𝑙𝑙	PRON
american_scientific_journal-4814	250	7	0	0	NUM
american_scientific_journal-4814	250	8	�	�	PROPN
american_scientific_journal-4814	250	9	[	[	X
american_scientific_journal-4814	250	10	�	�	NOUN
american_scientific_journal-4814	250	11	̈	̈	SYM
american_scientific_journal-4814	250	12	�	�	NOUN
american_scientific_journal-4814	250	13	𝑔𝑛𝑛(𝑡𝑡	𝑔𝑛𝑛(𝑡𝑡	NOUN
american_scientific_journal-4814	250	14	)	)	PUNCT
american_scientific_journal-4814	251	1	+	+	NUM
american_scientific_journal-4814	251	2	𝜑𝜑𝑛𝑛2𝑔𝑔𝑛𝑛(𝑡𝑡	𝜑𝜑𝑛𝑛2𝑔𝑔𝑛𝑛(𝑡𝑡	NOUN
american_scientific_journal-4814	251	3	)	)	PUNCT
american_scientific_journal-4814	251	4	]	]	PUNCT
american_scientific_journal-4814	252	1	+	+	CCONJ
american_scientific_journal-4814	252	2	3𝑛𝑛02	3𝑛𝑛02	NUM
american_scientific_journal-4814	252	3	�	�	NOUN
american_scientific_journal-4814	252	4	𝜌𝜌(𝑏𝑏	𝜌𝜌(𝑏𝑏	PROPN
american_scientific_journal-4814	252	5	+	+	CCONJ
american_scientific_journal-4814	252	6	𝑠𝑠)𝑈𝑈𝑘𝑘∗(𝑠𝑠)𝑑𝑑𝑠𝑠𝑔𝑔𝑛𝑛(𝑡𝑡	𝑠𝑠)𝑈𝑈𝑘𝑘∗(𝑠𝑠)𝑑𝑑𝑠𝑠𝑔𝑔𝑛𝑛(𝑡𝑡	PROPN
american_scientific_journal-4814	252	7	)	)	PUNCT
american_scientific_journal-4814	252	8	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-4814	252	9	0	0	NUM
american_scientific_journal-4814	252	10	�	�	PROPN
american_scientific_journal-4814	252	11	∞	∞	PROPN
american_scientific_journal-4814	252	12	𝑛𝑛=1	𝑛𝑛=1	NOUN
american_scientific_journal-4814	252	13	+	+	CCONJ
american_scientific_journal-4814	252	14	3	3	NUM
american_scientific_journal-4814	252	15	2	2	NUM
american_scientific_journal-4814	252	16	𝑛𝑛02	𝑛𝑛02	PROPN
american_scientific_journal-4814	252	17	�	�	PROPN
american_scientific_journal-4814	252	18	𝜃𝜃𝑛𝑛𝜃𝜃𝑘𝑘	𝜃𝜃𝑛𝑛𝜃𝜃𝑘𝑘	NOUN
american_scientific_journal-4814	252	19	�	�	PROPN
american_scientific_journal-4814	252	20	𝑆𝑆	𝑆𝑆	PROPN
american_scientific_journal-4814	252	21	�	�	PROPN
american_scientific_journal-4814	252	22	1∗(𝑠𝑠)𝑈𝑈𝑛𝑛∗′(𝑠𝑠)𝑈𝑈𝑘𝑘∗′(𝑠𝑠)𝑑𝑑𝑠𝑠𝑔𝑔𝑛𝑛(𝑡𝑡	1∗(𝑠𝑠)𝑈𝑈𝑛𝑛∗′(𝑠𝑠)𝑈𝑈𝑘𝑘∗′(𝑠𝑠)𝑑𝑑𝑠𝑠𝑔𝑔𝑛𝑛(𝑡𝑡	NUM
american_scientific_journal-4814	252	23	)	)	PUNCT
american_scientific_journal-4814	252	24	𝑙𝑙	𝑙𝑙	VERB
american_scientific_journal-4814	252	25	0	0	NUM
american_scientific_journal-4814	252	26	∞	∞	PROPN
american_scientific_journal-4814	252	27	𝑛𝑛=1	𝑛𝑛=1	NOUN
american_scientific_journal-4814	252	28	=	=	PRON
american_scientific_journal-4814	252	29	−𝜃𝜃𝑘𝑘	−𝜃𝜃𝑘𝑘	VERB
american_scientific_journal-4814	252	30	�	�	NOUN
american_scientific_journal-4814	252	31	𝜌𝜌(𝑏𝑏	𝜌𝜌(𝑏𝑏	PROPN
american_scientific_journal-4814	252	32	+	+	CCONJ
american_scientific_journal-4814	252	33	𝑠𝑠)𝑈𝑈𝑘𝑘∗(𝑠𝑠)𝑑𝑑𝑠𝑠	𝑠𝑠)𝑈𝑈𝑘𝑘∗(𝑠𝑠)𝑑𝑑𝑠𝑠	PROPN
american_scientific_journal-4814	252	34	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-4814	252	35	0	0	NUM
american_scientific_journal-4814	252	36	�	�	PROPN
american_scientific_journal-4814	252	37	�	�	PROPN
american_scientific_journal-4814	252	38	̈	̈	X
american_scientific_journal-4814	252	39	�	�	NOUN
american_scientific_journal-4814	252	40	𝜆(𝑡𝑡	𝜆(𝑡𝑡	NOUN
american_scientific_journal-4814	252	41	)	)	PUNCT
american_scientific_journal-4814	252	42	+	+	CCONJ
american_scientific_journal-4814	252	43	3𝑛𝑛02𝜆𝜆(𝑡𝑡)	3𝑛𝑛02𝜆𝜆(𝑡𝑡)	NUM
american_scientific_journal-4814	252	44	�	�	NOUN
american_scientific_journal-4814	252	45	.	.	PUNCT
american_scientific_journal-4814	252	46	one	one	PRON
american_scientific_journal-4814	252	47	gets	get	VERB
american_scientific_journal-4814	252	48	after	after	ADP
american_scientific_journal-4814	252	49	some	some	DET
american_scientific_journal-4814	252	50	similar	similar	ADJ
american_scientific_journal-4814	252	51	calculations	calculation	NOUN
american_scientific_journal-4814	252	52	the	the	DET
american_scientific_journal-4814	252	53	equations	equation	NOUN
american_scientific_journal-4814	252	54	describing	describe	VERB
american_scientific_journal-4814	252	55	the	the	DET
american_scientific_journal-4814	252	56	motion	motion	NOUN
american_scientific_journal-4814	252	57	of	of	ADP
american_scientific_journal-4814	252	58	(	(	PUNCT
american_scientific_journal-4814	252	59	𝐵𝐵𝐵𝐵𝑖𝑖	𝐵𝐵𝐵𝐵𝑖𝑖	PROPN
american_scientific_journal-4814	252	60	)	)	PUNCT
american_scientific_journal-4814	252	61	and	and	CCONJ
american_scientific_journal-4814	252	62	the	the	DET
american_scientific_journal-4814	252	63	motion	motion	NOUN
american_scientific_journal-4814	252	64	of	of	ADP
american_scientific_journal-4814	252	65	(	(	PUNCT
american_scientific_journal-4814	252	66	𝑇𝑇𝑆𝑆𝑖𝑖	𝑇𝑇𝑆𝑆𝑖𝑖	PROPN
american_scientific_journal-4814	252	67	)	)	PUNCT
american_scientific_journal-4814	252	68	.	.	PUNCT
american_scientific_journal-4814	253	1	one	one	NUM
american_scientific_journal-4814	253	2	makes	make	VERB
american_scientific_journal-4814	253	3	the	the	DET
american_scientific_journal-4814	253	4	summation	summation	NOUN
american_scientific_journal-4814	253	5	of	of	ADP
american_scientific_journal-4814	253	6	these	these	DET
american_scientific_journal-4814	253	7	three	three	NUM
american_scientific_journal-4814	253	8	equations	equation	NOUN
american_scientific_journal-4814	253	9	.	.	PUNCT
american_scientific_journal-4814	254	1	using	use	VERB
american_scientific_journal-4814	254	2	the	the	DET
american_scientific_journal-4814	254	3	equations	equation	NOUN
american_scientific_journal-4814	254	4	of	of	ADP
american_scientific_journal-4814	254	5	eigenfrequencies	eigenfrequencie	NOUN
american_scientific_journal-4814	254	6	(	(	PUNCT
american_scientific_journal-4814	254	7	13	13	NUM
american_scientific_journal-4814	254	8	)	)	PUNCT
american_scientific_journal-4814	254	9	and	and	CCONJ
american_scientific_journal-4814	254	10	making	make	VERB
american_scientific_journal-4814	254	11	a	a	DET
american_scientific_journal-4814	254	12	summation	summation	NOUN
american_scientific_journal-4814	254	13	on	on	ADP
american_scientific_journal-4814	254	14	i	i	PRON
american_scientific_journal-4814	254	15	,	,	PUNCT
american_scientific_journal-4814	254	16	the	the	DET
american_scientific_journal-4814	254	17	equation	equation	NOUN
american_scientific_journal-4814	254	18	above	above	ADV
american_scientific_journal-4814	254	19	becomes	become	VERB
american_scientific_journal-4814	254	20	:	:	PUNCT
american_scientific_journal-4814	254	21	�	�	PROPN
american_scientific_journal-4814	254	22	𝜃𝜃𝑛𝑛𝜃𝜃𝑘𝑘	𝜃𝜃𝑛𝑛𝜃𝜃𝑘𝑘	NOUN
american_scientific_journal-4814	254	23	�	�	PROPN
american_scientific_journal-4814	254	24	2	2	NUM
american_scientific_journal-4814	254	25	�	�	PROPN
american_scientific_journal-4814	254	26	�	�	PROPN
american_scientific_journal-4814	254	27	𝜌𝜌𝑈𝑈𝑛𝑛∗(𝑠𝑠)𝑈𝑈𝑘𝑘∗(𝑠𝑠)𝑑𝑑𝑠𝑠	𝜌𝜌𝑈𝑈𝑛𝑛∗(𝑠𝑠)𝑈𝑈𝑘𝑘∗(𝑠𝑠)𝑑𝑑𝑠𝑠	PROPN
american_scientific_journal-4814	254	28	𝑙𝑙	𝑙𝑙	ADP
american_scientific_journal-4814	254	29	0	0	NUM
american_scientific_journal-4814	254	30	+	+	NUM
american_scientific_journal-4814	254	31	�	�	PROPN
american_scientific_journal-4814	254	32	𝜎𝜎𝑒𝑒𝛼𝛼𝑛𝑛∗(𝑠𝑠)𝛼𝛼𝑘𝑘∗(𝑠𝑠)𝑑𝑑𝑠𝑠	𝜎𝜎𝑒𝑒𝛼𝛼𝑛𝑛∗(𝑠𝑠)𝛼𝛼𝑘𝑘∗(𝑠𝑠)𝑑𝑑𝑠𝑠	NOUN
american_scientific_journal-4814	254	33	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-4814	254	34	0	0	NUM
american_scientific_journal-4814	255	1	+	+	CCONJ
american_scientific_journal-4814	255	2	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-4814	255	3	�	�	PROPN
american_scientific_journal-4814	255	4	𝑈𝑈𝑛𝑛∗(𝑙𝑙)𝑈𝑈𝑘𝑘∗(𝑙𝑙	𝑈𝑈𝑛𝑛∗(𝑙𝑙)𝑈𝑈𝑘𝑘∗(𝑙𝑙	NOUN
american_scientific_journal-4814	255	5	)	)	PUNCT
american_scientific_journal-4814	255	6	�	�	PROPN
american_scientific_journal-4814	255	7	−	−	PROPN
american_scientific_journal-4814	255	8	𝐶𝐶	𝐶𝐶	PROPN
american_scientific_journal-4814	255	9	�	�	PROPN
american_scientific_journal-4814	255	10	[	[	X
american_scientific_journal-4814	255	11	�	�	PROPN
american_scientific_journal-4814	255	12	̈	̈	SYM
american_scientific_journal-4814	255	13	�	�	NOUN
american_scientific_journal-4814	255	14	𝑔𝑛𝑛(𝑡𝑡	𝑔𝑛𝑛(𝑡𝑡	NOUN
american_scientific_journal-4814	255	15	)	)	PUNCT
american_scientific_journal-4814	256	1	+	+	NUM
american_scientific_journal-4814	256	2	𝜑𝜑𝑛𝑛2𝑔𝑔𝑛𝑛(𝑡𝑡	𝜑𝜑𝑛𝑛2𝑔𝑔𝑛𝑛(𝑡𝑡	NOUN
american_scientific_journal-4814	256	3	)	)	PUNCT
american_scientific_journal-4814	256	4	]	]	PUNCT
american_scientific_journal-4814	257	1	∞	∞	NUM
american_scientific_journal-4814	257	2	𝑛𝑛=1	𝑛𝑛=1	PROPN
american_scientific_journal-4814	257	3	+	+	SYM
american_scientific_journal-4814	257	4	3𝑛𝑛02	3𝑛𝑛02	NUM
american_scientific_journal-4814	257	5	�	�	PROPN
american_scientific_journal-4814	257	6	𝜃𝜃𝑛𝑛𝜃𝜃𝑘𝑘	𝜃𝜃𝑛𝑛𝜃𝜃𝑘𝑘	NOUN
american_scientific_journal-4814	257	7	�	�	PROPN
american_scientific_journal-4814	257	8	�	�	PROPN
american_scientific_journal-4814	257	9	𝑆𝑆	𝑆𝑆	PROPN
american_scientific_journal-4814	257	10	�	�	PROPN
american_scientific_journal-4814	257	11	1∗(𝑠𝑠)𝑈𝑈𝑛𝑛∗′(𝑠𝑠)𝑈𝑈𝑘𝑘∗′(𝑠𝑠)𝑑𝑑𝑠𝑠	1∗(𝑠𝑠)𝑈𝑈𝑛𝑛∗′(𝑠𝑠)𝑈𝑈𝑘𝑘∗′(𝑠𝑠)𝑑𝑑𝑠𝑠	PROPN
american_scientific_journal-4814	257	12	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-4814	257	13	0	0	NUM
american_scientific_journal-4814	258	1	+	+	NUM
american_scientific_journal-4814	258	2	�	�	PROPN
american_scientific_journal-4814	258	3	𝑒𝑒𝑇𝑇	𝑒𝑒𝑇𝑇	PROPN
american_scientific_journal-4814	258	4	�	�	NOUN
american_scientific_journal-4814	258	5	1∗(𝑠𝑠)𝛼𝛼𝑛𝑛∗′(𝑠𝑠)𝛼𝛼𝑘𝑘∗′(𝑠𝑠)𝑑𝑑𝑠𝑠	1∗(𝑠𝑠)𝛼𝛼𝑛𝑛∗′(𝑠𝑠)𝛼𝛼𝑘𝑘∗′(𝑠𝑠)𝑑𝑑𝑠𝑠	PROPN
american_scientific_journal-4814	258	6	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-4814	258	7	0	0	NUM
american_scientific_journal-4814	258	8	−	−	PROPN
american_scientific_journal-4814	258	9	𝐶𝐶	𝐶𝐶	PROPN
american_scientific_journal-4814	258	10	�	�	PROPN
american_scientific_journal-4814	258	11	𝑔𝑔𝑛𝑛(𝑡𝑡	𝑔𝑔𝑛𝑛(𝑡𝑡	PROPN
american_scientific_journal-4814	258	12	)	)	PUNCT
american_scientific_journal-4814	258	13	∞	∞	PROPN
american_scientific_journal-4814	258	14	𝑛𝑛=1	𝑛𝑛=1	NOUN
american_scientific_journal-4814	258	15	=	=	SYM
american_scientific_journal-4814	258	16	𝐶𝐶𝜃𝜃𝑘𝑘	𝐶𝐶𝜃𝜃𝑘𝑘	PROPN
american_scientific_journal-4814	258	17	�	�	PROPN
american_scientific_journal-4814	258	18	�	�	PROPN
american_scientific_journal-4814	258	19	̈	̈	X
american_scientific_journal-4814	258	20	�	�	NOUN
american_scientific_journal-4814	258	21	𝜆(𝑡𝑡	𝜆(𝑡𝑡	NOUN
american_scientific_journal-4814	258	22	)	)	PUNCT
american_scientific_journal-4814	258	23	+	+	CCONJ
american_scientific_journal-4814	258	24	3𝑛𝑛02𝜆𝜆(𝑡𝑡)	3𝑛𝑛02𝜆𝜆(𝑡𝑡)	NUM
american_scientific_journal-4814	258	25	�	�	NOUN
american_scientific_journal-4814	258	26	.	.	PUNCT
american_scientific_journal-4814	259	1	one	one	NUM
american_scientific_journal-4814	259	2	uses	use	VERB
american_scientific_journal-4814	259	3	normalized	normalize	VERB
american_scientific_journal-4814	259	4	orthogonality	orthogonality	NOUN
american_scientific_journal-4814	259	5	property	property	NOUN
american_scientific_journal-4814	259	6	(	(	PUNCT
american_scientific_journal-4814	259	7	15	15	NUM
american_scientific_journal-4814	259	8	)	)	PUNCT
american_scientific_journal-4814	259	9	and	and	CCONJ
american_scientific_journal-4814	259	10	the	the	DET
american_scientific_journal-4814	259	11	expression	expression	NOUN
american_scientific_journal-4814	259	12	of	of	ADP
american_scientific_journal-4814	259	13	𝑚𝑚𝑛𝑛𝑘𝑘	𝑚𝑚𝑛𝑛𝑘𝑘	NOUN
american_scientific_journal-4814	259	14	(	(	PUNCT
american_scientific_journal-4814	259	15	19	19	NUM
american_scientific_journal-4814	259	16	):	):	PUNCT
american_scientific_journal-4814	259	17	�	�	PROPN
american_scientific_journal-4814	259	18	𝛿𝛿𝑛𝑛𝑘𝑘[	𝛿𝛿𝑛𝑛𝑘𝑘[	PROPN
american_scientific_journal-4814	259	19	�	�	PROPN
american_scientific_journal-4814	259	20	̈	̈	SYM
american_scientific_journal-4814	259	21	�	�	NOUN
american_scientific_journal-4814	259	22	𝑔𝑛𝑛(𝑡𝑡	𝑔𝑛𝑛(𝑡𝑡	NOUN
american_scientific_journal-4814	259	23	)	)	PUNCT
american_scientific_journal-4814	259	24	+	+	NUM
american_scientific_journal-4814	259	25	𝜑𝜑𝑛𝑛2𝑔𝑔𝑛𝑛(𝑡𝑡	𝜑𝜑𝑛𝑛2𝑔𝑔𝑛𝑛(𝑡𝑡	NOUN
american_scientific_journal-4814	259	26	)	)	PUNCT
american_scientific_journal-4814	259	27	]	]	PUNCT
american_scientific_journal-4814	260	1	∞	∞	NUM
american_scientific_journal-4814	260	2	𝑛𝑛=1	𝑛𝑛=1	NOUN
american_scientific_journal-4814	260	3	+	+	SYM
american_scientific_journal-4814	260	4	3𝑛𝑛02	3𝑛𝑛02	NUM
american_scientific_journal-4814	260	5	�	�	NOUN
american_scientific_journal-4814	260	6	𝑚𝑚𝑛𝑛𝑘𝑘𝑔𝑔𝑛𝑛(𝑡𝑡	𝑚𝑚𝑛𝑛𝑘𝑘𝑔𝑔𝑛𝑛(𝑡𝑡	NOUN
american_scientific_journal-4814	260	7	)	)	PUNCT
american_scientific_journal-4814	260	8	∞	∞	NUM
american_scientific_journal-4814	260	9	𝑛𝑛=1	𝑛𝑛=1	NOUN
american_scientific_journal-4814	260	10	=	=	SYM
american_scientific_journal-4814	260	11	𝐶𝐶𝜃𝜃𝑘𝑘	𝐶𝐶𝜃𝜃𝑘𝑘	PROPN
american_scientific_journal-4814	260	12	�	�	PROPN
american_scientific_journal-4814	260	13	�	�	PROPN
american_scientific_journal-4814	260	14	̈	̈	X
american_scientific_journal-4814	260	15	�	�	NOUN
american_scientific_journal-4814	260	16	𝜆(𝑡𝑡	𝜆(𝑡𝑡	NOUN
american_scientific_journal-4814	260	17	)	)	PUNCT
american_scientific_journal-4814	260	18	+	+	CCONJ
american_scientific_journal-4814	260	19	3𝑛𝑛02𝜆𝜆(𝑡𝑡)	3𝑛𝑛02𝜆𝜆(𝑡𝑡)	NUM
american_scientific_journal-4814	260	20	�	�	NOUN
american_scientific_journal-4814	260	21	.	.	PUNCT
american_scientific_journal-4814	260	22	•	•	NUM
american_scientific_journal-4814	260	23	appendix	appendix	VERB
american_scientific_journal-4814	260	24	4	4	NUM
american_scientific_journal-4814	260	25	one	one	NUM
american_scientific_journal-4814	260	26	multiplies	multiplie	NOUN
american_scientific_journal-4814	260	27	the	the	DET
american_scientific_journal-4814	260	28	previous	previous	ADJ
american_scientific_journal-4814	260	29	equation	equation	NOUN
american_scientific_journal-4814	260	30	by	by	ADP
american_scientific_journal-4814	260	31	(	(	PUNCT
american_scientific_journal-4814	260	32	−1)𝑖𝑖(𝑏𝑏	−1)𝑖𝑖(𝑏𝑏	PROPN
american_scientific_journal-4814	260	33	+	+	CCONJ
american_scientific_journal-4814	260	34	𝑠𝑠	𝑠𝑠	X
american_scientific_journal-4814	260	35	)	)	PUNCT
american_scientific_journal-4814	260	36	the	the	DET
american_scientific_journal-4814	260	37	equation	equation	NOUN
american_scientific_journal-4814	260	38	(	(	PUNCT
american_scientific_journal-4814	260	39	a	a	NOUN
american_scientific_journal-4814	260	40	)	)	PUNCT
american_scientific_journal-4814	260	41	of	of	ADP
american_scientific_journal-4814	260	42	the	the	DET
american_scientific_journal-4814	260	43	appendix	appendix	NOUN
american_scientific_journal-4814	260	44	3	3	NUM
american_scientific_journal-4814	260	45	,	,	PUNCT
american_scientific_journal-4814	260	46	then	then	ADV
american_scientific_journal-4814	260	47	one	one	NUM
american_scientific_journal-4814	260	48	integrates	integrate	NOUN
american_scientific_journal-4814	260	49	along	along	ADP
american_scientific_journal-4814	260	50	(	(	PUNCT
american_scientific_journal-4814	260	51	𝑆𝑆𝑆𝑆𝑖𝑖	𝑆𝑆𝑆𝑆𝑖𝑖	PROPN
american_scientific_journal-4814	260	52	)	)	PUNCT
american_scientific_journal-4814	260	53	.	.	PUNCT
american_scientific_journal-4814	261	1	after	after	ADP
american_scientific_journal-4814	261	2	calculation	calculation	NOUN
american_scientific_journal-4814	261	3	one	one	NOUN
american_scientific_journal-4814	261	4	gets	get	VERB
american_scientific_journal-4814	261	5	:	:	PUNCT
american_scientific_journal-4814	261	6	�	�	PROPN
american_scientific_journal-4814	261	7	𝜃𝜃𝑛𝑛	𝜃𝜃𝑛𝑛	PROPN
american_scientific_journal-4814	261	8	�	�	PROPN
american_scientific_journal-4814	261	9	𝜌𝜌	𝜌𝜌	PROPN
american_scientific_journal-4814	261	10	�	�	PROPN
american_scientific_journal-4814	261	11	(𝑏𝑏	(𝑏𝑏	PUNCT
american_scientific_journal-4814	261	12	+	+	CCONJ
american_scientific_journal-4814	261	13	𝑠𝑠)𝑈𝑈𝑛𝑛∗(𝑠𝑠)𝑑𝑑𝑠𝑠	𝑠𝑠)𝑈𝑈𝑛𝑛∗(𝑠𝑠)𝑑𝑑𝑠𝑠	PROPN
american_scientific_journal-4814	261	14	𝑙𝑙	𝑙𝑙	INTJ
american_scientific_journal-4814	261	15	0	0	NUM
american_scientific_journal-4814	262	1	+	+	CCONJ
american_scientific_journal-4814	262	2	𝜌𝜌	𝜌𝜌	PROPN
american_scientific_journal-4814	262	3	�	�	PROPN
american_scientific_journal-4814	262	4	(𝑏𝑏	(𝑏𝑏	PUNCT
american_scientific_journal-4814	262	5	+	+	NUM
american_scientific_journal-4814	262	6	𝑠𝑠)2𝑑𝑑𝑠𝑠	𝑠𝑠)2𝑑𝑑𝑠𝑠	X
american_scientific_journal-4814	262	7	𝑙𝑙	𝑙𝑙	X
american_scientific_journal-4814	262	8	0	0	NUM
american_scientific_journal-4814	262	9	�	�	PROPN
american_scientific_journal-4814	262	10	[	[	X
american_scientific_journal-4814	262	11	�	�	NOUN
american_scientific_journal-4814	262	12	̈	̈	SYM
american_scientific_journal-4814	262	13	�	�	NOUN
american_scientific_journal-4814	262	14	𝑔𝑛𝑛(𝑡𝑡	𝑔𝑛𝑛(𝑡𝑡	NOUN
american_scientific_journal-4814	262	15	)	)	PUNCT
american_scientific_journal-4814	263	1	+	+	NUM
american_scientific_journal-4814	263	2	𝜑𝜑𝑛𝑛2𝑔𝑔𝑛𝑛(𝑡𝑡	𝜑𝜑𝑛𝑛2𝑔𝑔𝑛𝑛(𝑡𝑡	NOUN
american_scientific_journal-4814	263	3	)	)	PUNCT
american_scientific_journal-4814	263	4	]	]	PUNCT
american_scientific_journal-4814	264	1	∞	∞	NUM
american_scientific_journal-4814	264	2	𝑛𝑛=1	𝑛𝑛=1	PROPN
american_scientific_journal-4814	264	3	+	+	PUNCT
american_scientific_journal-4814	264	4	3𝑛𝑛02𝜌𝜌	3𝑛𝑛02𝜌𝜌	NUM
american_scientific_journal-4814	264	5	�	�	NOUN
american_scientific_journal-4814	264	6	𝜃𝜃𝑛𝑛𝑔𝑔𝑛𝑛(𝑡𝑡	𝜃𝜃𝑛𝑛𝑔𝑔𝑛𝑛(𝑡𝑡	NOUN
american_scientific_journal-4814	264	7	)	)	PUNCT
american_scientific_journal-4814	264	8	∞	∞	PROPN
american_scientific_journal-4814	264	9	𝑛𝑛=1	𝑛𝑛=1	PROPN
american_scientific_journal-4814	264	10	�	�	PROPN
american_scientific_journal-4814	264	11	�	�	PROPN
american_scientific_journal-4814	264	12	(	(	PUNCT
american_scientific_journal-4814	264	13	𝑏𝑏	𝑏𝑏	NOUN
american_scientific_journal-4814	264	14	+	+	CCONJ
american_scientific_journal-4814	264	15	𝑠𝑠)2𝑑𝑑𝑠𝑠	𝑠𝑠)2𝑑𝑑𝑠𝑠	X
american_scientific_journal-4814	264	16	𝑙𝑙	𝑙𝑙	X
american_scientific_journal-4814	264	17	0	0	PUNCT
american_scientific_journal-4814	265	1	+	+	CCONJ
american_scientific_journal-4814	265	2	1	1	NUM
american_scientific_journal-4814	265	3	2	2	NUM
american_scientific_journal-4814	265	4	�	�	NOUN
american_scientific_journal-4814	265	5	[	[	X
american_scientific_journal-4814	265	6	(	(	PUNCT
american_scientific_journal-4814	265	7	𝑏𝑏	𝑏𝑏	NOUN
american_scientific_journal-4814	265	8	+	+	NUM
american_scientific_journal-4814	265	9	𝑙𝑙)2	𝑙𝑙)2	PROPN
american_scientific_journal-4814	265	10	−	−	PROPN
american_scientific_journal-4814	265	11	(	(	PUNCT
american_scientific_journal-4814	265	12	𝑏𝑏	𝑏𝑏	NOUN
american_scientific_journal-4814	265	13	+	+	NUM
american_scientific_journal-4814	265	14	𝑠𝑠)2]𝑈𝑈𝑛𝑛∗′(𝑠𝑠)𝑑𝑑𝑠𝑠	𝑠𝑠)2]𝑈𝑈𝑛𝑛∗′(𝑠𝑠)𝑑𝑑𝑠𝑠	PROPN
american_scientific_journal-4814	265	15	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-4814	265	16	0	0	NUM
american_scientific_journal-4814	265	17	�	�	PROPN
american_scientific_journal-4814	265	18	=	=	SYM
american_scientific_journal-4814	265	19	−𝜌𝜌	−𝜌𝜌	PROPN
american_scientific_journal-4814	265	20	�	�	PROPN
american_scientific_journal-4814	265	21	(𝑏𝑏	(𝑏𝑏	PUNCT
american_scientific_journal-4814	265	22	+	+	NUM
american_scientific_journal-4814	265	23	𝑠𝑠)2𝑑𝑑𝑠𝑠	𝑠𝑠)2𝑑𝑑𝑠𝑠	X
american_scientific_journal-4814	265	24	𝑙𝑙	𝑙𝑙	X
american_scientific_journal-4814	265	25	0	0	NUM
american_scientific_journal-4814	265	26	�	�	PROPN
american_scientific_journal-4814	265	27	�	�	PROPN
american_scientific_journal-4814	265	28	̈	̈	X
american_scientific_journal-4814	265	29	�	�	NOUN
american_scientific_journal-4814	265	30	𝜆(𝑡𝑡	𝜆(𝑡𝑡	NOUN
american_scientific_journal-4814	265	31	)	)	PUNCT
american_scientific_journal-4814	265	32	+	+	CCONJ
american_scientific_journal-4814	265	33	3𝑛𝑛02𝜆𝜆(𝑡𝑡)	3𝑛𝑛02𝜆𝜆(𝑡𝑡)	NUM
american_scientific_journal-4814	265	34	�	�	NOUN
american_scientific_journal-4814	265	35	.	.	PUNCT
american_scientific_journal-4814	266	1	one	one	PRON
american_scientific_journal-4814	266	2	gets	get	VERB
american_scientific_journal-4814	266	3	after	after	ADP
american_scientific_journal-4814	266	4	some	some	DET
american_scientific_journal-4814	266	5	similar	similar	ADJ
american_scientific_journal-4814	266	6	calculations	calculation	NOUN
american_scientific_journal-4814	266	7	the	the	DET
american_scientific_journal-4814	266	8	equations	equation	NOUN
american_scientific_journal-4814	266	9	describing	describe	VERB
american_scientific_journal-4814	266	10	the	the	DET
american_scientific_journal-4814	266	11	motion	motion	NOUN
american_scientific_journal-4814	266	12	of	of	ADP
american_scientific_journal-4814	266	13	(	(	PUNCT
american_scientific_journal-4814	266	14	𝐵𝐵𝐵𝐵𝑖𝑖	𝐵𝐵𝐵𝐵𝑖𝑖	PROPN
american_scientific_journal-4814	266	15	)	)	PUNCT
american_scientific_journal-4814	266	16	and	and	CCONJ
american_scientific_journal-4814	266	17	the	the	DET
american_scientific_journal-4814	266	18	motion	motion	NOUN
american_scientific_journal-4814	266	19	of	of	ADP
american_scientific_journal-4814	266	20	(	(	PUNCT
american_scientific_journal-4814	266	21	𝑇𝑇𝑆𝑆𝑖𝑖	𝑇𝑇𝑆𝑆𝑖𝑖	PROPN
american_scientific_journal-4814	266	22	)	)	PUNCT
american_scientific_journal-4814	266	23	.	.	PUNCT
american_scientific_journal-4814	267	1	one	one	NUM
american_scientific_journal-4814	267	2	makes	make	VERB
american_scientific_journal-4814	267	3	the	the	DET
american_scientific_journal-4814	267	4	summation	summation	NOUN
american_scientific_journal-4814	267	5	of	of	ADP
american_scientific_journal-4814	267	6	these	these	DET
american_scientific_journal-4814	267	7	three	three	NUM
american_scientific_journal-4814	267	8	equations	equation	NOUN
american_scientific_journal-4814	267	9	.	.	PUNCT
american_scientific_journal-4814	268	1	using	use	VERB
american_scientific_journal-4814	268	2	the	the	DET
american_scientific_journal-4814	268	3	equations	equation	NOUN
american_scientific_journal-4814	268	4	of	of	ADP
american_scientific_journal-4814	268	5	eigenfrequencies	eigenfrequencie	NOUN
american_scientific_journal-4814	268	6	(	(	PUNCT
american_scientific_journal-4814	268	7	13	13	NUM
american_scientific_journal-4814	268	8	)	)	PUNCT
american_scientific_journal-4814	268	9	and	and	CCONJ
american_scientific_journal-4814	268	10	making	make	VERB
american_scientific_journal-4814	268	11	a	a	DET
american_scientific_journal-4814	268	12	summation	summation	NOUN
american_scientific_journal-4814	268	13	,	,	PUNCT
american_scientific_journal-4814	268	14	the	the	DET
american_scientific_journal-4814	268	15	equation	equation	NOUN
american_scientific_journal-4814	268	16	above	above	ADV
american_scientific_journal-4814	268	17	becomes	become	VERB
american_scientific_journal-4814	268	18	:	:	PUNCT
american_scientific_journal-4814	268	19	american	american	ADJ
american_scientific_journal-4814	268	20	scientific	scientific	ADJ
american_scientific_journal-4814	268	21	research	research	PROPN
american_scientific_journal-4814	268	22	journal	journal	NOUN
american_scientific_journal-4814	268	23	for	for	ADP
american_scientific_journal-4814	268	24	engineering	engineering	NOUN
american_scientific_journal-4814	268	25	,	,	PUNCT
american_scientific_journal-4814	268	26	technology	technology	NOUN
american_scientific_journal-4814	268	27	,	,	PUNCT
american_scientific_journal-4814	268	28	and	and	CCONJ
american_scientific_journal-4814	268	29	sciences	science	NOUN
american_scientific_journal-4814	268	30	(	(	PUNCT
american_scientific_journal-4814	268	31	asrjets	asrjet	NOUN
american_scientific_journal-4814	268	32	)	)	PUNCT
american_scientific_journal-4814	268	33	(	(	PUNCT
american_scientific_journal-4814	268	34	2019	2019	NUM
american_scientific_journal-4814	268	35	)	)	PUNCT
american_scientific_journal-4814	268	36	volume	volume	NOUN
american_scientific_journal-4814	268	37	55	55	NUM
american_scientific_journal-4814	268	38	,	,	PUNCT
american_scientific_journal-4814	268	39	no	no	DET
american_scientific_journal-4814	268	40	1	1	NUM
american_scientific_journal-4814	268	41	,	,	PUNCT
american_scientific_journal-4814	268	42	pp	pp	ADP
american_scientific_journal-4814	268	43	50	50	NUM
american_scientific_journal-4814	268	44	-	-	SYM
american_scientific_journal-4814	268	45	68	68	NUM
american_scientific_journal-4814	268	46	67	67	NUM
american_scientific_journal-4814	269	1	[	[	X
american_scientific_journal-4814	269	2	2ℒ	2ℒ	PROPN
american_scientific_journal-4814	269	3	−	−	PROPN
american_scientific_journal-4814	269	4	𝐶𝐶]	𝐶𝐶]	PROPN
american_scientific_journal-4814	269	5	�	�	PROPN
american_scientific_journal-4814	269	6	𝜃𝜃𝑛𝑛[	𝜃𝜃𝑛𝑛[	NOUN
american_scientific_journal-4814	269	7	�	�	PROPN
american_scientific_journal-4814	269	8	̈	̈	SYM
american_scientific_journal-4814	269	9	�	�	NOUN
american_scientific_journal-4814	269	10	𝑔𝑛𝑛(𝑡𝑡	𝑔𝑛𝑛(𝑡𝑡	NOUN
american_scientific_journal-4814	269	11	)	)	PUNCT
american_scientific_journal-4814	270	1	+	+	NUM
american_scientific_journal-4814	270	2	𝜑𝜑𝑛𝑛2𝑔𝑔𝑛𝑛(𝑡𝑡	𝜑𝜑𝑛𝑛2𝑔𝑔𝑛𝑛(𝑡𝑡	NOUN
american_scientific_journal-4814	270	3	)	)	PUNCT
american_scientific_journal-4814	270	4	]	]	PUNCT
american_scientific_journal-4814	271	1	∞	∞	NUM
american_scientific_journal-4814	271	2	𝑛𝑛=1	𝑛𝑛=1	PROPN
american_scientific_journal-4814	271	3	+	+	SYM
american_scientific_journal-4814	271	4	3𝑛𝑛02	3𝑛𝑛02	NUM
american_scientific_journal-4814	271	5	�	�	NOUN
american_scientific_journal-4814	271	6	𝜃𝜃𝑛𝑛𝐶𝐶𝑛𝑛∗𝑔𝑔𝑛𝑛(𝑡𝑡	𝜃𝜃𝑛𝑛𝐶𝐶𝑛𝑛∗𝑔𝑔𝑛𝑛(𝑡𝑡	NOUN
american_scientific_journal-4814	271	7	)	)	PUNCT
american_scientific_journal-4814	271	8	∞	∞	PROPN
american_scientific_journal-4814	271	9	𝑛𝑛=1	𝑛𝑛=1	NOUN
american_scientific_journal-4814	271	10	=	=	SYM
american_scientific_journal-4814	271	11	−2ℒ	−2ℒ	PROPN
american_scientific_journal-4814	271	12	�	�	PROPN
american_scientific_journal-4814	271	13	�	�	PROPN
american_scientific_journal-4814	271	14	̈	̈	X
american_scientific_journal-4814	271	15	�	�	NOUN
american_scientific_journal-4814	271	16	𝜆(𝑡𝑡	𝜆(𝑡𝑡	NOUN
american_scientific_journal-4814	271	17	)	)	PUNCT
american_scientific_journal-4814	271	18	+	+	CCONJ
american_scientific_journal-4814	271	19	3𝑛𝑛02𝜆𝜆(𝑡𝑡)	3𝑛𝑛02𝜆𝜆(𝑡𝑡)	NUM
american_scientific_journal-4814	271	20	�	�	NOUN
american_scientific_journal-4814	271	21	.	.	PUNCT
american_scientific_journal-4814	272	1	with	with	ADP
american_scientific_journal-4814	272	2	:	:	PUNCT
american_scientific_journal-4814	272	3	𝐶𝐶𝑛𝑛∗	𝐶𝐶𝑛𝑛∗	PROPN
american_scientific_journal-4814	272	4	=	=	SYM
american_scientific_journal-4814	272	5	�	�	PROPN
american_scientific_journal-4814	272	6	𝑆𝑆	𝑆𝑆	PROPN
american_scientific_journal-4814	272	7	�	�	PROPN
american_scientific_journal-4814	272	8	1∗(𝑠𝑠)𝑈𝑈𝑛𝑛∗′(𝑠𝑠)𝑑𝑑𝑠𝑠	1∗(𝑠𝑠)𝑈𝑈𝑛𝑛∗′(𝑠𝑠)𝑑𝑑𝑠𝑠	NUM
american_scientific_journal-4814	272	9	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-4814	272	10	0	0	NUM
american_scientific_journal-4814	272	11	+	+	NUM
american_scientific_journal-4814	272	12	�	�	PROPN
american_scientific_journal-4814	272	13	𝑒𝑒𝑇𝑇	𝑒𝑒𝑇𝑇	NOUN
american_scientific_journal-4814	272	14	�	�	NOUN
american_scientific_journal-4814	272	15	1∗(𝑠𝑠)𝛼𝛼𝑛𝑛∗′(𝑠𝑠)𝑑𝑑𝑠𝑠	1∗(𝑠𝑠)𝛼𝛼𝑛𝑛∗′(𝑠𝑠)𝑑𝑑𝑠𝑠	NOUN
american_scientific_journal-4814	272	16	+	+	CCONJ
american_scientific_journal-4814	272	17	𝑏𝑏𝑒𝑒𝑇𝑇	𝑏𝑏𝑒𝑒𝑇𝑇	PROPN
american_scientific_journal-4814	272	18	�	�	NOUN
american_scientific_journal-4814	272	19	1∗(0)𝛼𝛼𝑛𝑛∗′(0	1∗(0)𝛼𝛼𝑛𝑛∗′(0	NUM
american_scientific_journal-4814	272	20	)	)	PUNCT
american_scientific_journal-4814	272	21	𝑙𝑙	𝑙𝑙	NOUN
american_scientific_journal-4814	272	22	0	0	NUM
american_scientific_journal-4814	273	1	+	+	CCONJ
american_scientific_journal-4814	273	2	2ℒ.	2ℒ.	NUM
american_scientific_journal-4814	273	3	one	one	PRON
american_scientific_journal-4814	273	4	uses	use	VERB
american_scientific_journal-4814	273	5	the	the	DET
american_scientific_journal-4814	273	6	equation	equation	NOUN
american_scientific_journal-4814	273	7	of	of	ADP
american_scientific_journal-4814	273	8	generalized	generalized	ADJ
american_scientific_journal-4814	273	9	coordinates	coordinate	NOUN
american_scientific_journal-4814	273	10	(	(	PUNCT
american_scientific_journal-4814	273	11	18	18	NUM
american_scientific_journal-4814	273	12	)	)	PUNCT
american_scientific_journal-4814	273	13	and	and	CCONJ
american_scientific_journal-4814	273	14	after	after	ADP
american_scientific_journal-4814	273	15	some	some	DET
american_scientific_journal-4814	273	16	manipulations	manipulation	NOUN
american_scientific_journal-4814	273	17	:	:	PUNCT
american_scientific_journal-4814	273	18	�	�	PROPN
american_scientific_journal-4814	273	19	̈	̈	X
american_scientific_journal-4814	273	20	�	�	NOUN
american_scientific_journal-4814	273	21	𝜆(𝑡𝑡	𝜆(𝑡𝑡	NOUN
american_scientific_journal-4814	273	22	)	)	PUNCT
american_scientific_journal-4814	273	23	�	�	PROPN
american_scientific_journal-4814	274	1	𝐶𝐶(2ℒ	𝐶𝐶(2ℒ	PROPN
american_scientific_journal-4814	274	2	−	−	NOUN
american_scientific_journal-4814	274	3	𝐶𝐶)	𝐶𝐶)	PROPN
american_scientific_journal-4814	274	4	�	�	NOUN
american_scientific_journal-4814	274	5	𝜃𝜃𝑛𝑛2	𝜃𝜃𝑛𝑛2	ADJ
american_scientific_journal-4814	274	6	∞	∞	NUM
american_scientific_journal-4814	274	7	𝑛𝑛=1	𝑛𝑛=1	NOUN
american_scientific_journal-4814	274	8	+	+	CCONJ
american_scientific_journal-4814	274	9	2ℒ	2ℒ	PROPN
american_scientific_journal-4814	274	10	�	�	PROPN
american_scientific_journal-4814	274	11	+	+	CCONJ
american_scientific_journal-4814	274	12	3𝑛𝑛02	3𝑛𝑛02	NUM
american_scientific_journal-4814	274	13	�	�	PROPN
american_scientific_journal-4814	274	14	𝜆𝜆(𝑡𝑡	𝜆𝜆(𝑡𝑡	PROPN
american_scientific_journal-4814	274	15	)	)	PUNCT
american_scientific_journal-4814	274	16	�	�	PROPN
american_scientific_journal-4814	275	1	𝐶𝐶(2ℒ	𝐶𝐶(2ℒ	PROPN
american_scientific_journal-4814	275	2	−	−	NOUN
american_scientific_journal-4814	275	3	𝐶𝐶)	𝐶𝐶)	PROPN
american_scientific_journal-4814	275	4	�	�	NOUN
american_scientific_journal-4814	275	5	𝜃𝜃𝑛𝑛2	𝜃𝜃𝑛𝑛2	ADJ
american_scientific_journal-4814	275	6	∞	∞	NUM
american_scientific_journal-4814	275	7	𝑛𝑛=1	𝑛𝑛=1	NOUN
american_scientific_journal-4814	275	8	+	+	CCONJ
american_scientific_journal-4814	275	9	2ℒ	2ℒ	PROPN
american_scientific_journal-4814	275	10	�	�	PROPN
american_scientific_journal-4814	275	11	+	+	CCONJ
american_scientific_journal-4814	275	12	�	�	PROPN
american_scientific_journal-4814	275	13	𝜃𝜃𝑛𝑛	𝜃𝜃𝑛𝑛	PROPN
american_scientific_journal-4814	275	14	�	�	PROPN
american_scientific_journal-4814	275	15	𝐶𝐶𝑛𝑛∗𝑔𝑔𝑛𝑛(𝑡𝑡	𝐶𝐶𝑛𝑛∗𝑔𝑔𝑛𝑛(𝑡𝑡	PROPN
american_scientific_journal-4814	275	16	)	)	PUNCT
american_scientific_journal-4814	276	1	−	−	PROPN
american_scientific_journal-4814	277	1	𝐶𝐶(2ℳ	𝐶𝐶(2ℳ	PROPN
american_scientific_journal-4814	277	2	−	−	PROPN
american_scientific_journal-4814	277	3	𝐶𝐶)	𝐶𝐶)	PROPN
american_scientific_journal-4814	277	4	�	�	NOUN
american_scientific_journal-4814	277	5	𝑚𝑚𝑛𝑛𝑝𝑝𝑔𝑔𝑝𝑝(𝑡𝑡	𝑚𝑚𝑛𝑛𝑝𝑝𝑔𝑔𝑝𝑝(𝑡𝑡	NOUN
american_scientific_journal-4814	277	6	)	)	PUNCT
american_scientific_journal-4814	277	7	∞	∞	PROPN
american_scientific_journal-4814	277	8	𝑝𝑝=1	𝑝𝑝=1	ADP
american_scientific_journal-4814	277	9	�	�	PROPN
american_scientific_journal-4814	277	10	∞	∞	PROPN
american_scientific_journal-4814	277	11	𝑛𝑛=1	𝑛𝑛=1	PROPN
american_scientific_journal-4814	277	12	�	�	PROPN
american_scientific_journal-4814	277	13	=	=	SYM
american_scientific_journal-4814	277	14	0	0	PROPN
american_scientific_journal-4814	277	15	.	.	PUNCT
american_scientific_journal-4814	278	1	the	the	DET
american_scientific_journal-4814	278	2	left	left	ADJ
american_scientific_journal-4814	278	3	side	side	NOUN
american_scientific_journal-4814	278	4	of	of	ADP
american_scientific_journal-4814	278	5	the	the	DET
american_scientific_journal-4814	278	6	preceding	precede	VERB
american_scientific_journal-4814	278	7	equation	equation	NOUN
american_scientific_journal-4814	278	8	which	which	PRON
american_scientific_journal-4814	278	9	is	be	AUX
american_scientific_journal-4814	278	10	a	a	DET
american_scientific_journal-4814	278	11	polynomial	polynomial	ADJ
american_scientific_journal-4814	278	12	in	in	ADP
american_scientific_journal-4814	278	13	𝑛𝑛0	𝑛𝑛0	NOUN
american_scientific_journal-4814	278	14	is	be	AUX
american_scientific_journal-4814	278	15	equal	equal	ADJ
american_scientific_journal-4814	278	16	to	to	ADP
american_scientific_journal-4814	278	17	zero	zero	NUM
american_scientific_journal-4814	278	18	whatever	whatever	DET
american_scientific_journal-4814	278	19	𝑛𝑛0	𝑛𝑛0	NOUN
american_scientific_journal-4814	278	20	.	.	PUNCT
american_scientific_journal-4814	279	1	one	one	NUM
american_scientific_journal-4814	279	2	deduces	deduce	VERB
american_scientific_journal-4814	279	3	:	:	PUNCT
american_scientific_journal-4814	279	4	�	�	NOUN
american_scientific_journal-4814	279	5	̈	̈	X
american_scientific_journal-4814	279	6	�	�	NOUN
american_scientific_journal-4814	279	7	𝜆(𝑡𝑡	𝜆(𝑡𝑡	NOUN
american_scientific_journal-4814	279	8	)	)	PUNCT
american_scientific_journal-4814	279	9	�	�	PROPN
american_scientific_journal-4814	279	10	𝐶𝐶(2ℒ	𝐶𝐶(2ℒ	PROPN
american_scientific_journal-4814	279	11	−	−	NOUN
american_scientific_journal-4814	279	12	𝐶𝐶)	𝐶𝐶)	PROPN
american_scientific_journal-4814	279	13	�	�	NOUN
american_scientific_journal-4814	279	14	𝜃𝜃𝑛𝑛2	𝜃𝜃𝑛𝑛2	ADJ
american_scientific_journal-4814	279	15	∞	∞	NUM
american_scientific_journal-4814	279	16	𝑛𝑛=1	𝑛𝑛=1	NOUN
american_scientific_journal-4814	279	17	+	+	CCONJ
american_scientific_journal-4814	279	18	2ℒ	2ℒ	PROPN
american_scientific_journal-4814	279	19	�	�	PROPN
american_scientific_journal-4814	279	20	=	=	SYM
american_scientific_journal-4814	279	21	0	0	NOUN
american_scientific_journal-4814	279	22	this	this	DET
american_scientific_journal-4814	279	23	equation	equation	NOUN
american_scientific_journal-4814	279	24	is	be	AUX
american_scientific_journal-4814	279	25	available	available	ADJ
american_scientific_journal-4814	279	26	whatever	whatever	PRON
american_scientific_journal-4814	279	27	the	the	DET
american_scientific_journal-4814	279	28	parameter	parameter	NOUN
american_scientific_journal-4814	279	29	time	time	NOUN
american_scientific_journal-4814	279	30	𝑡𝑡.	𝑡𝑡.	SCONJ
american_scientific_journal-4814	279	31	finally	finally	ADV
american_scientific_journal-4814	279	32	:	:	PUNCT
american_scientific_journal-4814	279	33	�	�	VERB
american_scientific_journal-4814	279	34	𝜃𝜃𝑛𝑛2	𝜃𝜃𝑛𝑛2	ADJ
american_scientific_journal-4814	279	35	∞	∞	NUM
american_scientific_journal-4814	279	36	𝑛𝑛=1	𝑛𝑛=1	NOUN
american_scientific_journal-4814	279	37	=	=	SYM
american_scientific_journal-4814	279	38	2ℒ	2ℒ	PROPN
american_scientific_journal-4814	279	39	𝐶𝐶(𝐶𝐶	𝐶𝐶(𝐶𝐶	PROPN
american_scientific_journal-4814	279	40	−	−	PROPN
american_scientific_journal-4814	279	41	2ℒ	2ℒ	NOUN
american_scientific_journal-4814	279	42	)	)	PUNCT
american_scientific_journal-4814	279	43	.	.	PUNCT
american_scientific_journal-4814	280	1	•	•	NUM
american_scientific_journal-4814	280	2	appendix	appendix	NOUN
american_scientific_journal-4814	280	3	5	5	NUM
american_scientific_journal-4814	280	4	figure	figure	NOUN
american_scientific_journal-4814	280	5	5	5	NUM
american_scientific_journal-4814	280	6	:	:	PUNCT
american_scientific_journal-4814	280	7	representation	representation	NOUN
american_scientific_journal-4814	280	8	of	of	ADP
american_scientific_journal-4814	280	9	the	the	DET
american_scientific_journal-4814	280	10	function	function	NOUN
american_scientific_journal-4814	280	11	𝑖𝑖𝑁𝑁	𝑖𝑖𝑁𝑁	PUNCT
american_scientific_journal-4814	280	12	as	as	ADP
american_scientific_journal-4814	280	13	a	a	DET
american_scientific_journal-4814	280	14	function	function	NOUN
american_scientific_journal-4814	280	15	of	of	ADP
american_scientific_journal-4814	280	16	𝑁𝑁.	𝑁𝑁.	X
american_scientific_journal-4814	280	17	0	0	NUM
american_scientific_journal-4814	280	18	5	5	NUM
american_scientific_journal-4814	280	19	10	10	NUM
american_scientific_journal-4814	280	20	15	15	NUM
american_scientific_journal-4814	280	21	20	20	NUM
american_scientific_journal-4814	280	22	25	25	NUM
american_scientific_journal-4814	280	23	30	30	NUM
american_scientific_journal-4814	280	24	35	35	NUM
american_scientific_journal-4814	280	25	0	0	NUM
american_scientific_journal-4814	280	26	1	1	NUM
american_scientific_journal-4814	280	27	2	2	NUM
american_scientific_journal-4814	280	28	3	3	NUM
american_scientific_journal-4814	280	29	4	4	NUM
american_scientific_journal-4814	280	30	x	x	SYM
american_scientific_journal-4814	280	31	10	10	NUM
american_scientific_journal-4814	280	32	-5	-5	NUM
american_scientific_journal-4814	280	33	va	va	NOUN
american_scientific_journal-4814	280	34	lu	lu	PROPN
american_scientific_journal-4814	280	35	e	e	PROPN
american_scientific_journal-4814	280	36	of	of	ADP
american_scientific_journal-4814	280	37	s	s	PART
american_scientific_journal-4814	280	38	um	um	INTJ
american_scientific_journal-4814	280	39	m	m	VERB
american_scientific_journal-4814	280	40	on	on	ADP
american_scientific_journal-4814	280	41	s	s	NOUN
american_scientific_journal-4814	280	42	number	number	NOUN
american_scientific_journal-4814	280	43	of	of	ADP
american_scientific_journal-4814	280	44	frequency	frequency	NOUN
american_scientific_journal-4814	280	45	overall	overall	ADJ
american_scientific_journal-4814	280	46	american	american	PROPN
american_scientific_journal-4814	280	47	scientific	scientific	ADJ
american_scientific_journal-4814	280	48	research	research	NOUN
american_scientific_journal-4814	280	49	journal	journal	NOUN
american_scientific_journal-4814	280	50	for	for	ADP
american_scientific_journal-4814	280	51	engineering	engineering	NOUN
american_scientific_journal-4814	280	52	,	,	PUNCT
american_scientific_journal-4814	280	53	technology	technology	NOUN
american_scientific_journal-4814	280	54	,	,	PUNCT
american_scientific_journal-4814	280	55	and	and	CCONJ
american_scientific_journal-4814	280	56	sciences	science	NOUN
american_scientific_journal-4814	280	57	(	(	PUNCT
american_scientific_journal-4814	280	58	asrjets	asrjet	NOUN
american_scientific_journal-4814	280	59	)	)	PUNCT
american_scientific_journal-4814	280	60	(	(	PUNCT
american_scientific_journal-4814	280	61	2019	2019	NUM
american_scientific_journal-4814	280	62	)	)	PUNCT
american_scientific_journal-4814	280	63	volume	volume	NOUN
american_scientific_journal-4814	280	64	55	55	NUM
american_scientific_journal-4814	280	65	,	,	PUNCT
american_scientific_journal-4814	280	66	no	no	DET
american_scientific_journal-4814	280	67	1	1	NUM
american_scientific_journal-4814	280	68	,	,	PUNCT
american_scientific_journal-4814	280	69	pp	pp	ADP
american_scientific_journal-4814	280	70	50	50	NUM
american_scientific_journal-4814	280	71	-	-	SYM
american_scientific_journal-4814	280	72	68	68	NUM
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american_scientific_journal-4814	280	76	:	:	PUNCT
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american_scientific_journal-4814	280	84	𝜑𝜑𝑛𝑛/2𝜋𝜋	𝜑𝜑𝑛𝑛/2𝜋𝜋	VERB
american_scientific_journal-4814	280	85	=	=	SYM
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american_scientific_journal-4814	281	3	:	:	PUNCT
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american_scientific_journal-4814	281	11	𝜑𝜑𝑛𝑛/2𝜋𝜋	𝜑𝜑𝑛𝑛/2𝜋𝜋	X
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american_scientific_journal-4814	282	1	figure	figure	VERB
american_scientific_journal-4814	282	2	8	8	NUM
american_scientific_journal-4814	282	3	:	:	PUNCT
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american_scientific_journal-4814	282	5	of	of	ADP
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american_scientific_journal-4814	282	8	solar	solar	ADJ
american_scientific_journal-4814	282	9	arrays	array	NOUN
american_scientific_journal-4814	282	10	(	(	PUNCT
american_scientific_journal-4814	282	11	𝜑𝜑𝑛𝑛/2𝜋𝜋	𝜑𝜑𝑛𝑛/2𝜋𝜋	X
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american_scientific_journal-4814	283	2	5	5	NUM
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american_scientific_journal-4814	283	4	15	15	NUM
american_scientific_journal-4814	283	5	20	20	NUM
american_scientific_journal-4814	283	6	25	25	NUM
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american_scientific_journal-4814	283	10	0	0	NUM
american_scientific_journal-4814	283	11	1	1	NUM
american_scientific_journal-4814	283	12	2	2	NUM
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american_scientific_journal-4814	283	21	gt	gt	PROPN
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american_scientific_journal-4814	283	31	m	m	VERB
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american_scientific_journal-4814	284	1	en	en	INTJ
american_scientific_journal-4814	284	2	gt	gt	PROPN
american_scientific_journal-4814	284	3	h	h	PROPN
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american_scientific_journal-4814	284	5	th	th	X
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american_scientific_journal-4814	284	8	te	te	PROPN
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american_scientific_journal-4814	284	14	er	er	INTJ
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american_scientific_journal-4814	284	16	0	0	NUM
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american_scientific_journal-4814	284	20	20	20	NUM
american_scientific_journal-4814	284	21	25	25	NUM
american_scientific_journal-4814	284	22	30	30	NUM
american_scientific_journal-4814	284	23	-2	-2	NOUN
american_scientific_journal-4814	284	24	-1	-1	NOUN
american_scientific_journal-4814	284	25	0	0	NUM
american_scientific_journal-4814	284	26	1	1	NUM
american_scientific_journal-4814	284	27	2	2	NUM
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american_scientific_journal-4814	284	29	of	of	ADP
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american_scientific_journal-4814	284	31	(	(	PUNCT
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american_scientific_journal-4814	285	1	en	en	INTJ
american_scientific_journal-4814	285	2	gt	gt	PROPN
american_scientific_journal-4814	285	3	h	h	PROPN
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american_scientific_journal-4814	285	5	th	th	X
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american_scientific_journal-4814	285	10	ce	ce	PROPN
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american_scientific_journal-4814	285	12	m	m	VERB
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american_scientific_journal-4814	285	14	er	er	INTJ
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