id	sid	tid	token	lemma	pos
ejpam-5398	1	1	european	european	PROPN
ejpam-5398	1	2	journal	journal	PROPN
ejpam-5398	1	3	of	of	ADP
ejpam-5398	1	4	pure	pure	ADJ
ejpam-5398	1	5	and	and	CCONJ
ejpam-5398	1	6	applied	apply	VERB
ejpam-5398	1	7	mathematics	mathematic	NOUN
ejpam-5398	1	8	vol	vol	NOUN
ejpam-5398	1	9	.	.	PROPN
ejpam-5398	2	1	17	17	NUM
ejpam-5398	2	2	,	,	PUNCT
ejpam-5398	2	3	no	no	INTJ
ejpam-5398	2	4	.	.	NOUN
ejpam-5398	2	5	4	4	NUM
ejpam-5398	2	6	,	,	PUNCT
ejpam-5398	2	7	2024	2024	NUM
ejpam-5398	2	8	,	,	PUNCT
ejpam-5398	2	9	2878	2878	NUM
ejpam-5398	2	10	-	-	SYM
ejpam-5398	2	11	2897	2897	NUM
ejpam-5398	2	12	issn	issn	PROPN
ejpam-5398	2	13	1307	1307	NUM
ejpam-5398	2	14	-	-	SYM
ejpam-5398	2	15	5543	5543	NUM
ejpam-5398	2	16	–	–	PUNCT
ejpam-5398	3	1	ejpam.com	ejpam.com	X
ejpam-5398	3	2	published	publish	VERB
ejpam-5398	3	3	by	by	ADP
ejpam-5398	3	4	new	new	PROPN
ejpam-5398	3	5	york	york	PROPN
ejpam-5398	3	6	business	business	PROPN
ejpam-5398	3	7	global	global	PROPN
ejpam-5398	3	8	a	a	DET
ejpam-5398	3	9	novel	novel	ADJ
ejpam-5398	3	10	inspection	inspection	NOUN
ejpam-5398	3	11	of	of	ADP
ejpam-5398	3	12	a	a	DET
ejpam-5398	3	13	time	time	NOUN
ejpam-5398	3	14	-	-	PUNCT
ejpam-5398	3	15	delayed	delay	VERB
ejpam-5398	3	16	rolling	rolling	NOUN
ejpam-5398	3	17	of	of	ADP
ejpam-5398	3	18	a	a	DET
ejpam-5398	3	19	rigid	rigid	ADJ
ejpam-5398	3	20	rod	rod	NOUN
ejpam-5398	3	21	khalid	khalid	PROPN
ejpam-5398	3	22	alluhydan1	alluhydan1	PROPN
ejpam-5398	3	23	,	,	PUNCT
ejpam-5398	3	24	galal	galal	PROPN
ejpam-5398	3	25	m.	m.	NOUN
ejpam-5398	3	26	moatimid2	moatimid2	PROPN
ejpam-5398	3	27	,	,	PUNCT
ejpam-5398	3	28	t.	t.	PROPN
ejpam-5398	3	29	s.	s.	PROPN
ejpam-5398	3	30	amer3	amer3	PROPN
ejpam-5398	3	31	,	,	PUNCT
ejpam-5398	3	32	a.	a.	PROPN
ejpam-5398	3	33	a.	a.	PROPN
ejpam-5398	3	34	galal4,∗	galal4,∗	PROPN
ejpam-5398	3	35	1	1	NUM
ejpam-5398	3	36	department	department	NOUN
ejpam-5398	3	37	of	of	ADP
ejpam-5398	3	38	mechanical	mechanical	ADJ
ejpam-5398	3	39	engineering	engineering	NOUN
ejpam-5398	3	40	,	,	PUNCT
ejpam-5398	3	41	college	college	NOUN
ejpam-5398	3	42	of	of	ADP
ejpam-5398	3	43	engineering	engineering	NOUN
ejpam-5398	3	44	,	,	PUNCT
ejpam-5398	3	45	king	king	PROPN
ejpam-5398	3	46	saud	saud	PROPN
ejpam-5398	3	47	university	university	PROPN
ejpam-5398	3	48	,	,	PUNCT
ejpam-5398	3	49	p.o	p.o	PROPN
ejpam-5398	3	50	box	box	PROPN
ejpam-5398	3	51	800	800	NUM
ejpam-5398	3	52	,	,	PUNCT
ejpam-5398	3	53	riyadh	riyadh	NOUN
ejpam-5398	3	54	11421	11421	NUM
ejpam-5398	3	55	,	,	PUNCT
ejpam-5398	3	56	saudi	saudi	PROPN
ejpam-5398	3	57	arabia	arabia	PROPN
ejpam-5398	3	58	2	2	NUM
ejpam-5398	3	59	department	department	NOUN
ejpam-5398	3	60	of	of	ADP
ejpam-5398	3	61	mathematics	mathematic	NOUN
ejpam-5398	3	62	,	,	PUNCT
ejpam-5398	3	63	faculty	faculty	NOUN
ejpam-5398	3	64	of	of	ADP
ejpam-5398	3	65	education	education	NOUN
ejpam-5398	3	66	,	,	PUNCT
ejpam-5398	3	67	ain	ain	PROPN
ejpam-5398	3	68	shams	shams	PROPN
ejpam-5398	3	69	university	university	PROPN
ejpam-5398	3	70	,	,	PUNCT
ejpam-5398	3	71	egypt	egypt	PROPN
ejpam-5398	3	72	3	3	NUM
ejpam-5398	3	73	department	department	NOUN
ejpam-5398	3	74	of	of	ADP
ejpam-5398	3	75	mathematics	mathematic	NOUN
ejpam-5398	3	76	,	,	PUNCT
ejpam-5398	3	77	faculty	faculty	NOUN
ejpam-5398	3	78	of	of	ADP
ejpam-5398	3	79	science	science	NOUN
ejpam-5398	3	80	,	,	PUNCT
ejpam-5398	3	81	tanta	tanta	PROPN
ejpam-5398	3	82	university	university	PROPN
ejpam-5398	3	83	,	,	PUNCT
ejpam-5398	3	84	tanta	tanta	PROPN
ejpam-5398	3	85	31527	31527	NUM
ejpam-5398	3	86	,	,	PUNCT
ejpam-5398	3	87	egypt	egypt	PROPN
ejpam-5398	3	88	4	4	NUM
ejpam-5398	3	89	department	department	NOUN
ejpam-5398	3	90	of	of	ADP
ejpam-5398	3	91	engineering	engineering	NOUN
ejpam-5398	3	92	physics	physics	PROPN
ejpam-5398	3	93	and	and	CCONJ
ejpam-5398	3	94	mathematics	mathematic	NOUN
ejpam-5398	3	95	,	,	PUNCT
ejpam-5398	3	96	faculty	faculty	NOUN
ejpam-5398	3	97	of	of	ADP
ejpam-5398	3	98	engineering	engineering	PROPN
ejpam-5398	3	99	,	,	PUNCT
ejpam-5398	3	100	tanta	tanta	PROPN
ejpam-5398	3	101	university	university	PROPN
ejpam-5398	3	102	,	,	PUNCT
ejpam-5398	3	103	tanta	tanta	PROPN
ejpam-5398	3	104	31734	31734	NUM
ejpam-5398	3	105	,	,	PUNCT
ejpam-5398	3	106	egypt	egypt	PROPN
ejpam-5398	3	107	abstract	abstract	PROPN
ejpam-5398	3	108	.	.	PUNCT
ejpam-5398	4	1	the	the	DET
ejpam-5398	4	2	work	work	NOUN
ejpam-5398	4	3	examines	examine	VERB
ejpam-5398	4	4	the	the	DET
ejpam-5398	4	5	stability	stability	NOUN
ejpam-5398	4	6	configuration	configuration	NOUN
ejpam-5398	4	7	of	of	ADP
ejpam-5398	4	8	a	a	DET
ejpam-5398	4	9	rolling	rolling	ADJ
ejpam-5398	4	10	rigid	rigid	ADJ
ejpam-5398	4	11	rod	rod	NOUN
ejpam-5398	4	12	in	in	ADP
ejpam-5398	4	13	the	the	DET
ejpam-5398	4	14	presence	presence	NOUN
ejpam-5398	4	15	of	of	ADP
ejpam-5398	4	16	a	a	DET
ejpam-5398	4	17	time	time	NOUN
ejpam-5398	4	18	-	-	PUNCT
ejpam-5398	4	19	delayed	delay	VERB
ejpam-5398	4	20	(	(	PUNCT
ejpam-5398	4	21	td	td	NOUN
ejpam-5398	4	22	)	)	PUNCT
ejpam-5398	4	23	in	in	ADP
ejpam-5398	4	24	a	a	DET
ejpam-5398	4	25	square	square	ADJ
ejpam-5398	4	26	position	position	NOUN
ejpam-5398	4	27	as	as	ADV
ejpam-5398	4	28	well	well	ADV
ejpam-5398	4	29	as	as	ADP
ejpam-5398	4	30	velocity	velocity	NOUN
ejpam-5398	4	31	.	.	PUNCT
ejpam-5398	5	1	examining	examine	VERB
ejpam-5398	5	2	time	time	NOUN
ejpam-5398	5	3	-	-	PUNCT
ejpam-5398	5	4	delayed	delay	VERB
ejpam-5398	5	5	rolling	rolling	ADJ
ejpam-5398	5	6	rigid	rigid	ADJ
ejpam-5398	5	7	rod	rod	NOUN
ejpam-5398	5	8	bridges	bridge	NOUN
ejpam-5398	5	9	presents	present	VERB
ejpam-5398	5	10	real	real	ADJ
ejpam-5398	5	11	engineering	engineering	NOUN
ejpam-5398	5	12	challenges	challenge	NOUN
ejpam-5398	5	13	and	and	CCONJ
ejpam-5398	5	14	raises	raise	VERB
ejpam-5398	5	15	significant	significant	ADJ
ejpam-5398	5	16	theoretical	theoretical	ADJ
ejpam-5398	5	17	questions	question	NOUN
ejpam-5398	5	18	,	,	PUNCT
ejpam-5398	5	19	making	make	VERB
ejpam-5398	5	20	it	it	PRON
ejpam-5398	5	21	a	a	DET
ejpam-5398	5	22	desirable	desirable	ADJ
ejpam-5398	5	23	problem	problem	NOUN
ejpam-5398	5	24	in	in	ADP
ejpam-5398	5	25	applied	applied	ADJ
ejpam-5398	5	26	and	and	CCONJ
ejpam-5398	5	27	theoretical	theoretical	ADJ
ejpam-5398	5	28	contexts	contexts	NOUN
ejpam-5398	5	29	.	.	PUNCT
ejpam-5398	6	1	it	it	PRON
ejpam-5398	6	2	is	be	AUX
ejpam-5398	6	3	recommended	recommend	VERB
ejpam-5398	6	4	to	to	PART
ejpam-5398	6	5	use	use	VERB
ejpam-5398	6	6	the	the	DET
ejpam-5398	6	7	non	non	ADJ
ejpam-5398	6	8	-	-	ADJ
ejpam-5398	6	9	perturbative	perturbative	ADJ
ejpam-5398	6	10	approach	approach	NOUN
ejpam-5398	6	11	(	(	PUNCT
ejpam-5398	6	12	npa	npa	NOUN
ejpam-5398	6	13	)	)	PUNCT
ejpam-5398	6	14	to	to	PART
ejpam-5398	6	15	find	find	VERB
ejpam-5398	6	16	an	an	DET
ejpam-5398	6	17	equivalent	equivalent	ADJ
ejpam-5398	6	18	linearized	linearize	VERB
ejpam-5398	6	19	differential	differential	ADJ
ejpam-5398	6	20	equation	equation	NOUN
ejpam-5398	6	21	.	.	PUNCT
ejpam-5398	7	1	actually	actually	ADV
ejpam-5398	7	2	,	,	PUNCT
ejpam-5398	7	3	the	the	DET
ejpam-5398	7	4	npa	npa	NOUN
ejpam-5398	7	5	is	be	AUX
ejpam-5398	7	6	based	base	VERB
ejpam-5398	7	7	on	on	ADP
ejpam-5398	7	8	the	the	DET
ejpam-5398	7	9	he	he	PRON
ejpam-5398	7	10	’s	’s	PART
ejpam-5398	7	11	frequency	frequency	NOUN
ejpam-5398	7	12	formula	formula	NOUN
ejpam-5398	7	13	(	(	PUNCT
ejpam-5398	7	14	hff	hff	NOUN
ejpam-5398	7	15	)	)	PUNCT
ejpam-5398	7	16	.	.	PUNCT
ejpam-5398	8	1	the	the	DET
ejpam-5398	8	2	mathematica	mathematica	PROPN
ejpam-5398	8	3	software	software	PROPN
ejpam-5398	8	4	(	(	PUNCT
ejpam-5398	8	5	ms	ms	NOUN
ejpam-5398	8	6	)	)	PUNCT
ejpam-5398	8	7	is	be	AUX
ejpam-5398	8	8	used	use	VERB
ejpam-5398	8	9	to	to	PART
ejpam-5398	8	10	compare	compare	VERB
ejpam-5398	8	11	and	and	CCONJ
ejpam-5398	8	12	assess	assess	VERB
ejpam-5398	8	13	of	of	ADP
ejpam-5398	8	14	this	this	DET
ejpam-5398	8	15	suitability	suitability	NOUN
ejpam-5398	8	16	.	.	PUNCT
ejpam-5398	9	1	using	use	VERB
ejpam-5398	9	2	the	the	DET
ejpam-5398	9	3	appropriate	appropriate	ADJ
ejpam-5398	9	4	numerical	numerical	ADJ
ejpam-5398	9	5	methodology	methodology	NOUN
ejpam-5398	9	6	(	(	PUNCT
ejpam-5398	9	7	nm	nm	NOUN
ejpam-5398	9	8	)	)	PUNCT
ejpam-5398	9	9	,	,	PUNCT
ejpam-5398	9	10	a	a	DET
ejpam-5398	9	11	matching	matching	NOUN
ejpam-5398	9	12	between	between	ADP
ejpam-5398	9	13	the	the	DET
ejpam-5398	9	14	strong	strong	ADJ
ejpam-5398	9	15	nonlinear	nonlinear	ADJ
ejpam-5398	9	16	ordinary	ordinary	ADJ
ejpam-5398	9	17	differential	differential	ADJ
ejpam-5398	9	18	equation	equation	NOUN
ejpam-5398	9	19	(	(	PUNCT
ejpam-5398	9	20	ode	ode	PROPN
ejpam-5398	9	21	)	)	PUNCT
ejpam-5398	9	22	and	and	CCONJ
ejpam-5398	9	23	the	the	DET
ejpam-5398	9	24	equivalent	equivalent	ADJ
ejpam-5398	9	25	analytical	analytical	ADJ
ejpam-5398	9	26	linear	linear	NOUN
ejpam-5398	9	27	one	one	NUM
ejpam-5398	9	28	is	be	AUX
ejpam-5398	9	29	obtained	obtain	VERB
ejpam-5398	9	30	.	.	PUNCT
ejpam-5398	10	1	this	this	DET
ejpam-5398	10	2	matching	matching	NOUN
ejpam-5398	10	3	has	have	AUX
ejpam-5398	10	4	revealed	reveal	VERB
ejpam-5398	10	5	a	a	DET
ejpam-5398	10	6	very	very	ADV
ejpam-5398	10	7	significant	significant	ADJ
ejpam-5398	10	8	agreement	agreement	NOUN
ejpam-5398	10	9	for	for	ADP
ejpam-5398	10	10	different	different	ADJ
ejpam-5398	10	11	criteria	criterion	NOUN
ejpam-5398	10	12	.	.	PUNCT
ejpam-5398	11	1	stated	state	VERB
ejpam-5398	11	2	differently	differently	ADV
ejpam-5398	11	3	,	,	PUNCT
ejpam-5398	11	4	the	the	DET
ejpam-5398	11	5	new	new	ADJ
ejpam-5398	11	6	performance	performance	NOUN
ejpam-5398	11	7	appears	appear	VERB
ejpam-5398	11	8	powerful	powerful	ADJ
ejpam-5398	11	9	,	,	PUNCT
ejpam-5398	11	10	promising	promising	ADJ
ejpam-5398	11	11	,	,	PUNCT
ejpam-5398	11	12	and	and	CCONJ
ejpam-5398	11	13	beneficial	beneficial	ADJ
ejpam-5398	11	14	,	,	PUNCT
ejpam-5398	11	15	and	and	CCONJ
ejpam-5398	11	16	it	it	PRON
ejpam-5398	11	17	may	may	AUX
ejpam-5398	11	18	be	be	AUX
ejpam-5398	11	19	applied	apply	VERB
ejpam-5398	11	20	to	to	ADP
ejpam-5398	11	21	different	different	ADJ
ejpam-5398	11	22	classes	class	NOUN
ejpam-5398	11	23	of	of	ADP
ejpam-5398	11	24	nonlinear	nonlinear	ADJ
ejpam-5398	11	25	oscillators	oscillator	NOUN
ejpam-5398	11	26	.	.	PUNCT
ejpam-5398	12	1	it	it	PRON
ejpam-5398	12	2	is	be	AUX
ejpam-5398	12	3	well	well	ADV
ejpam-5398	12	4	-	-	PUNCT
ejpam-5398	12	5	precision	precision	NOUN
ejpam-5398	12	6	,	,	PUNCT
ejpam-5398	12	7	flexible	flexible	ADJ
ejpam-5398	12	8	,	,	PUNCT
ejpam-5398	12	9	and	and	CCONJ
ejpam-5398	12	10	convenient	convenient	ADJ
ejpam-5398	12	11	.	.	PUNCT
ejpam-5398	13	1	the	the	DET
ejpam-5398	13	2	new	new	ADJ
ejpam-5398	13	3	approach	approach	NOUN
ejpam-5398	13	4	has	have	VERB
ejpam-5398	13	5	many	many	ADJ
ejpam-5398	13	6	advantages	advantage	NOUN
ejpam-5398	13	7	in	in	ADP
ejpam-5398	13	8	contrast	contrast	NOUN
ejpam-5398	13	9	to	to	ADP
ejpam-5398	13	10	all	all	DET
ejpam-5398	13	11	other	other	ADJ
ejpam-5398	13	12	perturbed	perturb	VERB
ejpam-5398	13	13	methods	method	NOUN
ejpam-5398	13	14	.	.	PUNCT
ejpam-5398	14	1	it	it	PRON
ejpam-5398	14	2	avoids	avoid	VERB
ejpam-5398	14	3	the	the	DET
ejpam-5398	14	4	usage	usage	NOUN
ejpam-5398	14	5	of	of	ADP
ejpam-5398	14	6	the	the	DET
ejpam-5398	14	7	taylor	taylor	PROPN
ejpam-5398	14	8	expansion	expansion	NOUN
ejpam-5398	14	9	in	in	ADP
ejpam-5398	14	10	expanding	expand	VERB
ejpam-5398	14	11	the	the	DET
ejpam-5398	14	12	restoring	restore	VERB
ejpam-5398	14	13	forces	force	NOUN
ejpam-5398	14	14	;	;	PUNCT
ejpam-5398	14	15	particularly	particularly	ADV
ejpam-5398	14	16	in	in	ADP
ejpam-5398	14	17	the	the	DET
ejpam-5398	14	18	topic	topic	NOUN
ejpam-5398	14	19	of	of	ADP
ejpam-5398	14	20	the	the	DET
ejpam-5398	14	21	dynamical	dynamical	ADJ
ejpam-5398	14	22	systems	system	NOUN
ejpam-5398	14	23	.	.	PUNCT
ejpam-5398	15	1	therefore	therefore	ADV
ejpam-5398	15	2	,	,	PUNCT
ejpam-5398	15	3	the	the	DET
ejpam-5398	15	4	stability	stability	NOUN
ejpam-5398	15	5	analysis	analysis	NOUN
ejpam-5398	15	6	is	be	AUX
ejpam-5398	15	7	analyzed	analyze	VERB
ejpam-5398	15	8	and	and	CCONJ
ejpam-5398	15	9	the	the	DET
ejpam-5398	15	10	current	current	ADJ
ejpam-5398	15	11	work	work	NOUN
ejpam-5398	15	12	no	no	ADV
ejpam-5398	15	13	longer	long	ADV
ejpam-5398	15	14	incorporates	incorporate	VERB
ejpam-5398	15	15	this	this	DET
ejpam-5398	15	16	shortcoming	shortcoming	NOUN
ejpam-5398	15	17	.	.	PUNCT
ejpam-5398	16	1	furthermore	furthermore	ADV
ejpam-5398	16	2	,	,	PUNCT
ejpam-5398	16	3	the	the	DET
ejpam-5398	16	4	temporal	temporal	ADJ
ejpam-5398	16	5	histories	history	NOUN
ejpam-5398	16	6	of	of	ADP
ejpam-5398	16	7	the	the	DET
ejpam-5398	16	8	obtained	obtain	VERB
ejpam-5398	16	9	novel	novel	ADJ
ejpam-5398	16	10	outcomes	outcome	NOUN
ejpam-5398	16	11	and	and	CCONJ
ejpam-5398	16	12	their	their	PRON
ejpam-5398	16	13	various	various	ADJ
ejpam-5398	16	14	stable	stable	ADJ
ejpam-5398	16	15	zones	zone	NOUN
ejpam-5398	16	16	are	be	AUX
ejpam-5398	16	17	accomplished	accomplish	VERB
ejpam-5398	16	18	.	.	PUNCT
ejpam-5398	17	1	it	it	PRON
ejpam-5398	17	2	is	be	AUX
ejpam-5398	17	3	possible	possible	ADJ
ejpam-5398	17	4	to	to	PART
ejpam-5398	17	5	examine	examine	VERB
ejpam-5398	17	6	the	the	DET
ejpam-5398	17	7	relevance	relevance	NOUN
ejpam-5398	17	8	of	of	ADP
ejpam-5398	17	9	the	the	DET
ejpam-5398	17	10	employed	employ	VERB
ejpam-5398	17	11	parameter	parameter	NOUN
ejpam-5398	17	12	and	and	CCONJ
ejpam-5398	17	13	demonstrate	demonstrate	VERB
ejpam-5398	17	14	the	the	DET
ejpam-5398	17	15	precision	precision	NOUN
ejpam-5398	17	16	of	of	ADP
ejpam-5398	17	17	the	the	DET
ejpam-5398	17	18	outcomes	outcome	NOUN
ejpam-5398	17	19	through	through	ADP
ejpam-5398	17	20	an	an	DET
ejpam-5398	17	21	exploration	exploration	NOUN
ejpam-5398	17	22	of	of	ADP
ejpam-5398	17	23	the	the	DET
ejpam-5398	17	24	data	datum	NOUN
ejpam-5398	17	25	.	.	PUNCT
ejpam-5398	18	1	it	it	PRON
ejpam-5398	18	2	is	be	AUX
ejpam-5398	18	3	found	find	VERB
ejpam-5398	18	4	that	that	SCONJ
ejpam-5398	18	5	periodic	periodic	ADJ
ejpam-5398	18	6	solutions	solution	NOUN
ejpam-5398	18	7	provide	provide	VERB
ejpam-5398	18	8	reliable	reliable	ADJ
ejpam-5398	18	9	and	and	CCONJ
ejpam-5398	18	10	predictable	predictable	ADJ
ejpam-5398	18	11	behavior	behavior	NOUN
ejpam-5398	18	12	in	in	ADP
ejpam-5398	18	13	a	a	DET
ejpam-5398	18	14	system	system	NOUN
ejpam-5398	18	15	,	,	PUNCT
ejpam-5398	18	16	whereas	whereas	SCONJ
ejpam-5398	18	17	phase	phase	NOUN
ejpam-5398	18	18	plane	plane	NOUN
ejpam-5398	18	19	diagrams	diagram	NOUN
ejpam-5398	18	20	offer	offer	VERB
ejpam-5398	18	21	a	a	DET
ejpam-5398	18	22	visual	visual	ADJ
ejpam-5398	18	23	and	and	CCONJ
ejpam-5398	18	24	quantitative	quantitative	ADJ
ejpam-5398	18	25	comprehension	comprehension	NOUN
ejpam-5398	18	26	of	of	ADP
ejpam-5398	18	27	dynamics	dynamic	NOUN
ejpam-5398	18	28	and	and	CCONJ
ejpam-5398	18	29	stability	stability	NOUN
ejpam-5398	18	30	.	.	PUNCT
ejpam-5398	19	1	this	this	DET
ejpam-5398	19	2	appreciation	appreciation	NOUN
ejpam-5398	19	3	is	be	AUX
ejpam-5398	19	4	vital	vital	ADJ
ejpam-5398	19	5	for	for	ADP
ejpam-5398	19	6	ensuring	ensure	VERB
ejpam-5398	19	7	safe	safe	ADJ
ejpam-5398	19	8	operation	operation	NOUN
ejpam-5398	19	9	under	under	ADP
ejpam-5398	19	10	different	different	ADJ
ejpam-5398	19	11	conditions	condition	NOUN
ejpam-5398	19	12	.	.	PUNCT
ejpam-5398	20	1	2020	2020	NUM
ejpam-5398	20	2	mathematics	mathematic	NOUN
ejpam-5398	20	3	subject	subject	NOUN
ejpam-5398	20	4	classifications	classification	NOUN
ejpam-5398	20	5	:	:	PUNCT
ejpam-5398	20	6	70k20	70k20	NUM
ejpam-5398	20	7	,	,	PUNCT
ejpam-5398	20	8	70q05	70q05	NUM
ejpam-5398	20	9	,	,	PUNCT
ejpam-5398	20	10	70k05	70k05	NUM
ejpam-5398	20	11	,	,	PUNCT
ejpam-5398	20	12	70k40	70k40	NUM
ejpam-5398	20	13	key	key	ADJ
ejpam-5398	20	14	words	word	NOUN
ejpam-5398	20	15	and	and	CCONJ
ejpam-5398	20	16	phrases	phrase	NOUN
ejpam-5398	20	17	:	:	PUNCT
ejpam-5398	20	18	rolling	roll	VERB
ejpam-5398	20	19	rigid	rigid	ADJ
ejpam-5398	20	20	rod	rod	NOUN
ejpam-5398	20	21	,	,	PUNCT
ejpam-5398	20	22	nonlinear	nonlinear	ADJ
ejpam-5398	20	23	vibrations	vibration	NOUN
ejpam-5398	20	24	,	,	PUNCT
ejpam-5398	20	25	square	square	ADJ
ejpam-5398	20	26	position	position	NOUN
ejpam-5398	20	27	-	-	PUNCT
ejpam-5398	20	28	velocity	velocity	NOUN
ejpam-5398	20	29	time	time	NOUN
ejpam-5398	20	30	delay	delay	NOUN
ejpam-5398	20	31	,	,	PUNCT
ejpam-5398	20	32	he	he	PRON
ejpam-5398	20	33	’s	’	VERB
ejpam-5398	20	34	frequency	frequency	NOUN
ejpam-5398	20	35	formula	formula	NOUN
ejpam-5398	20	36	,	,	PUNCT
ejpam-5398	20	37	non	non	ADJ
ejpam-5398	20	38	-	-	ADJ
ejpam-5398	20	39	perturbative	perturbative	ADJ
ejpam-5398	20	40	approach	approach	NOUN
ejpam-5398	20	41	,	,	PUNCT
ejpam-5398	20	42	stability	stability	NOUN
ejpam-5398	20	43	configuration	configuration	NOUN
ejpam-5398	20	44	∗corresponding	∗corresponde	VERB
ejpam-5398	20	45	author	author	NOUN
ejpam-5398	20	46	.	.	PUNCT
ejpam-5398	21	1	doi	doi	NOUN
ejpam-5398	21	2	:	:	PUNCT
ejpam-5398	21	3	https://doi.org/10.29020/nybg.ejpam.v17i4.5398	https://doi.org/10.29020/nybg.ejpam.v17i4.5398	NUM
ejpam-5398	21	4	email	email	NOUN
ejpam-5398	21	5	address	address	NOUN
ejpam-5398	21	6	:	:	PUNCT
ejpam-5398	21	7	abdallah.galal@f-eng.tanta.edu.eg	abdallah.galal@f-eng.tanta.edu.eg	PROPN
ejpam-5398	21	8	(	(	PUNCT
ejpam-5398	21	9	a.	a.	NOUN
ejpam-5398	21	10	a.	a.	PROPN
ejpam-5398	21	11	galal	galal	PROPN
ejpam-5398	21	12	)	)	PUNCT
ejpam-5398	21	13	,	,	PUNCT
ejpam-5398	21	14	kalluhydan@ksu.edu.sa	kalluhydan@ksu.edu.sa	PROPN
ejpam-5398	21	15	(	(	PUNCT
ejpam-5398	21	16	k.	k.	PROPN
ejpam-5398	21	17	alluhydan	alluhydan	PROPN
ejpam-5398	21	18	)	)	PUNCT
ejpam-5398	21	19	,	,	PUNCT
ejpam-5398	21	20	tarek.saleh@science.tanta.edu.eg	tarek.saleh@science.tanta.edu.eg	X
ejpam-5398	21	21	(	(	PUNCT
ejpam-5398	21	22	t.	t.	PROPN
ejpam-5398	21	23	s.	s.	PROPN
ejpam-5398	21	24	amer	amer	PROPN
ejpam-5398	21	25	)	)	PUNCT
ejpam-5398	21	26	,	,	PUNCT
ejpam-5398	21	27	gal	gal	ADJ
ejpam-5398	21	28	moa@edu.asu.edu.eg	moa@edu.asu.edu.eg	PROPN
ejpam-5398	21	29	(	(	PUNCT
ejpam-5398	21	30	g.	g.	PROPN
ejpam-5398	21	31	m.	m.	PROPN
ejpam-5398	21	32	moatimid	moatimid	PROPN
ejpam-5398	21	33	)	)	PUNCT
ejpam-5398	21	34	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5398	21	35	2878	2878	NUM
ejpam-5398	21	36	copyright	copyright	NOUN
ejpam-5398	21	37	:	:	PUNCT
ejpam-5398	21	38	©	©	PROPN
ejpam-5398	21	39	2024	2024	NUM
ejpam-5398	21	40	the	the	DET
ejpam-5398	21	41	author(s	author(s	NOUN
ejpam-5398	21	42	)	)	PUNCT
ejpam-5398	21	43	.	.	PUNCT
ejpam-5398	22	1	(	(	PUNCT
ejpam-5398	22	2	cc	cc	NOUN
ejpam-5398	22	3	by	by	ADP
ejpam-5398	22	4	-	-	PUNCT
ejpam-5398	22	5	nc	nc	PROPN
ejpam-5398	22	6	4.0	4.0	NUM
ejpam-5398	22	7	)	)	PUNCT
ejpam-5398	22	8	a.	a.	NOUN
ejpam-5398	22	9	a.	a.	NOUN
ejpam-5398	22	10	galal	galal	PROPN
ejpam-5398	22	11	et	et	PROPN
ejpam-5398	22	12	al	al	PROPN
ejpam-5398	22	13	.	.	PUNCT
ejpam-5398	22	14	/	/	SYM
ejpam-5398	22	15	eur	eur	PROPN
ejpam-5398	22	16	.	.	PUNCT
ejpam-5398	23	1	j.	j.	PROPN
ejpam-5398	23	2	pure	pure	PROPN
ejpam-5398	23	3	appl	appl	PROPN
ejpam-5398	23	4	.	.	PROPN
ejpam-5398	23	5	math	math	PROPN
ejpam-5398	23	6	,	,	PUNCT
ejpam-5398	23	7	17	17	NUM
ejpam-5398	23	8	(	(	PUNCT
ejpam-5398	23	9	4	4	NUM
ejpam-5398	23	10	)	)	PUNCT
ejpam-5398	23	11	(	(	PUNCT
ejpam-5398	23	12	2024	2024	NUM
ejpam-5398	23	13	)	)	PUNCT
ejpam-5398	23	14	,	,	PUNCT
ejpam-5398	23	15	2878	2878	NUM
ejpam-5398	23	16	-	-	SYM
ejpam-5398	23	17	2897	2897	NUM
ejpam-5398	23	18	2879	2879	NUM
ejpam-5398	23	19	nomenclature	nomenclature	NOUN
ejpam-5398	23	20	l	l	NOUN
ejpam-5398	23	21	:	:	PUNCT
ejpam-5398	23	22	length	length	NOUN
ejpam-5398	23	23	of	of	ADP
ejpam-5398	23	24	the	the	DET
ejpam-5398	23	25	rod	rod	NOUN
ejpam-5398	23	26	.	.	PUNCT
ejpam-5398	24	1	θ	θ	X
ejpam-5398	24	2	:	:	PUNCT
ejpam-5398	24	3	angular	angular	ADJ
ejpam-5398	24	4	displacement	displacement	NOUN
ejpam-5398	24	5	.	.	PUNCT
ejpam-5398	25	1	t	t	NOUN
ejpam-5398	25	2	:	:	PUNCT
ejpam-5398	25	3	time	time	NOUN
ejpam-5398	25	4	.	.	PUNCT
ejpam-5398	26	1	·	·	PUNCT
ejpam-5398	26	2	:	:	PUNCT
ejpam-5398	26	3	time	time	NOUN
ejpam-5398	26	4	derivative	derivative	ADJ
ejpam-5398	26	5	.	.	PUNCT
ejpam-5398	27	1	τ	τ	X
ejpam-5398	27	2	:	:	PUNCT
ejpam-5398	27	3	time	time	NOUN
ejpam-5398	27	4	-	-	PUNCT
ejpam-5398	27	5	decay	decay	NOUN
ejpam-5398	27	6	.	.	PUNCT
ejpam-5398	28	1	m	m	VERB
ejpam-5398	28	2	:	:	PUNCT
ejpam-5398	28	3	uniform	uniform	ADJ
ejpam-5398	28	4	rigid	rigid	ADJ
ejpam-5398	28	5	rod	rod	NOUN
ejpam-5398	28	6	’s	’s	PART
ejpam-5398	28	7	mass	mass	NOUN
ejpam-5398	28	8	.	.	PUNCT
ejpam-5398	29	1	g	g	NOUN
ejpam-5398	29	2	:	:	PUNCT
ejpam-5398	29	3	gravity	gravity	NOUN
ejpam-5398	29	4	’s	’s	PART
ejpam-5398	29	5	acceleration	acceleration	NOUN
ejpam-5398	29	6	.	.	PUNCT
ejpam-5398	30	1	2r	2r	NUM
ejpam-5398	30	2	:	:	PUNCT
ejpam-5398	30	3	circular	circular	ADJ
ejpam-5398	30	4	surface	surface	NOUN
ejpam-5398	30	5	diameter	diameter	NOUN
ejpam-5398	30	6	.	.	PUNCT
ejpam-5398	31	1	c.m	c.m	INTJ
ejpam-5398	31	2	:	:	PUNCT
ejpam-5398	31	3	center	center	NOUN
ejpam-5398	31	4	of	of	ADP
ejpam-5398	31	5	mass	mass	NOUN
ejpam-5398	31	6	of	of	ADP
ejpam-5398	31	7	the	the	DET
ejpam-5398	31	8	uniform	uniform	ADJ
ejpam-5398	31	9	rod	rod	NOUN
ejpam-5398	31	10	.	.	PUNCT
ejpam-5398	32	1	a	a	DET
ejpam-5398	32	2	,	,	PUNCT
ejpam-5398	32	3	b	b	NOUN
ejpam-5398	32	4	:	:	PUNCT
ejpam-5398	32	5	non	non	ADJ
ejpam-5398	32	6	-	-	ADJ
ejpam-5398	32	7	dimensional	dimensional	ADJ
ejpam-5398	32	8	quantities	quantity	NOUN
ejpam-5398	32	9	.	.	PUNCT
ejpam-5398	33	1	1	1	X
ejpam-5398	33	2	.	.	X
ejpam-5398	33	3	introduction	introduction	NOUN
ejpam-5398	33	4	there	there	PRON
ejpam-5398	33	5	are	be	VERB
ejpam-5398	33	6	various	various	ADJ
ejpam-5398	33	7	amounts	amount	NOUN
ejpam-5398	33	8	of	of	ADP
ejpam-5398	33	9	nonlinear	nonlinear	ADJ
ejpam-5398	33	10	phenomena	phenomenon	NOUN
ejpam-5398	33	11	present	present	ADJ
ejpam-5398	33	12	in	in	ADP
ejpam-5398	33	13	all	all	DET
ejpam-5398	33	14	practical	practical	ADJ
ejpam-5398	33	15	structures	structure	NOUN
ejpam-5398	33	16	.	.	PUNCT
ejpam-5398	34	1	the	the	DET
ejpam-5398	34	2	nonlinearity	nonlinearity	NOUN
ejpam-5398	34	3	’s	’s	PART
ejpam-5398	34	4	characteristics	characteristic	NOUN
ejpam-5398	34	5	are	be	AUX
ejpam-5398	34	6	usually	usually	ADV
ejpam-5398	34	7	understated	understate	VERB
ejpam-5398	34	8	enough	enough	ADV
ejpam-5398	34	9	to	to	PART
ejpam-5398	34	10	be	be	AUX
ejpam-5398	34	11	not	not	PART
ejpam-5398	34	12	ignored	ignore	VERB
ejpam-5398	34	13	.	.	PUNCT
ejpam-5398	35	1	consequently	consequently	ADV
ejpam-5398	35	2	,	,	PUNCT
ejpam-5398	35	3	the	the	DET
ejpam-5398	35	4	linear	linear	PROPN
ejpam-5398	35	5	theories	theory	NOUN
ejpam-5398	35	6	can	can	AUX
ejpam-5398	35	7	not	not	PART
ejpam-5398	35	8	be	be	AUX
ejpam-5398	35	9	used	use	VERB
ejpam-5398	35	10	to	to	PART
ejpam-5398	35	11	study	study	VERB
ejpam-5398	35	12	the	the	DET
ejpam-5398	35	13	dynamics	dynamic	NOUN
ejpam-5398	35	14	and	and	CCONJ
ejpam-5398	35	15	behavior	behavior	NOUN
ejpam-5398	35	16	of	of	ADP
ejpam-5398	35	17	these	these	DET
ejpam-5398	35	18	systems	system	NOUN
ejpam-5398	35	19	.	.	PUNCT
ejpam-5398	36	1	on	on	ADP
ejpam-5398	36	2	the	the	DET
ejpam-5398	36	3	other	other	ADJ
ejpam-5398	36	4	hand	hand	NOUN
ejpam-5398	36	5	,	,	PUNCT
ejpam-5398	36	6	many	many	ADJ
ejpam-5398	36	7	structures	structure	NOUN
ejpam-5398	36	8	in	in	ADP
ejpam-5398	36	9	the	the	DET
ejpam-5398	36	10	real	real	ADJ
ejpam-5398	36	11	-	-	PUNCT
ejpam-5398	36	12	world	world	NOUN
ejpam-5398	36	13	have	have	VERB
ejpam-5398	36	14	large	large	ADJ
ejpam-5398	36	15	nonlinearities	nonlinearitie	NOUN
ejpam-5398	36	16	that	that	PRON
ejpam-5398	36	17	make	make	VERB
ejpam-5398	36	18	linear	linear	ADJ
ejpam-5398	36	19	theories	theory	NOUN
ejpam-5398	36	20	out	out	ADP
ejpam-5398	36	21	-	-	PUNCT
ejpam-5398	36	22	of	of	ADP
ejpam-5398	36	23	-	-	PUNCT
ejpam-5398	36	24	date	date	NOUN
ejpam-5398	36	25	.	.	PUNCT
ejpam-5398	37	1	furthermore	furthermore	ADV
ejpam-5398	37	2	,	,	PUNCT
ejpam-5398	37	3	the	the	DET
ejpam-5398	37	4	system	system	NOUN
ejpam-5398	37	5	richer	rich	ADJ
ejpam-5398	37	6	the	the	DET
ejpam-5398	37	7	dynamical	dynamical	ADJ
ejpam-5398	37	8	behavior	behavior	NOUN
ejpam-5398	37	9	,	,	PUNCT
ejpam-5398	37	10	such	such	ADJ
ejpam-5398	37	11	as	as	ADP
ejpam-5398	37	12	period	period	NOUN
ejpam-5398	37	13	doubling	double	VERB
ejpam-5398	37	14	,	,	PUNCT
ejpam-5398	37	15	quasi	quasi	ADJ
ejpam-5398	37	16	-	-	ADJ
ejpam-5398	37	17	periodic	periodic	ADJ
ejpam-5398	37	18	behavior	behavior	NOUN
ejpam-5398	37	19	,	,	PUNCT
ejpam-5398	37	20	and	and	CCONJ
ejpam-5398	37	21	chaotic	chaotic	ADJ
ejpam-5398	37	22	response	response	NOUN
ejpam-5398	37	23	,	,	PUNCT
ejpam-5398	37	24	may	may	AUX
ejpam-5398	37	25	be	be	AUX
ejpam-5398	37	26	disregarded	disregard	VERB
ejpam-5398	37	27	if	if	SCONJ
ejpam-5398	37	28	linear	linear	ADJ
ejpam-5398	37	29	techniques	technique	NOUN
ejpam-5398	37	30	are	be	AUX
ejpam-5398	37	31	applied	apply	VERB
ejpam-5398	37	32	to	to	ADP
ejpam-5398	37	33	highly	highly	ADV
ejpam-5398	37	34	nonlinear	nonlinear	ADJ
ejpam-5398	37	35	systems	system	NOUN
ejpam-5398	37	36	.	.	PUNCT
ejpam-5398	38	1	therefore	therefore	ADV
ejpam-5398	38	2	,	,	PUNCT
ejpam-5398	38	3	a	a	DET
ejpam-5398	38	4	full	full	ADJ
ejpam-5398	38	5	understanding	understanding	NOUN
ejpam-5398	38	6	of	of	ADP
ejpam-5398	38	7	nonlinear	nonlinear	ADJ
ejpam-5398	38	8	system	system	NOUN
ejpam-5398	38	9	dynamics	dynamic	NOUN
ejpam-5398	38	10	is	be	AUX
ejpam-5398	38	11	necessary	necessary	ADJ
ejpam-5398	38	12	to	to	PART
ejpam-5398	38	13	comprehend	comprehend	VERB
ejpam-5398	38	14	organizational	organizational	ADJ
ejpam-5398	38	15	dynamics	dynamic	NOUN
ejpam-5398	38	16	.	.	PUNCT
ejpam-5398	39	1	differential	differential	ADJ
ejpam-5398	39	2	equation	equation	NOUN
ejpam-5398	39	3	systems	system	NOUN
ejpam-5398	39	4	,	,	PUNCT
ejpam-5398	39	5	ordinary	ordinary	ADJ
ejpam-5398	39	6	or	or	CCONJ
ejpam-5398	39	7	partial	partial	ADJ
ejpam-5398	39	8	,	,	PUNCT
ejpam-5398	39	9	are	be	AUX
ejpam-5398	39	10	widely	widely	ADV
ejpam-5398	39	11	recognized	recognize	VERB
ejpam-5398	39	12	for	for	ADP
ejpam-5398	39	13	their	their	PRON
ejpam-5398	39	14	ability	ability	NOUN
ejpam-5398	39	15	to	to	PART
ejpam-5398	39	16	represent	represent	VERB
ejpam-5398	39	17	a	a	DET
ejpam-5398	39	18	wide	wide	ADJ
ejpam-5398	39	19	range	range	NOUN
ejpam-5398	39	20	of	of	ADP
ejpam-5398	39	21	engineering	engineering	NOUN
ejpam-5398	39	22	systems	system	NOUN
ejpam-5398	39	23	.	.	PUNCT
ejpam-5398	40	1	with	with	ADP
ejpam-5398	40	2	a	a	DET
ejpam-5398	40	3	few	few	ADJ
ejpam-5398	40	4	exclusions	exclusion	NOUN
ejpam-5398	40	5	,	,	PUNCT
ejpam-5398	40	6	their	their	PRON
ejpam-5398	40	7	exact	exact	ADJ
ejpam-5398	40	8	solutions	solution	NOUN
ejpam-5398	40	9	seem	seem	VERB
ejpam-5398	40	10	too	too	ADV
ejpam-5398	40	11	challenging	challenging	ADJ
ejpam-5398	40	12	and	and	CCONJ
ejpam-5398	40	13	unachievable	unachievable	ADJ
ejpam-5398	40	14	.	.	PUNCT
ejpam-5398	41	1	in	in	ADP
ejpam-5398	41	2	order	order	NOUN
ejpam-5398	41	3	to	to	PART
ejpam-5398	41	4	make	make	VERB
ejpam-5398	41	5	handling	handle	VERB
ejpam-5398	41	6	numerous	numerous	ADJ
ejpam-5398	41	7	nonlinear	nonlinear	ADJ
ejpam-5398	41	8	equations	equation	NOUN
ejpam-5398	41	9	easier	easy	ADJ
ejpam-5398	41	10	,	,	PUNCT
ejpam-5398	41	11	many	many	ADJ
ejpam-5398	41	12	academics	academic	NOUN
ejpam-5398	41	13	are	be	AUX
ejpam-5398	41	14	focused	focus	VERB
ejpam-5398	41	15	their	their	PRON
ejpam-5398	41	16	attention	attention	NOUN
ejpam-5398	41	17	on	on	ADP
ejpam-5398	41	18	the	the	DET
ejpam-5398	41	19	approximation	approximation	NOUN
ejpam-5398	41	20	solutions	solution	NOUN
ejpam-5398	41	21	for	for	ADP
ejpam-5398	41	22	specific	specific	ADJ
ejpam-5398	41	23	weak	weak	ADJ
ejpam-5398	41	24	nonlinear	nonlinear	ADJ
ejpam-5398	41	25	issues	issue	NOUN
ejpam-5398	41	26	,	,	PUNCT
ejpam-5398	41	27	such	such	ADJ
ejpam-5398	41	28	as	as	ADP
ejpam-5398	41	29	the	the	DET
ejpam-5398	41	30	mean	mean	ADJ
ejpam-5398	41	31	approach	approach	NOUN
ejpam-5398	41	32	and	and	CCONJ
ejpam-5398	41	33	the	the	DET
ejpam-5398	41	34	procedure	procedure	NOUN
ejpam-5398	41	35	of	of	ADP
ejpam-5398	41	36	extremely	extremely	ADV
ejpam-5398	41	37	tiny	tiny	ADJ
ejpam-5398	41	38	parameters	parameter	NOUN
ejpam-5398	41	39	[	[	X
ejpam-5398	41	40	9	9	NUM
ejpam-5398	41	41	,	,	PUNCT
ejpam-5398	41	42	10	10	NUM
ejpam-5398	41	43	,	,	PUNCT
ejpam-5398	41	44	35	35	NUM
ejpam-5398	41	45	,	,	PUNCT
ejpam-5398	41	46	42	42	NUM
ejpam-5398	41	47	]	]	PUNCT
ejpam-5398	41	48	.	.	PUNCT
ejpam-5398	42	1	analysis	analysis	NOUN
ejpam-5398	42	2	was	be	AUX
ejpam-5398	42	3	done	do	VERB
ejpam-5398	42	4	on	on	ADP
ejpam-5398	42	5	the	the	DET
ejpam-5398	42	6	magnetic	magnetic	ADJ
ejpam-5398	42	7	spherical	spherical	ADJ
ejpam-5398	42	8	pendulum	pendulum	NOUN
ejpam-5398	42	9	problem	problem	NOUN
ejpam-5398	42	10	[	[	X
ejpam-5398	42	11	16	16	NUM
ejpam-5398	42	12	]	]	PUNCT
ejpam-5398	42	13	.	.	PUNCT
ejpam-5398	43	1	the	the	DET
ejpam-5398	43	2	issue	issue	NOUN
ejpam-5398	43	3	was	be	AUX
ejpam-5398	43	4	investigated	investigate	VERB
ejpam-5398	43	5	using	use	VERB
ejpam-5398	43	6	the	the	DET
ejpam-5398	43	7	advanced	advanced	ADJ
ejpam-5398	43	8	nonlinear	nonlinear	ADJ
ejpam-5398	43	9	frequency	frequency	NOUN
ejpam-5398	43	10	,	,	PUNCT
ejpam-5398	43	11	additionally	additionally	ADV
ejpam-5398	43	12	with	with	ADP
ejpam-5398	43	13	the	the	DET
ejpam-5398	43	14	homotopy	homotopy	NOUN
ejpam-5398	43	15	perturbation	perturbation	NOUN
ejpam-5398	43	16	method	method	NOUN
ejpam-5398	43	17	(	(	PUNCT
ejpam-5398	43	18	hpm	hpm	NOUN
ejpam-5398	43	19	)	)	PUNCT
ejpam-5398	43	20	,	,	PUNCT
ejpam-5398	43	21	and	and	CCONJ
ejpam-5398	43	22	the	the	DET
ejpam-5398	43	23	laplace	laplace	NOUN
ejpam-5398	43	24	transforms	transform	VERB
ejpam-5398	43	25	.	.	PUNCT
ejpam-5398	44	1	it	it	PRON
ejpam-5398	44	2	was	be	AUX
ejpam-5398	44	3	studied	study	VERB
ejpam-5398	44	4	how	how	SCONJ
ejpam-5398	44	5	to	to	PART
ejpam-5398	44	6	move	move	VERB
ejpam-5398	44	7	a	a	DET
ejpam-5398	44	8	simple	simple	ADJ
ejpam-5398	44	9	pendulum	pendulum	NOUN
ejpam-5398	44	10	with	with	ADP
ejpam-5398	44	11	a	a	DET
ejpam-5398	44	12	light	light	ADJ
ejpam-5398	44	13	spring	spring	NOUN
ejpam-5398	44	14	and	and	CCONJ
ejpam-5398	44	15	a	a	DET
ejpam-5398	44	16	rolling	rolling	ADJ
ejpam-5398	44	17	wheel	wheel	NOUN
ejpam-5398	44	18	attachment	attachment	NOUN
ejpam-5398	45	1	[	[	X
ejpam-5398	45	2	14	14	NUM
ejpam-5398	45	3	]	]	PUNCT
ejpam-5398	45	4	.	.	PUNCT
ejpam-5398	46	1	the	the	DET
ejpam-5398	46	2	basic	basic	ADJ
ejpam-5398	46	3	motion	motion	NOUN
ejpam-5398	46	4	equation	equation	NOUN
ejpam-5398	46	5	experienced	experience	VERB
ejpam-5398	46	6	a	a	DET
ejpam-5398	46	7	transformation	transformation	NOUN
ejpam-5398	46	8	into	into	ADP
ejpam-5398	46	9	high	high	ADJ
ejpam-5398	46	10	nonlinear	nonlinear	ADJ
ejpam-5398	46	11	ode	ode	NOUN
ejpam-5398	46	12	under	under	ADP
ejpam-5398	46	13	specific	specific	ADJ
ejpam-5398	46	14	conditions	condition	NOUN
ejpam-5398	46	15	.	.	PUNCT
ejpam-5398	47	1	the	the	DET
ejpam-5398	47	2	complicated	complicated	ADJ
ejpam-5398	47	3	behavior	behavior	NOUN
ejpam-5398	47	4	of	of	ADP
ejpam-5398	47	5	a	a	DET
ejpam-5398	47	6	perturbed	perturb	VERB
ejpam-5398	47	7	van	van	PROPN
ejpam-5398	47	8	der	der	ADJ
ejpam-5398	47	9	pol	pol	PROPN
ejpam-5398	47	10	-	-	PUNCT
ejpam-5398	47	11	duffing	duffe	VERB
ejpam-5398	47	12	oscillator	oscillator	NOUN
ejpam-5398	47	13	was	be	AUX
ejpam-5398	47	14	effectively	effectively	ADV
ejpam-5398	47	15	reduced	reduce	VERB
ejpam-5398	47	16	by	by	ADP
ejpam-5398	47	17	utilizing	utilize	VERB
ejpam-5398	47	18	td	td	NOUN
ejpam-5398	47	19	position	position	NOUN
ejpam-5398	47	20	and	and	CCONJ
ejpam-5398	47	21	velocity	velocity	NOUN
ejpam-5398	47	22	[	[	X
ejpam-5398	47	23	15	15	NUM
ejpam-5398	47	24	]	]	PUNCT
ejpam-5398	47	25	.	.	PUNCT
ejpam-5398	48	1	a	a	DET
ejpam-5398	48	2	time	time	NOUN
ejpam-5398	48	3	delay	delay	NOUN
ejpam-5398	48	4	was	be	AUX
ejpam-5398	48	5	implemented	implement	VERB
ejpam-5398	48	6	as	as	ADP
ejpam-5398	48	7	an	an	DET
ejpam-5398	48	8	additional	additional	ADJ
ejpam-5398	48	9	protection	protection	NOUN
ejpam-5398	48	10	to	to	PART
ejpam-5398	48	11	prevent	prevent	VERB
ejpam-5398	48	12	the	the	DET
ejpam-5398	48	13	system	system	NOUN
ejpam-5398	48	14	under	under	ADP
ejpam-5398	48	15	examination	examination	NOUN
ejpam-5398	48	16	from	from	ADP
ejpam-5398	48	17	undergoing	undergo	VERB
ejpam-5398	48	18	the	the	DET
ejpam-5398	48	19	nonlinear	nonlinear	ADJ
ejpam-5398	48	20	vibrations	vibration	NOUN
ejpam-5398	48	21	.	.	PUNCT
ejpam-5398	49	1	the	the	DET
ejpam-5398	49	2	issue	issue	NOUN
ejpam-5398	49	3	of	of	ADP
ejpam-5398	49	4	this	this	DET
ejpam-5398	49	5	work	work	NOUN
ejpam-5398	49	6	was	be	AUX
ejpam-5398	49	7	especially	especially	ADV
ejpam-5398	49	8	current	current	ADJ
ejpam-5398	49	9	since	since	SCONJ
ejpam-5398	49	10	technologies	technology	NOUN
ejpam-5398	49	11	with	with	ADP
ejpam-5398	49	12	a	a	DET
ejpam-5398	49	13	td	td	NOUN
ejpam-5398	49	14	are	be	AUX
ejpam-5398	49	15	the	the	DET
ejpam-5398	49	16	subject	subject	NOUN
ejpam-5398	49	17	of	of	ADP
ejpam-5398	49	18	many	many	ADJ
ejpam-5398	49	19	investigations	investigation	NOUN
ejpam-5398	49	20	recently	recently	ADV
ejpam-5398	49	21	.	.	PUNCT
ejpam-5398	50	1	over	over	ADP
ejpam-5398	50	2	the	the	DET
ejpam-5398	50	3	recent	recent	ADJ
ejpam-5398	50	4	years	year	NOUN
ejpam-5398	50	5	,	,	PUNCT
ejpam-5398	50	6	the	the	DET
ejpam-5398	50	7	techniques	technique	NOUN
ejpam-5398	50	8	involving	involve	VERB
ejpam-5398	50	9	td	td	NOUN
ejpam-5398	50	10	have	have	AUX
ejpam-5398	50	11	increasingly	increasingly	ADV
ejpam-5398	50	12	drawn	draw	VERB
ejpam-5398	50	13	interest	interest	NOUN
ejpam-5398	50	14	.	.	PUNCT
ejpam-5398	51	1	henceforth	henceforth	ADV
ejpam-5398	51	2	,	,	PUNCT
ejpam-5398	51	3	research	research	NOUN
ejpam-5398	51	4	was	be	AUX
ejpam-5398	51	5	conducted	conduct	VERB
ejpam-5398	51	6	on	on	ADP
ejpam-5398	51	7	a	a	DET
ejpam-5398	51	8	td	td	NOUN
ejpam-5398	51	9	controller	controller	NOUN
ejpam-5398	51	10	for	for	ADP
ejpam-5398	51	11	a	a	DET
ejpam-5398	51	12	damped	damped	NOUN
ejpam-5398	51	13	,	,	PUNCT
ejpam-5398	51	14	nonlinear	nonlinear	ADJ
ejpam-5398	51	15	,	,	PUNCT
ejpam-5398	51	16	excited	excited	ADJ
ejpam-5398	51	17	duffing	duffing	NOUN
ejpam-5398	51	18	oscillator	oscillator	NOUN
ejpam-5398	51	19	(	(	PUNCT
ejpam-5398	51	20	do	do	AUX
ejpam-5398	51	21	)	)	PUNCT
ejpam-5398	52	1	[	[	X
ejpam-5398	52	2	19	19	NUM
ejpam-5398	52	3	]	]	PUNCT
ejpam-5398	52	4	.	.	PUNCT
ejpam-5398	53	1	the	the	DET
ejpam-5398	53	2	modified	modify	VERB
ejpam-5398	53	3	periodic	periodic	ADJ
ejpam-5398	53	4	solution	solution	NOUN
ejpam-5398	53	5	that	that	PRON
ejpam-5398	53	6	forms	form	VERB
ejpam-5398	53	7	the	the	DET
ejpam-5398	53	8	basis	basis	NOUN
ejpam-5398	53	9	of	of	ADP
ejpam-5398	53	10	the	the	DET
ejpam-5398	53	11	current	current	ADJ
ejpam-5398	53	12	investigation	investigation	NOUN
ejpam-5398	53	13	is	be	AUX
ejpam-5398	53	14	called	call	VERB
ejpam-5398	53	15	the	the	DET
ejpam-5398	53	16	hff	hff	NOUN
ejpam-5398	53	17	.	.	PUNCT
ejpam-5398	54	1	the	the	DET
ejpam-5398	54	2	examination	examination	NOUN
ejpam-5398	54	3	of	of	ADP
ejpam-5398	54	4	a.	a.	PROPN
ejpam-5398	54	5	a.	a.	PROPN
ejpam-5398	54	6	galal	galal	PROPN
ejpam-5398	54	7	et	et	PROPN
ejpam-5398	54	8	al	al	PROPN
ejpam-5398	54	9	.	.	PUNCT
ejpam-5398	54	10	/	/	SYM
ejpam-5398	54	11	eur	eur	PROPN
ejpam-5398	54	12	.	.	PUNCT
ejpam-5398	55	1	j.	j.	PROPN
ejpam-5398	55	2	pure	pure	PROPN
ejpam-5398	55	3	appl	appl	PROPN
ejpam-5398	55	4	.	.	PROPN
ejpam-5398	55	5	math	math	PROPN
ejpam-5398	55	6	,	,	PUNCT
ejpam-5398	55	7	17	17	NUM
ejpam-5398	55	8	(	(	PUNCT
ejpam-5398	55	9	4	4	NUM
ejpam-5398	55	10	)	)	PUNCT
ejpam-5398	55	11	(	(	PUNCT
ejpam-5398	55	12	2024	2024	NUM
ejpam-5398	55	13	)	)	PUNCT
ejpam-5398	55	14	,	,	PUNCT
ejpam-5398	55	15	2878	2878	NUM
ejpam-5398	55	16	-	-	SYM
ejpam-5398	55	17	2897	2897	NUM
ejpam-5398	55	18	2880	2880	NUM
ejpam-5398	55	19	the	the	DET
ejpam-5398	55	20	stability	stability	NOUN
ejpam-5398	55	21	analysis	analysis	NOUN
ejpam-5398	55	22	concerning	concern	VERB
ejpam-5398	55	23	the	the	DET
ejpam-5398	55	24	disturbed	disturbed	ADJ
ejpam-5398	55	25	pendulum	pendulum	NOUN
ejpam-5398	55	26	movement	movement	NOUN
ejpam-5398	55	27	was	be	AUX
ejpam-5398	55	28	conducted	conduct	VERB
ejpam-5398	55	29	using	use	VERB
ejpam-5398	55	30	the	the	DET
ejpam-5398	55	31	adapted	adapted	ADJ
ejpam-5398	55	32	hpm	hpm	NOUN
ejpam-5398	55	33	.	.	PUNCT
ejpam-5398	56	1	the	the	DET
ejpam-5398	56	2	td	td	NOUN
ejpam-5398	56	3	for	for	ADP
ejpam-5398	56	4	position	position	NOUN
ejpam-5398	56	5	and	and	CCONJ
ejpam-5398	56	6	velocity	velocity	NOUN
ejpam-5398	56	7	are	be	AUX
ejpam-5398	56	8	employed	employ	VERB
ejpam-5398	56	9	in	in	ADP
ejpam-5398	56	10	order	order	NOUN
ejpam-5398	56	11	to	to	PART
ejpam-5398	56	12	reduce	reduce	VERB
ejpam-5398	56	13	the	the	DET
ejpam-5398	56	14	complex	complex	ADJ
ejpam-5398	56	15	oscillation	oscillation	NOUN
ejpam-5398	56	16	’s	’s	PART
ejpam-5398	56	17	behavior	behavior	NOUN
ejpam-5398	56	18	of	of	ADP
ejpam-5398	56	19	the	the	DET
ejpam-5398	56	20	framework	framework	NOUN
ejpam-5398	56	21	under	under	ADP
ejpam-5398	56	22	consideration	consideration	NOUN
ejpam-5398	56	23	.	.	PUNCT
ejpam-5398	57	1	additional	additional	ADJ
ejpam-5398	57	2	progress	progress	NOUN
ejpam-5398	57	3	in	in	ADP
ejpam-5398	57	4	this	this	DET
ejpam-5398	57	5	field	field	NOUN
ejpam-5398	57	6	was	be	AUX
ejpam-5398	57	7	performed	perform	VERB
ejpam-5398	57	8	[	[	X
ejpam-5398	57	9	2	2	NUM
ejpam-5398	57	10	,	,	PUNCT
ejpam-5398	57	11	24	24	NUM
ejpam-5398	57	12	]	]	PUNCT
ejpam-5398	57	13	.	.	PUNCT
ejpam-5398	58	1	a	a	DET
ejpam-5398	58	2	precise	precise	ADJ
ejpam-5398	58	3	solution	solution	NOUN
ejpam-5398	58	4	for	for	ADP
ejpam-5398	58	5	a	a	DET
ejpam-5398	58	6	nonlinear	nonlinear	ADJ
ejpam-5398	58	7	oscillator	oscillator	NOUN
ejpam-5398	58	8	with	with	ADP
ejpam-5398	58	9	a	a	DET
ejpam-5398	58	10	mass	mass	NOUN
ejpam-5398	58	11	that	that	PRON
ejpam-5398	58	12	depends	depend	VERB
ejpam-5398	58	13	on	on	ADP
ejpam-5398	58	14	the	the	DET
ejpam-5398	58	15	position	position	NOUN
ejpam-5398	58	16	of	of	ADP
ejpam-5398	58	17	the	the	DET
ejpam-5398	58	18	coordinate	coordinate	NOUN
ejpam-5398	58	19	was	be	AUX
ejpam-5398	58	20	derived	derive	VERB
ejpam-5398	58	21	[	[	X
ejpam-5398	58	22	1	1	NUM
ejpam-5398	58	23	]	]	PUNCT
ejpam-5398	58	24	.	.	PUNCT
ejpam-5398	59	1	the	the	DET
ejpam-5398	59	2	findings	finding	NOUN
ejpam-5398	59	3	collected	collect	VERB
ejpam-5398	59	4	demonstrated	demonstrate	VERB
ejpam-5398	59	5	that	that	SCONJ
ejpam-5398	59	6	the	the	DET
ejpam-5398	59	7	proposed	propose	VERB
ejpam-5398	59	8	technique	technique	NOUN
ejpam-5398	59	9	was	be	AUX
ejpam-5398	59	10	a	a	DET
ejpam-5398	59	11	promising	promising	ADJ
ejpam-5398	59	12	tool	tool	NOUN
ejpam-5398	59	13	for	for	ADP
ejpam-5398	59	14	solving	solve	VERB
ejpam-5398	59	15	the	the	DET
ejpam-5398	59	16	van	van	PROPN
ejpam-5398	59	17	der	der	ADJ
ejpam-5398	59	18	pol	pol	PROPN
ejpam-5398	59	19	oscillator	oscillator	NOUN
ejpam-5398	59	20	and	and	CCONJ
ejpam-5398	59	21	providing	provide	VERB
ejpam-5398	59	22	information	information	NOUN
ejpam-5398	59	23	on	on	ADP
ejpam-5398	59	24	the	the	DET
ejpam-5398	59	25	phase	phase	NOUN
ejpam-5398	59	26	portrait	portrait	NOUN
ejpam-5398	59	27	,	,	PUNCT
ejpam-5398	59	28	so	so	ADV
ejpam-5398	59	29	proving	prove	VERB
ejpam-5398	59	30	the	the	DET
ejpam-5398	59	31	stability	stability	NOUN
ejpam-5398	59	32	of	of	ADP
ejpam-5398	59	33	the	the	DET
ejpam-5398	59	34	system	system	NOUN
ejpam-5398	59	35	[	[	X
ejpam-5398	59	36	3	3	NUM
ejpam-5398	59	37	]	]	PUNCT
ejpam-5398	59	38	.	.	PUNCT
ejpam-5398	60	1	the	the	DET
ejpam-5398	60	2	study	study	NOUN
ejpam-5398	60	3	reported	report	VERB
ejpam-5398	60	4	the	the	DET
ejpam-5398	60	5	use	use	NOUN
ejpam-5398	60	6	of	of	ADP
ejpam-5398	60	7	firstand	firstand	NOUN
ejpam-5398	60	8	second	second	ADJ
ejpam-5398	60	9	-	-	PUNCT
ejpam-5398	60	10	order	order	NOUN
ejpam-5398	60	11	difference	difference	NOUN
ejpam-5398	60	12	techniques	technique	NOUN
ejpam-5398	60	13	to	to	PART
ejpam-5398	60	14	find	find	VERB
ejpam-5398	60	15	numerical	numerical	ADJ
ejpam-5398	60	16	solutions	solution	NOUN
ejpam-5398	60	17	for	for	ADP
ejpam-5398	60	18	initial	initial	ADJ
ejpam-5398	60	19	boundary	boundary	ADJ
ejpam-5398	60	20	value	value	NOUN
ejpam-5398	60	21	issues	issue	NOUN
ejpam-5398	60	22	of	of	ADP
ejpam-5398	60	23	both	both	CCONJ
ejpam-5398	60	24	homogeneous	homogeneous	ADJ
ejpam-5398	60	25	and	and	CCONJ
ejpam-5398	60	26	nonhomogeneous	nonhomogeneous	ADJ
ejpam-5398	60	27	helmholtz	helmholtz	NOUN
ejpam-5398	60	28	equations	equation	NOUN
ejpam-5398	60	29	[	[	X
ejpam-5398	60	30	5	5	NUM
ejpam-5398	60	31	]	]	PUNCT
ejpam-5398	60	32	.	.	PUNCT
ejpam-5398	61	1	the	the	DET
ejpam-5398	61	2	stability	stability	NOUN
ejpam-5398	61	3	of	of	ADP
ejpam-5398	61	4	these	these	DET
ejpam-5398	61	5	procedures	procedure	NOUN
ejpam-5398	61	6	is	be	AUX
ejpam-5398	61	7	thoroughly	thoroughly	ADV
ejpam-5398	61	8	examined	examine	VERB
ejpam-5398	61	9	,	,	PUNCT
ejpam-5398	61	10	guaranteeing	guarantee	VERB
ejpam-5398	61	11	their	their	PRON
ejpam-5398	61	12	dependability	dependability	NOUN
ejpam-5398	61	13	and	and	CCONJ
ejpam-5398	61	14	convergence	convergence	NOUN
ejpam-5398	61	15	over	over	ADP
ejpam-5398	61	16	a	a	DET
ejpam-5398	61	17	broad	broad	ADJ
ejpam-5398	61	18	spectrum	spectrum	NOUN
ejpam-5398	61	19	of	of	ADP
ejpam-5398	61	20	problem	problem	NOUN
ejpam-5398	61	21	situations	situation	NOUN
ejpam-5398	61	22	.	.	PUNCT
ejpam-5398	62	1	an	an	DET
ejpam-5398	62	2	approach	approach	NOUN
ejpam-5398	62	3	that	that	PRON
ejpam-5398	62	4	is	be	AUX
ejpam-5398	62	5	dependable	dependable	ADJ
ejpam-5398	62	6	and	and	CCONJ
ejpam-5398	62	7	utilizes	utilize	VERB
ejpam-5398	62	8	an	an	DET
ejpam-5398	62	9	adapted	adapted	ADJ
ejpam-5398	62	10	version	version	NOUN
ejpam-5398	62	11	of	of	ADP
ejpam-5398	62	12	the	the	DET
ejpam-5398	62	13	conventional	conventional	ADJ
ejpam-5398	62	14	differential	differential	ADJ
ejpam-5398	62	15	transform	transform	NOUN
ejpam-5398	62	16	method	method	NOUN
ejpam-5398	62	17	was	be	AUX
ejpam-5398	62	18	introduced	introduce	VERB
ejpam-5398	62	19	[	[	PUNCT
ejpam-5398	62	20	4	4	NUM
ejpam-5398	62	21	]	]	PUNCT
ejpam-5398	62	22	.	.	PUNCT
ejpam-5398	63	1	the	the	DET
ejpam-5398	63	2	results	result	NOUN
ejpam-5398	63	3	collected	collect	VERB
ejpam-5398	63	4	demonstrated	demonstrate	VERB
ejpam-5398	63	5	that	that	SCONJ
ejpam-5398	63	6	the	the	DET
ejpam-5398	63	7	proposed	propose	VERB
ejpam-5398	63	8	technique	technique	NOUN
ejpam-5398	63	9	is	be	AUX
ejpam-5398	63	10	a	a	DET
ejpam-5398	63	11	highly	highly	ADV
ejpam-5398	63	12	promising	promising	ADJ
ejpam-5398	63	13	tool	tool	NOUN
ejpam-5398	63	14	for	for	ADP
ejpam-5398	63	15	solving	solve	VERB
ejpam-5398	63	16	the	the	DET
ejpam-5398	63	17	van	van	PROPN
ejpam-5398	63	18	der	der	ADJ
ejpam-5398	63	19	pol	pol	PROPN
ejpam-5398	63	20	oscillator	oscillator	NOUN
ejpam-5398	63	21	and	and	CCONJ
ejpam-5398	63	22	providing	provide	VERB
ejpam-5398	63	23	accurate	accurate	ADJ
ejpam-5398	63	24	information	information	NOUN
ejpam-5398	63	25	on	on	ADP
ejpam-5398	63	26	the	the	DET
ejpam-5398	63	27	phase	phase	NOUN
ejpam-5398	63	28	portrait	portrait	NOUN
ejpam-5398	63	29	,	,	PUNCT
ejpam-5398	63	30	so	so	ADV
ejpam-5398	63	31	proving	prove	VERB
ejpam-5398	63	32	the	the	DET
ejpam-5398	63	33	system	system	NOUN
ejpam-5398	63	34	’s	’s	PART
ejpam-5398	63	35	stability	stability	NOUN
ejpam-5398	63	36	.	.	PUNCT
ejpam-5398	64	1	in	in	ADP
ejpam-5398	64	2	real	real	ADJ
ejpam-5398	64	3	-	-	PUNCT
ejpam-5398	64	4	life	life	NOUN
ejpam-5398	64	5	,	,	PUNCT
ejpam-5398	64	6	there	there	PRON
ejpam-5398	64	7	have	have	AUX
ejpam-5398	64	8	been	be	AUX
ejpam-5398	64	9	situations	situation	NOUN
ejpam-5398	64	10	where	where	SCONJ
ejpam-5398	64	11	objects	object	NOUN
ejpam-5398	64	12	are	be	AUX
ejpam-5398	64	13	just	just	ADV
ejpam-5398	64	14	tangentially	tangentially	ADV
ejpam-5398	64	15	attached	attach	VERB
ejpam-5398	64	16	to	to	ADP
ejpam-5398	64	17	their	their	PRON
ejpam-5398	64	18	framework	framework	NOUN
ejpam-5398	64	19	,	,	PUNCT
ejpam-5398	64	20	allowing	allow	VERB
ejpam-5398	64	21	rocks	rock	NOUN
ejpam-5398	64	22	to	to	PART
ejpam-5398	64	23	fall	fall	VERB
ejpam-5398	64	24	on	on	ADP
ejpam-5398	64	25	nearby	nearby	ADJ
ejpam-5398	64	26	materials	material	NOUN
ejpam-5398	64	27	.	.	PUNCT
ejpam-5398	65	1	these	these	PRON
ejpam-5398	65	2	include	include	VERB
ejpam-5398	65	3	radioactive	radioactive	ADJ
ejpam-5398	65	4	fuel	fuel	NOUN
ejpam-5398	65	5	cells	cell	NOUN
ejpam-5398	65	6	in	in	ADP
ejpam-5398	65	7	reactors	reactor	NOUN
ejpam-5398	65	8	,	,	PUNCT
ejpam-5398	65	9	air	air	NOUN
ejpam-5398	65	10	extraction	extraction	NOUN
ejpam-5398	65	11	columns	column	NOUN
ejpam-5398	65	12	,	,	PUNCT
ejpam-5398	65	13	petroleum	petroleum	NOUN
ejpam-5398	65	14	cracking	cracking	NOUN
ejpam-5398	65	15	towers	tower	NOUN
ejpam-5398	65	16	,	,	PUNCT
ejpam-5398	65	17	and	and	CCONJ
ejpam-5398	65	18	liquid	liquid	ADJ
ejpam-5398	65	19	petrol	petrol	NOUN
ejpam-5398	65	20	tanks	tank	NOUN
ejpam-5398	65	21	.	.	PUNCT
ejpam-5398	66	1	undeniably	undeniably	ADV
ejpam-5398	66	2	,	,	PUNCT
ejpam-5398	66	3	the	the	DET
ejpam-5398	66	4	most	most	ADV
ejpam-5398	66	5	lucid	lucid	ADJ
ejpam-5398	66	6	illustration	illustration	NOUN
ejpam-5398	66	7	of	of	ADP
ejpam-5398	66	8	structural	structural	ADJ
ejpam-5398	66	9	responses	response	NOUN
ejpam-5398	66	10	during	during	ADP
ejpam-5398	66	11	seismic	seismic	ADJ
ejpam-5398	66	12	activities	activity	NOUN
ejpam-5398	66	13	is	be	AUX
ejpam-5398	66	14	their	their	PRON
ejpam-5398	66	15	rocking	rock	VERB
ejpam-5398	66	16	motion	motion	NOUN
ejpam-5398	66	17	.	.	PUNCT
ejpam-5398	67	1	despite	despite	SCONJ
ejpam-5398	67	2	the	the	DET
ejpam-5398	67	3	seemingly	seemingly	ADV
ejpam-5398	67	4	straightforward	straightforward	ADJ
ejpam-5398	67	5	nature	nature	NOUN
ejpam-5398	67	6	of	of	ADP
ejpam-5398	67	7	this	this	DET
ejpam-5398	67	8	phenomenon	phenomenon	NOUN
ejpam-5398	67	9	,	,	PUNCT
ejpam-5398	67	10	the	the	DET
ejpam-5398	67	11	swaying	swaying	NOUN
ejpam-5398	67	12	and	and	CCONJ
ejpam-5398	67	13	toppling	topple	VERB
ejpam-5398	67	14	of	of	ADP
ejpam-5398	67	15	rigid	rigid	ADJ
ejpam-5398	67	16	structures	structure	NOUN
ejpam-5398	67	17	in	in	ADP
ejpam-5398	67	18	response	response	NOUN
ejpam-5398	67	19	to	to	ADP
ejpam-5398	67	20	basic	basic	ADJ
ejpam-5398	67	21	stimuli	stimulus	NOUN
ejpam-5398	67	22	present	present	VERB
ejpam-5398	67	23	significant	significant	ADJ
ejpam-5398	67	24	challenges	challenge	NOUN
ejpam-5398	67	25	.	.	PUNCT
ejpam-5398	68	1	the	the	DET
ejpam-5398	68	2	primary	primary	ADJ
ejpam-5398	68	3	inspiration	inspiration	NOUN
ejpam-5398	68	4	for	for	ADP
ejpam-5398	68	5	comprehending	comprehend	VERB
ejpam-5398	68	6	this	this	DET
ejpam-5398	68	7	rocking	rock	VERB
ejpam-5398	68	8	issue	issue	NOUN
ejpam-5398	68	9	stems	stem	VERB
ejpam-5398	68	10	from	from	ADP
ejpam-5398	68	11	the	the	DET
ejpam-5398	68	12	potential	potential	NOUN
ejpam-5398	68	13	to	to	PART
ejpam-5398	68	14	utilize	utilize	VERB
ejpam-5398	68	15	it	it	PRON
ejpam-5398	68	16	as	as	ADP
ejpam-5398	68	17	a	a	DET
ejpam-5398	68	18	preventive	preventive	ADJ
ejpam-5398	68	19	measure	measure	NOUN
ejpam-5398	68	20	.	.	PUNCT
ejpam-5398	69	1	this	this	DET
ejpam-5398	69	2	understanding	understanding	NOUN
ejpam-5398	69	3	could	could	AUX
ejpam-5398	69	4	be	be	AUX
ejpam-5398	69	5	instrumental	instrumental	ADJ
ejpam-5398	69	6	in	in	ADP
ejpam-5398	69	7	safeguarding	safeguard	VERB
ejpam-5398	69	8	structures	structure	NOUN
ejpam-5398	69	9	,	,	PUNCT
ejpam-5398	69	10	furnishings	furnishing	NOUN
ejpam-5398	69	11	,	,	PUNCT
ejpam-5398	69	12	and	and	CCONJ
ejpam-5398	69	13	apparatus	apparatus	NOUN
ejpam-5398	69	14	from	from	ADP
ejpam-5398	69	15	collapsing	collapse	VERB
ejpam-5398	69	16	and	and	CCONJ
ejpam-5398	69	17	posing	pose	VERB
ejpam-5398	69	18	threats	threat	NOUN
ejpam-5398	69	19	to	to	ADP
ejpam-5398	69	20	human	human	ADJ
ejpam-5398	69	21	safety	safety	NOUN
ejpam-5398	69	22	during	during	ADP
ejpam-5398	69	23	the	the	DET
ejpam-5398	69	24	tremors	tremor	NOUN
ejpam-5398	69	25	of	of	ADP
ejpam-5398	69	26	an	an	DET
ejpam-5398	69	27	earthquake	earthquake	NOUN
ejpam-5398	69	28	.	.	PUNCT
ejpam-5398	70	1	early	early	ADJ
ejpam-5398	70	2	and	and	CCONJ
ejpam-5398	70	3	good	good	ADJ
ejpam-5398	70	4	results	result	NOUN
ejpam-5398	70	5	were	be	AUX
ejpam-5398	70	6	obtained	obtain	VERB
ejpam-5398	70	7	from	from	ADP
ejpam-5398	70	8	the	the	DET
ejpam-5398	70	9	shaking	shaking	NOUN
ejpam-5398	70	10	of	of	ADP
ejpam-5398	70	11	the	the	DET
ejpam-5398	70	12	isolation	isolation	NOUN
ejpam-5398	70	13	system	system	NOUN
ejpam-5398	70	14	[	[	X
ejpam-5398	70	15	13	13	NUM
ejpam-5398	70	16	,	,	PUNCT
ejpam-5398	70	17	41	41	NUM
ejpam-5398	70	18	]	]	PUNCT
ejpam-5398	70	19	.	.	PUNCT
ejpam-5398	71	1	the	the	DET
ejpam-5398	71	2	first	first	ADJ
ejpam-5398	71	3	-	-	PUNCT
ejpam-5398	71	4	order	order	NOUN
ejpam-5398	71	5	approximations	approximation	NOUN
ejpam-5398	71	6	of	of	ADP
ejpam-5398	71	7	the	the	DET
ejpam-5398	71	8	iterative	iterative	NOUN
ejpam-5398	71	9	perturbation	perturbation	NOUN
ejpam-5398	71	10	technique	technique	NOUN
ejpam-5398	71	11	are	be	AUX
ejpam-5398	71	12	explored	explore	VERB
ejpam-5398	71	13	to	to	PART
ejpam-5398	71	14	mimic	mimic	VERB
ejpam-5398	71	15	pertains	pertain	NOUN
ejpam-5398	71	16	to	to	ADP
ejpam-5398	71	17	the	the	DET
ejpam-5398	71	18	oscillation	oscillation	NOUN
ejpam-5398	71	19	patterns	pattern	NOUN
ejpam-5398	71	20	observed	observe	VERB
ejpam-5398	71	21	in	in	ADP
ejpam-5398	71	22	a	a	DET
ejpam-5398	71	23	stiff	stiff	ADJ
ejpam-5398	71	24	bar	bar	NOUN
ejpam-5398	71	25	that	that	PRON
ejpam-5398	71	26	sways	sway	VERB
ejpam-5398	71	27	reciprocally	reciprocally	ADV
ejpam-5398	71	28	on	on	ADP
ejpam-5398	71	29	a	a	DET
ejpam-5398	71	30	cylindrical	cylindrical	ADJ
ejpam-5398	71	31	surface	surface	NOUN
ejpam-5398	71	32	without	without	ADP
ejpam-5398	71	33	any	any	DET
ejpam-5398	71	34	slippage	slippage	NOUN
ejpam-5398	71	35	,	,	PUNCT
ejpam-5398	71	36	along	along	ADP
ejpam-5398	71	37	with	with	ADP
ejpam-5398	71	38	the	the	DET
ejpam-5398	71	39	cubic	cubic	ADJ
ejpam-5398	71	40	-	-	PUNCT
ejpam-5398	71	41	quintic	quintic	ADJ
ejpam-5398	71	42	do	do	NOUN
ejpam-5398	71	43	[	[	X
ejpam-5398	71	44	6	6	NUM
ejpam-5398	71	45	]	]	PUNCT
ejpam-5398	71	46	.	.	PUNCT
ejpam-5398	72	1	an	an	DET
ejpam-5398	72	2	investigation	investigation	NOUN
ejpam-5398	72	3	of	of	ADP
ejpam-5398	72	4	the	the	DET
ejpam-5398	72	5	movement	movement	NOUN
ejpam-5398	72	6	of	of	ADP
ejpam-5398	72	7	a	a	DET
ejpam-5398	72	8	rigid	rigid	ADJ
ejpam-5398	72	9	rod	rod	NOUN
ejpam-5398	72	10	swaying	sway	VERB
ejpam-5398	72	11	back	back	ADV
ejpam-5398	72	12	and	and	CCONJ
ejpam-5398	72	13	cubic	cubic	ADJ
ejpam-5398	72	14	-	-	PUNCT
ejpam-5398	72	15	quintic	quintic	ADJ
ejpam-5398	72	16	do	do	AUX
ejpam-5398	72	17	employed	employ	VERB
ejpam-5398	72	18	he	he	PRON
ejpam-5398	72	19	’s	’	VERB
ejpam-5398	72	20	energy	energy	NOUN
ejpam-5398	72	21	balancing	balance	VERB
ejpam-5398	72	22	approach	approach	NOUN
ejpam-5398	72	23	[	[	X
ejpam-5398	72	24	11	11	NUM
ejpam-5398	72	25	]	]	PUNCT
ejpam-5398	72	26	.	.	PUNCT
ejpam-5398	73	1	it	it	PRON
ejpam-5398	73	2	is	be	AUX
ejpam-5398	73	3	found	find	VERB
ejpam-5398	73	4	that	that	SCONJ
ejpam-5398	73	5	this	this	DET
ejpam-5398	73	6	approach	approach	NOUN
ejpam-5398	73	7	does	do	AUX
ejpam-5398	73	8	not	not	PART
ejpam-5398	73	9	require	require	VERB
ejpam-5398	73	10	the	the	DET
ejpam-5398	73	11	linearization	linearization	NOUN
ejpam-5398	73	12	process	process	NOUN
ejpam-5398	73	13	or	or	CCONJ
ejpam-5398	73	14	small	small	ADJ
ejpam-5398	73	15	perturbations	perturbation	NOUN
ejpam-5398	73	16	,	,	PUNCT
ejpam-5398	73	17	and	and	CCONJ
ejpam-5398	73	18	it	it	PRON
ejpam-5398	73	19	is	be	AUX
ejpam-5398	73	20	very	very	ADV
ejpam-5398	73	21	practical	practical	ADJ
ejpam-5398	73	22	and	and	CCONJ
ejpam-5398	73	23	efficient	efficient	ADJ
ejpam-5398	73	24	.	.	PUNCT
ejpam-5398	74	1	the	the	DET
ejpam-5398	74	2	problem	problem	NOUN
ejpam-5398	74	3	of	of	ADP
ejpam-5398	74	4	a	a	DET
ejpam-5398	74	5	stiff	stiff	ADJ
ejpam-5398	74	6	rod	rod	NOUN
ejpam-5398	74	7	rocking	rock	VERB
ejpam-5398	74	8	while	while	SCONJ
ejpam-5398	74	9	slipping	slip	VERB
ejpam-5398	74	10	on	on	ADP
ejpam-5398	74	11	a	a	DET
ejpam-5398	74	12	stiff	stiff	ADJ
ejpam-5398	74	13	circular	circular	ADJ
ejpam-5398	74	14	surface	surface	NOUN
ejpam-5398	74	15	was	be	AUX
ejpam-5398	74	16	examined	examine	VERB
ejpam-5398	74	17	[	[	X
ejpam-5398	74	18	17	17	NUM
ejpam-5398	74	19	]	]	PUNCT
ejpam-5398	74	20	.	.	PUNCT
ejpam-5398	75	1	from	from	ADP
ejpam-5398	75	2	the	the	DET
ejpam-5398	75	3	principles	principle	NOUN
ejpam-5398	75	4	of	of	ADP
ejpam-5398	75	5	the	the	DET
ejpam-5398	75	6	euler	euler	PROPN
ejpam-5398	75	7	-	-	PUNCT
ejpam-5398	75	8	lagrange	lagrange	NOUN
ejpam-5398	75	9	theorem	theorem	NOUN
ejpam-5398	75	10	,	,	PUNCT
ejpam-5398	75	11	one	one	PRON
ejpam-5398	75	12	can	can	AUX
ejpam-5398	75	13	potentially	potentially	ADV
ejpam-5398	75	14	derive	derive	VERB
ejpam-5398	75	15	the	the	DET
ejpam-5398	75	16	overarching	overarching	ADJ
ejpam-5398	75	17	equation	equation	NOUN
ejpam-5398	75	18	governing	govern	VERB
ejpam-5398	75	19	motion	motion	NOUN
ejpam-5398	75	20	.	.	PUNCT
ejpam-5398	76	1	analysis	analysis	NOUN
ejpam-5398	76	2	was	be	AUX
ejpam-5398	76	3	done	do	VERB
ejpam-5398	76	4	on	on	ADP
ejpam-5398	76	5	the	the	DET
ejpam-5398	76	6	stability	stability	NOUN
ejpam-5398	76	7	analysis	analysis	NOUN
ejpam-5398	76	8	of	of	ADP
ejpam-5398	76	9	a	a	DET
ejpam-5398	76	10	rocking	rock	VERB
ejpam-5398	76	11	rigid	rigid	ADJ
ejpam-5398	76	12	rod	rod	NOUN
ejpam-5398	76	13	using	use	VERB
ejpam-5398	76	14	td	td	NOUN
ejpam-5398	76	15	square	square	ADJ
ejpam-5398	76	16	position	position	NOUN
ejpam-5398	76	17	as	as	ADV
ejpam-5398	76	18	well	well	ADV
ejpam-5398	76	19	as	as	ADP
ejpam-5398	76	20	velocity	velocity	NOUN
ejpam-5398	76	21	[	[	X
ejpam-5398	76	22	17	17	NUM
ejpam-5398	76	23	]	]	PUNCT
ejpam-5398	76	24	.	.	PUNCT
ejpam-5398	77	1	the	the	DET
ejpam-5398	77	2	td	td	PROPN
ejpam-5398	77	3	technologies	technology	NOUN
ejpam-5398	77	4	have	have	AUX
ejpam-5398	77	5	been	be	AUX
ejpam-5398	77	6	the	the	DET
ejpam-5398	77	7	subject	subject	NOUN
ejpam-5398	77	8	of	of	ADP
ejpam-5398	77	9	several	several	ADJ
ejpam-5398	77	10	researches	research	NOUN
ejpam-5398	77	11	lately	lately	ADV
ejpam-5398	77	12	;	;	PUNCT
ejpam-5398	77	13	therefore	therefore	ADV
ejpam-5398	77	14	this	this	DET
ejpam-5398	77	15	topic	topic	NOUN
ejpam-5398	77	16	of	of	ADP
ejpam-5398	77	17	investigation	investigation	NOUN
ejpam-5398	77	18	was	be	AUX
ejpam-5398	77	19	especially	especially	ADV
ejpam-5398	77	20	relevant	relevant	ADJ
ejpam-5398	77	21	.	.	PUNCT
ejpam-5398	78	1	the	the	DET
ejpam-5398	78	2	td	td	NOUN
ejpam-5398	78	3	served	serve	VERB
ejpam-5398	78	4	as	as	ADP
ejpam-5398	78	5	a	a	DET
ejpam-5398	78	6	supplementary	supplementary	ADJ
ejpam-5398	78	7	protection	protection	NOUN
ejpam-5398	78	8	against	against	ADP
ejpam-5398	78	9	the	the	DET
ejpam-5398	78	10	nonlinearly	nonlinearly	ADV
ejpam-5398	78	11	oscillating	oscillate	VERB
ejpam-5398	78	12	system	system	NOUN
ejpam-5398	78	13	that	that	PRON
ejpam-5398	78	14	was	be	AUX
ejpam-5398	78	15	being	be	AUX
ejpam-5398	78	16	examined	examine	VERB
ejpam-5398	78	17	.	.	PUNCT
ejpam-5398	79	1	in	in	ADP
ejpam-5398	79	2	all	all	DET
ejpam-5398	79	3	the	the	DET
ejpam-5398	79	4	previous	previous	ADJ
ejpam-5398	79	5	efforts	effort	NOUN
ejpam-5398	79	6	,	,	PUNCT
ejpam-5398	79	7	the	the	DET
ejpam-5398	79	8	restorative	restorative	ADJ
ejpam-5398	79	9	powers	power	NOUN
ejpam-5398	79	10	were	be	AUX
ejpam-5398	79	11	weakened	weaken	VERB
ejpam-5398	79	12	through	through	ADP
ejpam-5398	79	13	the	the	DET
ejpam-5398	79	14	application	application	NOUN
ejpam-5398	79	15	of	of	ADP
ejpam-5398	79	16	the	the	DET
ejpam-5398	79	17	taylor	taylor	PROPN
ejpam-5398	79	18	expansion	expansion	NOUN
ejpam-5398	79	19	.	.	PUNCT
ejpam-5398	80	1	on	on	ADP
ejpam-5398	80	2	the	the	DET
ejpam-5398	80	3	other	other	ADJ
ejpam-5398	80	4	hand	hand	NOUN
ejpam-5398	80	5	,	,	PUNCT
ejpam-5398	80	6	the	the	DET
ejpam-5398	80	7	current	current	ADJ
ejpam-5398	80	8	representation	representation	NOUN
ejpam-5398	80	9	is	be	AUX
ejpam-5398	80	10	incomparable	incomparable	ADJ
ejpam-5398	80	11	in	in	SCONJ
ejpam-5398	80	12	that	that	SCONJ
ejpam-5398	80	13	it	it	PRON
ejpam-5398	80	14	maintains	maintain	VERB
ejpam-5398	80	15	these	these	DET
ejpam-5398	80	16	forces	force	NOUN
ejpam-5398	80	17	.	.	PUNCT
ejpam-5398	81	1	recently	recently	ADV
ejpam-5398	81	2	,	,	PUNCT
ejpam-5398	81	3	the	the	DET
ejpam-5398	81	4	hff	hff	NOUN
ejpam-5398	81	5	were	be	AUX
ejpam-5398	81	6	adopted	adopt	VERB
ejpam-5398	81	7	a.	a.	NOUN
ejpam-5398	81	8	a.	a.	NOUN
ejpam-5398	81	9	galal	galal	PROPN
ejpam-5398	81	10	et	et	PROPN
ejpam-5398	81	11	al	al	PROPN
ejpam-5398	81	12	.	.	PUNCT
ejpam-5398	81	13	/	/	SYM
ejpam-5398	81	14	eur	eur	PROPN
ejpam-5398	81	15	.	.	PUNCT
ejpam-5398	82	1	j.	j.	PROPN
ejpam-5398	82	2	pure	pure	PROPN
ejpam-5398	82	3	appl	appl	PROPN
ejpam-5398	82	4	.	.	PROPN
ejpam-5398	82	5	math	math	PROPN
ejpam-5398	82	6	,	,	PUNCT
ejpam-5398	82	7	17	17	NUM
ejpam-5398	82	8	(	(	PUNCT
ejpam-5398	82	9	4	4	NUM
ejpam-5398	82	10	)	)	PUNCT
ejpam-5398	82	11	(	(	PUNCT
ejpam-5398	82	12	2024	2024	NUM
ejpam-5398	82	13	)	)	PUNCT
ejpam-5398	82	14	,	,	PUNCT
ejpam-5398	82	15	2878	2878	NUM
ejpam-5398	82	16	-	-	SYM
ejpam-5398	82	17	2897	2897	NUM
ejpam-5398	82	18	2881	2881	NUM
ejpam-5398	82	19	in	in	ADP
ejpam-5398	82	20	analyzing	analyze	VERB
ejpam-5398	82	21	several	several	ADJ
ejpam-5398	82	22	works	work	NOUN
ejpam-5398	82	23	in	in	ADP
ejpam-5398	82	24	the	the	DET
ejpam-5398	82	25	dynamical	dynamical	ADJ
ejpam-5398	82	26	system	system	NOUN
ejpam-5398	82	27	as	as	ADV
ejpam-5398	82	28	well	well	ADV
ejpam-5398	82	29	as	as	ADP
ejpam-5398	82	30	the	the	DET
ejpam-5398	82	31	electrohydrodynamics	electrohydrodynamic	NOUN
ejpam-5398	82	32	stability	stability	NOUN
ejpam-5398	82	33	[	[	X
ejpam-5398	82	34	8	8	NUM
ejpam-5398	82	35	,	,	PUNCT
ejpam-5398	82	36	18	18	NUM
ejpam-5398	82	37	,	,	PUNCT
ejpam-5398	82	38	20–23	20–23	NOUN
ejpam-5398	82	39	,	,	PUNCT
ejpam-5398	82	40	25–34	25–34	NUM
ejpam-5398	82	41	]	]	PUNCT
ejpam-5398	82	42	.	.	PUNCT
ejpam-5398	83	1	nonlinear	nonlinear	ADJ
ejpam-5398	83	2	oscillations	oscillation	NOUN
ejpam-5398	83	3	are	be	AUX
ejpam-5398	83	4	a	a	DET
ejpam-5398	83	5	part	part	NOUN
ejpam-5398	83	6	of	of	ADP
ejpam-5398	83	7	ordinary	ordinary	ADJ
ejpam-5398	83	8	life	life	NOUN
ejpam-5398	83	9	and	and	CCONJ
ejpam-5398	83	10	comparable	comparable	ADJ
ejpam-5398	83	11	technical	technical	ADJ
ejpam-5398	83	12	systems	system	NOUN
ejpam-5398	83	13	.	.	PUNCT
ejpam-5398	84	1	nonlinear	nonlinear	ADJ
ejpam-5398	84	2	vibrations	vibration	NOUN
ejpam-5398	84	3	,	,	PUNCT
ejpam-5398	84	4	as	as	ADP
ejpam-5398	84	5	one	one	NUM
ejpam-5398	84	6	of	of	ADP
ejpam-5398	84	7	the	the	DET
ejpam-5398	84	8	most	most	ADV
ejpam-5398	84	9	significant	significant	ADJ
ejpam-5398	84	10	and	and	CCONJ
ejpam-5398	84	11	often	often	ADV
ejpam-5398	84	12	used	use	VERB
ejpam-5398	84	13	prototypes	prototype	NOUN
ejpam-5398	84	14	in	in	ADP
ejpam-5398	84	15	dynamic	dynamic	ADJ
ejpam-5398	84	16	structures	structure	NOUN
ejpam-5398	84	17	,	,	PUNCT
ejpam-5398	84	18	are	be	AUX
ejpam-5398	84	19	vital	vital	ADJ
ejpam-5398	84	20	in	in	ADP
ejpam-5398	84	21	considering	consider	VERB
ejpam-5398	84	22	different	different	ADJ
ejpam-5398	84	23	nonlinear	nonlinear	ADJ
ejpam-5398	84	24	occurrences	occurrence	NOUN
ejpam-5398	84	25	in	in	ADP
ejpam-5398	84	26	electrical	electrical	ADJ
ejpam-5398	84	27	manufacturing	manufacturing	NOUN
ejpam-5398	84	28	and	and	CCONJ
ejpam-5398	84	29	industry	industry	NOUN
ejpam-5398	84	30	.	.	PUNCT
ejpam-5398	85	1	the	the	DET
ejpam-5398	85	2	hff	hff	PROPN
ejpam-5398	85	3	is	be	AUX
ejpam-5398	85	4	the	the	DET
ejpam-5398	85	5	most	most	ADV
ejpam-5398	85	6	straightforward	straightforward	ADJ
ejpam-5398	85	7	way	way	NOUN
ejpam-5398	85	8	to	to	PART
ejpam-5398	85	9	calculate	calculate	VERB
ejpam-5398	85	10	the	the	DET
ejpam-5398	85	11	frequencyamplitude	frequencyamplitude	NOUN
ejpam-5398	85	12	relationship	relationship	NOUN
ejpam-5398	85	13	,	,	PUNCT
ejpam-5398	85	14	while	while	SCONJ
ejpam-5398	85	15	analyzing	analyze	VERB
ejpam-5398	85	16	different	different	ADJ
ejpam-5398	85	17	classes	class	NOUN
ejpam-5398	85	18	of	of	ADP
ejpam-5398	85	19	nonlinear	nonlinear	ADJ
ejpam-5398	85	20	dynamical	dynamical	ADJ
ejpam-5398	85	21	systems	system	NOUN
ejpam-5398	85	22	.	.	PUNCT
ejpam-5398	86	1	the	the	DET
ejpam-5398	86	2	calculation	calculation	NOUN
ejpam-5398	86	3	of	of	ADP
ejpam-5398	86	4	the	the	DET
ejpam-5398	86	5	remaining	remain	VERB
ejpam-5398	86	6	values	value	NOUN
ejpam-5398	86	7	is	be	AUX
ejpam-5398	86	8	compared	compare	VERB
ejpam-5398	86	9	with	with	ADP
ejpam-5398	86	10	the	the	DET
ejpam-5398	86	11	formulation	formulation	NOUN
ejpam-5398	86	12	of	of	ADP
ejpam-5398	86	13	frequencyamplitude	frequencyamplitude	NOUN
ejpam-5398	86	14	and	and	CCONJ
ejpam-5398	86	15	its	its	PRON
ejpam-5398	86	16	diverse	diverse	ADJ
ejpam-5398	86	17	versions	version	NOUN
ejpam-5398	86	18	[	[	X
ejpam-5398	86	19	40	40	NUM
ejpam-5398	86	20	]	]	PUNCT
ejpam-5398	86	21	.	.	PUNCT
ejpam-5398	87	1	this	this	DET
ejpam-5398	87	2	study	study	NOUN
ejpam-5398	87	3	suggested	suggest	VERB
ejpam-5398	87	4	introducing	introduce	VERB
ejpam-5398	87	5	a	a	DET
ejpam-5398	87	6	free	free	ADJ
ejpam-5398	87	7	parameter	parameter	NOUN
ejpam-5398	87	8	to	to	PART
ejpam-5398	87	9	offer	offer	VERB
ejpam-5398	87	10	an	an	DET
ejpam-5398	87	11	accurate	accurate	ADJ
ejpam-5398	87	12	estimation	estimation	NOUN
ejpam-5398	87	13	of	of	ADP
ejpam-5398	87	14	the	the	DET
ejpam-5398	87	15	nonlinear	nonlinear	ADJ
ejpam-5398	87	16	oscillator	oscillator	NOUN
ejpam-5398	87	17	frequency	frequency	NOUN
ejpam-5398	87	18	and	and	CCONJ
ejpam-5398	87	19	to	to	PART
ejpam-5398	87	20	reduce	reduce	VERB
ejpam-5398	87	21	the	the	DET
ejpam-5398	87	22	number	number	NOUN
ejpam-5398	87	23	of	of	ADP
ejpam-5398	87	24	techniques	technique	NOUN
ejpam-5398	87	25	needed	need	VERB
ejpam-5398	87	26	for	for	ADP
ejpam-5398	87	27	the	the	DET
ejpam-5398	87	28	residual	residual	ADJ
ejpam-5398	87	29	computation	computation	NOUN
ejpam-5398	87	30	.	.	PUNCT
ejpam-5398	88	1	using	use	VERB
ejpam-5398	88	2	residuals	residual	NOUN
ejpam-5398	88	3	from	from	ADP
ejpam-5398	88	4	two	two	NUM
ejpam-5398	88	5	trial	trial	NOUN
ejpam-5398	88	6	solutions	solution	NOUN
ejpam-5398	88	7	,	,	PUNCT
ejpam-5398	88	8	the	the	DET
ejpam-5398	88	9	hff	hff	NOUN
ejpam-5398	88	10	is	be	AUX
ejpam-5398	88	11	used	use	VERB
ejpam-5398	88	12	to	to	PART
ejpam-5398	88	13	find	find	VERB
ejpam-5398	88	14	the	the	DET
ejpam-5398	88	15	nonlinear	nonlinear	ADJ
ejpam-5398	88	16	oscillator	oscillator	NOUN
ejpam-5398	88	17	frequency	frequency	NOUN
ejpam-5398	88	18	and	and	CCONJ
ejpam-5398	88	19	amplitude	amplitude	NOUN
ejpam-5398	88	20	relationship	relationship	NOUN
ejpam-5398	89	1	[	[	X
ejpam-5398	89	2	37	37	NUM
ejpam-5398	89	3	]	]	PUNCT
ejpam-5398	89	4	.	.	PUNCT
ejpam-5398	90	1	this	this	DET
ejpam-5398	90	2	approach	approach	NOUN
ejpam-5398	90	3	can	can	AUX
ejpam-5398	90	4	still	still	ADV
ejpam-5398	90	5	be	be	AUX
ejpam-5398	90	6	improved	improve	VERB
ejpam-5398	90	7	,	,	PUNCT
ejpam-5398	90	8	even	even	ADV
ejpam-5398	90	9	in	in	ADP
ejpam-5398	90	10	the	the	DET
ejpam-5398	90	11	unlikely	unlikely	ADJ
ejpam-5398	90	12	event	event	NOUN
ejpam-5398	90	13	that	that	SCONJ
ejpam-5398	90	14	an	an	DET
ejpam-5398	90	15	extremely	extremely	ADV
ejpam-5398	90	16	precise	precise	ADJ
ejpam-5398	90	17	response	response	NOUN
ejpam-5398	90	18	is	be	AUX
ejpam-5398	90	19	produced	produce	VERB
ejpam-5398	90	20	.	.	PUNCT
ejpam-5398	91	1	for	for	ADP
ejpam-5398	91	2	nonlinear	nonlinear	ADJ
ejpam-5398	91	3	oscillators	oscillator	NOUN
ejpam-5398	91	4	,	,	PUNCT
ejpam-5398	91	5	the	the	DET
ejpam-5398	91	6	hff	hff	NOUN
ejpam-5398	91	7	offered	offer	VERB
ejpam-5398	91	8	the	the	DET
ejpam-5398	91	9	most	most	ADV
ejpam-5398	91	10	straightforward	straightforward	ADJ
ejpam-5398	91	11	and	and	CCONJ
ejpam-5398	91	12	precise	precise	ADJ
ejpam-5398	91	13	frequency	frequency	NOUN
ejpam-5398	91	14	formulation	formulation	NOUN
ejpam-5398	91	15	[	[	X
ejpam-5398	91	16	36	36	NUM
ejpam-5398	91	17	]	]	PUNCT
ejpam-5398	91	18	.	.	PUNCT
ejpam-5398	92	1	the	the	DET
ejpam-5398	92	2	un	un	PROPN
ejpam-5398	92	3	-	-	ADJ
ejpam-5398	92	4	damped	damped	ADJ
ejpam-5398	92	5	do	do	NOUN
ejpam-5398	92	6	and	and	CCONJ
ejpam-5398	92	7	its	its	PRON
ejpam-5398	92	8	related	related	ADJ
ejpam-5398	92	9	family	family	NOUN
ejpam-5398	92	10	are	be	AUX
ejpam-5398	92	11	successfully	successfully	ADV
ejpam-5398	92	12	resolved	resolve	VERB
ejpam-5398	92	13	with	with	ADP
ejpam-5398	92	14	it	it	PRON
ejpam-5398	92	15	[	[	X
ejpam-5398	92	16	7	7	NUM
ejpam-5398	92	17	]	]	PUNCT
ejpam-5398	92	18	.	.	PUNCT
ejpam-5398	93	1	the	the	DET
ejpam-5398	93	2	complexity	complexity	NOUN
ejpam-5398	93	3	characteristic	characteristic	ADJ
ejpam-5398	93	4	in	in	ADP
ejpam-5398	93	5	evaluating	evaluate	VERB
ejpam-5398	93	6	the	the	DET
ejpam-5398	93	7	do	do	NOUN
ejpam-5398	93	8	with	with	ADP
ejpam-5398	93	9	advanced	advanced	ADJ
ejpam-5398	93	10	nonlinearity	nonlinearity	NOUN
ejpam-5398	93	11	,	,	PUNCT
ejpam-5398	93	12	as	as	ADV
ejpam-5398	93	13	well	well	ADV
ejpam-5398	93	14	as	as	ADP
ejpam-5398	93	15	the	the	DET
ejpam-5398	93	16	quadratic	quadratic	ADJ
ejpam-5398	93	17	damping	damp	VERB
ejpam-5398	93	18	equation	equation	NOUN
ejpam-5398	93	19	,	,	PUNCT
ejpam-5398	93	20	has	have	AUX
ejpam-5398	93	21	marked	mark	VERB
ejpam-5398	93	22	this	this	DET
ejpam-5398	93	23	subject	subject	NOUN
ejpam-5398	93	24	as	as	ADP
ejpam-5398	93	25	a	a	DET
ejpam-5398	93	26	critical	critical	ADJ
ejpam-5398	93	27	area	area	NOUN
ejpam-5398	93	28	necessitating	necessitate	VERB
ejpam-5398	93	29	comprehensive	comprehensive	ADJ
ejpam-5398	93	30	investigation	investigation	NOUN
ejpam-5398	93	31	for	for	ADP
ejpam-5398	93	32	more	more	ADV
ejpam-5398	93	33	accurate	accurate	ADJ
ejpam-5398	93	34	solutions	solution	NOUN
ejpam-5398	93	35	.	.	PUNCT
ejpam-5398	94	1	since	since	SCONJ
ejpam-5398	94	2	linear	linear	PROPN
ejpam-5398	94	3	equations	equation	NOUN
ejpam-5398	94	4	are	be	AUX
ejpam-5398	94	5	frequently	frequently	ADV
ejpam-5398	94	6	perfect	perfect	ADJ
ejpam-5398	94	7	solutions	solution	NOUN
ejpam-5398	94	8	,	,	PUNCT
ejpam-5398	94	9	the	the	DET
ejpam-5398	94	10	hff	hff	NOUN
ejpam-5398	94	11	for	for	ADP
ejpam-5398	94	12	damped	damped	ADJ
ejpam-5398	94	13	nonlinear	nonlinear	ADJ
ejpam-5398	94	14	oscillation	oscillation	NOUN
ejpam-5398	94	15	is	be	AUX
ejpam-5398	94	16	a	a	DET
ejpam-5398	94	17	hot	hot	ADJ
ejpam-5398	94	18	topic	topic	NOUN
ejpam-5398	94	19	.	.	PUNCT
ejpam-5398	95	1	the	the	DET
ejpam-5398	95	2	extremely	extremely	ADV
ejpam-5398	95	3	accurate	accurate	ADJ
ejpam-5398	95	4	solution	solution	NOUN
ejpam-5398	95	5	,	,	PUNCT
ejpam-5398	95	6	also	also	ADV
ejpam-5398	95	7	known	know	VERB
ejpam-5398	95	8	as	as	ADP
ejpam-5398	95	9	the	the	DET
ejpam-5398	95	10	linearized	linearize	VERB
ejpam-5398	95	11	equation	equation	NOUN
ejpam-5398	95	12	solution	solution	NOUN
ejpam-5398	95	13	,	,	PUNCT
ejpam-5398	95	14	illustrated	illustrate	VERB
ejpam-5398	95	15	how	how	SCONJ
ejpam-5398	95	16	to	to	PART
ejpam-5398	95	17	approach	approach	VERB
ejpam-5398	95	18	the	the	DET
ejpam-5398	95	19	nonlinear	nonlinear	ADJ
ejpam-5398	95	20	issue	issue	NOUN
ejpam-5398	95	21	.	.	PUNCT
ejpam-5398	96	1	an	an	DET
ejpam-5398	96	2	exact	exact	ADJ
ejpam-5398	96	3	solution	solution	NOUN
ejpam-5398	96	4	is	be	AUX
ejpam-5398	96	5	obtained	obtain	VERB
ejpam-5398	96	6	when	when	SCONJ
ejpam-5398	96	7	equations	equation	NOUN
ejpam-5398	96	8	having	have	VERB
ejpam-5398	96	9	constant	constant	ADJ
ejpam-5398	96	10	coefficients	coefficient	NOUN
ejpam-5398	96	11	are	be	AUX
ejpam-5398	96	12	made	make	VERB
ejpam-5398	96	13	linear	linear	ADJ
ejpam-5398	96	14	through	through	ADP
ejpam-5398	96	15	the	the	DET
ejpam-5398	96	16	application	application	NOUN
ejpam-5398	96	17	of	of	ADP
ejpam-5398	96	18	the	the	DET
ejpam-5398	96	19	hpm	hpm	NOUN
ejpam-5398	96	20	.	.	PUNCT
ejpam-5398	97	1	the	the	DET
ejpam-5398	97	2	existing	exist	VERB
ejpam-5398	97	3	study	study	NOUN
ejpam-5398	97	4	aims	aim	VERB
ejpam-5398	97	5	to	to	PART
ejpam-5398	97	6	utilize	utilize	VERB
ejpam-5398	97	7	the	the	DET
ejpam-5398	97	8	hff	hff	NOUN
ejpam-5398	97	9	in	in	ADP
ejpam-5398	97	10	identifying	identify	VERB
ejpam-5398	97	11	the	the	DET
ejpam-5398	97	12	frequency	frequency	NOUN
ejpam-5398	97	13	of	of	ADP
ejpam-5398	97	14	a	a	DET
ejpam-5398	97	15	nonlinear	nonlinear	ADJ
ejpam-5398	97	16	oscillation	oscillation	NOUN
ejpam-5398	97	17	,	,	PUNCT
ejpam-5398	97	18	which	which	PRON
ejpam-5398	97	19	may	may	AUX
ejpam-5398	97	20	be	be	AUX
ejpam-5398	97	21	subject	subject	ADJ
ejpam-5398	97	22	to	to	ADP
ejpam-5398	97	23	linear	linear	ADJ
ejpam-5398	97	24	or	or	CCONJ
ejpam-5398	97	25	nonlinear	nonlinear	ADJ
ejpam-5398	97	26	damping	damp	VERB
ejpam-5398	97	27	forces	force	NOUN
ejpam-5398	97	28	.	.	PUNCT
ejpam-5398	98	1	the	the	DET
ejpam-5398	98	2	td	td	PROPN
ejpam-5398	98	3	rolling	rolling	NOUN
ejpam-5398	98	4	of	of	ADP
ejpam-5398	98	5	a	a	DET
ejpam-5398	98	6	rigid	rigid	ADJ
ejpam-5398	98	7	rod	rod	NOUN
ejpam-5398	98	8	is	be	AUX
ejpam-5398	98	9	the	the	DET
ejpam-5398	98	10	occurrence	occurrence	NOUN
ejpam-5398	98	11	in	in	ADP
ejpam-5398	98	12	which	which	PRON
ejpam-5398	98	13	the	the	DET
ejpam-5398	98	14	rolling	rolling	ADJ
ejpam-5398	98	15	motion	motion	NOUN
ejpam-5398	98	16	of	of	ADP
ejpam-5398	98	17	a	a	DET
ejpam-5398	98	18	rod	rod	NOUN
ejpam-5398	98	19	is	be	AUX
ejpam-5398	98	20	affected	affect	VERB
ejpam-5398	98	21	by	by	ADP
ejpam-5398	98	22	a	a	DET
ejpam-5398	98	23	delay	delay	NOUN
ejpam-5398	98	24	in	in	ADP
ejpam-5398	98	25	the	the	DET
ejpam-5398	98	26	application	application	NOUN
ejpam-5398	98	27	of	of	ADP
ejpam-5398	98	28	forces	force	NOUN
ejpam-5398	98	29	or	or	CCONJ
ejpam-5398	98	30	torques	torque	NOUN
ejpam-5398	98	31	.	.	PUNCT
ejpam-5398	99	1	this	this	DET
ejpam-5398	99	2	delay	delay	NOUN
ejpam-5398	99	3	can	can	AUX
ejpam-5398	99	4	lead	lead	VERB
ejpam-5398	99	5	to	to	ADP
ejpam-5398	99	6	intricate	intricate	ADJ
ejpam-5398	99	7	dynamics	dynamic	NOUN
ejpam-5398	99	8	,	,	PUNCT
ejpam-5398	99	9	such	such	ADJ
ejpam-5398	99	10	as	as	ADP
ejpam-5398	99	11	oscillations	oscillation	NOUN
ejpam-5398	99	12	,	,	PUNCT
ejpam-5398	99	13	alterations	alteration	NOUN
ejpam-5398	99	14	in	in	ADP
ejpam-5398	99	15	stability	stability	NOUN
ejpam-5398	99	16	,	,	PUNCT
ejpam-5398	99	17	or	or	CCONJ
ejpam-5398	99	18	changing	change	VERB
ejpam-5398	99	19	rolling	rolling	ADJ
ejpam-5398	99	20	trajectories	trajectory	NOUN
ejpam-5398	99	21	.	.	PUNCT
ejpam-5398	100	1	the	the	DET
ejpam-5398	100	2	td	td	NOUN
ejpam-5398	100	3	in	in	ADP
ejpam-5398	100	4	mechanical	mechanical	ADJ
ejpam-5398	100	5	systems	system	NOUN
ejpam-5398	100	6	frequently	frequently	ADV
ejpam-5398	100	7	occurs	occur	VERB
ejpam-5398	100	8	as	as	ADP
ejpam-5398	100	9	a	a	DET
ejpam-5398	100	10	result	result	NOUN
ejpam-5398	100	11	of	of	ADP
ejpam-5398	100	12	factors	factor	NOUN
ejpam-5398	100	13	such	such	ADJ
ejpam-5398	100	14	as	as	ADP
ejpam-5398	100	15	control	control	NOUN
ejpam-5398	100	16	system	system	NOUN
ejpam-5398	100	17	feedback	feedback	NOUN
ejpam-5398	100	18	,	,	PUNCT
ejpam-5398	100	19	material	material	ADJ
ejpam-5398	100	20	deformation	deformation	NOUN
ejpam-5398	100	21	,	,	PUNCT
ejpam-5398	100	22	or	or	CCONJ
ejpam-5398	100	23	delayed	delay	VERB
ejpam-5398	100	24	actuation	actuation	NOUN
ejpam-5398	100	25	.	.	PUNCT
ejpam-5398	101	1	several	several	ADJ
ejpam-5398	101	2	distinguished	distinguished	ADJ
ejpam-5398	101	3	uses	use	NOUN
ejpam-5398	101	4	can	can	AUX
ejpam-5398	101	5	be	be	AUX
ejpam-5398	101	6	concisely	concisely	ADV
ejpam-5398	101	7	summarized	summarize	VERB
ejpam-5398	101	8	as	as	SCONJ
ejpam-5398	101	9	follows	follow	VERB
ejpam-5398	101	10	:	:	PUNCT
ejpam-5398	101	11	the	the	DET
ejpam-5398	101	12	td	td	NOUN
ejpam-5398	101	13	rolling	rolling	NOUN
ejpam-5398	101	14	can	can	AUX
ejpam-5398	101	15	have	have	VERB
ejpam-5398	101	16	a	a	DET
ejpam-5398	101	17	considerable	considerable	ADJ
ejpam-5398	101	18	impact	impact	NOUN
ejpam-5398	101	19	on	on	ADP
ejpam-5398	101	20	the	the	DET
ejpam-5398	101	21	movement	movement	NOUN
ejpam-5398	101	22	control	control	NOUN
ejpam-5398	101	23	of	of	ADP
ejpam-5398	101	24	robotic	robotic	ADJ
ejpam-5398	101	25	manipulators	manipulator	NOUN
ejpam-5398	101	26	or	or	CCONJ
ejpam-5398	101	27	mobile	mobile	NOUN
ejpam-5398	101	28	robots	robot	NOUN
ejpam-5398	101	29	,	,	PUNCT
ejpam-5398	101	30	especially	especially	ADV
ejpam-5398	101	31	when	when	SCONJ
ejpam-5398	101	32	precise	precise	ADJ
ejpam-5398	101	33	control	control	NOUN
ejpam-5398	101	34	is	be	AUX
ejpam-5398	101	35	required	require	VERB
ejpam-5398	101	36	.	.	PUNCT
ejpam-5398	102	1	gaining	gain	VERB
ejpam-5398	102	2	comprehension	comprehension	NOUN
ejpam-5398	102	3	of	of	ADP
ejpam-5398	102	4	this	this	DET
ejpam-5398	102	5	td	td	NOUN
ejpam-5398	102	6	can	can	AUX
ejpam-5398	102	7	aid	aid	VERB
ejpam-5398	102	8	in	in	ADP
ejpam-5398	102	9	formulating	formulate	VERB
ejpam-5398	102	10	enhanced	enhanced	ADJ
ejpam-5398	102	11	control	control	NOUN
ejpam-5398	102	12	algorithms	algorithm	NOUN
ejpam-5398	102	13	to	to	PART
ejpam-5398	102	14	alleviate	alleviate	VERB
ejpam-5398	102	15	unwanted	unwanted	ADJ
ejpam-5398	102	16	oscillations	oscillation	NOUN
ejpam-5398	102	17	or	or	CCONJ
ejpam-5398	102	18	instability	instability	NOUN
ejpam-5398	102	19	.	.	PUNCT
ejpam-5398	103	1	the	the	DET
ejpam-5398	103	2	td	td	NOUN
ejpam-5398	103	3	rolling	rolling	NOUN
ejpam-5398	103	4	can	can	AUX
ejpam-5398	103	5	be	be	AUX
ejpam-5398	103	6	employed	employ	VERB
ejpam-5398	103	7	in	in	ADP
ejpam-5398	103	8	engineering	engineering	NOUN
ejpam-5398	103	9	structures	structure	NOUN
ejpam-5398	103	10	to	to	PART
ejpam-5398	103	11	serve	serve	VERB
ejpam-5398	103	12	as	as	ADP
ejpam-5398	103	13	vibration	vibration	NOUN
ejpam-5398	103	14	damping	damp	VERB
ejpam-5398	103	15	systems	system	NOUN
ejpam-5398	103	16	.	.	PUNCT
ejpam-5398	104	1	engineers	engineer	NOUN
ejpam-5398	104	2	can	can	AUX
ejpam-5398	104	3	enhance	enhance	VERB
ejpam-5398	104	4	the	the	DET
ejpam-5398	104	5	stability	stability	NOUN
ejpam-5398	104	6	and	and	CCONJ
ejpam-5398	104	7	durability	durability	NOUN
ejpam-5398	104	8	of	of	ADP
ejpam-5398	104	9	structures	structure	NOUN
ejpam-5398	104	10	by	by	ADP
ejpam-5398	104	11	implementing	implement	VERB
ejpam-5398	104	12	controlled	control	VERB
ejpam-5398	104	13	delays	delay	NOUN
ejpam-5398	104	14	to	to	PART
ejpam-5398	104	15	mitigate	mitigate	VERB
ejpam-5398	104	16	or	or	CCONJ
ejpam-5398	104	17	counter	counter	VERB
ejpam-5398	104	18	undesired	undesired	ADJ
ejpam-5398	104	19	vibrations	vibration	NOUN
ejpam-5398	104	20	.	.	PUNCT
ejpam-5398	105	1	understanding	understand	VERB
ejpam-5398	105	2	the	the	DET
ejpam-5398	105	3	delayed	delay	VERB
ejpam-5398	105	4	rolling	rolling	ADJ
ejpam-5398	105	5	behavior	behavior	NOUN
ejpam-5398	105	6	of	of	ADP
ejpam-5398	105	7	conveyor	conveyor	NOUN
ejpam-5398	105	8	systems	system	NOUN
ejpam-5398	105	9	,	,	PUNCT
ejpam-5398	105	10	particularly	particularly	ADV
ejpam-5398	105	11	when	when	SCONJ
ejpam-5398	105	12	handling	handle	VERB
ejpam-5398	105	13	elongated	elongate	VERB
ejpam-5398	105	14	objects	object	NOUN
ejpam-5398	105	15	such	such	ADJ
ejpam-5398	105	16	as	as	ADP
ejpam-5398	105	17	rods	rod	NOUN
ejpam-5398	105	18	,	,	PUNCT
ejpam-5398	105	19	can	can	AUX
ejpam-5398	105	20	result	result	VERB
ejpam-5398	105	21	in	in	ADP
ejpam-5398	105	22	improved	improved	ADJ
ejpam-5398	105	23	design	design	NOUN
ejpam-5398	105	24	and	and	CCONJ
ejpam-5398	105	25	control	control	NOUN
ejpam-5398	105	26	strategies	strategy	NOUN
ejpam-5398	105	27	to	to	PART
ejpam-5398	105	28	prevent	prevent	VERB
ejpam-5398	105	29	jams	jam	NOUN
ejpam-5398	105	30	or	or	CCONJ
ejpam-5398	105	31	misalignment	misalignment	NOUN
ejpam-5398	105	32	during	during	ADP
ejpam-5398	105	33	material	material	NOUN
ejpam-5398	105	34	transport	transport	NOUN
ejpam-5398	105	35	.	.	PUNCT
ejpam-5398	106	1	at	at	ADP
ejpam-5398	106	2	the	the	DET
ejpam-5398	106	3	micro	micro	ADJ
ejpam-5398	106	4	and	and	CCONJ
ejpam-5398	106	5	nano	nano	NOUN
ejpam-5398	106	6	scales	scale	NOUN
ejpam-5398	106	7	,	,	PUNCT
ejpam-5398	106	8	the	the	DET
ejpam-5398	106	9	td	td	NOUN
ejpam-5398	106	10	can	can	AUX
ejpam-5398	106	11	be	be	AUX
ejpam-5398	106	12	more	more	ADV
ejpam-5398	106	13	pronounced	pronounced	ADJ
ejpam-5398	106	14	because	because	SCONJ
ejpam-5398	106	15	of	of	ADP
ejpam-5398	106	16	the	the	DET
ejpam-5398	106	17	slower	slow	ADJ
ejpam-5398	106	18	a.	a.	NOUN
ejpam-5398	106	19	a.	a.	PROPN
ejpam-5398	106	20	galal	galal	PROPN
ejpam-5398	106	21	et	et	PROPN
ejpam-5398	106	22	al	al	PROPN
ejpam-5398	106	23	.	.	PUNCT
ejpam-5398	106	24	/	/	SYM
ejpam-5398	106	25	eur	eur	PROPN
ejpam-5398	106	26	.	.	PUNCT
ejpam-5398	107	1	j.	j.	PROPN
ejpam-5398	107	2	pure	pure	PROPN
ejpam-5398	107	3	appl	appl	PROPN
ejpam-5398	107	4	.	.	PROPN
ejpam-5398	107	5	math	math	PROPN
ejpam-5398	107	6	,	,	PUNCT
ejpam-5398	107	7	17	17	NUM
ejpam-5398	107	8	(	(	PUNCT
ejpam-5398	107	9	4	4	NUM
ejpam-5398	107	10	)	)	PUNCT
ejpam-5398	107	11	(	(	PUNCT
ejpam-5398	107	12	2024	2024	NUM
ejpam-5398	107	13	)	)	PUNCT
ejpam-5398	107	14	,	,	PUNCT
ejpam-5398	107	15	2878	2878	NUM
ejpam-5398	107	16	-	-	SYM
ejpam-5398	107	17	2897	2897	NUM
ejpam-5398	107	18	2882	2882	NUM
ejpam-5398	107	19	response	response	NOUN
ejpam-5398	107	20	times	time	NOUN
ejpam-5398	107	21	in	in	ADP
ejpam-5398	107	22	actuation	actuation	NOUN
ejpam-5398	107	23	and	and	CCONJ
ejpam-5398	107	24	sensing	sensing	NOUN
ejpam-5398	107	25	.	.	PUNCT
ejpam-5398	108	1	precision	precision	NOUN
ejpam-5398	108	2	is	be	AUX
ejpam-5398	108	3	crucial	crucial	ADJ
ejpam-5398	108	4	when	when	SCONJ
ejpam-5398	108	5	developing	develop	VERB
ejpam-5398	108	6	instruments	instrument	NOUN
ejpam-5398	108	7	,	,	PUNCT
ejpam-5398	108	8	as	as	SCONJ
ejpam-5398	108	9	even	even	ADV
ejpam-5398	108	10	slight	slight	ADJ
ejpam-5398	108	11	delays	delay	NOUN
ejpam-5398	108	12	can	can	AUX
ejpam-5398	108	13	have	have	VERB
ejpam-5398	108	14	a	a	DET
ejpam-5398	108	15	significant	significant	ADJ
ejpam-5398	108	16	impact	impact	NOUN
ejpam-5398	108	17	on	on	ADP
ejpam-5398	108	18	the	the	DET
ejpam-5398	108	19	performance	performance	NOUN
ejpam-5398	108	20	and	and	CCONJ
ejpam-5398	108	21	accuracy	accuracy	NOUN
ejpam-5398	108	22	of	of	ADP
ejpam-5398	108	23	the	the	DET
ejpam-5398	108	24	device	device	NOUN
ejpam-5398	108	25	.	.	PUNCT
ejpam-5398	109	1	understanding	understand	VERB
ejpam-5398	109	2	td	td	NOUN
ejpam-5398	109	3	rolling	rolling	NOUN
ejpam-5398	109	4	can	can	AUX
ejpam-5398	109	5	improve	improve	VERB
ejpam-5398	109	6	the	the	DET
ejpam-5398	109	7	dependability	dependability	NOUN
ejpam-5398	109	8	and	and	CCONJ
ejpam-5398	109	9	predictability	predictability	NOUN
ejpam-5398	109	10	of	of	ADP
ejpam-5398	109	11	deployment	deployment	NOUN
ejpam-5398	109	12	mechanisms	mechanism	NOUN
ejpam-5398	109	13	in	in	ADP
ejpam-5398	109	14	military	military	ADJ
ejpam-5398	109	15	electronics	electronic	NOUN
ejpam-5398	109	16	,	,	PUNCT
ejpam-5398	109	17	especially	especially	ADV
ejpam-5398	109	18	in	in	ADP
ejpam-5398	109	19	situations	situation	NOUN
ejpam-5398	109	20	when	when	SCONJ
ejpam-5398	109	21	timing	timing	NOUN
ejpam-5398	109	22	and	and	CCONJ
ejpam-5398	109	23	synchronization	synchronization	NOUN
ejpam-5398	109	24	are	be	AUX
ejpam-5398	109	25	critical	critical	ADJ
ejpam-5398	109	26	.	.	PUNCT
ejpam-5398	110	1	this	this	DET
ejpam-5398	110	2	understanding	understanding	NOUN
ejpam-5398	110	3	ensures	ensure	VERB
ejpam-5398	110	4	that	that	SCONJ
ejpam-5398	110	5	systems	system	NOUN
ejpam-5398	110	6	function	function	VERB
ejpam-5398	110	7	appropriately	appropriately	ADV
ejpam-5398	110	8	under	under	ADP
ejpam-5398	110	9	time	time	NOUN
ejpam-5398	110	10	-	-	PUNCT
ejpam-5398	110	11	sensitive	sensitive	ADJ
ejpam-5398	110	12	conditions	condition	NOUN
ejpam-5398	110	13	.	.	PUNCT
ejpam-5398	111	1	when	when	SCONJ
ejpam-5398	111	2	designing	design	VERB
ejpam-5398	111	3	tires	tire	NOUN
ejpam-5398	111	4	or	or	CCONJ
ejpam-5398	111	5	rolling	rolling	ADJ
ejpam-5398	111	6	elements	element	NOUN
ejpam-5398	111	7	for	for	ADP
ejpam-5398	111	8	automotive	automotive	ADJ
ejpam-5398	111	9	and	and	CCONJ
ejpam-5398	111	10	aerospace	aerospace	NOUN
ejpam-5398	111	11	applications	application	NOUN
ejpam-5398	111	12	,	,	PUNCT
ejpam-5398	111	13	including	include	VERB
ejpam-5398	111	14	the	the	DET
ejpam-5398	111	15	effects	effect	NOUN
ejpam-5398	111	16	of	of	ADP
ejpam-5398	111	17	time	time	NOUN
ejpam-5398	111	18	-	-	PUNCT
ejpam-5398	111	19	delayed	delay	VERB
ejpam-5398	111	20	rolling	rolling	NOUN
ejpam-5398	111	21	can	can	AUX
ejpam-5398	111	22	enhance	enhance	VERB
ejpam-5398	111	23	the	the	DET
ejpam-5398	111	24	precision	precision	NOUN
ejpam-5398	111	25	of	of	ADP
ejpam-5398	111	26	simulations	simulation	NOUN
ejpam-5398	111	27	and	and	CCONJ
ejpam-5398	111	28	optimize	optimize	VERB
ejpam-5398	111	29	the	the	DET
ejpam-5398	111	30	performance	performance	NOUN
ejpam-5398	111	31	of	of	ADP
ejpam-5398	111	32	these	these	DET
ejpam-5398	111	33	components	component	NOUN
ejpam-5398	111	34	in	in	ADP
ejpam-5398	111	35	dynamic	dynamic	ADJ
ejpam-5398	111	36	settings	setting	NOUN
ejpam-5398	111	37	,	,	PUNCT
ejpam-5398	111	38	especially	especially	ADV
ejpam-5398	111	39	in	in	ADP
ejpam-5398	111	40	highspeed	highspeed	NOUN
ejpam-5398	111	41	or	or	CCONJ
ejpam-5398	111	42	high	high	ADJ
ejpam-5398	111	43	-	-	PUNCT
ejpam-5398	111	44	stress	stress	NOUN
ejpam-5398	111	45	environments	environment	NOUN
ejpam-5398	111	46	.	.	PUNCT
ejpam-5398	112	1	comprehending	comprehend	VERB
ejpam-5398	112	2	and	and	CCONJ
ejpam-5398	112	3	controlling	control	VERB
ejpam-5398	112	4	these	these	DET
ejpam-5398	112	5	delays	delay	NOUN
ejpam-5398	112	6	are	be	AUX
ejpam-5398	112	7	essential	essential	ADJ
ejpam-5398	112	8	for	for	ADP
ejpam-5398	112	9	maximizing	maximize	VERB
ejpam-5398	112	10	performance	performance	NOUN
ejpam-5398	112	11	and	and	CCONJ
ejpam-5398	112	12	guaranteeing	guarantee	VERB
ejpam-5398	112	13	the	the	DET
ejpam-5398	112	14	stability	stability	NOUN
ejpam-5398	112	15	and	and	CCONJ
ejpam-5398	112	16	dependability	dependability	NOUN
ejpam-5398	112	17	of	of	ADP
ejpam-5398	112	18	the	the	DET
ejpam-5398	112	19	system	system	NOUN
ejpam-5398	112	20	.	.	PUNCT
ejpam-5398	113	1	owing	owe	VERB
ejpam-5398	113	2	to	to	ADP
ejpam-5398	113	3	the	the	DET
ejpam-5398	113	4	aforementioned	aforementioned	ADJ
ejpam-5398	113	5	potentials	potential	NOUN
ejpam-5398	113	6	,	,	PUNCT
ejpam-5398	113	7	their	their	PRON
ejpam-5398	113	8	exceptional	exceptional	ADJ
ejpam-5398	113	9	sensitivity	sensitivity	NOUN
ejpam-5398	113	10	to	to	ADP
ejpam-5398	113	11	dynamic	dynamic	ADJ
ejpam-5398	113	12	loading	loading	NOUN
ejpam-5398	113	13	,	,	PUNCT
ejpam-5398	113	14	geometric	geometric	ADJ
ejpam-5398	113	15	variations	variation	NOUN
ejpam-5398	113	16	,	,	PUNCT
ejpam-5398	113	17	and	and	CCONJ
ejpam-5398	113	18	dissipation	dissipation	NOUN
ejpam-5398	113	19	challenges	challenge	NOUN
ejpam-5398	113	20	,	,	PUNCT
ejpam-5398	113	21	assessing	assess	VERB
ejpam-5398	113	22	the	the	DET
ejpam-5398	113	23	rocking	rocking	NOUN
ejpam-5398	113	24	and	and	CCONJ
ejpam-5398	113	25	toppling	topple	VERB
ejpam-5398	113	26	reactions	reaction	NOUN
ejpam-5398	113	27	of	of	ADP
ejpam-5398	113	28	rigid	rigid	ADJ
ejpam-5398	113	29	blocks	block	NOUN
ejpam-5398	113	30	during	during	ADP
ejpam-5398	113	31	motion	motion	NOUN
ejpam-5398	113	32	events	event	NOUN
ejpam-5398	113	33	presents	present	VERB
ejpam-5398	113	34	a	a	DET
ejpam-5398	113	35	substantial	substantial	ADJ
ejpam-5398	113	36	challenge	challenge	NOUN
ejpam-5398	113	37	.	.	PUNCT
ejpam-5398	114	1	therefore	therefore	ADV
ejpam-5398	114	2	,	,	PUNCT
ejpam-5398	114	3	examining	examine	VERB
ejpam-5398	114	4	the	the	DET
ejpam-5398	114	5	dynamic	dynamic	ADJ
ejpam-5398	114	6	behavior	behavior	NOUN
ejpam-5398	114	7	of	of	ADP
ejpam-5398	114	8	a	a	DET
ejpam-5398	114	9	rigid	rigid	ADJ
ejpam-5398	114	10	rocking	rocking	NOUN
ejpam-5398	114	11	rod	rod	NOUN
ejpam-5398	114	12	over	over	ADP
ejpam-5398	114	13	a	a	DET
ejpam-5398	114	14	circular	circular	ADJ
ejpam-5398	114	15	surface	surface	NOUN
ejpam-5398	114	16	under	under	ADP
ejpam-5398	114	17	the	the	DET
ejpam-5398	114	18	assumption	assumption	NOUN
ejpam-5398	114	19	of	of	ADP
ejpam-5398	114	20	pure	pure	ADJ
ejpam-5398	114	21	rolling	rolling	NOUN
ejpam-5398	114	22	without	without	ADP
ejpam-5398	114	23	slippage	slippage	NOUN
ejpam-5398	114	24	is	be	AUX
ejpam-5398	114	25	the	the	DET
ejpam-5398	114	26	aim	aim	NOUN
ejpam-5398	114	27	of	of	ADP
ejpam-5398	114	28	this	this	DET
ejpam-5398	114	29	paper	paper	NOUN
ejpam-5398	114	30	.	.	PUNCT
ejpam-5398	115	1	according	accord	VERB
ejpam-5398	115	2	to	to	ADP
ejpam-5398	115	3	classical	classical	ADJ
ejpam-5398	115	4	mechanics	mechanic	NOUN
ejpam-5398	115	5	,	,	PUNCT
ejpam-5398	115	6	the	the	DET
ejpam-5398	115	7	motion	motion	NOUN
ejpam-5398	115	8	’s	’s	PART
ejpam-5398	115	9	governing	govern	VERB
ejpam-5398	115	10	equation	equation	NOUN
ejpam-5398	115	11	is	be	AUX
ejpam-5398	115	12	controlled	control	VERB
ejpam-5398	115	13	as	as	ADP
ejpam-5398	115	14	a	a	DET
ejpam-5398	115	15	nonlinear	nonlinear	ADJ
ejpam-5398	115	16	ode	ode	NOUN
ejpam-5398	115	17	with	with	ADP
ejpam-5398	115	18	highly	highly	ADV
ejpam-5398	115	19	nonlinear	nonlinear	ADJ
ejpam-5398	115	20	orders	order	NOUN
ejpam-5398	115	21	.	.	PUNCT
ejpam-5398	116	1	regarding	regard	VERB
ejpam-5398	116	2	the	the	DET
ejpam-5398	116	3	innovative	innovative	ADJ
ejpam-5398	116	4	approach	approach	NOUN
ejpam-5398	116	5	or	or	CCONJ
ejpam-5398	116	6	noteworthy	noteworthy	ADJ
ejpam-5398	116	7	outcomes	outcome	NOUN
ejpam-5398	116	8	,	,	PUNCT
ejpam-5398	116	9	it	it	PRON
ejpam-5398	116	10	is	be	AUX
ejpam-5398	116	11	vital	vital	ADJ
ejpam-5398	116	12	to	to	PART
ejpam-5398	116	13	emphasize	emphasize	VERB
ejpam-5398	116	14	the	the	DET
ejpam-5398	116	15	following	following	NOUN
ejpam-5398	116	16	:	:	PUNCT
ejpam-5398	116	17	the	the	DET
ejpam-5398	116	18	new	new	ADJ
ejpam-5398	116	19	technique	technique	NOUN
ejpam-5398	116	20	yields	yield	VERB
ejpam-5398	116	21	highly	highly	ADV
ejpam-5398	116	22	nonlinear	nonlinear	ADJ
ejpam-5398	116	23	ode	ode	NOUN
ejpam-5398	116	24	that	that	PRON
ejpam-5398	116	25	exactly	exactly	ADV
ejpam-5398	116	26	has	have	VERB
ejpam-5398	116	27	the	the	DET
ejpam-5398	116	28	same	same	ADJ
ejpam-5398	116	29	behavior	behavior	NOUN
ejpam-5398	116	30	as	as	ADP
ejpam-5398	116	31	the	the	DET
ejpam-5398	116	32	existing	exist	VERB
ejpam-5398	116	33	nonlinear	nonlinear	ADJ
ejpam-5398	116	34	one	one	NUM
ejpam-5398	116	35	.	.	PUNCT
ejpam-5398	117	1	there	there	PRON
ejpam-5398	117	2	must	must	AUX
ejpam-5398	117	3	be	be	AUX
ejpam-5398	117	4	a	a	DET
ejpam-5398	117	5	harmonious	harmonious	ADJ
ejpam-5398	117	6	correlation	correlation	NOUN
ejpam-5398	117	7	between	between	ADP
ejpam-5398	117	8	the	the	DET
ejpam-5398	117	9	mathematical	mathematical	ADJ
ejpam-5398	117	10	expressions	expression	NOUN
ejpam-5398	117	11	for	for	ADP
ejpam-5398	117	12	the	the	DET
ejpam-5398	117	13	new	new	ADJ
ejpam-5398	117	14	method	method	NOUN
ejpam-5398	117	15	to	to	PART
ejpam-5398	117	16	work	work	VERB
ejpam-5398	117	17	.	.	PUNCT
ejpam-5398	118	1	all	all	DET
ejpam-5398	118	2	traditional	traditional	ADJ
ejpam-5398	118	3	methods	method	NOUN
ejpam-5398	118	4	utilize	utilize	VERB
ejpam-5398	118	5	the	the	DET
ejpam-5398	118	6	taylor	taylor	PROPN
ejpam-5398	118	7	series	series	PROPN
ejpam-5398	118	8	expansion	expansion	NOUN
ejpam-5398	118	9	to	to	PART
ejpam-5398	118	10	reduce	reduce	VERB
ejpam-5398	118	11	the	the	DET
ejpam-5398	118	12	complexity	complexity	NOUN
ejpam-5398	118	13	of	of	ADP
ejpam-5398	118	14	the	the	DET
ejpam-5398	118	15	specified	specified	ADJ
ejpam-5398	118	16	issue	issue	NOUN
ejpam-5398	118	17	in	in	ADP
ejpam-5398	118	18	the	the	DET
ejpam-5398	118	19	presence	presence	NOUN
ejpam-5398	118	20	of	of	ADP
ejpam-5398	118	21	restoring	restore	VERB
ejpam-5398	118	22	forces	force	NOUN
ejpam-5398	118	23	.	.	PUNCT
ejpam-5398	119	1	the	the	DET
ejpam-5398	119	2	current	current	ADJ
ejpam-5398	119	3	paper	paper	NOUN
ejpam-5398	119	4	has	have	AUX
ejpam-5398	119	5	no	no	ADV
ejpam-5398	119	6	longer	long	ADV
ejpam-5398	119	7	encompasses	encompass	VERB
ejpam-5398	119	8	this	this	DET
ejpam-5398	119	9	shortcoming	shortcoming	NOUN
ejpam-5398	119	10	.	.	PUNCT
ejpam-5398	120	1	we	we	PRON
ejpam-5398	120	2	can	can	AUX
ejpam-5398	120	3	examine	examine	VERB
ejpam-5398	120	4	the	the	DET
ejpam-5398	120	5	problem	problem	NOUN
ejpam-5398	120	6	’s	’s	PART
ejpam-5398	120	7	stability	stability	NOUN
ejpam-5398	120	8	analysis	analysis	NOUN
ejpam-5398	120	9	thanks	thank	NOUN
ejpam-5398	120	10	to	to	ADP
ejpam-5398	120	11	the	the	DET
ejpam-5398	120	12	current	current	ADJ
ejpam-5398	120	13	methodology	methodology	NOUN
ejpam-5398	120	14	,	,	PUNCT
ejpam-5398	120	15	which	which	PRON
ejpam-5398	120	16	is	be	AUX
ejpam-5398	120	17	not	not	PART
ejpam-5398	120	18	possible	possible	ADJ
ejpam-5398	120	19	with	with	ADP
ejpam-5398	120	20	other	other	ADJ
ejpam-5398	120	21	conventional	conventional	ADJ
ejpam-5398	120	22	techniques	technique	NOUN
ejpam-5398	120	23	.	.	PUNCT
ejpam-5398	121	1	lastly	lastly	ADV
ejpam-5398	121	2	,	,	PUNCT
ejpam-5398	121	3	the	the	DET
ejpam-5398	121	4	novel	novel	ADJ
ejpam-5398	121	5	approach	approach	NOUN
ejpam-5398	121	6	seems	seem	VERB
ejpam-5398	121	7	to	to	PART
ejpam-5398	121	8	be	be	AUX
ejpam-5398	121	9	an	an	DET
ejpam-5398	121	10	easy	easy	ADJ
ejpam-5398	121	11	-	-	PUNCT
ejpam-5398	121	12	to	to	ADP
ejpam-5398	121	13	-	-	PUNCT
ejpam-5398	121	14	use	use	VERB
ejpam-5398	121	15	,	,	PUNCT
ejpam-5398	121	16	worthwhile	worthwhile	ADJ
ejpam-5398	121	17	,	,	PUNCT
ejpam-5398	121	18	and	and	CCONJ
ejpam-5398	121	19	interesting	interesting	ADJ
ejpam-5398	121	20	tool	tool	NOUN
ejpam-5398	121	21	.	.	PUNCT
ejpam-5398	122	1	it	it	PRON
ejpam-5398	122	2	is	be	AUX
ejpam-5398	122	3	useful	useful	ADJ
ejpam-5398	122	4	for	for	ADP
ejpam-5398	122	5	the	the	DET
ejpam-5398	122	6	analysis	analysis	NOUN
ejpam-5398	122	7	of	of	ADP
ejpam-5398	122	8	several	several	ADJ
ejpam-5398	122	9	types	type	NOUN
ejpam-5398	122	10	of	of	ADP
ejpam-5398	122	11	nonlinear	nonlinear	ADJ
ejpam-5398	122	12	oscillators	oscillator	NOUN
ejpam-5398	122	13	.	.	PUNCT
ejpam-5398	123	1	to	to	PART
ejpam-5398	123	2	cartelize	cartelize	VERB
ejpam-5398	123	3	the	the	DET
ejpam-5398	123	4	presentation	presentation	NOUN
ejpam-5398	123	5	of	of	ADP
ejpam-5398	123	6	the	the	DET
ejpam-5398	123	7	paper	paper	NOUN
ejpam-5398	123	8	,	,	PUNCT
ejpam-5398	123	9	the	the	DET
ejpam-5398	123	10	remaining	remain	VERB
ejpam-5398	123	11	text	text	NOUN
ejpam-5398	123	12	is	be	AUX
ejpam-5398	123	13	organized	organize	VERB
ejpam-5398	123	14	as	as	SCONJ
ejpam-5398	123	15	follows	follow	VERB
ejpam-5398	123	16	:	:	PUNCT
ejpam-5398	123	17	the	the	DET
ejpam-5398	123	18	npa	npa	NOUN
ejpam-5398	123	19	yields	yield	VERB
ejpam-5398	123	20	an	an	DET
ejpam-5398	123	21	equivalent	equivalent	ADJ
ejpam-5398	123	22	linear	linear	ADJ
ejpam-5398	123	23	equation	equation	NOUN
ejpam-5398	123	24	in	in	ADP
ejpam-5398	123	25	§	§	PROPN
ejpam-5398	123	26	2	2	NUM
ejpam-5398	123	27	.	.	PUNCT
ejpam-5398	124	1	this	this	DET
ejpam-5398	124	2	section	section	NOUN
ejpam-5398	124	3	presents	present	VERB
ejpam-5398	124	4	a	a	DET
ejpam-5398	124	5	confirmation	confirmation	NOUN
ejpam-5398	124	6	using	use	VERB
ejpam-5398	124	7	the	the	DET
ejpam-5398	124	8	numerical	numerical	ADJ
ejpam-5398	124	9	solution	solution	NOUN
ejpam-5398	124	10	via	via	ADP
ejpam-5398	124	11	nm	nm	PROPN
ejpam-5398	124	12	.	.	PUNCT
ejpam-5398	125	1	the	the	DET
ejpam-5398	125	2	graphical	graphical	ADJ
ejpam-5398	125	3	plots	plot	NOUN
ejpam-5398	125	4	,	,	PUNCT
ejpam-5398	125	5	including	include	VERB
ejpam-5398	125	6	time	time	NOUN
ejpam-5398	125	7	history	history	NOUN
ejpam-5398	125	8	and	and	CCONJ
ejpam-5398	125	9	stability	stability	NOUN
ejpam-5398	125	10	,	,	PUNCT
ejpam-5398	125	11	are	be	AUX
ejpam-5398	125	12	presented	present	VERB
ejpam-5398	125	13	in	in	ADP
ejpam-5398	125	14	§	§	PROPN
ejpam-5398	125	15	3	3	NUM
ejpam-5398	125	16	together	together	ADV
ejpam-5398	125	17	with	with	ADP
ejpam-5398	125	18	their	their	PRON
ejpam-5398	125	19	interpretations	interpretation	NOUN
ejpam-5398	125	20	based	base	VERB
ejpam-5398	125	21	on	on	ADP
ejpam-5398	125	22	the	the	DET
ejpam-5398	125	23	obtained	obtain	VERB
ejpam-5398	125	24	data	datum	NOUN
ejpam-5398	125	25	.	.	PUNCT
ejpam-5398	126	1	lately	lately	ADV
ejpam-5398	126	2	,	,	PUNCT
ejpam-5398	126	3	closing	closing	NOUN
ejpam-5398	126	4	thoughts	thought	NOUN
ejpam-5398	126	5	are	be	AUX
ejpam-5398	126	6	offered	offer	VERB
ejpam-5398	126	7	in	in	ADP
ejpam-5398	126	8	§	§	PROPN
ejpam-5398	126	9	4	4	NUM
ejpam-5398	126	10	.	.	NOUN
ejpam-5398	126	11	2	2	NUM
ejpam-5398	126	12	.	.	X
ejpam-5398	126	13	methodology	methodology	NOUN
ejpam-5398	126	14	structure	structure	NOUN
ejpam-5398	126	15	the	the	DET
ejpam-5398	126	16	improvement	improvement	NOUN
ejpam-5398	126	17	of	of	ADP
ejpam-5398	126	18	the	the	DET
ejpam-5398	126	19	existing	exist	VERB
ejpam-5398	126	20	equation	equation	NOUN
ejpam-5398	126	21	is	be	AUX
ejpam-5398	126	22	used	use	VERB
ejpam-5398	126	23	to	to	PART
ejpam-5398	126	24	analyze	analyze	VERB
ejpam-5398	126	25	the	the	DET
ejpam-5398	126	26	motion	motion	NOUN
ejpam-5398	126	27	of	of	ADP
ejpam-5398	126	28	a	a	DET
ejpam-5398	126	29	solid	solid	ADJ
ejpam-5398	126	30	rod	rod	NOUN
ejpam-5398	126	31	that	that	PRON
ejpam-5398	126	32	rocks	rock	VERB
ejpam-5398	126	33	.	.	PUNCT
ejpam-5398	127	1	the	the	DET
ejpam-5398	127	2	suitable	suitable	ADJ
ejpam-5398	127	3	response	response	NOUN
ejpam-5398	127	4	to	to	ADP
ejpam-5398	127	5	the	the	DET
ejpam-5398	127	6	periodic	periodic	ADJ
ejpam-5398	127	7	motions	motion	NOUN
ejpam-5398	127	8	remains	remain	VERB
ejpam-5398	127	9	challenging	challenge	VERB
ejpam-5398	127	10	due	due	ADJ
ejpam-5398	127	11	to	to	ADP
ejpam-5398	127	12	the	the	DET
ejpam-5398	127	13	structures	structure	NOUN
ejpam-5398	127	14	of	of	ADP
ejpam-5398	127	15	related	relate	VERB
ejpam-5398	127	16	essential	essential	ADJ
ejpam-5398	127	17	equations	equation	NOUN
ejpam-5398	127	18	.	.	PUNCT
ejpam-5398	128	1	therefore	therefore	ADV
ejpam-5398	128	2	,	,	PUNCT
ejpam-5398	128	3	the	the	DET
ejpam-5398	128	4	goal	goal	NOUN
ejpam-5398	128	5	of	of	ADP
ejpam-5398	128	6	this	this	DET
ejpam-5398	128	7	work	work	NOUN
ejpam-5398	128	8	is	be	AUX
ejpam-5398	128	9	to	to	PART
ejpam-5398	128	10	find	find	VERB
ejpam-5398	128	11	periodic	periodic	ADJ
ejpam-5398	128	12	a.	a.	NOUN
ejpam-5398	128	13	a.	a.	NOUN
ejpam-5398	128	14	galal	galal	PROPN
ejpam-5398	128	15	et	et	PROPN
ejpam-5398	128	16	al	al	PROPN
ejpam-5398	128	17	.	.	PUNCT
ejpam-5398	128	18	/	/	SYM
ejpam-5398	128	19	eur	eur	PROPN
ejpam-5398	128	20	.	.	PUNCT
ejpam-5398	129	1	j.	j.	PROPN
ejpam-5398	129	2	pure	pure	PROPN
ejpam-5398	129	3	appl	appl	PROPN
ejpam-5398	129	4	.	.	PROPN
ejpam-5398	129	5	math	math	PROPN
ejpam-5398	129	6	,	,	PUNCT
ejpam-5398	129	7	17	17	NUM
ejpam-5398	129	8	(	(	PUNCT
ejpam-5398	129	9	4	4	NUM
ejpam-5398	129	10	)	)	PUNCT
ejpam-5398	129	11	(	(	PUNCT
ejpam-5398	129	12	2024	2024	NUM
ejpam-5398	129	13	)	)	PUNCT
ejpam-5398	129	14	,	,	PUNCT
ejpam-5398	129	15	2878	2878	NUM
ejpam-5398	129	16	-	-	SYM
ejpam-5398	129	17	2897	2897	NUM
ejpam-5398	129	18	2883	2883	NUM
ejpam-5398	129	19	figure	figure	NOUN
ejpam-5398	129	20	1	1	NUM
ejpam-5398	129	21	:	:	PUNCT
ejpam-5398	129	22	sketches	sketch	VERB
ejpam-5398	129	23	the	the	DET
ejpam-5398	129	24	model	model	NOUN
ejpam-5398	129	25	being	be	AUX
ejpam-5398	129	26	examined	examine	VERB
ejpam-5398	129	27	.	.	PUNCT
ejpam-5398	130	1	analytical	analytical	ADJ
ejpam-5398	130	2	solutions	solution	NOUN
ejpam-5398	130	3	using	use	VERB
ejpam-5398	130	4	a	a	DET
ejpam-5398	130	5	more	more	ADV
ejpam-5398	130	6	straightforward	straightforward	ADJ
ejpam-5398	130	7	scheme	scheme	NOUN
ejpam-5398	130	8	for	for	ADP
ejpam-5398	130	9	this	this	DET
ejpam-5398	130	10	type	type	NOUN
ejpam-5398	130	11	of	of	ADP
ejpam-5398	130	12	dynamical	dynamical	ADJ
ejpam-5398	130	13	system	system	NOUN
ejpam-5398	130	14	.	.	PUNCT
ejpam-5398	131	1	in	in	ADP
ejpam-5398	131	2	this	this	DET
ejpam-5398	131	3	instance	instance	NOUN
ejpam-5398	131	4	,	,	PUNCT
ejpam-5398	131	5	any	any	DET
ejpam-5398	131	6	other	other	ADJ
ejpam-5398	131	7	conventional	conventional	ADJ
ejpam-5398	131	8	perturbation	perturbation	NOUN
ejpam-5398	131	9	method	method	NOUN
ejpam-5398	131	10	in	in	ADP
ejpam-5398	131	11	addition	addition	NOUN
ejpam-5398	131	12	to	to	ADP
ejpam-5398	131	13	the	the	DET
ejpam-5398	131	14	taylor	taylor	PROPN
ejpam-5398	131	15	expansion	expansion	NOUN
ejpam-5398	131	16	is	be	AUX
ejpam-5398	131	17	not	not	PART
ejpam-5398	131	18	required	require	VERB
ejpam-5398	131	19	.	.	PUNCT
ejpam-5398	132	1	the	the	DET
ejpam-5398	132	2	subject	subject	NOUN
ejpam-5398	132	3	under	under	ADP
ejpam-5398	132	4	research	research	NOUN
ejpam-5398	132	5	is	be	AUX
ejpam-5398	132	6	established	establish	VERB
ejpam-5398	132	7	by	by	ADP
ejpam-5398	132	8	a	a	DET
ejpam-5398	132	9	consistently	consistently	ADV
ejpam-5398	132	10	inflexible	inflexible	ADJ
ejpam-5398	132	11	rod	rod	NOUN
ejpam-5398	132	12	actively	actively	ADV
ejpam-5398	132	13	rolling	roll	VERB
ejpam-5398	132	14	across	across	ADP
ejpam-5398	132	15	a	a	DET
ejpam-5398	132	16	circular	circular	ADJ
ejpam-5398	132	17	surface	surface	NOUN
ejpam-5398	132	18	without	without	ADP
ejpam-5398	132	19	sliding	slide	VERB
ejpam-5398	132	20	.	.	PUNCT
ejpam-5398	133	1	the	the	DET
ejpam-5398	133	2	length	length	NOUN
ejpam-5398	133	3	and	and	CCONJ
ejpam-5398	133	4	the	the	DET
ejpam-5398	133	5	mass	mass	NOUN
ejpam-5398	133	6	of	of	ADP
ejpam-5398	133	7	the	the	DET
ejpam-5398	133	8	rod	rod	NOUN
ejpam-5398	133	9	are	be	AUX
ejpam-5398	133	10	both	both	PRON
ejpam-5398	133	11	been	be	AUX
ejpam-5398	133	12	retained	retain	VERB
ejpam-5398	133	13	.	.	PUNCT
ejpam-5398	134	1	the	the	DET
ejpam-5398	134	2	rod	rod	NOUN
ejpam-5398	134	3	is	be	AUX
ejpam-5398	134	4	first	first	ADV
ejpam-5398	134	5	resting	rest	VERB
ejpam-5398	134	6	horizontally	horizontally	ADV
ejpam-5398	134	7	at	at	ADP
ejpam-5398	134	8	the	the	DET
ejpam-5398	134	9	tangency	tangency	NOUN
ejpam-5398	134	10	point	point	NOUN
ejpam-5398	134	11	,	,	PUNCT
ejpam-5398	134	12	which	which	PRON
ejpam-5398	134	13	is	be	AUX
ejpam-5398	134	14	situated	situate	VERB
ejpam-5398	134	15	at	at	ADP
ejpam-5398	134	16	the	the	DET
ejpam-5398	134	17	center	center	NOUN
ejpam-5398	134	18	of	of	ADP
ejpam-5398	134	19	mass	mass	NOUN
ejpam-5398	134	20	(	(	PUNCT
ejpam-5398	134	21	c.m	c.m	NOUN
ejpam-5398	134	22	.	.	PROPN
ejpam-5398	134	23	)	)	PUNCT
ejpam-5398	134	24	,	,	PUNCT
ejpam-5398	134	25	as	as	SCONJ
ejpam-5398	134	26	shown	show	VERB
ejpam-5398	134	27	in	in	ADP
ejpam-5398	134	28	fig	fig	NOUN
ejpam-5398	134	29	.	.	PUNCT
ejpam-5398	135	1	(	(	PUNCT
ejpam-5398	135	2	1	1	NUM
ejpam-5398	135	3	)	)	PUNCT
ejpam-5398	135	4	.	.	PUNCT
ejpam-5398	136	1	the	the	DET
ejpam-5398	136	2	arc	arc	NOUN
ejpam-5398	136	3	rθ	rθ	VERB
ejpam-5398	136	4	with	with	ADP
ejpam-5398	136	5	no	no	DET
ejpam-5398	136	6	-	-	PUNCT
ejpam-5398	136	7	slip	slip	NOUN
ejpam-5398	136	8	motion	motion	NOUN
ejpam-5398	136	9	,	,	PUNCT
ejpam-5398	136	10	which	which	PRON
ejpam-5398	136	11	is	be	AUX
ejpam-5398	136	12	defined	define	VERB
ejpam-5398	136	13	as	as	ADP
ejpam-5398	136	14	a	a	DET
ejpam-5398	136	15	small	small	ADJ
ejpam-5398	136	16	movement	movement	NOUN
ejpam-5398	136	17	on	on	ADP
ejpam-5398	136	18	the	the	DET
ejpam-5398	136	19	circle	circle	NOUN
ejpam-5398	136	20	,	,	PUNCT
ejpam-5398	136	21	must	must	AUX
ejpam-5398	136	22	eventually	eventually	ADV
ejpam-5398	136	23	be	be	AUX
ejpam-5398	136	24	used	use	VERB
ejpam-5398	136	25	to	to	PART
ejpam-5398	136	26	characterize	characterize	VERB
ejpam-5398	136	27	the	the	DET
ejpam-5398	136	28	distance	distance	NOUN
ejpam-5398	136	29	between	between	ADP
ejpam-5398	136	30	the	the	DET
ejpam-5398	136	31	center	center	NOUN
ejpam-5398	136	32	of	of	ADP
ejpam-5398	136	33	mass	mass	NOUN
ejpam-5398	136	34	and	and	CCONJ
ejpam-5398	136	35	the	the	DET
ejpam-5398	136	36	tangency	tangency	NOUN
ejpam-5398	136	37	point	point	NOUN
ejpam-5398	136	38	.	.	PUNCT
ejpam-5398	137	1	currently	currently	ADV
ejpam-5398	137	2	,	,	PUNCT
ejpam-5398	137	3	going	go	VERB
ejpam-5398	137	4	back	back	ADV
ejpam-5398	137	5	to	to	ADP
ejpam-5398	137	6	our	our	PRON
ejpam-5398	137	7	earlier	early	ADJ
ejpam-5398	137	8	work	work	NOUN
ejpam-5398	137	9	[	[	X
ejpam-5398	137	10	17	17	NUM
ejpam-5398	137	11	]	]	PUNCT
ejpam-5398	137	12	,	,	PUNCT
ejpam-5398	137	13	we	we	PRON
ejpam-5398	137	14	can	can	AUX
ejpam-5398	137	15	extract	extract	VERB
ejpam-5398	137	16	the	the	DET
ejpam-5398	137	17	uniform	uniform	ADJ
ejpam-5398	137	18	stiff	stiff	ADJ
ejpam-5398	137	19	swinging	swinging	NOUN
ejpam-5398	137	20	rod	rod	NOUN
ejpam-5398	137	21	’s	’s	PART
ejpam-5398	137	22	regulating	regulate	VERB
ejpam-5398	137	23	equation	equation	NOUN
ejpam-5398	137	24	of	of	ADP
ejpam-5398	137	25	motion	motion	NOUN
ejpam-5398	137	26	,	,	PUNCT
ejpam-5398	137	27	which	which	PRON
ejpam-5398	137	28	took	take	VERB
ejpam-5398	137	29	the	the	DET
ejpam-5398	137	30	following	follow	VERB
ejpam-5398	137	31	form	form	NOUN
ejpam-5398	137	32	[	[	X
ejpam-5398	137	33	17	17	NUM
ejpam-5398	137	34	]	]	X
ejpam-5398	137	35	:	:	PUNCT
ejpam-5398	137	36	ml2	ml2	PROPN
ejpam-5398	137	37	12	12	NUM
ejpam-5398	137	38	θ̈	θ̈	CCONJ
ejpam-5398	138	1	+	+	NUM
ejpam-5398	138	2	mr2	mr2	NOUN
ejpam-5398	138	3	(	(	PUNCT
ejpam-5398	138	4	θ̇2θ̈	θ̇2θ̈	PUNCT
ejpam-5398	138	5	+	+	CCONJ
ejpam-5398	138	6	θ̈θ̇2	θ̈θ̇2	X
ejpam-5398	138	7	)	)	PUNCT
ejpam-5398	139	1	+	+	ADP
ejpam-5398	139	2	mg	mg	PROPN
ejpam-5398	139	3	cos	co	NOUN
ejpam-5398	139	4	θ	θ	PROPN
ejpam-5398	139	5	=	=	SYM
ejpam-5398	139	6	0	0	PROPN
ejpam-5398	139	7	.	.	PUNCT
ejpam-5398	140	1	(	(	PUNCT
ejpam-5398	140	2	1	1	X
ejpam-5398	140	3	)	)	PUNCT
ejpam-5398	140	4	the	the	DET
ejpam-5398	140	5	foundation	foundation	NOUN
ejpam-5398	140	6	of	of	ADP
ejpam-5398	140	7	this	this	DET
ejpam-5398	140	8	article	article	NOUN
ejpam-5398	140	9	provides	provide	VERB
ejpam-5398	140	10	a	a	DET
ejpam-5398	140	11	comprehensive	comprehensive	ADJ
ejpam-5398	140	12	inventory	inventory	NOUN
ejpam-5398	140	13	of	of	ADP
ejpam-5398	140	14	all	all	DET
ejpam-5398	140	15	the	the	DET
ejpam-5398	140	16	variables	variable	NOUN
ejpam-5398	140	17	employed	employ	VERB
ejpam-5398	140	18	in	in	ADP
ejpam-5398	140	19	eq	eq	ADP
ejpam-5398	140	20	.	.	PUNCT
ejpam-5398	141	1	(	(	PUNCT
ejpam-5398	141	2	1	1	NUM
ejpam-5398	141	3	)	)	PUNCT
ejpam-5398	141	4	.	.	PUNCT
ejpam-5398	142	1	the	the	DET
ejpam-5398	142	2	anticipated	anticipate	VERB
ejpam-5398	142	3	model	model	NOUN
ejpam-5398	142	4	’s	’s	PART
ejpam-5398	142	5	outline	outline	NOUN
ejpam-5398	142	6	is	be	AUX
ejpam-5398	142	7	illustrated	illustrate	VERB
ejpam-5398	142	8	in	in	ADP
ejpam-5398	142	9	fig	fig	NOUN
ejpam-5398	142	10	.	.	PUNCT
ejpam-5398	143	1	(	(	PUNCT
ejpam-5398	143	2	1	1	NUM
ejpam-5398	143	3	)	)	PUNCT
ejpam-5398	143	4	.	.	PUNCT
ejpam-5398	144	1	simply	simply	ADV
ejpam-5398	144	2	,	,	PUNCT
ejpam-5398	144	3	eq	eq	ADJ
ejpam-5398	144	4	.	.	PUNCT
ejpam-5398	145	1	(	(	PUNCT
ejpam-5398	145	2	1	1	X
ejpam-5398	145	3	)	)	PUNCT
ejpam-5398	145	4	will	will	AUX
ejpam-5398	145	5	be	be	AUX
ejpam-5398	145	6	converted	convert	VERB
ejpam-5398	145	7	to	to	ADP
ejpam-5398	145	8	the	the	DET
ejpam-5398	145	9	subsequent	subsequent	ADJ
ejpam-5398	145	10	simplified	simplified	ADJ
ejpam-5398	145	11	form	form	NOUN
ejpam-5398	145	12	:	:	PUNCT
ejpam-5398	145	13	θ̈	θ̈	NOUN
ejpam-5398	145	14	+	+	CCONJ
ejpam-5398	145	15	a(θ2θ̈	a(θ2θ̈	PROPN
ejpam-5398	145	16	+	+	CCONJ
ejpam-5398	145	17	θ̇2	θ̇2	PROPN
ejpam-5398	145	18	)	)	PUNCT
ejpam-5398	146	1	+	+	SYM
ejpam-5398	146	2	b	b	X
ejpam-5398	146	3	cos	cos	PROPN
ejpam-5398	146	4	θ	θ	PROPN
ejpam-5398	146	5	=	=	SYM
ejpam-5398	146	6	0	0	NUM
ejpam-5398	146	7	,	,	PUNCT
ejpam-5398	146	8	(	(	PUNCT
ejpam-5398	146	9	2	2	X
ejpam-5398	146	10	)	)	PUNCT
ejpam-5398	146	11	where	where	SCONJ
ejpam-5398	146	12	a	a	PRON
ejpam-5398	146	13	,	,	PUNCT
ejpam-5398	146	14	and	and	CCONJ
ejpam-5398	146	15	b	b	NOUN
ejpam-5398	146	16	are	be	AUX
ejpam-5398	146	17	two	two	NUM
ejpam-5398	146	18	non	non	ADJ
ejpam-5398	146	19	-	-	ADJ
ejpam-5398	146	20	dimensional	dimensional	ADJ
ejpam-5398	146	21	physical	physical	ADJ
ejpam-5398	146	22	quantities	quantity	NOUN
ejpam-5398	146	23	.	.	PUNCT
ejpam-5398	147	1	as	as	SCONJ
ejpam-5398	147	2	was	be	AUX
ejpam-5398	147	3	widely	widely	ADV
ejpam-5398	147	4	known	know	VERB
ejpam-5398	147	5	,	,	PUNCT
ejpam-5398	147	6	td	td	NOUN
ejpam-5398	147	7	controllers	controller	NOUN
ejpam-5398	147	8	were	be	AUX
ejpam-5398	147	9	proposed	propose	VERB
ejpam-5398	147	10	to	to	PART
ejpam-5398	147	11	control	control	VERB
ejpam-5398	147	12	the	the	DET
ejpam-5398	147	13	nonlinear	nonlinear	ADJ
ejpam-5398	147	14	disturbances	disturbance	NOUN
ejpam-5398	147	15	.	.	PUNCT
ejpam-5398	148	1	as	as	SCONJ
ejpam-5398	148	2	was	be	AUX
ejpam-5398	148	3	previously	previously	ADV
ejpam-5398	148	4	shown	show	VERB
ejpam-5398	148	5	,	,	PUNCT
ejpam-5398	148	6	the	the	DET
ejpam-5398	148	7	loop	loop	NOUN
ejpam-5398	148	8	delay	delay	NOUN
ejpam-5398	148	9	can	can	AUX
ejpam-5398	148	10	significantly	significantly	ADV
ejpam-5398	148	11	affect	affect	VERB
ejpam-5398	148	12	the	the	DET
ejpam-5398	148	13	stability	stability	NOUN
ejpam-5398	148	14	of	of	ADP
ejpam-5398	148	15	the	the	DET
ejpam-5398	148	16	system	system	NOUN
ejpam-5398	148	17	’	'	PUNCT
ejpam-5398	148	18	or	or	CCONJ
ejpam-5398	148	19	instability	instability	NOUN
ejpam-5398	148	20	.	.	PUNCT
ejpam-5398	149	1	however	however	ADV
ejpam-5398	149	2	,	,	PUNCT
ejpam-5398	149	3	when	when	SCONJ
ejpam-5398	149	4	the	the	DET
ejpam-5398	149	5	ideal	ideal	ADJ
ejpam-5398	149	6	td	td	NOUN
ejpam-5398	149	7	was	be	AUX
ejpam-5398	149	8	considered	consider	VERB
ejpam-5398	149	9	,	,	PUNCT
ejpam-5398	149	10	the	the	DET
ejpam-5398	149	11	subsequent	subsequent	ADJ
ejpam-5398	149	12	analytical	analytical	ADJ
ejpam-5398	149	13	and	and	CCONJ
ejpam-5398	149	14	numerical	numerical	ADJ
ejpam-5398	149	15	evaluations	evaluation	NOUN
ejpam-5398	149	16	demonstrated	demonstrate	VERB
ejpam-5398	149	17	that	that	SCONJ
ejpam-5398	149	18	the	the	DET
ejpam-5398	149	19	nonlinear	nonlinear	ADJ
ejpam-5398	149	20	position	position	NOUN
ejpam-5398	149	21	and	and	CCONJ
ejpam-5398	149	22	nonlinear	nonlinear	ADJ
ejpam-5398	149	23	velocity	velocity	NOUN
ejpam-5398	149	24	are	be	AUX
ejpam-5398	149	25	the	the	DET
ejpam-5398	149	26	best	good	ADJ
ejpam-5398	149	27	at	at	ADP
ejpam-5398	149	28	damping	damp	VERB
ejpam-5398	149	29	the	the	DET
ejpam-5398	149	30	vibration	vibration	NOUN
ejpam-5398	149	31	.	.	PUNCT
ejpam-5398	150	1	a	a	DET
ejpam-5398	150	2	simple	simple	ADJ
ejpam-5398	150	3	procedure	procedure	NOUN
ejpam-5398	150	4	for	for	ADP
ejpam-5398	150	5	determining	determine	VERB
ejpam-5398	150	6	the	the	DET
ejpam-5398	150	7	ideal	ideal	ADJ
ejpam-5398	150	8	loop	loop	NOUN
ejpam-5398	150	9	delay	delay	NOUN
ejpam-5398	150	10	values	value	NOUN
ejpam-5398	150	11	in	in	ADP
ejpam-5398	150	12	a	a	DET
ejpam-5398	150	13	way	way	NOUN
ejpam-5398	150	14	that	that	PRON
ejpam-5398	150	15	enhances	enhance	VERB
ejpam-5398	150	16	the	the	DET
ejpam-5398	150	17	system	system	NOUN
ejpam-5398	150	18	profile	profile	NOUN
ejpam-5398	150	19	was	be	AUX
ejpam-5398	150	20	suggested	suggest	VERB
ejpam-5398	150	21	[	[	X
ejpam-5398	150	22	38	38	NUM
ejpam-5398	150	23	]	]	PUNCT
ejpam-5398	150	24	.	.	PUNCT
ejpam-5398	151	1	moreover	moreover	ADV
ejpam-5398	151	2	,	,	PUNCT
ejpam-5398	151	3	the	the	DET
ejpam-5398	151	4	effectiveness	effectiveness	NOUN
ejpam-5398	151	5	of	of	ADP
ejpam-5398	151	6	six	six	NUM
ejpam-5398	151	7	iterations	iteration	NOUN
ejpam-5398	151	8	of	of	ADP
ejpam-5398	151	9	linear	linear	ADJ
ejpam-5398	151	10	and	and	CCONJ
ejpam-5398	151	11	nonlinear	nonlinear	ADJ
ejpam-5398	151	12	feedback	feedback	NOUN
ejpam-5398	151	13	controllers	controller	NOUN
ejpam-5398	151	14	for	for	ADP
ejpam-5398	151	15	position	position	NOUN
ejpam-5398	151	16	,	,	PUNCT
ejpam-5398	151	17	acceleration	acceleration	NOUN
ejpam-5398	151	18	,	,	PUNCT
ejpam-5398	151	19	and	and	CCONJ
ejpam-5398	151	20	velocity	velocity	NOUN
ejpam-5398	151	21	was	be	AUX
ejpam-5398	151	22	studied	study	VERB
ejpam-5398	151	23	[	[	PUNCT
ejpam-5398	151	24	38	38	NUM
ejpam-5398	151	25	]	]	PUNCT
ejpam-5398	151	26	.	.	PUNCT
ejpam-5398	152	1	it	it	PRON
ejpam-5398	152	2	was	be	AUX
ejpam-5398	152	3	discovered	discover	VERB
ejpam-5398	152	4	that	that	SCONJ
ejpam-5398	152	5	the	the	DET
ejpam-5398	152	6	best	good	ADJ
ejpam-5398	152	7	method	method	NOUN
ejpam-5398	152	8	for	for	ADP
ejpam-5398	152	9	reducing	reduce	VERB
ejpam-5398	152	10	vibration	vibration	NOUN
ejpam-5398	152	11	and	and	CCONJ
ejpam-5398	152	12	suppressing	suppress	VERB
ejpam-5398	152	13	bifurcations	bifurcation	NOUN
ejpam-5398	152	14	was	be	AUX
ejpam-5398	152	15	the	the	DET
ejpam-5398	152	16	td	td	NOUN
ejpam-5398	152	17	cubic	cubic	ADJ
ejpam-5398	152	18	acceleration	acceleration	NOUN
ejpam-5398	152	19	control	control	NOUN
ejpam-5398	152	20	.	.	PUNCT
ejpam-5398	153	1	in	in	ADP
ejpam-5398	153	2	view	view	NOUN
ejpam-5398	153	3	of	of	ADP
ejpam-5398	153	4	the	the	DET
ejpam-5398	153	5	previous	previous	ADJ
ejpam-5398	153	6	achievement	achievement	NOUN
ejpam-5398	153	7	,	,	PUNCT
ejpam-5398	153	8	we	we	PRON
ejpam-5398	153	9	consequently	consequently	ADV
ejpam-5398	153	10	incorporate	incorporate	VERB
ejpam-5398	153	11	the	the	DET
ejpam-5398	153	12	square	square	ADJ
ejpam-5398	153	13	td	td	NOUN
ejpam-5398	153	14	in	in	ADP
ejpam-5398	153	15	location	location	NOUN
ejpam-5398	153	16	and	and	CCONJ
ejpam-5398	153	17	velocity	velocity	NOUN
ejpam-5398	153	18	into	into	ADP
ejpam-5398	153	19	the	the	DET
ejpam-5398	153	20	existing	exist	VERB
ejpam-5398	153	21	model	model	NOUN
ejpam-5398	153	22	.	.	PUNCT
ejpam-5398	154	1	accordingly	accordingly	ADV
ejpam-5398	154	2	,	,	PUNCT
ejpam-5398	154	3	the	the	DET
ejpam-5398	154	4	basic	basic	ADJ
ejpam-5398	154	5	equation	equation	NOUN
ejpam-5398	154	6	of	of	ADP
ejpam-5398	154	7	motion	motion	NOUN
ejpam-5398	154	8	that	that	PRON
ejpam-5398	154	9	controls	control	VERB
ejpam-5398	154	10	all	all	DET
ejpam-5398	154	11	future	future	ADJ
ejpam-5398	154	12	motion	motion	NOUN
ejpam-5398	154	13	is	be	AUX
ejpam-5398	154	14	as	as	SCONJ
ejpam-5398	154	15	follows	follow	VERB
ejpam-5398	154	16	:	:	PUNCT
ejpam-5398	154	17	θ̈	θ̈	PROPN
ejpam-5398	155	1	+	+	CCONJ
ejpam-5398	155	2	a	a	DET
ejpam-5398	155	3	[	[	PUNCT
ejpam-5398	155	4	θ2θ̈(t−	θ2θ̈(t−	PROPN
ejpam-5398	155	5	τ	τ	PROPN
ejpam-5398	155	6	)	)	PUNCT
ejpam-5398	155	7	+	+	CCONJ
ejpam-5398	155	8	θθ̇2(t−	θθ̇2(t−	ADJ
ejpam-5398	155	9	τ	τ	X
ejpam-5398	155	10	)	)	PUNCT
ejpam-5398	155	11	]	]	PUNCT
ejpam-5398	156	1	+	+	CCONJ
ejpam-5398	156	2	bθ	bθ	PROPN
ejpam-5398	156	3	cos	co	NOUN
ejpam-5398	156	4	θ	θ	PROPN
ejpam-5398	156	5	=	=	SYM
ejpam-5398	156	6	0	0	PROPN
ejpam-5398	156	7	.	.	PUNCT
ejpam-5398	157	1	(	(	PUNCT
ejpam-5398	157	2	3	3	X
ejpam-5398	157	3	)	)	PUNCT
ejpam-5398	157	4	a.	a.	NOUN
ejpam-5398	157	5	a.	a.	NOUN
ejpam-5398	157	6	galal	galal	PROPN
ejpam-5398	157	7	et	et	PROPN
ejpam-5398	157	8	al	al	PROPN
ejpam-5398	157	9	.	.	PUNCT
ejpam-5398	157	10	/	/	SYM
ejpam-5398	157	11	eur	eur	PROPN
ejpam-5398	157	12	.	.	PUNCT
ejpam-5398	158	1	j.	j.	PROPN
ejpam-5398	158	2	pure	pure	PROPN
ejpam-5398	158	3	appl	appl	PROPN
ejpam-5398	158	4	.	.	PROPN
ejpam-5398	158	5	math	math	PROPN
ejpam-5398	158	6	,	,	PUNCT
ejpam-5398	158	7	17	17	NUM
ejpam-5398	158	8	(	(	PUNCT
ejpam-5398	158	9	4	4	NUM
ejpam-5398	158	10	)	)	PUNCT
ejpam-5398	158	11	(	(	PUNCT
ejpam-5398	158	12	2024	2024	NUM
ejpam-5398	158	13	)	)	PUNCT
ejpam-5398	158	14	,	,	PUNCT
ejpam-5398	158	15	2878	2878	NUM
ejpam-5398	158	16	-	-	SYM
ejpam-5398	158	17	2897	2897	NUM
ejpam-5398	158	18	2884	2884	NUM
ejpam-5398	158	19	one	one	NUM
ejpam-5398	158	20	could	could	AUX
ejpam-5398	158	21	ideally	ideally	ADV
ejpam-5398	158	22	imagine	imagine	VERB
ejpam-5398	158	23	the	the	DET
ejpam-5398	158	24	initial	initial	ADJ
ejpam-5398	158	25	conditions	condition	NOUN
ejpam-5398	158	26	(	(	PUNCT
ejpam-5398	158	27	ics	ics	NOUN
ejpam-5398	158	28	)	)	PUNCT
ejpam-5398	158	29	,	,	PUNCT
ejpam-5398	158	30	as	as	ADP
ejpam-5398	158	31	in	in	ADP
ejpam-5398	158	32	the	the	DET
ejpam-5398	158	33	next	next	ADJ
ejpam-5398	158	34	form	form	NOUN
ejpam-5398	158	35	:	:	PUNCT
ejpam-5398	158	36	θ(0	θ(0	PROPN
ejpam-5398	158	37	)	)	PUNCT
ejpam-5398	158	38	=	=	SYM
ejpam-5398	158	39	a	a	PRON
ejpam-5398	158	40	,	,	PUNCT
ejpam-5398	158	41	θ̇(0	θ̇(0	NOUN
ejpam-5398	158	42	)	)	PUNCT
ejpam-5398	158	43	=	=	SYM
ejpam-5398	158	44	0	0	X
ejpam-5398	158	45	.	.	PUNCT
ejpam-5398	159	1	(	(	PUNCT
ejpam-5398	159	2	4	4	X
ejpam-5398	159	3	)	)	PUNCT
ejpam-5398	159	4	at	at	ADP
ejpam-5398	159	5	this	this	DET
ejpam-5398	159	6	stage	stage	NOUN
ejpam-5398	159	7	,	,	PUNCT
ejpam-5398	159	8	returning	return	VERB
ejpam-5398	159	9	again	again	ADV
ejpam-5398	159	10	to	to	ADP
ejpam-5398	159	11	the	the	DET
ejpam-5398	159	12	fundamental	fundamental	ADJ
ejpam-5398	159	13	td	td	NOUN
ejpam-5398	159	14	as	as	SCONJ
ejpam-5398	159	15	given	give	VERB
ejpam-5398	159	16	in	in	ADP
ejpam-5398	159	17	eq	eq	ADP
ejpam-5398	159	18	.	.	PUNCT
ejpam-5398	160	1	(	(	PUNCT
ejpam-5398	160	2	3	3	NUM
ejpam-5398	160	3	)	)	PUNCT
ejpam-5398	160	4	,	,	PUNCT
ejpam-5398	160	5	the	the	DET
ejpam-5398	160	6	npa	npa	NOUN
ejpam-5398	160	7	enables	enable	VERB
ejpam-5398	160	8	us	we	PRON
ejpam-5398	160	9	to	to	PART
ejpam-5398	160	10	transform	transform	VERB
ejpam-5398	160	11	the	the	DET
ejpam-5398	160	12	nonlinear	nonlinear	ADJ
ejpam-5398	160	13	ode	ode	NOUN
ejpam-5398	160	14	as	as	SCONJ
ejpam-5398	160	15	shown	show	VERB
ejpam-5398	160	16	in	in	ADP
ejpam-5398	160	17	eq	eq	ADP
ejpam-5398	160	18	.	.	PUNCT
ejpam-5398	161	1	(	(	PUNCT
ejpam-5398	161	2	3	3	X
ejpam-5398	161	3	)	)	PUNCT
ejpam-5398	161	4	into	into	ADP
ejpam-5398	161	5	an	an	DET
ejpam-5398	161	6	equivalent	equivalent	ADJ
ejpam-5398	161	7	linear	linear	ADJ
ejpam-5398	161	8	one	one	NUM
ejpam-5398	161	9	as	as	ADP
ejpam-5398	161	10	ü	ü	PRON
ejpam-5398	161	11	+	+	CCONJ
ejpam-5398	161	12	ω2u	ω2u	NOUN
ejpam-5398	161	13	=	=	SYM
ejpam-5398	161	14	0	0	PUNCT
ejpam-5398	162	1	under	under	ADP
ejpam-5398	162	2	the	the	DET
ejpam-5398	162	3	similar	similar	ADJ
ejpam-5398	162	4	ics	ic	NOUN
ejpam-5398	162	5	that	that	PRON
ejpam-5398	162	6	are	be	AUX
ejpam-5398	162	7	given	give	VERB
ejpam-5398	162	8	in	in	ADP
ejpam-5398	162	9	eq	eq	ADP
ejpam-5398	162	10	.	.	PUNCT
ejpam-5398	163	1	(	(	PUNCT
ejpam-5398	163	2	4	4	NUM
ejpam-5398	163	3	)	)	PUNCT
ejpam-5398	163	4	,	,	PUNCT
ejpam-5398	163	5	where	where	SCONJ
ejpam-5398	163	6	ω2	ω2	ADJ
ejpam-5398	163	7	is	be	AUX
ejpam-5398	163	8	known	know	VERB
ejpam-5398	163	9	as	as	ADP
ejpam-5398	163	10	the	the	DET
ejpam-5398	163	11	total	total	ADJ
ejpam-5398	163	12	frequency	frequency	NOUN
ejpam-5398	163	13	that	that	PRON
ejpam-5398	163	14	depends	depend	VERB
ejpam-5398	163	15	on	on	ADP
ejpam-5398	163	16	all	all	DET
ejpam-5398	163	17	parameters	parameter	NOUN
ejpam-5398	163	18	of	of	ADP
ejpam-5398	163	19	the	the	DET
ejpam-5398	163	20	original	original	ADJ
ejpam-5398	163	21	system	system	NOUN
ejpam-5398	163	22	.	.	PUNCT
ejpam-5398	164	1	u	u	NOUN
ejpam-5398	164	2	=	=	PUNCT
ejpam-5398	164	3	a	a	DET
ejpam-5398	164	4	cos(ωt	cos(ωt	NOUN
ejpam-5398	164	5	)	)	PUNCT
ejpam-5398	164	6	,	,	PUNCT
ejpam-5398	164	7	u̇	u̇	PROPN
ejpam-5398	164	8	=	=	PUNCT
ejpam-5398	164	9	−aωcos(ωt	−aωcos(ωt	PROPN
ejpam-5398	164	10	)	)	PUNCT
ejpam-5398	164	11	,	,	PUNCT
ejpam-5398	164	12	and	and	CCONJ
ejpam-5398	164	13	ü	ü	X
ejpam-5398	164	14	=	=	SYM
ejpam-5398	164	15	−ω2u	−ω2u	NUM
ejpam-5398	164	16	,	,	PUNCT
ejpam-5398	164	17	(	(	PUNCT
ejpam-5398	164	18	5	5	X
ejpam-5398	164	19	)	)	PUNCT
ejpam-5398	164	20	where	where	SCONJ
ejpam-5398	164	21	a	a	PRON
ejpam-5398	164	22	is	be	AUX
ejpam-5398	164	23	the	the	DET
ejpam-5398	164	24	initial	initial	ADJ
ejpam-5398	164	25	oscillation	oscillation	NOUN
ejpam-5398	164	26	amplitude	amplitude	NOUN
ejpam-5398	164	27	.	.	PUNCT
ejpam-5398	165	1	appropriately	appropriately	ADV
ejpam-5398	165	2	,	,	PUNCT
ejpam-5398	165	3	the	the	DET
ejpam-5398	165	4	shift	shift	NOUN
ejpam-5398	165	5	of	of	ADP
ejpam-5398	165	6	the	the	DET
ejpam-5398	165	7	independent	independent	ADJ
ejpam-5398	165	8	time	time	NOUN
ejpam-5398	165	9	may	may	AUX
ejpam-5398	165	10	be	be	AUX
ejpam-5398	165	11	expressed	express	VERB
ejpam-5398	165	12	as	as	ADP
ejpam-5398	165	13	:	:	PUNCT
ejpam-5398	165	14	u(t−	u(t−	PROPN
ejpam-5398	165	15	τ	τ	PROPN
ejpam-5398	165	16	)	)	PUNCT
ejpam-5398	165	17	=	=	SYM
ejpam-5398	166	1	a	a	DET
ejpam-5398	166	2	cos(t−	cos(t−	INTJ
ejpam-5398	166	3	τ	τ	NOUN
ejpam-5398	166	4	)	)	PUNCT
ejpam-5398	166	5	=	=	SYM
ejpam-5398	166	6	a(cosωt	a(cosωt	NOUN
ejpam-5398	166	7	cosωτ	cosωτ	NOUN
ejpam-5398	166	8	+	+	CCONJ
ejpam-5398	166	9	sinωt	sinωt	NOUN
ejpam-5398	166	10	sinωτ	sinωτ	NOUN
ejpam-5398	166	11	)	)	PUNCT
ejpam-5398	167	1	=	=	SYM
ejpam-5398	167	2	u(t	u(t	NOUN
ejpam-5398	167	3	)	)	PUNCT
ejpam-5398	167	4	cosωt−	cosωt−	NOUN
ejpam-5398	167	5	1	1	NUM
ejpam-5398	167	6	ω	ω	NUM
ejpam-5398	167	7	u̇(t	u̇(t	NOUN
ejpam-5398	167	8	)	)	PUNCT
ejpam-5398	167	9	sinωτ	sinωτ	NOUN
ejpam-5398	167	10	.	.	PUNCT
ejpam-5398	168	1	(	(	PUNCT
ejpam-5398	168	2	6	6	X
ejpam-5398	168	3	)	)	PUNCT
ejpam-5398	168	4	it	it	PRON
ejpam-5398	168	5	follows	follow	VERB
ejpam-5398	168	6	that	that	SCONJ
ejpam-5398	168	7	ü(t−	ü(t−	PROPN
ejpam-5398	168	8	τ	τ	PROPN
ejpam-5398	168	9	)	)	PUNCT
ejpam-5398	168	10	=	=	SYM
ejpam-5398	168	11	u̇(t	u̇(t	NOUN
ejpam-5398	168	12	)	)	PUNCT
ejpam-5398	168	13	cosω(t	cosω(t	NOUN
ejpam-5398	168	14	)	)	PUNCT
ejpam-5398	168	15	+	+	NUM
ejpam-5398	168	16	ωu(t	ωu(t	NOUN
ejpam-5398	168	17	)	)	PUNCT
ejpam-5398	168	18	sinω(τ	sinω(τ	PROPN
ejpam-5398	168	19	)	)	PUNCT
ejpam-5398	168	20	.	.	PUNCT
ejpam-5398	169	1	(	(	PUNCT
ejpam-5398	169	2	7	7	NUM
ejpam-5398	169	3	)	)	PUNCT
ejpam-5398	169	4	eq	eq	NOUN
ejpam-5398	169	5	.	.	PUNCT
ejpam-5398	170	1	(	(	PUNCT
ejpam-5398	170	2	3	3	X
ejpam-5398	170	3	)	)	PUNCT
ejpam-5398	170	4	may	may	AUX
ejpam-5398	170	5	be	be	AUX
ejpam-5398	170	6	written	write	VERB
ejpam-5398	170	7	as	as	SCONJ
ejpam-5398	170	8	follows	follow	VERB
ejpam-5398	170	9	:	:	PUNCT
ejpam-5398	170	10	θ̈	θ̈	X
ejpam-5398	170	11	+	+	SYM
ejpam-5398	170	12	f(θ	f(θ	ADJ
ejpam-5398	170	13	,	,	PUNCT
ejpam-5398	170	14	θ̇	θ̇	ADJ
ejpam-5398	170	15	,	,	PUNCT
ejpam-5398	170	16	θ̈	θ̈	NOUN
ejpam-5398	170	17	)	)	PUNCT
ejpam-5398	170	18	+	+	X
ejpam-5398	170	19	f(θ	f(θ	ADJ
ejpam-5398	170	20	,	,	PUNCT
ejpam-5398	170	21	θ̇	θ̇	ADJ
ejpam-5398	170	22	,	,	PUNCT
ejpam-5398	170	23	θ̈	θ̈	NOUN
ejpam-5398	170	24	)	)	PUNCT
ejpam-5398	170	25	=	=	SYM
ejpam-5398	170	26	0	0	NUM
ejpam-5398	170	27	,	,	PUNCT
ejpam-5398	170	28	(	(	PUNCT
ejpam-5398	170	29	8)	8)	NUM
ejpam-5398	170	30	where	where	SCONJ
ejpam-5398	170	31	f(θ	f(θ	NOUN
ejpam-5398	170	32	,	,	PUNCT
ejpam-5398	170	33	θ̇	θ̇	X
ejpam-5398	170	34	,	,	PUNCT
ejpam-5398	170	35	θ̈	θ̈	NOUN
ejpam-5398	170	36	)	)	PUNCT
ejpam-5398	170	37	=	=	SYM
ejpam-5398	170	38	α(θ̈2	α(θ̈2	X
ejpam-5398	170	39	+	+	X
ejpam-5398	170	40	θ̇2	θ̇2	PROPN
ejpam-5398	170	41	)	)	PUNCT
ejpam-5398	170	42	cos2ωt+	cos2ωt+	PROPN
ejpam-5398	170	43	(	(	PUNCT
ejpam-5398	170	44	ω2θ̇2	ω2θ̇2	NUM
ejpam-5398	170	45	+	+	CCONJ
ejpam-5398	170	46	1	1	NUM
ejpam-5398	170	47	ω2	ω2	ADJ
ejpam-5398	170	48	θ̈2	θ̈2	NOUN
ejpam-5398	170	49	)	)	PUNCT
ejpam-5398	170	50	sin2ωt+	sin2ωt+	ADJ
ejpam-5398	170	51	bθ	bθ	PROPN
ejpam-5398	170	52	cos	cos	PROPN
ejpam-5398	170	53	θ	θ	PROPN
ejpam-5398	170	54	,	,	PUNCT
ejpam-5398	170	55	g(θ	g(θ	ADP
ejpam-5398	170	56	,	,	PUNCT
ejpam-5398	170	57	θ̇	θ̇	X
ejpam-5398	170	58	,	,	PUNCT
ejpam-5398	170	59	θ̈	θ̈	NOUN
ejpam-5398	170	60	)	)	PUNCT
ejpam-5398	171	1	=	=	NOUN
ejpam-5398	171	2	αω	αω	X
ejpam-5398	171	3	(	(	PUNCT
ejpam-5398	171	4	θ̇θ̈	θ̇θ̈	NUM
ejpam-5398	171	5	−	−	PROPN
ejpam-5398	171	6	1	1	NUM
ejpam-5398	171	7	ω2	ω2	NOUN
ejpam-5398	171	8	θ̇3	θ̇3	PROPN
ejpam-5398	171	9	)	)	PUNCT
ejpam-5398	171	10	sin	sin	NOUN
ejpam-5398	171	11	2ωt	2ωt	NOUN
ejpam-5398	171	12	.	.	PUNCT
ejpam-5398	172	1	(	(	PUNCT
ejpam-5398	172	2	9	9	X
ejpam-5398	172	3	)	)	PUNCT
ejpam-5398	172	4	an	an	DET
ejpam-5398	172	5	equivalent	equivalent	ADJ
ejpam-5398	172	6	frequency	frequency	NOUN
ejpam-5398	172	7	ω2	ω2	ADJ
ejpam-5398	172	8	eqv	eqv	NOUN
ejpam-5398	172	9	can	can	AUX
ejpam-5398	172	10	by	by	SCONJ
ejpam-5398	172	11	evaluated	evaluate	VERB
ejpam-5398	172	12	as	as	SCONJ
ejpam-5398	172	13	shown	show	VERB
ejpam-5398	172	14	previously	previously	ADV
ejpam-5398	172	15	by	by	ADP
ejpam-5398	172	16	moatimid	moatimid	PROPN
ejpam-5398	172	17	et	et	PROPN
ejpam-5398	172	18	al	al	PROPN
ejpam-5398	172	19	.	.	PUNCT
ejpam-5398	173	1	[	[	X
ejpam-5398	173	2	8	8	NUM
ejpam-5398	173	3	,	,	PUNCT
ejpam-5398	173	4	18	18	NUM
ejpam-5398	173	5	,	,	PUNCT
ejpam-5398	173	6	20–23	20–23	NOUN
ejpam-5398	173	7	,	,	PUNCT
ejpam-5398	173	8	25–34	25–34	NUM
ejpam-5398	173	9	]	]	PUNCT
ejpam-5398	173	10	in	in	ADP
ejpam-5398	173	11	the	the	DET
ejpam-5398	173	12	following	following	ADJ
ejpam-5398	173	13	manner	manner	NOUN
ejpam-5398	173	14	:	:	PUNCT
ejpam-5398	173	15	ω2	ω2	ADJ
ejpam-5398	173	16	eqv	eqv	NOUN
ejpam-5398	173	17	=	=	SYM
ejpam-5398	173	18	∫	∫	PROPN
ejpam-5398	173	19	2π	2π	NOUN
ejpam-5398	173	20	/	/	SYM
ejpam-5398	173	21	ω	ω	NUM
ejpam-5398	173	22	0	0	NUM
ejpam-5398	173	23	uf(u	uf(u	PROPN
ejpam-5398	173	24	,	,	PUNCT
ejpam-5398	173	25	u̇	u̇	PROPN
ejpam-5398	173	26	,	,	PUNCT
ejpam-5398	173	27	ü)dt∫	ü)dt∫	NOUN
ejpam-5398	173	28	2π	2π	NOUN
ejpam-5398	173	29	/	/	SYM
ejpam-5398	173	30	ω	ω	NOUN
ejpam-5398	173	31	0	0	PUNCT
ejpam-5398	173	32	u2dt	u2dt	PUNCT
ejpam-5398	173	33	=	=	SYM
ejpam-5398	173	34	2b	2b	NOUN
ejpam-5398	173	35	a	a	DET
ejpam-5398	173	36	(	(	PUNCT
ejpam-5398	173	37	j1(a)−aj2(a))−	j1(a)−aj2(a))−	NUM
ejpam-5398	173	38	1	1	NUM
ejpam-5398	173	39	2	2	NUM
ejpam-5398	173	40	aa2ω2	aa2ω2	PROPN
ejpam-5398	173	41	cos	cos	ADP
ejpam-5398	173	42	2ωt	2ωt	NOUN
ejpam-5398	173	43	,	,	PUNCT
ejpam-5398	173	44	(	(	PUNCT
ejpam-5398	173	45	10	10	NUM
ejpam-5398	173	46	)	)	PUNCT
ejpam-5398	173	47	where	where	SCONJ
ejpam-5398	173	48	j1(a	j1(a	NOUN
ejpam-5398	173	49	)	)	PUNCT
ejpam-5398	173	50	,	,	PUNCT
ejpam-5398	173	51	and	and	CCONJ
ejpam-5398	173	52	j2(a)are	j2(a)are	PRON
ejpam-5398	173	53	the	the	DET
ejpam-5398	173	54	first	first	ADJ
ejpam-5398	173	55	kind	kind	NOUN
ejpam-5398	173	56	of	of	ADP
ejpam-5398	173	57	bessel	bessel	ADJ
ejpam-5398	173	58	functions	function	NOUN
ejpam-5398	173	59	of	of	ADP
ejpam-5398	173	60	the	the	DET
ejpam-5398	173	61	argument	argument	NOUN
ejpam-5398	173	62	a	a	PRON
ejpam-5398	173	63	of	of	ADP
ejpam-5398	173	64	order	order	NOUN
ejpam-5398	173	65	one	one	NUM
ejpam-5398	173	66	and	and	CCONJ
ejpam-5398	173	67	two	two	NUM
ejpam-5398	173	68	,	,	PUNCT
ejpam-5398	173	69	respectively	respectively	ADV
ejpam-5398	173	70	.	.	PUNCT
ejpam-5398	174	1	additionally	additionally	ADV
ejpam-5398	174	2	,	,	PUNCT
ejpam-5398	174	3	following	follow	VERB
ejpam-5398	174	4	moatimid	moatimid	PROPN
ejpam-5398	174	5	et	et	PROPN
ejpam-5398	174	6	al	al	PROPN
ejpam-5398	174	7	.	.	PUNCT
ejpam-5398	175	1	[	[	X
ejpam-5398	175	2	8	8	NUM
ejpam-5398	175	3	,	,	PUNCT
ejpam-5398	175	4	23	23	NUM
ejpam-5398	175	5	,	,	PUNCT
ejpam-5398	175	6	27	27	NUM
ejpam-5398	175	7	,	,	PUNCT
ejpam-5398	175	8	28	28	NUM
ejpam-5398	175	9	]	]	PUNCT
ejpam-5398	175	10	,	,	PUNCT
ejpam-5398	175	11	the	the	DET
ejpam-5398	175	12	equivalent	equivalent	ADJ
ejpam-5398	175	13	damping	damp	VERB
ejpam-5398	175	14	term	term	NOUN
ejpam-5398	175	15	can	can	AUX
ejpam-5398	175	16	be	be	AUX
ejpam-5398	175	17	evaluated	evaluate	VERB
ejpam-5398	175	18	as	as	SCONJ
ejpam-5398	175	19	follows	follow	VERB
ejpam-5398	175	20	:	:	PUNCT
ejpam-5398	175	21	σeqv	σeqv	NOUN
ejpam-5398	175	22	=	=	SYM
ejpam-5398	175	23	∫	∫	NOUN
ejpam-5398	175	24	2π	2π	NOUN
ejpam-5398	175	25	/	/	SYM
ejpam-5398	176	1	ω	ω	NUM
ejpam-5398	176	2	0	0	NUM
ejpam-5398	176	3	u̇g(u	u̇g(u	PROPN
ejpam-5398	176	4	,	,	PUNCT
ejpam-5398	176	5	u̇	u̇	PROPN
ejpam-5398	176	6	,	,	PUNCT
ejpam-5398	176	7	ü)dt∫	ü)dt∫	NOUN
ejpam-5398	176	8	2π	2π	NOUN
ejpam-5398	176	9	/	/	SYM
ejpam-5398	176	10	ω	ω	NOUN
ejpam-5398	176	11	0	0	X
ejpam-5398	176	12	u̇2dt	u̇2dt	NUM
ejpam-5398	176	13	=	=	SYM
ejpam-5398	176	14	−1	−1	NOUN
ejpam-5398	176	15	2	2	NUM
ejpam-5398	176	16	aa2ω2	aa2ω2	PROPN
ejpam-5398	176	17	sin	sin	NOUN
ejpam-5398	176	18	2ωt	2ωt	NOUN
ejpam-5398	176	19	.	.	PUNCT
ejpam-5398	177	1	(	(	PUNCT
ejpam-5398	177	2	11	11	NUM
ejpam-5398	177	3	)	)	PUNCT
ejpam-5398	177	4	a.	a.	NOUN
ejpam-5398	177	5	a.	a.	NOUN
ejpam-5398	177	6	galal	galal	PROPN
ejpam-5398	177	7	et	et	PROPN
ejpam-5398	177	8	al	al	PROPN
ejpam-5398	177	9	.	.	PUNCT
ejpam-5398	177	10	/	/	SYM
ejpam-5398	177	11	eur	eur	PROPN
ejpam-5398	177	12	.	.	PUNCT
ejpam-5398	178	1	j.	j.	PROPN
ejpam-5398	178	2	pure	pure	PROPN
ejpam-5398	178	3	appl	appl	PROPN
ejpam-5398	178	4	.	.	PROPN
ejpam-5398	178	5	math	math	PROPN
ejpam-5398	178	6	,	,	PUNCT
ejpam-5398	178	7	17	17	NUM
ejpam-5398	178	8	(	(	PUNCT
ejpam-5398	178	9	4	4	NUM
ejpam-5398	178	10	)	)	PUNCT
ejpam-5398	178	11	(	(	PUNCT
ejpam-5398	178	12	2024	2024	NUM
ejpam-5398	178	13	)	)	PUNCT
ejpam-5398	178	14	,	,	PUNCT
ejpam-5398	178	15	2878	2878	NUM
ejpam-5398	178	16	-	-	SYM
ejpam-5398	178	17	2897	2897	NUM
ejpam-5398	178	18	2885	2885	NUM
ejpam-5398	178	19	the	the	DET
ejpam-5398	178	20	equivalent	equivalent	ADJ
ejpam-5398	178	21	linear	linear	PROPN
ejpam-5398	178	22	ode	ode	NOUN
ejpam-5398	178	23	can	can	AUX
ejpam-5398	178	24	now	now	ADV
ejpam-5398	178	25	be	be	AUX
ejpam-5398	178	26	constructed	construct	VERB
ejpam-5398	178	27	as	as	SCONJ
ejpam-5398	178	28	follows	follow	VERB
ejpam-5398	178	29	:	:	PUNCT
ejpam-5398	178	30	ü+	ü+	NUM
ejpam-5398	179	1	σeqvu̇+	σeqvu̇+	PROPN
ejpam-5398	179	2	ω2	ω2	ADJ
ejpam-5398	179	3	eqvu	eqvu	NOUN
ejpam-5398	179	4	=	=	SYM
ejpam-5398	179	5	0	0	NUM
ejpam-5398	179	6	.	.	PUNCT
ejpam-5398	180	1	(	(	PUNCT
ejpam-5398	180	2	12	12	NUM
ejpam-5398	180	3	)	)	PUNCT
ejpam-5398	180	4	furthermore	furthermore	ADV
ejpam-5398	180	5	,	,	PUNCT
ejpam-5398	180	6	the	the	DET
ejpam-5398	180	7	standard	standard	ADJ
ejpam-5398	180	8	normal	normal	ADJ
ejpam-5398	180	9	form	form	NOUN
ejpam-5398	180	10	may	may	AUX
ejpam-5398	180	11	be	be	AUX
ejpam-5398	180	12	achieved	achieve	VERB
ejpam-5398	180	13	concurrently	concurrently	ADV
ejpam-5398	180	14	with	with	ADP
ejpam-5398	180	15	the	the	DET
ejpam-5398	180	16	transformation	transformation	NOUN
ejpam-5398	180	17	u(t	u(t	NOUN
ejpam-5398	180	18	)	)	PUNCT
ejpam-5398	180	19	=	=	SYM
ejpam-5398	180	20	h(t)(−σeqvt/2	h(t)(−σeqvt/2	NOUN
ejpam-5398	180	21	)	)	PUNCT
ejpam-5398	180	22	.	.	PUNCT
ejpam-5398	181	1	following	follow	VERB
ejpam-5398	181	2	the	the	DET
ejpam-5398	181	3	standard	standard	ADJ
ejpam-5398	181	4	calculus	calculus	NOUN
ejpam-5398	181	5	,	,	PUNCT
ejpam-5398	181	6	the	the	DET
ejpam-5398	181	7	unknown	unknown	ADJ
ejpam-5398	181	8	function	function	NOUN
ejpam-5398	181	9	satisfies	satisfy	VERB
ejpam-5398	181	10	the	the	DET
ejpam-5398	181	11	following	follow	VERB
ejpam-5398	181	12	damped	damped	ADJ
ejpam-5398	181	13	-	-	PUNCT
ejpam-5398	181	14	simple	simple	ADJ
ejpam-5398	181	15	harmonic	harmonic	ADJ
ejpam-5398	181	16	differential	differential	NOUN
ejpam-5398	181	17	equation	equation	NOUN
ejpam-5398	181	18	:	:	PUNCT
ejpam-5398	181	19	ḧ+ω2h	ḧ+ω2h	PROPN
ejpam-5398	181	20	=	=	SYM
ejpam-5398	181	21	0	0	NUM
ejpam-5398	181	22	,	,	PUNCT
ejpam-5398	181	23	(	(	PUNCT
ejpam-5398	181	24	13	13	NUM
ejpam-5398	181	25	)	)	PUNCT
ejpam-5398	181	26	where	where	SCONJ
ejpam-5398	181	27	ω2	ω2	NOUN
ejpam-5398	181	28	=	=	SYM
ejpam-5398	181	29	ω2	ω2	ADJ
ejpam-5398	181	30	eqv	eqv	NOUN
ejpam-5398	181	31	−	−	PROPN
ejpam-5398	181	32	σ2	σ2	PROPN
ejpam-5398	181	33	eqv/4	eqv/4	PROPN
ejpam-5398	181	34	.	.	PUNCT
ejpam-5398	182	1	in	in	ADP
ejpam-5398	182	2	other	other	ADJ
ejpam-5398	182	3	words	word	NOUN
ejpam-5398	182	4	,	,	PUNCT
ejpam-5398	182	5	the	the	DET
ejpam-5398	182	6	equivalence	equivalence	NOUN
ejpam-5398	182	7	frequency	frequency	NOUN
ejpam-5398	182	8	can	can	AUX
ejpam-5398	182	9	be	be	AUX
ejpam-5398	182	10	obtained	obtain	VERB
ejpam-5398	182	11	by	by	ADP
ejpam-5398	182	12	combining	combine	VERB
ejpam-5398	182	13	the	the	DET
ejpam-5398	182	14	results	result	NOUN
ejpam-5398	182	15	in	in	ADP
ejpam-5398	182	16	eqs	eqs	PROPN
ejpam-5398	182	17	.	.	PUNCT
ejpam-5398	183	1	(	(	PUNCT
ejpam-5398	183	2	10	10	NUM
ejpam-5398	183	3	)	)	PUNCT
ejpam-5398	183	4	and	and	CCONJ
ejpam-5398	183	5	(	(	PUNCT
ejpam-5398	183	6	11	11	NUM
ejpam-5398	183	7	)	)	PUNCT
ejpam-5398	183	8	with	with	ADP
ejpam-5398	183	9	the	the	DET
ejpam-5398	183	10	previous	previous	ADJ
ejpam-5398	183	11	relation	relation	NOUN
ejpam-5398	183	12	to	to	PART
ejpam-5398	183	13	produce	produce	VERB
ejpam-5398	183	14	:	:	PUNCT
ejpam-5398	183	15	ω2	ω2	PROPN
ejpam-5398	183	16	=	=	SYM
ejpam-5398	183	17	2b	2b	X
ejpam-5398	183	18	a	a	DET
ejpam-5398	183	19	(	(	PUNCT
ejpam-5398	183	20	j1(a)−aj2(a))−	j1(a)−aj2(a))−	NUM
ejpam-5398	183	21	1	1	NUM
ejpam-5398	183	22	2	2	NUM
ejpam-5398	183	23	aa2ω2	aa2ω2	PROPN
ejpam-5398	183	24	cos	cos	ADP
ejpam-5398	183	25	2ωτ	2ωτ	NOUN
ejpam-5398	183	26	−	−	NUM
ejpam-5398	183	27	1	1	NUM
ejpam-5398	183	28	4	4	NUM
ejpam-5398	183	29	(	(	PUNCT
ejpam-5398	183	30	1	1	NUM
ejpam-5398	183	31	2	2	NUM
ejpam-5398	183	32	aa2ω2	aa2ω2	PROPN
ejpam-5398	183	33	sin	sin	NOUN
ejpam-5398	183	34	2ωτ	2ωτ	NOUN
ejpam-5398	183	35	)	)	PUNCT
ejpam-5398	183	36	2	2	NUM
ejpam-5398	183	37	.	.	PUNCT
ejpam-5398	184	1	(	(	PUNCT
ejpam-5398	184	2	14	14	NUM
ejpam-5398	184	3	)	)	PUNCT
ejpam-5398	184	4	indeed	indeed	ADV
ejpam-5398	184	5	,	,	PUNCT
ejpam-5398	184	6	the	the	DET
ejpam-5398	184	7	governing	govern	VERB
ejpam-5398	184	8	equation	equation	NOUN
ejpam-5398	184	9	of	of	ADP
ejpam-5398	184	10	the	the	DET
ejpam-5398	184	11	total	total	ADJ
ejpam-5398	184	12	frequency	frequency	NOUN
ejpam-5398	184	13	as	as	SCONJ
ejpam-5398	184	14	given	give	VERB
ejpam-5398	184	15	in	in	ADP
ejpam-5398	184	16	the	the	DET
ejpam-5398	184	17	previous	previous	ADJ
ejpam-5398	184	18	eq	eq	NOUN
ejpam-5398	184	19	.	.	PUNCT
ejpam-5398	185	1	(	(	PUNCT
ejpam-5398	185	2	14	14	NUM
ejpam-5398	185	3	)	)	PUNCT
ejpam-5398	185	4	is	be	AUX
ejpam-5398	185	5	a	a	DET
ejpam-5398	185	6	transcendental	transcendental	ADJ
ejpam-5398	185	7	one	one	NUM
ejpam-5398	185	8	.	.	PUNCT
ejpam-5398	186	1	therefore	therefore	ADV
ejpam-5398	186	2	,	,	PUNCT
ejpam-5398	186	3	the	the	DET
ejpam-5398	186	4	numerical	numerical	ADJ
ejpam-5398	186	5	stability	stability	NOUN
ejpam-5398	186	6	discussions	discussion	NOUN
ejpam-5398	186	7	are	be	AUX
ejpam-5398	186	8	plotted	plot	VERB
ejpam-5398	186	9	via	via	ADP
ejpam-5398	186	10	the	the	DET
ejpam-5398	186	11	command	command	NOUN
ejpam-5398	186	12	(	(	PUNCT
ejpam-5398	186	13	plotregion	plotregion	NOUN
ejpam-5398	186	14	)	)	PUNCT
ejpam-5398	186	15	in	in	ADP
ejpam-5398	186	16	the	the	DET
ejpam-5398	186	17	ms	ms	NOUN
ejpam-5398	186	18	,	,	PUNCT
ejpam-5398	186	19	for	for	ADP
ejpam-5398	186	20	this	this	DET
ejpam-5398	186	21	purpose	purpose	NOUN
ejpam-5398	186	22	,	,	PUNCT
ejpam-5398	186	23	see	see	VERB
ejpam-5398	186	24	the	the	DET
ejpam-5398	186	25	subsequent	subsequent	ADJ
ejpam-5398	186	26	figs	fig	NOUN
ejpam-5398	186	27	.	.	PUNCT
ejpam-5398	187	1	(	(	PUNCT
ejpam-5398	187	2	6	6	NUM
ejpam-5398	187	3	)	)	PUNCT
ejpam-5398	187	4	,	,	PUNCT
ejpam-5398	187	5	(	(	PUNCT
ejpam-5398	187	6	7),(8	7),(8	NOUN
ejpam-5398	187	7	)	)	PUNCT
ejpam-5398	187	8	,	,	PUNCT
ejpam-5398	187	9	and	and	CCONJ
ejpam-5398	187	10	(	(	PUNCT
ejpam-5398	187	11	9	9	NUM
ejpam-5398	187	12	)	)	PUNCT
ejpam-5398	187	13	.	.	PUNCT
ejpam-5398	188	1	additionally	additionally	ADV
ejpam-5398	188	2	,	,	PUNCT
ejpam-5398	188	3	because	because	SCONJ
ejpam-5398	188	4	the	the	DET
ejpam-5398	188	5	time	time	NOUN
ejpam-5398	188	6	-	-	PUNCT
ejpam-5398	188	7	delay	delay	NOUN
ejpam-5398	188	8	is	be	AUX
ejpam-5398	188	9	infinitesimal	infinitesimal	ADJ
ejpam-5398	188	10	,	,	PUNCT
ejpam-5398	188	11	employing	employ	VERB
ejpam-5398	188	12	taylor	taylor	NOUN
ejpam-5398	188	13	expansion	expansion	NOUN
ejpam-5398	188	14	,	,	PUNCT
ejpam-5398	188	15	then	then	ADV
ejpam-5398	188	16	eq	eq	ADP
ejpam-5398	188	17	.	.	PUNCT
ejpam-5398	189	1	(	(	PUNCT
ejpam-5398	189	2	14	14	NUM
ejpam-5398	189	3	)	)	PUNCT
ejpam-5398	189	4	will	will	AUX
ejpam-5398	189	5	be	be	AUX
ejpam-5398	189	6	polynomial	polynomial	ADJ
ejpam-5398	189	7	in	in	ADP
ejpam-5398	189	8	ω2	ω2	NUM
ejpam-5398	189	9	.	.	PUNCT
ejpam-5398	190	1	in	in	ADP
ejpam-5398	190	2	this	this	DET
ejpam-5398	190	3	case	case	NOUN
ejpam-5398	190	4	the	the	DET
ejpam-5398	190	5	stability	stability	NOUN
ejpam-5398	190	6	standard	standard	NOUN
ejpam-5398	190	7	requires	require	VERB
ejpam-5398	190	8	:	:	PUNCT
ejpam-5398	190	9	ω2	ω2	ADV
ejpam-5398	190	10	>	>	X
ejpam-5398	190	11	0	0	NUM
ejpam-5398	190	12	,	,	PUNCT
ejpam-5398	190	13	and	and	CCONJ
ejpam-5398	190	14	σeqv	σeqv	NOUN
ejpam-5398	190	15	>	>	X
ejpam-5398	190	16	0	0	X
ejpam-5398	190	17	.	.	PUNCT
ejpam-5398	191	1	(	(	PUNCT
ejpam-5398	191	2	15	15	NUM
ejpam-5398	191	3	)	)	PUNCT
ejpam-5398	191	4	to	to	PART
ejpam-5398	191	5	obtain	obtain	VERB
ejpam-5398	191	6	the	the	DET
ejpam-5398	191	7	value	value	NOUN
ejpam-5398	191	8	of	of	ADP
ejpam-5398	191	9	the	the	DET
ejpam-5398	191	10	equivalent	equivalent	ADJ
ejpam-5398	191	11	frequency	frequency	NOUN
ejpam-5398	191	12	,	,	PUNCT
ejpam-5398	191	13	consider	consider	VERB
ejpam-5398	191	14	the	the	DET
ejpam-5398	191	15	following	follow	VERB
ejpam-5398	191	16	data	datum	NOUN
ejpam-5398	191	17	sample	sample	NOUN
ejpam-5398	191	18	and	and	CCONJ
ejpam-5398	191	19	the	the	DET
ejpam-5398	191	20	ms	ms	NOUN
ejpam-5398	191	21	:	:	PUNCT
ejpam-5398	191	22	a	a	PRON
ejpam-5398	191	23	=	=	SYM
ejpam-5398	191	24	5.0	5.0	NUM
ejpam-5398	191	25	,	,	PUNCT
ejpam-5398	191	26	b	b	NOUN
ejpam-5398	191	27	=	=	SYM
ejpam-5398	191	28	3.0	3.0	NUM
ejpam-5398	191	29	,	,	PUNCT
ejpam-5398	192	1	τ	τ	PROPN
ejpam-5398	192	2	=	=	NOUN
ejpam-5398	192	3	0.01	0.01	NUM
ejpam-5398	192	4	,	,	PUNCT
ejpam-5398	192	5	and	and	CCONJ
ejpam-5398	192	6	a	a	DET
ejpam-5398	192	7	=	=	SYM
ejpam-5398	192	8	0.1	0.1	NUM
ejpam-5398	192	9	utilizing	utilize	VERB
ejpam-5398	192	10	the	the	DET
ejpam-5398	192	11	assistance	assistance	NOUN
ejpam-5398	192	12	of	of	ADP
ejpam-5398	192	13	the	the	DET
ejpam-5398	192	14	mathematica	mathematica	PROPN
ejpam-5398	192	15	software	software	PROPN
ejpam-5398	192	16	through	through	ADP
ejpam-5398	192	17	the	the	DET
ejpam-5398	192	18	command	command	NOUN
ejpam-5398	192	19	of	of	ADP
ejpam-5398	192	20	findroot	findroot	NOUN
ejpam-5398	192	21	,	,	PUNCT
ejpam-5398	192	22	the	the	DET
ejpam-5398	192	23	value	value	NOUN
ejpam-5398	192	24	of	of	ADP
ejpam-5398	192	25	the	the	DET
ejpam-5398	192	26	total	total	ADJ
ejpam-5398	192	27	frequency	frequency	NOUN
ejpam-5398	192	28	becomes	become	VERB
ejpam-5398	192	29	1.39425	1.39425	NUM
ejpam-5398	192	30	.	.	PUNCT
ejpam-5398	193	1	once	once	ADV
ejpam-5398	193	2	more	more	ADJ
ejpam-5398	193	3	,	,	PUNCT
ejpam-5398	193	4	eq	eq	NOUN
ejpam-5398	193	5	.	.	PUNCT
ejpam-5398	194	1	(	(	PUNCT
ejpam-5398	194	2	14	14	NUM
ejpam-5398	194	3	)	)	PUNCT
ejpam-5398	194	4	gives	give	VERB
ejpam-5398	194	5	the	the	DET
ejpam-5398	194	6	characteristic	characteristic	ADJ
ejpam-5398	194	7	equation	equation	NOUN
ejpam-5398	194	8	in	in	ADP
ejpam-5398	194	9	the	the	DET
ejpam-5398	194	10	total	total	ADJ
ejpam-5398	194	11	frequency	frequency	NOUN
ejpam-5398	194	12	equation	equation	NOUN
ejpam-5398	194	13	.	.	PUNCT
ejpam-5398	195	1	actually	actually	ADV
ejpam-5398	195	2	,	,	PUNCT
ejpam-5398	195	3	this	this	DET
ejpam-5398	195	4	equation	equation	NOUN
ejpam-5398	195	5	is	be	AUX
ejpam-5398	195	6	a	a	DET
ejpam-5398	195	7	transcendental	transcendental	ADJ
ejpam-5398	195	8	one	one	NUM
ejpam-5398	195	9	;	;	PUNCT
ejpam-5398	195	10	it	it	PRON
ejpam-5398	195	11	has	have	VERB
ejpam-5398	195	12	no	no	DET
ejpam-5398	195	13	exact	exact	ADJ
ejpam-5398	195	14	solution	solution	NOUN
ejpam-5398	195	15	.	.	PUNCT
ejpam-5398	196	1	to	to	PART
ejpam-5398	196	2	analyze	analyze	VERB
ejpam-5398	196	3	the	the	DET
ejpam-5398	196	4	stability	stability	NOUN
ejpam-5398	196	5	configuration	configuration	NOUN
ejpam-5398	196	6	,	,	PUNCT
ejpam-5398	196	7	we	we	PRON
ejpam-5398	196	8	are	be	AUX
ejpam-5398	196	9	forced	force	VERB
ejpam-5398	196	10	to	to	PART
ejpam-5398	196	11	adopt	adopt	VERB
ejpam-5398	196	12	the	the	DET
ejpam-5398	196	13	ms	ms	NOUN
ejpam-5398	196	14	via	via	ADP
ejpam-5398	196	15	the	the	DET
ejpam-5398	196	16	command	command	NOUN
ejpam-5398	196	17	plotregion	plotregion	NOUN
ejpam-5398	196	18	.	.	PUNCT
ejpam-5398	197	1	3	3	X
ejpam-5398	197	2	.	.	X
ejpam-5398	197	3	graphical	graphical	ADJ
ejpam-5398	197	4	representations	representation	NOUN
ejpam-5398	197	5	and	and	CCONJ
ejpam-5398	197	6	discussions	discussion	NOUN
ejpam-5398	197	7	of	of	ADP
ejpam-5398	197	8	the	the	DET
ejpam-5398	197	9	results	result	NOUN
ejpam-5398	197	10	the	the	DET
ejpam-5398	197	11	purpose	purpose	NOUN
ejpam-5398	197	12	of	of	ADP
ejpam-5398	197	13	the	the	DET
ejpam-5398	197	14	current	current	ADJ
ejpam-5398	197	15	section	section	NOUN
ejpam-5398	197	16	is	be	AUX
ejpam-5398	197	17	to	to	PART
ejpam-5398	197	18	highlight	highlight	VERB
ejpam-5398	197	19	the	the	DET
ejpam-5398	197	20	graphical	graphical	ADJ
ejpam-5398	197	21	representations	representation	NOUN
ejpam-5398	197	22	and	and	CCONJ
ejpam-5398	197	23	discuss	discuss	VERB
ejpam-5398	197	24	the	the	DET
ejpam-5398	197	25	achieved	achieve	VERB
ejpam-5398	197	26	results	result	NOUN
ejpam-5398	197	27	in	in	ADP
ejpam-5398	197	28	light	light	NOUN
ejpam-5398	197	29	of	of	ADP
ejpam-5398	197	30	the	the	DET
ejpam-5398	197	31	following	follow	VERB
ejpam-5398	197	32	data	datum	NOUN
ejpam-5398	197	33	of	of	ADP
ejpam-5398	197	34	the	the	DET
ejpam-5398	197	35	parameters	parameter	NOUN
ejpam-5398	197	36	:	:	PUNCT
ejpam-5398	197	37	a	a	PRON
ejpam-5398	197	38	=	=	X
ejpam-5398	197	39	(	(	PUNCT
ejpam-5398	197	40	0.8	0.8	NUM
ejpam-5398	197	41	,	,	PUNCT
ejpam-5398	197	42	0.9	0.9	NUM
ejpam-5398	197	43	,	,	PUNCT
ejpam-5398	197	44	1	1	NUM
ejpam-5398	197	45	)	)	PUNCT
ejpam-5398	197	46	,	,	PUNCT
ejpam-5398	197	47	b	b	X
ejpam-5398	197	48	=	=	SYM
ejpam-5398	197	49	(	(	PUNCT
ejpam-5398	197	50	0.1	0.1	NUM
ejpam-5398	197	51	,	,	PUNCT
ejpam-5398	197	52	0.5	0.5	NUM
ejpam-5398	197	53	,	,	PUNCT
ejpam-5398	197	54	1	1	NUM
ejpam-5398	197	55	,	,	PUNCT
ejpam-5398	197	56	1.5	1.5	NUM
ejpam-5398	197	57	)	)	PUNCT
ejpam-5398	197	58	,	,	PUNCT
ejpam-5398	197	59	a	a	PRON
ejpam-5398	197	60	=	=	X
ejpam-5398	197	61	(	(	PUNCT
ejpam-5398	197	62	0.1	0.1	NUM
ejpam-5398	197	63	,	,	PUNCT
ejpam-5398	197	64	0.5	0.5	NUM
ejpam-5398	197	65	,	,	PUNCT
ejpam-5398	197	66	1	1	NUM
ejpam-5398	197	67	,	,	PUNCT
ejpam-5398	197	68	1.5	1.5	NUM
ejpam-5398	197	69	)	)	PUNCT
ejpam-5398	197	70	,	,	PUNCT
ejpam-5398	197	71	τ	τ	X
ejpam-5398	197	72	=	=	PUNCT
ejpam-5398	197	73	(	(	PUNCT
ejpam-5398	197	74	0.1	0.1	NUM
ejpam-5398	197	75	,	,	PUNCT
ejpam-5398	197	76	0.5	0.5	NUM
ejpam-5398	197	77	,	,	PUNCT
ejpam-5398	197	78	1	1	NUM
ejpam-5398	197	79	)	)	PUNCT
ejpam-5398	197	80	.	.	PUNCT
ejpam-5398	198	1	it	it	PRON
ejpam-5398	198	2	is	be	AUX
ejpam-5398	198	3	easy	easy	ADJ
ejpam-5398	198	4	to	to	PART
ejpam-5398	198	5	access	access	VERB
ejpam-5398	198	6	to	to	PART
ejpam-5398	198	7	match	match	VERB
ejpam-5398	198	8	the	the	DET
ejpam-5398	198	9	numerical	numerical	ADJ
ejpam-5398	198	10	solution	solution	NOUN
ejpam-5398	198	11	(	(	PUNCT
ejpam-5398	198	12	ns	ns	NUM
ejpam-5398	198	13	)	)	PUNCT
ejpam-5398	198	14	of	of	ADP
ejpam-5398	198	15	the	the	DET
ejpam-5398	198	16	previous	previous	ADJ
ejpam-5398	198	17	eq	eq	X
ejpam-5398	198	18	.	.	PUNCT
ejpam-5398	199	1	(	(	PUNCT
ejpam-5398	199	2	3	3	NUM
ejpam-5398	199	3	)	)	PUNCT
ejpam-5398	199	4	via	via	ADP
ejpam-5398	199	5	the	the	DET
ejpam-5398	199	6	knowledge	knowledge	NOUN
ejpam-5398	199	7	of	of	ADP
ejpam-5398	199	8	ndsolve	ndsolve	NOUN
ejpam-5398	199	9	of	of	ADP
ejpam-5398	199	10	the	the	DET
ejpam-5398	199	11	ms	ms	NOUN
ejpam-5398	199	12	with	with	ADP
ejpam-5398	199	13	the	the	DET
ejpam-5398	199	14	solution	solution	NOUN
ejpam-5398	199	15	of	of	ADP
ejpam-5398	199	16	the	the	DET
ejpam-5398	199	17	equivalent	equivalent	ADJ
ejpam-5398	199	18	linear	linear	PROPN
ejpam-5398	199	19	ode	ode	PROPN
ejpam-5398	199	20	.	.	PUNCT
ejpam-5398	200	1	therefore	therefore	ADV
ejpam-5398	200	2	,	,	PUNCT
ejpam-5398	200	3	fig.(2	fig.(2	NOUN
ejpam-5398	200	4	)	)	PUNCT
ejpam-5398	200	5	is	be	AUX
ejpam-5398	200	6	graphed	graph	VERB
ejpam-5398	200	7	for	for	ADP
ejpam-5398	200	8	a	a	DET
ejpam-5398	200	9	=	=	SYM
ejpam-5398	200	10	1	1	NUM
ejpam-5398	200	11	,	,	PUNCT
ejpam-5398	200	12	a	a	DET
ejpam-5398	200	13	=	=	NOUN
ejpam-5398	200	14	0.1	0.1	NUM
ejpam-5398	200	15	,	,	PUNCT
ejpam-5398	200	16	and	and	CCONJ
ejpam-5398	200	17	b	b	X
ejpam-5398	200	18	=	=	SYM
ejpam-5398	200	19	1	1	NUM
ejpam-5398	200	20	when	when	SCONJ
ejpam-5398	200	21	the	the	DET
ejpam-5398	200	22	td	td	PROPN
ejpam-5398	200	23	parameter	parameter	NOUN
ejpam-5398	200	24	τ	τ	PROPN
ejpam-5398	200	25	has	have	VERB
ejpam-5398	200	26	the	the	DET
ejpam-5398	200	27	value	value	NOUN
ejpam-5398	200	28	0.1	0.1	NUM
ejpam-5398	200	29	.	.	PUNCT
ejpam-5398	201	1	as	as	SCONJ
ejpam-5398	201	2	seen	see	VERB
ejpam-5398	201	3	from	from	ADP
ejpam-5398	201	4	this	this	DET
ejpam-5398	201	5	comparison	comparison	NOUN
ejpam-5398	201	6	,	,	PUNCT
ejpam-5398	201	7	there	there	PRON
ejpam-5398	201	8	is	be	VERB
ejpam-5398	201	9	an	an	DET
ejpam-5398	201	10	excellent	excellent	ADJ
ejpam-5398	201	11	consistency	consistency	NOUN
ejpam-5398	201	12	a.	a.	NOUN
ejpam-5398	201	13	a.	a.	PROPN
ejpam-5398	201	14	galal	galal	PROPN
ejpam-5398	201	15	et	et	PROPN
ejpam-5398	201	16	al	al	PROPN
ejpam-5398	201	17	.	.	PUNCT
ejpam-5398	201	18	/	/	SYM
ejpam-5398	201	19	eur	eur	PROPN
ejpam-5398	201	20	.	.	PUNCT
ejpam-5398	202	1	j.	j.	PROPN
ejpam-5398	202	2	pure	pure	PROPN
ejpam-5398	202	3	appl	appl	PROPN
ejpam-5398	202	4	.	.	PROPN
ejpam-5398	202	5	math	math	PROPN
ejpam-5398	202	6	,	,	PUNCT
ejpam-5398	202	7	17	17	NUM
ejpam-5398	202	8	(	(	PUNCT
ejpam-5398	202	9	4	4	NUM
ejpam-5398	202	10	)	)	PUNCT
ejpam-5398	202	11	(	(	PUNCT
ejpam-5398	202	12	2024	2024	NUM
ejpam-5398	202	13	)	)	PUNCT
ejpam-5398	202	14	,	,	PUNCT
ejpam-5398	202	15	2878	2878	NUM
ejpam-5398	202	16	-	-	SYM
ejpam-5398	202	17	2897	2897	NUM
ejpam-5398	202	18	2886	2886	NUM
ejpam-5398	202	19	figure	figure	NOUN
ejpam-5398	202	20	2	2	NUM
ejpam-5398	202	21	:	:	PUNCT
ejpam-5398	202	22	explores	explore	VERB
ejpam-5398	202	23	the	the	DET
ejpam-5398	202	24	comparison	comparison	NOUN
ejpam-5398	202	25	connecting	connect	VERB
ejpam-5398	202	26	the	the	DET
ejpam-5398	202	27	as	as	ADV
ejpam-5398	202	28	and	and	CCONJ
ejpam-5398	202	29	ns	ns	ADJ
ejpam-5398	202	30	.	.	PROPN
ejpam-5398	203	1	concerning	concern	VERB
ejpam-5398	203	2	the	the	DET
ejpam-5398	203	3	analytical	analytical	ADJ
ejpam-5398	203	4	solution	solution	NOUN
ejpam-5398	203	5	and	and	CCONJ
ejpam-5398	203	6	numerical	numerical	ADJ
ejpam-5398	203	7	one	one	NUM
ejpam-5398	203	8	,	,	PUNCT
ejpam-5398	203	9	which	which	PRON
ejpam-5398	203	10	demonstrates	demonstrate	VERB
ejpam-5398	203	11	good	good	ADJ
ejpam-5398	203	12	accuracy	accuracy	NOUN
ejpam-5398	203	13	of	of	ADP
ejpam-5398	203	14	the	the	DET
ejpam-5398	203	15	npa	npa	NOUN
ejpam-5398	203	16	.	.	PUNCT
ejpam-5398	204	1	additionally	additionally	ADV
ejpam-5398	204	2	,	,	PUNCT
ejpam-5398	204	3	up	up	ADP
ejpam-5398	204	4	to	to	ADP
ejpam-5398	204	5	the	the	DET
ejpam-5398	204	6	time	time	NOUN
ejpam-5398	204	7	of	of	ADP
ejpam-5398	204	8	50	50	NUM
ejpam-5398	204	9	units	unit	NOUN
ejpam-5398	204	10	,	,	PUNCT
ejpam-5398	204	11	the	the	DET
ejpam-5398	204	12	ms	ms	NOUN
ejpam-5398	204	13	showed	show	VERB
ejpam-5398	204	14	that	that	SCONJ
ejpam-5398	204	15	the	the	DET
ejpam-5398	204	16	absolute	absolute	ADJ
ejpam-5398	204	17	error	error	NOUN
ejpam-5398	204	18	between	between	ADP
ejpam-5398	204	19	the	the	DET
ejpam-5398	204	20	analytical	analytical	ADJ
ejpam-5398	204	21	and	and	CCONJ
ejpam-5398	204	22	numerical	numerical	ADJ
ejpam-5398	204	23	solutions	solution	NOUN
ejpam-5398	204	24	is	be	AUX
ejpam-5398	204	25	0.002025	0.002025	NUM
ejpam-5398	204	26	.	.	PUNCT
ejpam-5398	205	1	to	to	PART
ejpam-5398	205	2	validate	validate	VERB
ejpam-5398	205	3	the	the	DET
ejpam-5398	205	4	absolute	absolute	ADJ
ejpam-5398	205	5	error	error	NOUN
ejpam-5398	205	6	between	between	ADP
ejpam-5398	205	7	them	they	PRON
ejpam-5398	205	8	,	,	PUNCT
ejpam-5398	205	9	table	table	NOUN
ejpam-5398	205	10	(	(	PUNCT
ejpam-5398	205	11	3	3	NUM
ejpam-5398	205	12	)	)	PUNCT
ejpam-5398	205	13	is	be	AUX
ejpam-5398	205	14	presented	present	VERB
ejpam-5398	205	15	.	.	PUNCT
ejpam-5398	206	1	the	the	DET
ejpam-5398	206	2	inspection	inspection	NOUN
ejpam-5398	206	3	of	of	ADP
ejpam-5398	206	4	the	the	DET
ejpam-5398	206	5	drawn	draw	VERB
ejpam-5398	206	6	curves	curve	NOUN
ejpam-5398	206	7	of	of	ADP
ejpam-5398	206	8	this	this	DET
ejpam-5398	206	9	figure	figure	NOUN
ejpam-5398	206	10	explores	explore	VERB
ejpam-5398	206	11	their	their	PRON
ejpam-5398	206	12	periodic	periodic	ADJ
ejpam-5398	206	13	forms	form	NOUN
ejpam-5398	206	14	which	which	PRON
ejpam-5398	206	15	give	give	VERB
ejpam-5398	206	16	an	an	DET
ejpam-5398	206	17	impression	impression	NOUN
ejpam-5398	206	18	of	of	ADP
ejpam-5398	206	19	the	the	DET
ejpam-5398	206	20	stability	stability	NOUN
ejpam-5398	206	21	and	and	CCONJ
ejpam-5398	206	22	steady	steady	ADJ
ejpam-5398	206	23	behavior	behavior	NOUN
ejpam-5398	206	24	of	of	ADP
ejpam-5398	206	25	mutual	mutual	ADJ
ejpam-5398	206	26	solutions	solution	NOUN
ejpam-5398	206	27	.	.	PUNCT
ejpam-5398	207	1	time	time	NOUN
ejpam-5398	207	2	analytical	analytical	ADJ
ejpam-5398	207	3	solution	solution	NOUN
ejpam-5398	207	4	approximate	approximate	ADJ
ejpam-5398	207	5	solution	solution	NOUN
ejpam-5398	207	6	absolute	absolute	ADJ
ejpam-5398	207	7	error	error	NOUN
ejpam-5398	207	8	0	0	NUM
ejpam-5398	207	9	1	1	NUM
ejpam-5398	207	10	1	1	NUM
ejpam-5398	207	11	0.0000000000000000	0.0000000000000000	NUM
ejpam-5398	207	12	5	5	NUM
ejpam-5398	207	13	-0.6367368984628483	-0.6367368984628483	NOUN
ejpam-5398	207	14	-0.6840673392798011	-0.6840673392798011	X
ejpam-5398	207	15	0.04733044081695281	0.04733044081695281	NUM
ejpam-5398	207	16	10	10	NUM
ejpam-5398	207	17	-0.1891322442718248	-0.1891322442718248	NOUN
ejpam-5398	207	18	-0.165428295011344	-0.165428295011344	NOUN
ejpam-5398	207	19	0.02370394927069039	0.02370394927069039	NUM
ejpam-5398	208	1	15	15	NUM
ejpam-5398	208	2	0.8775918556967678	0.8775918556967678	NUM
ejpam-5398	208	3	0.8671456885746593	0.8671456885746593	NUM
ejpam-5398	208	4	0.01044616712210844	0.01044616712210844	NUM
ejpam-5398	208	5	20	20	NUM
ejpam-5398	208	6	-0.9284579883534055	-0.9284579883534055	NOUN
ejpam-5398	208	7	-0.9463244488562964	-0.9463244488562964	NOUN
ejpam-5398	209	1	0.017866460211890867	0.017866460211890867	NUM
ejpam-5398	209	2	25	25	NUM
ejpam-5398	209	3	0.30437506401763743	0.30437506401763743	NUM
ejpam-5398	209	4	0.37993757885446146	0.37993757885446146	NUM
ejpam-5398	209	5	0.0755625143862673	0.0755625143862673	NUM
ejpam-5398	209	6	30	30	NUM
ejpam-5398	209	7	0.540334930370593	0.540334930370593	NUM
ejpam-5398	209	8	0.521267116029197	0.521267116029197	NUM
ejpam-5398	209	9	0.01906781434157334	0.01906781434157334	NUM
ejpam-5398	209	10	35	35	NUM
ejpam-5398	209	11	-0.9928774394082572	-0.9928774394082572	NOUN
ejpam-5398	209	12	-0.9734314088762631	-0.9734314088762631	NOUN
ejpam-5398	210	1	0.01944603040994164	0.01944603040994164	NUM
ejpam-5398	210	2	40	40	NUM
ejpam-5398	211	1	0.7240684722745052	0.7240684722745052	NUM
ejpam-5398	211	2	0.758824169662992	0.758824169662992	NUM
ejpam-5398	211	3	0.0347556793179396	0.0347556793179396	NUM
ejpam-5398	212	1	45	45	NUM
ejpam-5398	212	2	0.0707952127866591	0.0707952127866591	NUM
ejpam-5398	212	3	0.0599615698265702	0.0599615698265702	NUM
ejpam-5398	212	4	0.01083361589400279	0.01083361589400279	NUM
ejpam-5398	212	5	50	50	NUM
ejpam-5398	212	6	-0.8142243207060901	-0.8142243207060901	NOUN
ejpam-5398	212	7	-0.8215978344057133	-0.8215978344057133	VERB
ejpam-5398	212	8	0.007373513699623246	0.007373513699623246	NUM
ejpam-5398	212	9	the	the	DET
ejpam-5398	212	10	solutions	solution	NOUN
ejpam-5398	212	11	of	of	ADP
ejpam-5398	212	12	eq.(3	eq.(3	NOUN
ejpam-5398	212	13	)	)	PUNCT
ejpam-5398	212	14	at	at	ADP
ejpam-5398	212	15	various	various	ADJ
ejpam-5398	212	16	values	value	NOUN
ejpam-5398	212	17	of	of	ADP
ejpam-5398	212	18	a	a	DET
ejpam-5398	212	19	,	,	PUNCT
ejpam-5398	212	20	a	a	PRON
ejpam-5398	212	21	,	,	PUNCT
ejpam-5398	212	22	and	and	CCONJ
ejpam-5398	212	23	b	b	NOUN
ejpam-5398	212	24	are	be	AUX
ejpam-5398	212	25	plotted	plot	VERB
ejpam-5398	212	26	,	,	PUNCT
ejpam-5398	212	27	respectively	respectively	ADV
ejpam-5398	212	28	,	,	PUNCT
ejpam-5398	212	29	in	in	ADP
ejpam-5398	212	30	figs	fig	NOUN
ejpam-5398	212	31	.	.	PUNCT
ejpam-5398	213	1	(	(	PUNCT
ejpam-5398	213	2	(	(	PUNCT
ejpam-5398	213	3	3	3	NUM
ejpam-5398	213	4	)	)	PUNCT
ejpam-5398	213	5	,	,	PUNCT
ejpam-5398	213	6	(	(	PUNCT
ejpam-5398	213	7	4	4	NUM
ejpam-5398	213	8	)	)	PUNCT
ejpam-5398	213	9	,	,	PUNCT
ejpam-5398	213	10	and	and	CCONJ
ejpam-5398	213	11	(	(	PUNCT
ejpam-5398	213	12	5	5	NUM
ejpam-5398	213	13	)	)	PUNCT
ejpam-5398	213	14	)	)	PUNCT
ejpam-5398	213	15	.	.	PUNCT
ejpam-5398	214	1	the	the	DET
ejpam-5398	214	2	curves	curve	NOUN
ejpam-5398	214	3	in	in	ADP
ejpam-5398	214	4	fig	fig	NOUN
ejpam-5398	214	5	.	.	PUNCT
ejpam-5398	215	1	(	(	PUNCT
ejpam-5398	215	2	3	3	X
ejpam-5398	215	3	)	)	PUNCT
ejpam-5398	215	4	are	be	AUX
ejpam-5398	215	5	calculated	calculate	VERB
ejpam-5398	215	6	when	when	SCONJ
ejpam-5398	215	7	a	a	DET
ejpam-5398	215	8	=	=	NOUN
ejpam-5398	215	9	0.8	0.8	NUM
ejpam-5398	215	10	,	,	PUNCT
ejpam-5398	215	11	0.9	0.9	NUM
ejpam-5398	215	12	,	,	PUNCT
ejpam-5398	215	13	and	and	CCONJ
ejpam-5398	215	14	1	1	NUM
ejpam-5398	215	15	and	and	CCONJ
ejpam-5398	215	16	with	with	ADP
ejpam-5398	215	17	the	the	DET
ejpam-5398	215	18	similar	similar	ADJ
ejpam-5398	215	19	amounts	amount	NOUN
ejpam-5398	215	20	of	of	ADP
ejpam-5398	215	21	other	other	ADJ
ejpam-5398	215	22	factors	factor	NOUN
ejpam-5398	215	23	as	as	SCONJ
ejpam-5398	215	24	shown	show	VERB
ejpam-5398	215	25	in	in	ADP
ejpam-5398	215	26	fig	fig	NOUN
ejpam-5398	215	27	.	.	PUNCT
ejpam-5398	216	1	(	(	PUNCT
ejpam-5398	216	2	2	2	NUM
ejpam-5398	216	3	)	)	PUNCT
ejpam-5398	216	4	,	,	PUNCT
ejpam-5398	216	5	while	while	SCONJ
ejpam-5398	216	6	curves	curve	NOUN
ejpam-5398	216	7	in	in	ADP
ejpam-5398	216	8	fig	fig	NOUN
ejpam-5398	216	9	.	.	PUNCT
ejpam-5398	217	1	(	(	PUNCT
ejpam-5398	217	2	4	4	X
ejpam-5398	217	3	)	)	PUNCT
ejpam-5398	217	4	are	be	AUX
ejpam-5398	217	5	drawn	draw	VERB
ejpam-5398	217	6	at	at	ADP
ejpam-5398	217	7	a	a	DET
ejpam-5398	217	8	=	=	SYM
ejpam-5398	217	9	(	(	PUNCT
ejpam-5398	217	10	0	0	NUM
ejpam-5398	217	11	,	,	PUNCT
ejpam-5398	217	12	1	1	NUM
ejpam-5398	217	13	,	,	PUNCT
ejpam-5398	217	14	0.5	0.5	NUM
ejpam-5398	217	15	,	,	PUNCT
ejpam-5398	217	16	1	1	NUM
ejpam-5398	217	17	)	)	PUNCT
ejpam-5398	217	18	,	,	PUNCT
ejpam-5398	217	19	a	a	PRON
ejpam-5398	217	20	=	=	SYM
ejpam-5398	217	21	1	1	NUM
ejpam-5398	217	22	,	,	PUNCT
ejpam-5398	217	23	b	b	NOUN
ejpam-5398	217	24	=	=	SYM
ejpam-5398	217	25	1	1	NUM
ejpam-5398	217	26	,	,	PUNCT
ejpam-5398	217	27	and	and	CCONJ
ejpam-5398	217	28	τ	τ	PROPN
ejpam-5398	217	29	=	=	NOUN
ejpam-5398	217	30	0.1	0.1	NUM
ejpam-5398	217	31	.	.	PUNCT
ejpam-5398	218	1	in	in	ADP
ejpam-5398	218	2	addition	addition	NOUN
ejpam-5398	218	3	,	,	PUNCT
ejpam-5398	218	4	the	the	DET
ejpam-5398	218	5	variation	variation	NOUN
ejpam-5398	218	6	of	of	ADP
ejpam-5398	218	7	a.	a.	PROPN
ejpam-5398	218	8	a.	a.	PROPN
ejpam-5398	218	9	galal	galal	PROPN
ejpam-5398	218	10	et	et	PROPN
ejpam-5398	218	11	al	al	PROPN
ejpam-5398	218	12	.	.	PUNCT
ejpam-5398	218	13	/	/	SYM
ejpam-5398	218	14	eur	eur	PROPN
ejpam-5398	218	15	.	.	PUNCT
ejpam-5398	219	1	j.	j.	PROPN
ejpam-5398	219	2	pure	pure	PROPN
ejpam-5398	219	3	appl	appl	PROPN
ejpam-5398	219	4	.	.	PROPN
ejpam-5398	219	5	math	math	PROPN
ejpam-5398	219	6	,	,	PUNCT
ejpam-5398	219	7	17	17	NUM
ejpam-5398	219	8	(	(	PUNCT
ejpam-5398	219	9	4	4	NUM
ejpam-5398	219	10	)	)	PUNCT
ejpam-5398	219	11	(	(	PUNCT
ejpam-5398	219	12	2024	2024	NUM
ejpam-5398	219	13	)	)	PUNCT
ejpam-5398	219	14	,	,	PUNCT
ejpam-5398	219	15	2878	2878	NUM
ejpam-5398	219	16	-	-	SYM
ejpam-5398	219	17	2897	2897	NUM
ejpam-5398	219	18	2887	2887	NUM
ejpam-5398	219	19	the	the	DET
ejpam-5398	219	20	value	value	NOUN
ejpam-5398	219	21	of	of	ADP
ejpam-5398	219	22	b	b	NOUN
ejpam-5398	219	23	is	be	AUX
ejpam-5398	219	24	examined	examine	VERB
ejpam-5398	219	25	in	in	ADP
ejpam-5398	219	26	fig	fig	NOUN
ejpam-5398	219	27	.	.	PUNCT
ejpam-5398	220	1	(	(	PUNCT
ejpam-5398	220	2	5	5	NUM
ejpam-5398	220	3	)	)	PUNCT
ejpam-5398	220	4	at	at	ADP
ejpam-5398	220	5	a	a	DET
ejpam-5398	220	6	=	=	NOUN
ejpam-5398	220	7	a	a	PRON
ejpam-5398	220	8	=	=	SYM
ejpam-5398	220	9	b	b	NOUN
ejpam-5398	220	10	=	=	SYM
ejpam-5398	220	11	1	1	NUM
ejpam-5398	220	12	,	,	PUNCT
ejpam-5398	220	13	and	and	CCONJ
ejpam-5398	220	14	τ	τ	PROPN
ejpam-5398	220	15	=	=	NOUN
ejpam-5398	220	16	0.1	0.1	NUM
ejpam-5398	220	17	.	.	PUNCT
ejpam-5398	221	1	the	the	DET
ejpam-5398	221	2	parts	part	NOUN
ejpam-5398	221	3	(	(	PUNCT
ejpam-5398	221	4	a	a	NOUN
ejpam-5398	221	5	)	)	PUNCT
ejpam-5398	221	6	of	of	ADP
ejpam-5398	221	7	these	these	DET
ejpam-5398	221	8	figures	figure	NOUN
ejpam-5398	221	9	show	show	VERB
ejpam-5398	221	10	the	the	DET
ejpam-5398	221	11	temporal	temporal	ADJ
ejpam-5398	221	12	history	history	NOUN
ejpam-5398	221	13	of	of	ADP
ejpam-5398	221	14	θ	θ	PROPN
ejpam-5398	221	15	according	accord	VERB
ejpam-5398	221	16	to	to	ADP
ejpam-5398	221	17	the	the	DET
ejpam-5398	221	18	variation	variation	NOUN
ejpam-5398	221	19	of	of	ADP
ejpam-5398	221	20	the	the	DET
ejpam-5398	221	21	above	above	ADV
ejpam-5398	221	22	-	-	PUNCT
ejpam-5398	221	23	mentioned	mention	VERB
ejpam-5398	221	24	parameters	parameter	NOUN
ejpam-5398	221	25	.	.	PUNCT
ejpam-5398	222	1	these	these	DET
ejpam-5398	222	2	curves	curve	NOUN
ejpam-5398	222	3	have	have	VERB
ejpam-5398	222	4	a	a	DET
ejpam-5398	222	5	decaying	decay	VERB
ejpam-5398	222	6	form	form	NOUN
ejpam-5398	222	7	,	,	PUNCT
ejpam-5398	222	8	where	where	SCONJ
ejpam-5398	222	9	the	the	DET
ejpam-5398	222	10	amplitudes	amplitude	NOUN
ejpam-5398	222	11	of	of	ADP
ejpam-5398	222	12	the	the	DET
ejpam-5398	222	13	waves	wave	NOUN
ejpam-5398	222	14	are	be	AUX
ejpam-5398	222	15	improved	improve	VERB
ejpam-5398	222	16	with	with	ADP
ejpam-5398	222	17	the	the	DET
ejpam-5398	222	18	rise	rise	NOUN
ejpam-5398	222	19	of	of	ADP
ejpam-5398	222	20	a	a	DET
ejpam-5398	222	21	values	value	NOUN
ejpam-5398	222	22	,	,	PUNCT
ejpam-5398	222	23	and	and	CCONJ
ejpam-5398	222	24	the	the	DET
ejpam-5398	222	25	wave	wave	NOUN
ejpam-5398	222	26	number	number	NOUN
ejpam-5398	222	27	increases	increase	VERB
ejpam-5398	222	28	with	with	ADP
ejpam-5398	222	29	time	time	NOUN
ejpam-5398	222	30	,	,	PUNCT
ejpam-5398	222	31	as	as	SCONJ
ejpam-5398	222	32	seen	see	VERB
ejpam-5398	222	33	in	in	ADP
ejpam-5398	222	34	fig	fig	NOUN
ejpam-5398	222	35	.	.	PUNCT
ejpam-5398	223	1	(	(	PUNCT
ejpam-5398	223	2	3a	3a	NUM
ejpam-5398	223	3	)	)	PUNCT
ejpam-5398	223	4	.	.	PUNCT
ejpam-5398	224	1	the	the	DET
ejpam-5398	224	2	number	number	NOUN
ejpam-5398	224	3	of	of	ADP
ejpam-5398	224	4	oscillations	oscillation	NOUN
ejpam-5398	224	5	and	and	CCONJ
ejpam-5398	224	6	their	their	PRON
ejpam-5398	224	7	wave	wave	NOUN
ejpam-5398	224	8	’s	’s	PART
ejpam-5398	224	9	number	number	NOUN
ejpam-5398	224	10	,	,	PUNCT
ejpam-5398	224	11	are	be	AUX
ejpam-5398	224	12	shown	show	VERB
ejpam-5398	224	13	in	in	ADP
ejpam-5398	224	14	fig	fig	NOUN
ejpam-5398	224	15	.	.	PUNCT
ejpam-5398	225	1	4(a	4(a	NUM
ejpam-5398	225	2	)	)	PUNCT
ejpam-5398	226	1	,	,	PUNCT
ejpam-5398	226	2	remain	remain	VERB
ejpam-5398	226	3	stationary	stationary	ADJ
ejpam-5398	226	4	with	with	ADP
ejpam-5398	226	5	the	the	DET
ejpam-5398	226	6	change	change	NOUN
ejpam-5398	226	7	of	of	ADP
ejpam-5398	226	8	a	a	DET
ejpam-5398	226	9	values	value	NOUN
ejpam-5398	226	10	,	,	PUNCT
ejpam-5398	226	11	in	in	ADP
ejpam-5398	226	12	which	which	PRON
ejpam-5398	226	13	their	their	PRON
ejpam-5398	226	14	amplitudes	amplitude	NOUN
ejpam-5398	226	15	decrease	decrease	VERB
ejpam-5398	226	16	with	with	ADP
ejpam-5398	226	17	the	the	DET
ejpam-5398	226	18	increase	increase	NOUN
ejpam-5398	226	19	of	of	ADP
ejpam-5398	226	20	the	the	DET
ejpam-5398	226	21	values	value	NOUN
ejpam-5398	226	22	of	of	ADP
ejpam-5398	226	23	a.	a.	NOUN
ejpam-5398	226	24	however	however	ADV
ejpam-5398	226	25	,	,	PUNCT
ejpam-5398	226	26	the	the	DET
ejpam-5398	226	27	change	change	NOUN
ejpam-5398	226	28	of	of	ADP
ejpam-5398	226	29	the	the	DET
ejpam-5398	226	30	values	value	NOUN
ejpam-5398	226	31	b	b	PROPN
ejpam-5398	226	32	of	of	ADP
ejpam-5398	226	33	has	have	VERB
ejpam-5398	226	34	a	a	DET
ejpam-5398	226	35	positive	positive	ADJ
ejpam-5398	226	36	impact	impact	NOUN
ejpam-5398	226	37	on	on	ADP
ejpam-5398	226	38	the	the	DET
ejpam-5398	226	39	behavior	behavior	NOUN
ejpam-5398	226	40	of	of	ADP
ejpam-5398	226	41	the	the	DET
ejpam-5398	226	42	waves	wave	NOUN
ejpam-5398	226	43	describing	describe	VERB
ejpam-5398	226	44	θ	θ	NOUN
ejpam-5398	226	45	,	,	PUNCT
ejpam-5398	226	46	as	as	SCONJ
ejpam-5398	226	47	seen	see	VERB
ejpam-5398	226	48	in	in	ADP
ejpam-5398	226	49	fig	fig	NOUN
ejpam-5398	226	50	.	.	PUNCT
ejpam-5398	227	1	(	(	PUNCT
ejpam-5398	227	2	5a	5a	NUM
ejpam-5398	227	3	)	)	PUNCT
ejpam-5398	227	4	.	.	PUNCT
ejpam-5398	228	1	looking	look	VERB
ejpam-5398	228	2	at	at	ADP
ejpam-5398	228	3	the	the	DET
ejpam-5398	228	4	curves	curve	NOUN
ejpam-5398	228	5	of	of	ADP
ejpam-5398	228	6	this	this	DET
ejpam-5398	228	7	figure	figure	NOUN
ejpam-5398	228	8	,	,	PUNCT
ejpam-5398	228	9	in	in	ADP
ejpam-5398	228	10	more	more	ADJ
ejpam-5398	228	11	detail	detail	NOUN
ejpam-5398	228	12	,	,	PUNCT
ejpam-5398	228	13	reveals	reveal	VERB
ejpam-5398	228	14	that	that	SCONJ
ejpam-5398	228	15	the	the	DET
ejpam-5398	228	16	fluctuation	fluctuation	NOUN
ejpam-5398	228	17	numbers	number	NOUN
ejpam-5398	228	18	increase	increase	VERB
ejpam-5398	228	19	with	with	ADP
ejpam-5398	228	20	the	the	DET
ejpam-5398	228	21	increase	increase	NOUN
ejpam-5398	228	22	of	of	ADP
ejpam-5398	228	23	the	the	DET
ejpam-5398	228	24	values	value	NOUN
ejpam-5398	228	25	of	of	ADP
ejpam-5398	228	26	b	b	NOUN
ejpam-5398	228	27	,	,	PUNCT
ejpam-5398	228	28	i.e.	i.e.	X
ejpam-5398	228	29	,	,	PUNCT
ejpam-5398	228	30	as	as	SCONJ
ejpam-5398	228	31	the	the	DET
ejpam-5398	228	32	wavelength	wavelength	NOUN
ejpam-5398	228	33	decreases	decrease	VERB
ejpam-5398	228	34	,	,	PUNCT
ejpam-5398	228	35	even	even	ADV
ejpam-5398	228	36	though	though	SCONJ
ejpam-5398	228	37	the	the	DET
ejpam-5398	228	38	amplitudes	amplitude	NOUN
ejpam-5398	228	39	of	of	ADP
ejpam-5398	228	40	these	these	DET
ejpam-5398	228	41	curves	curve	NOUN
ejpam-5398	228	42	persist	persist	VERB
ejpam-5398	228	43	unaffected	unaffected	ADJ
ejpam-5398	228	44	.	.	PUNCT
ejpam-5398	229	1	when	when	SCONJ
ejpam-5398	229	2	we	we	PRON
ejpam-5398	229	3	going	go	VERB
ejpam-5398	229	4	to	to	PART
ejpam-5398	229	5	compare	compare	VERB
ejpam-5398	229	6	the	the	DET
ejpam-5398	229	7	curves	curve	NOUN
ejpam-5398	229	8	of	of	ADP
ejpam-5398	229	9	fig	fig	NOUN
ejpam-5398	229	10	.	.	PUNCT
ejpam-5398	230	1	(	(	PUNCT
ejpam-5398	230	2	3a	3a	NUM
ejpam-5398	230	3	)	)	PUNCT
ejpam-5398	230	4	,	,	PUNCT
ejpam-5398	230	5	fig	fig	NOUN
ejpam-5398	230	6	.	.	PUNCT
ejpam-5398	231	1	(	(	PUNCT
ejpam-5398	231	2	4a	4a	NOUN
ejpam-5398	231	3	)	)	PUNCT
ejpam-5398	231	4	,	,	PUNCT
ejpam-5398	231	5	and	and	CCONJ
ejpam-5398	231	6	fig	fig	NOUN
ejpam-5398	231	7	.	.	PUNCT
ejpam-5398	232	1	(	(	PUNCT
ejpam-5398	232	2	5a	5a	NUM
ejpam-5398	232	3	)	)	PUNCT
ejpam-5398	232	4	with	with	ADP
ejpam-5398	232	5	each	each	DET
ejpam-5398	232	6	other	other	ADJ
ejpam-5398	232	7	,	,	PUNCT
ejpam-5398	232	8	one	one	PRON
ejpam-5398	232	9	can	can	AUX
ejpam-5398	232	10	say	say	VERB
ejpam-5398	232	11	that	that	SCONJ
ejpam-5398	232	12	the	the	DET
ejpam-5398	232	13	number	number	NOUN
ejpam-5398	232	14	of	of	ADP
ejpam-5398	232	15	wave	wave	NOUN
ejpam-5398	232	16	fluctuations	fluctuation	NOUN
ejpam-5398	232	17	rises	rise	VERB
ejpam-5398	232	18	with	with	ADP
ejpam-5398	232	19	the	the	DET
ejpam-5398	232	20	change	change	NOUN
ejpam-5398	232	21	of	of	ADP
ejpam-5398	232	22	a	a	DET
ejpam-5398	232	23	than	than	ADP
ejpam-5398	232	24	with	with	ADP
ejpam-5398	232	25	the	the	DET
ejpam-5398	232	26	difference	difference	NOUN
ejpam-5398	232	27	between	between	ADP
ejpam-5398	232	28	both	both	PRON
ejpam-5398	232	29	a	a	PRON
ejpam-5398	232	30	and	and	CCONJ
ejpam-5398	232	31	b.	b.	PROPN
ejpam-5398	232	32	moreover	moreover	ADV
ejpam-5398	232	33	,	,	PUNCT
ejpam-5398	232	34	these	these	DET
ejpam-5398	232	35	waves	wave	NOUN
ejpam-5398	232	36	have	have	VERB
ejpam-5398	232	37	variable	variable	ADJ
ejpam-5398	232	38	amplitudes	amplitude	NOUN
ejpam-5398	232	39	,	,	PUNCT
ejpam-5398	232	40	as	as	SCONJ
ejpam-5398	232	41	seen	see	VERB
ejpam-5398	232	42	in	in	ADP
ejpam-5398	232	43	figs	fig	NOUN
ejpam-5398	232	44	.	.	PUNCT
ejpam-5398	233	1	(	(	PUNCT
ejpam-5398	233	2	4a	4a	NUM
ejpam-5398	233	3	)	)	PUNCT
ejpam-5398	233	4	and	and	CCONJ
ejpam-5398	233	5	(	(	PUNCT
ejpam-5398	233	6	5a	5a	NUM
ejpam-5398	233	7	)	)	PUNCT
ejpam-5398	233	8	,	,	PUNCT
ejpam-5398	233	9	but	but	CCONJ
ejpam-5398	233	10	in	in	ADP
ejpam-5398	233	11	fig	fig	NOUN
ejpam-5398	233	12	.	.	PUNCT
ejpam-5398	234	1	(	(	PUNCT
ejpam-5398	234	2	5a	5a	NUM
ejpam-5398	234	3	)	)	PUNCT
ejpam-5398	234	4	,	,	PUNCT
ejpam-5398	234	5	they	they	PRON
ejpam-5398	234	6	remain	remain	VERB
ejpam-5398	234	7	constant	constant	ADJ
ejpam-5398	234	8	.	.	PUNCT
ejpam-5398	235	1	figs	fig	NOUN
ejpam-5398	235	2	.	.	PUNCT
ejpam-5398	236	1	(	(	PUNCT
ejpam-5398	236	2	3b	3b	NUM
ejpam-5398	236	3	)	)	PUNCT
ejpam-5398	236	4	,	,	PUNCT
ejpam-5398	236	5	(	(	PUNCT
ejpam-5398	236	6	4b	4b	PROPN
ejpam-5398	236	7	)	)	PUNCT
ejpam-5398	236	8	,	,	PUNCT
ejpam-5398	236	9	and	and	CCONJ
ejpam-5398	236	10	(	(	PUNCT
ejpam-5398	236	11	5b	5b	X
ejpam-5398	236	12	)	)	PUNCT
ejpam-5398	236	13	reveal	reveal	VERB
ejpam-5398	236	14	the	the	DET
ejpam-5398	236	15	corresponding	correspond	VERB
ejpam-5398	236	16	diagrams	diagram	NOUN
ejpam-5398	236	17	of	of	ADP
ejpam-5398	236	18	phase	phase	NOUN
ejpam-5398	236	19	planes	plane	NOUN
ejpam-5398	236	20	which	which	PRON
ejpam-5398	236	21	have	have	VERB
ejpam-5398	236	22	the	the	DET
ejpam-5398	236	23	forms	form	NOUN
ejpam-5398	236	24	of	of	ADP
ejpam-5398	236	25	closed	closed	ADJ
ejpam-5398	236	26	curves	curve	NOUN
ejpam-5398	236	27	to	to	PART
ejpam-5398	236	28	maintain	maintain	VERB
ejpam-5398	236	29	the	the	DET
ejpam-5398	236	30	stability	stability	NOUN
ejpam-5398	236	31	of	of	ADP
ejpam-5398	236	32	the	the	DET
ejpam-5398	236	33	solutions	solution	NOUN
ejpam-5398	236	34	.	.	PUNCT
ejpam-5398	237	1	the	the	DET
ejpam-5398	237	2	drawn	draw	VERB
ejpam-5398	237	3	curves	curve	NOUN
ejpam-5398	237	4	in	in	ADP
ejpam-5398	237	5	figs	fig	NOUN
ejpam-5398	237	6	.	.	PUNCT
ejpam-5398	238	1	(	(	PUNCT
ejpam-5398	238	2	3b	3b	NUM
ejpam-5398	238	3	)	)	PUNCT
ejpam-5398	238	4	and	and	CCONJ
ejpam-5398	238	5	(	(	PUNCT
ejpam-5398	238	6	4b	4b	X
ejpam-5398	238	7	)	)	PUNCT
ejpam-5398	238	8	are	be	AUX
ejpam-5398	238	9	close	close	ADJ
ejpam-5398	238	10	to	to	ADP
ejpam-5398	238	11	each	each	DET
ejpam-5398	238	12	other	other	ADJ
ejpam-5398	238	13	and	and	CCONJ
ejpam-5398	238	14	take	take	VERB
ejpam-5398	238	15	the	the	DET
ejpam-5398	238	16	direction	direction	NOUN
ejpam-5398	238	17	inward	inward	ADV
ejpam-5398	238	18	,	,	PUNCT
ejpam-5398	238	19	which	which	PRON
ejpam-5398	238	20	indicates	indicate	VERB
ejpam-5398	238	21	the	the	DET
ejpam-5398	238	22	stability	stability	NOUN
ejpam-5398	238	23	and	and	CCONJ
ejpam-5398	238	24	stationary	stationary	ADJ
ejpam-5398	238	25	behavior	behavior	NOUN
ejpam-5398	238	26	of	of	ADP
ejpam-5398	238	27	the	the	DET
ejpam-5398	238	28	solution	solution	NOUN
ejpam-5398	238	29	.	.	PUNCT
ejpam-5398	239	1	the	the	DET
ejpam-5398	239	2	reason	reason	NOUN
ejpam-5398	239	3	is	be	AUX
ejpam-5398	239	4	due	due	ADJ
ejpam-5398	239	5	to	to	ADP
ejpam-5398	239	6	the	the	DET
ejpam-5398	239	7	change	change	NOUN
ejpam-5398	239	8	in	in	ADP
ejpam-5398	239	9	the	the	DET
ejpam-5398	239	10	amplitudes	amplitude	NOUN
ejpam-5398	239	11	of	of	ADP
ejpam-5398	239	12	the	the	DET
ejpam-5398	239	13	waves	wave	NOUN
ejpam-5398	239	14	.	.	PUNCT
ejpam-5398	240	1	on	on	ADP
ejpam-5398	240	2	the	the	DET
ejpam-5398	240	3	other	other	ADJ
ejpam-5398	240	4	hand	hand	NOUN
ejpam-5398	240	5	,	,	PUNCT
ejpam-5398	240	6	one	one	PRON
ejpam-5398	240	7	finds	find	VERB
ejpam-5398	240	8	that	that	SCONJ
ejpam-5398	240	9	these	these	DET
ejpam-5398	240	10	curves	curve	NOUN
ejpam-5398	240	11	take	take	VERB
ejpam-5398	240	12	symmetrical	symmetrical	ADJ
ejpam-5398	240	13	closed	closed	ADJ
ejpam-5398	240	14	forms	form	NOUN
ejpam-5398	240	15	,	,	PUNCT
ejpam-5398	240	16	as	as	SCONJ
ejpam-5398	240	17	shown	show	VERB
ejpam-5398	240	18	in	in	ADP
ejpam-5398	240	19	fig	fig	NOUN
ejpam-5398	240	20	.	.	PUNCT
ejpam-5398	241	1	(	(	PUNCT
ejpam-5398	241	2	5b	5b	NUM
ejpam-5398	241	3	)	)	PUNCT
ejpam-5398	241	4	because	because	SCONJ
ejpam-5398	241	5	the	the	DET
ejpam-5398	241	6	amplitudes	amplitude	NOUN
ejpam-5398	241	7	of	of	ADP
ejpam-5398	241	8	the	the	DET
ejpam-5398	241	9	drawn	draw	VERB
ejpam-5398	241	10	waves	wave	NOUN
ejpam-5398	241	11	in	in	ADP
ejpam-5398	241	12	this	this	DET
ejpam-5398	241	13	figure	figure	NOUN
ejpam-5398	241	14	don	don	NOUN
ejpam-5398	241	15	not	not	PART
ejpam-5398	241	16	change	change	VERB
ejpam-5398	241	17	to	to	ADP
ejpam-5398	241	18	some	some	DET
ejpam-5398	241	19	extent	extent	NOUN
ejpam-5398	241	20	.	.	PUNCT
ejpam-5398	242	1	however	however	ADV
ejpam-5398	242	2	,	,	PUNCT
ejpam-5398	242	3	this	this	DET
ejpam-5398	242	4	interpretation	interpretation	NOUN
ejpam-5398	242	5	confirms	confirm	VERB
ejpam-5398	242	6	the	the	DET
ejpam-5398	242	7	validity	validity	NOUN
ejpam-5398	242	8	of	of	ADP
ejpam-5398	242	9	what	what	PRON
ejpam-5398	242	10	has	have	AUX
ejpam-5398	242	11	been	be	AUX
ejpam-5398	242	12	discussed	discuss	VERB
ejpam-5398	242	13	in	in	ADP
ejpam-5398	242	14	the	the	DET
ejpam-5398	242	15	previous	previous	ADJ
ejpam-5398	242	16	discussion	discussion	NOUN
ejpam-5398	242	17	.	.	PUNCT
ejpam-5398	243	1	the	the	DET
ejpam-5398	243	2	symmetry	symmetry	NOUN
ejpam-5398	243	3	in	in	ADP
ejpam-5398	243	4	the	the	DET
ejpam-5398	243	5	phase	phase	NOUN
ejpam-5398	243	6	plane	plane	NOUN
ejpam-5398	243	7	curves	curve	NOUN
ejpam-5398	243	8	for	for	ADP
ejpam-5398	243	9	periodic	periodic	ADJ
ejpam-5398	243	10	waves	wave	NOUN
ejpam-5398	243	11	arises	arise	VERB
ejpam-5398	243	12	due	due	ADP
ejpam-5398	243	13	to	to	ADP
ejpam-5398	243	14	the	the	DET
ejpam-5398	243	15	nature	nature	NOUN
ejpam-5398	243	16	of	of	ADP
ejpam-5398	243	17	the	the	DET
ejpam-5398	243	18	underlying	underlying	ADJ
ejpam-5398	243	19	differential	differential	ADJ
ejpam-5398	243	20	equations	equation	NOUN
ejpam-5398	243	21	governing	govern	VERB
ejpam-5398	243	22	the	the	DET
ejpam-5398	243	23	system	system	NOUN
ejpam-5398	243	24	.	.	PUNCT
ejpam-5398	244	1	these	these	DET
ejpam-5398	244	2	curves	curve	NOUN
ejpam-5398	244	3	represent	represent	VERB
ejpam-5398	244	4	the	the	DET
ejpam-5398	244	5	relationship	relationship	NOUN
ejpam-5398	244	6	between	between	ADP
ejpam-5398	244	7	a	a	DET
ejpam-5398	244	8	system	system	NOUN
ejpam-5398	244	9	’s	’s	PART
ejpam-5398	244	10	position	position	NOUN
ejpam-5398	244	11	and	and	CCONJ
ejpam-5398	244	12	its	its	PRON
ejpam-5398	244	13	velocity	velocity	NOUN
ejpam-5398	244	14	as	as	SCONJ
ejpam-5398	244	15	it	it	PRON
ejpam-5398	244	16	evolves	evolve	VERB
ejpam-5398	244	17	over	over	ADP
ejpam-5398	244	18	time	time	NOUN
ejpam-5398	244	19	.	.	PUNCT
ejpam-5398	245	1	the	the	DET
ejpam-5398	245	2	symmetry	symmetry	NOUN
ejpam-5398	245	3	of	of	ADP
ejpam-5398	245	4	these	these	DET
ejpam-5398	245	5	curves	curve	NOUN
ejpam-5398	245	6	backs	back	NOUN
ejpam-5398	245	7	to	to	ADP
ejpam-5398	245	8	the	the	DET
ejpam-5398	245	9	following	following	ADJ
ejpam-5398	245	10	reasons	reason	NOUN
ejpam-5398	245	11	:	:	PUNCT
ejpam-5398	245	12	in	in	ADP
ejpam-5398	245	13	a	a	DET
ejpam-5398	245	14	periodic	periodic	ADJ
ejpam-5398	245	15	system	system	NOUN
ejpam-5398	245	16	,	,	PUNCT
ejpam-5398	245	17	the	the	DET
ejpam-5398	245	18	motion	motion	NOUN
ejpam-5398	245	19	repeats	repeat	VERB
ejpam-5398	245	20	itself	itself	PRON
ejpam-5398	245	21	after	after	ADP
ejpam-5398	245	22	a	a	DET
ejpam-5398	245	23	certain	certain	ADJ
ejpam-5398	245	24	time	time	NOUN
ejpam-5398	245	25	period	period	NOUN
ejpam-5398	245	26	.	.	PUNCT
ejpam-5398	246	1	this	this	PRON
ejpam-5398	246	2	implies	imply	VERB
ejpam-5398	246	3	that	that	SCONJ
ejpam-5398	246	4	for	for	ADP
ejpam-5398	246	5	every	every	DET
ejpam-5398	246	6	point	point	NOUN
ejpam-5398	246	7	in	in	ADP
ejpam-5398	246	8	the	the	DET
ejpam-5398	246	9	phase	phase	NOUN
ejpam-5398	246	10	plane	plane	NOUN
ejpam-5398	246	11	,	,	PUNCT
ejpam-5398	246	12	the	the	DET
ejpam-5398	246	13	system	system	NOUN
ejpam-5398	246	14	will	will	AUX
ejpam-5398	246	15	return	return	VERB
ejpam-5398	246	16	to	to	ADP
ejpam-5398	246	17	the	the	DET
ejpam-5398	246	18	same	same	ADJ
ejpam-5398	246	19	point	point	NOUN
ejpam-5398	246	20	after	after	ADP
ejpam-5398	246	21	one	one	NUM
ejpam-5398	246	22	period	period	NOUN
ejpam-5398	246	23	.	.	PUNCT
ejpam-5398	247	1	this	this	DET
ejpam-5398	247	2	repetitive	repetitive	ADJ
ejpam-5398	247	3	motion	motion	NOUN
ejpam-5398	247	4	is	be	AUX
ejpam-5398	247	5	a	a	DET
ejpam-5398	247	6	key	key	ADJ
ejpam-5398	247	7	factor	factor	NOUN
ejpam-5398	247	8	leading	lead	VERB
ejpam-5398	247	9	to	to	ADP
ejpam-5398	247	10	the	the	DET
ejpam-5398	247	11	closed	closed	ADJ
ejpam-5398	247	12	curves	curve	NOUN
ejpam-5398	247	13	in	in	ADP
ejpam-5398	247	14	the	the	DET
ejpam-5398	247	15	phase	phase	NOUN
ejpam-5398	247	16	plane	plane	NOUN
ejpam-5398	247	17	.	.	PUNCT
ejpam-5398	248	1	in	in	ADP
ejpam-5398	248	2	conservative	conservative	ADJ
ejpam-5398	248	3	systems	system	NOUN
ejpam-5398	248	4	,	,	PUNCT
ejpam-5398	248	5	the	the	DET
ejpam-5398	248	6	total	total	ADJ
ejpam-5398	248	7	mechanical	mechanical	ADJ
ejpam-5398	248	8	energy	energy	NOUN
ejpam-5398	248	9	is	be	AUX
ejpam-5398	248	10	constant	constant	ADJ
ejpam-5398	248	11	.	.	PUNCT
ejpam-5398	249	1	this	this	DET
ejpam-5398	249	2	constancy	constancy	NOUN
ejpam-5398	249	3	is	be	AUX
ejpam-5398	249	4	mirrored	mirror	VERB
ejpam-5398	249	5	in	in	ADP
ejpam-5398	249	6	the	the	DET
ejpam-5398	249	7	symmetry	symmetry	NOUN
ejpam-5398	249	8	of	of	ADP
ejpam-5398	249	9	the	the	DET
ejpam-5398	249	10	phase	phase	NOUN
ejpam-5398	249	11	plane	plane	NOUN
ejpam-5398	249	12	.	.	PUNCT
ejpam-5398	250	1	as	as	ADP
ejpam-5398	250	2	the	the	DET
ejpam-5398	250	3	system	system	NOUN
ejpam-5398	250	4	oscillates	oscillate	NOUN
ejpam-5398	250	5	,	,	PUNCT
ejpam-5398	250	6	energy	energy	NOUN
ejpam-5398	250	7	continuously	continuously	ADV
ejpam-5398	250	8	shifts	shift	NOUN
ejpam-5398	250	9	between	between	ADP
ejpam-5398	250	10	kinetic	kinetic	ADJ
ejpam-5398	250	11	and	and	CCONJ
ejpam-5398	250	12	potential	potential	ADJ
ejpam-5398	250	13	forms	form	NOUN
ejpam-5398	250	14	,	,	PUNCT
ejpam-5398	250	15	resulting	result	VERB
ejpam-5398	250	16	in	in	ADP
ejpam-5398	250	17	symmetric	symmetric	ADJ
ejpam-5398	250	18	trajectories	trajectory	NOUN
ejpam-5398	250	19	in	in	ADP
ejpam-5398	250	20	the	the	DET
ejpam-5398	250	21	phase	phase	NOUN
ejpam-5398	250	22	plane	plane	NOUN
ejpam-5398	250	23	.	.	PUNCT
ejpam-5398	251	1	if	if	SCONJ
ejpam-5398	251	2	the	the	DET
ejpam-5398	251	3	system	system	NOUN
ejpam-5398	251	4	is	be	AUX
ejpam-5398	251	5	linear	linear	ADJ
ejpam-5398	251	6	,	,	PUNCT
ejpam-5398	251	7	the	the	DET
ejpam-5398	251	8	phase	phase	NOUN
ejpam-5398	251	9	plane	plane	NOUN
ejpam-5398	251	10	trajectories	trajectory	NOUN
ejpam-5398	251	11	are	be	AUX
ejpam-5398	251	12	elliptical	elliptical	ADJ
ejpam-5398	251	13	and	and	CCONJ
ejpam-5398	251	14	perfectly	perfectly	ADV
ejpam-5398	251	15	symmetric	symmetric	ADJ
ejpam-5398	251	16	about	about	ADP
ejpam-5398	251	17	the	the	DET
ejpam-5398	251	18	origin	origin	NOUN
ejpam-5398	251	19	.	.	PUNCT
ejpam-5398	252	1	this	this	DET
ejpam-5398	252	2	symmetry	symmetry	NOUN
ejpam-5398	252	3	is	be	AUX
ejpam-5398	252	4	due	due	ADJ
ejpam-5398	252	5	to	to	ADP
ejpam-5398	252	6	the	the	DET
ejpam-5398	252	7	linear	linear	ADJ
ejpam-5398	252	8	relationship	relationship	NOUN
ejpam-5398	252	9	between	between	ADP
ejpam-5398	252	10	the	the	DET
ejpam-5398	252	11	restoring	restore	VERB
ejpam-5398	252	12	force	force	NOUN
ejpam-5398	252	13	and	and	CCONJ
ejpam-5398	252	14	displacement	displacement	NOUN
ejpam-5398	252	15	in	in	ADP
ejpam-5398	252	16	harmonic	harmonic	ADJ
ejpam-5398	252	17	motion	motion	NOUN
ejpam-5398	252	18	.	.	PUNCT
ejpam-5398	253	1	even	even	ADV
ejpam-5398	253	2	in	in	ADP
ejpam-5398	253	3	nonlinear	nonlinear	ADJ
ejpam-5398	253	4	systems	system	NOUN
ejpam-5398	253	5	,	,	PUNCT
ejpam-5398	253	6	if	if	SCONJ
ejpam-5398	253	7	the	the	DET
ejpam-5398	253	8	nonlinearities	nonlinearitie	NOUN
ejpam-5398	253	9	are	be	AUX
ejpam-5398	253	10	symmetric	symmetric	ADJ
ejpam-5398	253	11	,	,	PUNCT
ejpam-5398	253	12	the	the	DET
ejpam-5398	253	13	phase	phase	NOUN
ejpam-5398	253	14	plane	plane	NOUN
ejpam-5398	253	15	curves	curve	NOUN
ejpam-5398	253	16	can	can	AUX
ejpam-5398	253	17	remain	remain	VERB
ejpam-5398	253	18	symmetric	symmetric	ADJ
ejpam-5398	253	19	.	.	PUNCT
ejpam-5398	254	1	although	although	SCONJ
ejpam-5398	254	2	the	the	DET
ejpam-5398	254	3	type	type	NOUN
ejpam-5398	254	4	and	and	CCONJ
ejpam-5398	254	5	degree	degree	NOUN
ejpam-5398	254	6	of	of	ADP
ejpam-5398	254	7	nonlinearity	nonlinearity	NOUN
ejpam-5398	254	8	may	may	AUX
ejpam-5398	254	9	change	change	VERB
ejpam-5398	254	10	the	the	DET
ejpam-5398	254	11	shape	shape	NOUN
ejpam-5398	254	12	of	of	ADP
ejpam-5398	254	13	the	the	DET
ejpam-5398	254	14	curves	curve	NOUN
ejpam-5398	254	15	,	,	PUNCT
ejpam-5398	254	16	symmetry	symmetry	NOUN
ejpam-5398	254	17	in	in	ADP
ejpam-5398	254	18	the	the	DET
ejpam-5398	254	19	potential	potential	ADJ
ejpam-5398	254	20	function	function	NOUN
ejpam-5398	254	21	frequently	frequently	ADV
ejpam-5398	254	22	leads	lead	VERB
ejpam-5398	254	23	to	to	ADP
ejpam-5398	254	24	symmetric	symmetric	ADJ
ejpam-5398	254	25	trajectories	trajectory	NOUN
ejpam-5398	254	26	in	in	ADP
ejpam-5398	254	27	the	the	DET
ejpam-5398	254	28	phase	phase	NOUN
ejpam-5398	254	29	plane	plane	NOUN
ejpam-5398	254	30	.	.	PUNCT
ejpam-5398	255	1	for	for	ADP
ejpam-5398	255	2	more	more	ADJ
ejpam-5398	255	3	convenience	convenience	NOUN
ejpam-5398	255	4	,	,	PUNCT
ejpam-5398	255	5	since	since	SCONJ
ejpam-5398	255	6	the	the	DET
ejpam-5398	255	7	td	td	NOUN
ejpam-5398	255	8	must	must	AUX
ejpam-5398	255	9	be	be	AUX
ejpam-5398	255	10	of	of	ADP
ejpam-5398	255	11	a	a	DET
ejpam-5398	255	12	positive	positive	ADJ
ejpam-5398	255	13	real	real	ADJ
ejpam-5398	255	14	value	value	NOUN
ejpam-5398	255	15	,	,	PUNCT
ejpam-5398	255	16	the	the	DET
ejpam-5398	255	17	inequality	inequality	NOUN
ejpam-5398	255	18	eq	eq	ADP
ejpam-5398	255	19	.	.	PUNCT
ejpam-5398	256	1	(	(	PUNCT
ejpam-5398	256	2	15	15	NUM
ejpam-5398	256	3	)	)	PUNCT
ejpam-5398	256	4	has	have	AUX
ejpam-5398	256	5	been	be	AUX
ejpam-5398	256	6	drawn	draw	VERB
ejpam-5398	256	7	to	to	PART
ejpam-5398	256	8	reflect	reflect	VERB
ejpam-5398	256	9	the	the	DET
ejpam-5398	256	10	influences	influence	NOUN
ejpam-5398	256	11	of	of	ADP
ejpam-5398	256	12	the	the	DET
ejpam-5398	256	13	physical	physical	ADJ
ejpam-5398	256	14	parameters	parameter	NOUN
ejpam-5398	256	15	a.a	a.a	PROPN
ejpam-5398	256	16	,	,	PUNCT
ejpam-5398	256	17	and	and	CCONJ
ejpam-5398	256	18	b	b	NOUN
ejpam-5398	256	19	,	,	PUNCT
ejpam-5398	256	20	as	as	SCONJ
ejpam-5398	256	21	explored	explore	VERB
ejpam-5398	256	22	in	in	ADP
ejpam-5398	256	23	figs	fig	NOUN
ejpam-5398	256	24	(	(	PUNCT
ejpam-5398	256	25	6,7,8	6,7,8	NUM
ejpam-5398	256	26	)	)	PUNCT
ejpam-5398	256	27	,	,	PUNCT
ejpam-5398	256	28	and	and	CCONJ
ejpam-5398	256	29	(	(	PUNCT
ejpam-5398	256	30	9	9	NUM
ejpam-5398	256	31	)	)	PUNCT
ejpam-5398	256	32	.	.	PUNCT
ejpam-5398	257	1	these	these	DET
ejpam-5398	257	2	figures	figure	NOUN
ejpam-5398	257	3	are	be	AUX
ejpam-5398	257	4	graphed	graph	VERB
ejpam-5398	257	5	to	to	PART
ejpam-5398	257	6	show	show	VERB
ejpam-5398	257	7	the	the	DET
ejpam-5398	257	8	drawn	draw	VERB
ejpam-5398	257	9	a.	a.	NOUN
ejpam-5398	257	10	a.	a.	NOUN
ejpam-5398	257	11	galal	galal	PROPN
ejpam-5398	257	12	et	et	PROPN
ejpam-5398	257	13	al	al	PROPN
ejpam-5398	257	14	.	.	PUNCT
ejpam-5398	257	15	/	/	SYM
ejpam-5398	257	16	eur	eur	PROPN
ejpam-5398	257	17	.	.	PUNCT
ejpam-5398	258	1	j.	j.	PROPN
ejpam-5398	258	2	pure	pure	PROPN
ejpam-5398	258	3	appl	appl	PROPN
ejpam-5398	258	4	.	.	PROPN
ejpam-5398	258	5	math	math	PROPN
ejpam-5398	258	6	,	,	PUNCT
ejpam-5398	258	7	17	17	NUM
ejpam-5398	258	8	(	(	PUNCT
ejpam-5398	258	9	4	4	NUM
ejpam-5398	258	10	)	)	PUNCT
ejpam-5398	258	11	(	(	PUNCT
ejpam-5398	258	12	2024	2024	NUM
ejpam-5398	258	13	)	)	PUNCT
ejpam-5398	258	14	,	,	PUNCT
ejpam-5398	258	15	2878	2878	NUM
ejpam-5398	258	16	-	-	SYM
ejpam-5398	258	17	2897	2897	NUM
ejpam-5398	258	18	2888	2888	NUM
ejpam-5398	258	19	figure	figure	NOUN
ejpam-5398	258	20	3	3	NUM
ejpam-5398	258	21	:	:	PUNCT
ejpam-5398	258	22	(	(	PUNCT
ejpam-5398	258	23	a	a	X
ejpam-5398	258	24	)	)	PUNCT
ejpam-5398	258	25	explores	explore	VERB
ejpam-5398	258	26	curves	curve	NOUN
ejpam-5398	258	27	of	of	ADP
ejpam-5398	258	28	at	at	ADP
ejpam-5398	258	29	different	different	ADJ
ejpam-5398	258	30	amounts	amount	NOUN
ejpam-5398	258	31	of	of	ADP
ejpam-5398	258	32	θ(t	θ(t	PROPN
ejpam-5398	258	33	)	)	PUNCT
ejpam-5398	258	34	,	,	PUNCT
ejpam-5398	258	35	and	and	CCONJ
ejpam-5398	258	36	(	(	PUNCT
ejpam-5398	258	37	b	b	X
ejpam-5398	258	38	)	)	PUNCT
ejpam-5398	258	39	reveals	reveal	VERB
ejpam-5398	258	40	the	the	DET
ejpam-5398	258	41	phase	phase	NOUN
ejpam-5398	258	42	plane	plane	NOUN
ejpam-5398	258	43	trajectories	trajectory	NOUN
ejpam-5398	258	44	in	in	ADP
ejpam-5398	258	45	(	(	PUNCT
ejpam-5398	258	46	a	a	NOUN
ejpam-5398	258	47	)	)	PUNCT
ejpam-5398	258	48	.	.	PUNCT
ejpam-5398	259	1	figure	figure	VERB
ejpam-5398	259	2	4	4	NUM
ejpam-5398	259	3	:	:	PUNCT
ejpam-5398	259	4	(	(	PUNCT
ejpam-5398	259	5	a	a	X
ejpam-5398	259	6	)	)	PUNCT
ejpam-5398	259	7	demonstrates	demonstrate	VERB
ejpam-5398	259	8	curves	curve	NOUN
ejpam-5398	259	9	of	of	ADP
ejpam-5398	259	10	θ(t	θ(t	PROPN
ejpam-5398	259	11	)	)	PUNCT
ejpam-5398	259	12	at	at	ADP
ejpam-5398	259	13	different	different	ADJ
ejpam-5398	259	14	amounts	amount	NOUN
ejpam-5398	259	15	of	of	ADP
ejpam-5398	259	16	a	a	PRON
ejpam-5398	259	17	,	,	PUNCT
ejpam-5398	259	18	and	and	CCONJ
ejpam-5398	259	19	(	(	PUNCT
ejpam-5398	259	20	b	b	X
ejpam-5398	259	21	)	)	PUNCT
ejpam-5398	259	22	shows	show	VERB
ejpam-5398	259	23	the	the	DET
ejpam-5398	259	24	phase	phase	NOUN
ejpam-5398	259	25	plane	plane	NOUN
ejpam-5398	259	26	diagrams	diagram	NOUN
ejpam-5398	259	27	in	in	ADP
ejpam-5398	259	28	(	(	PUNCT
ejpam-5398	259	29	a	a	NOUN
ejpam-5398	259	30	)	)	PUNCT
ejpam-5398	259	31	.	.	PUNCT
ejpam-5398	260	1	stable	stable	ADJ
ejpam-5398	260	2	/	/	SYM
ejpam-5398	260	3	unstable	unstable	ADJ
ejpam-5398	260	4	zones	zone	NOUN
ejpam-5398	260	5	,	,	PUNCT
ejpam-5398	260	6	in	in	ADP
ejpam-5398	260	7	which	which	PRON
ejpam-5398	260	8	the	the	DET
ejpam-5398	260	9	green	green	ADJ
ejpam-5398	260	10	areas	area	NOUN
ejpam-5398	260	11	denote	denote	VERB
ejpam-5398	260	12	the	the	DET
ejpam-5398	260	13	stabile	stabile	ADJ
ejpam-5398	260	14	zones	zone	NOUN
ejpam-5398	260	15	,	,	PUNCT
ejpam-5398	260	16	while	while	SCONJ
ejpam-5398	260	17	the	the	DET
ejpam-5398	260	18	white	white	ADJ
ejpam-5398	260	19	ones	one	NOUN
ejpam-5398	260	20	express	express	VERB
ejpam-5398	260	21	the	the	DET
ejpam-5398	260	22	unstable	unstable	ADJ
ejpam-5398	260	23	areas	area	NOUN
ejpam-5398	260	24	.	.	PUNCT
ejpam-5398	261	1	these	these	DET
ejpam-5398	261	2	zones	zone	NOUN
ejpam-5398	261	3	are	be	AUX
ejpam-5398	261	4	plotted	plot	VERB
ejpam-5398	261	5	in	in	ADP
ejpam-5398	261	6	view	view	NOUN
ejpam-5398	261	7	the	the	DET
ejpam-5398	261	8	intersection	intersection	NOUN
ejpam-5398	261	9	of	of	ADP
ejpam-5398	261	10	the	the	DET
ejpam-5398	261	11	instability	instability	NOUN
ejpam-5398	261	12	and	and	CCONJ
ejpam-5398	261	13	stability	stability	NOUN
ejpam-5398	261	14	regions	region	NOUN
ejpam-5398	261	15	of	of	ADP
ejpam-5398	261	16	the	the	DET
ejpam-5398	261	17	inequalities	inequality	NOUN
ejpam-5398	261	18	eq	eq	ADJ
ejpam-5398	261	19	.	.	PUNCT
ejpam-5398	262	1	(	(	PUNCT
ejpam-5398	262	2	15	15	NUM
ejpam-5398	262	3	)	)	PUNCT
ejpam-5398	262	4	.	.	PUNCT
ejpam-5398	263	1	fig	fig	NOUN
ejpam-5398	263	2	.	.	PUNCT
ejpam-5398	264	1	(	(	PUNCT
ejpam-5398	264	2	6	6	X
ejpam-5398	264	3	)	)	PUNCT
ejpam-5398	264	4	show	show	VERB
ejpam-5398	264	5	the	the	DET
ejpam-5398	264	6	variation	variation	NOUN
ejpam-5398	264	7	of	of	ADP
ejpam-5398	264	8	these	these	DET
ejpam-5398	264	9	zones	zone	NOUN
ejpam-5398	264	10	according	accord	VERB
ejpam-5398	264	11	to	to	ADP
ejpam-5398	264	12	the	the	DET
ejpam-5398	264	13	various	various	ADJ
ejpam-5398	264	14	values	value	NOUN
ejpam-5398	264	15	of	of	ADP
ejpam-5398	264	16	a	a	PRON
ejpam-5398	264	17	=	=	X
ejpam-5398	264	18	(	(	PUNCT
ejpam-5398	264	19	0.4	0.4	NUM
ejpam-5398	264	20	,	,	PUNCT
ejpam-5398	264	21	0.7	0.7	NUM
ejpam-5398	264	22	,	,	PUNCT
ejpam-5398	264	23	1	1	NUM
ejpam-5398	264	24	)	)	PUNCT
ejpam-5398	264	25	at	at	ADP
ejpam-5398	264	26	a	a	DET
ejpam-5398	264	27	=	=	SYM
ejpam-5398	264	28	b	b	NOUN
ejpam-5398	264	29	=	=	NOUN
ejpam-5398	264	30	0.01	0.01	NUM
ejpam-5398	264	31	,	,	PUNCT
ejpam-5398	264	32	while	while	SCONJ
ejpam-5398	264	33	parts	part	NOUN
ejpam-5398	264	34	of	of	ADP
ejpam-5398	264	35	fig	fig	NOUN
ejpam-5398	264	36	.	.	PUNCT
ejpam-5398	265	1	(	(	PUNCT
ejpam-5398	265	2	7	7	X
ejpam-5398	265	3	)	)	PUNCT
ejpam-5398	265	4	are	be	AUX
ejpam-5398	265	5	drawn	draw	VERB
ejpam-5398	265	6	when	when	SCONJ
ejpam-5398	265	7	a	a	PRON
ejpam-5398	265	8	=	=	X
ejpam-5398	265	9	(	(	PUNCT
ejpam-5398	265	10	0.4	0.4	NUM
ejpam-5398	265	11	,	,	PUNCT
ejpam-5398	265	12	0.7	0.7	NUM
ejpam-5398	265	13	)	)	PUNCT
ejpam-5398	265	14	and	and	CCONJ
ejpam-5398	265	15	a	a	DET
ejpam-5398	265	16	=	=	SYM
ejpam-5398	265	17	b	b	NOUN
ejpam-5398	265	18	=	=	SYM
ejpam-5398	265	19	1	1	X
ejpam-5398	265	20	.	.	PUNCT
ejpam-5398	265	21	looking	look	VERB
ejpam-5398	265	22	at	at	ADP
ejpam-5398	265	23	the	the	DET
ejpam-5398	265	24	parts	part	NOUN
ejpam-5398	265	25	(	(	PUNCT
ejpam-5398	265	26	a	a	NOUN
ejpam-5398	265	27	)	)	PUNCT
ejpam-5398	265	28	and	and	CCONJ
ejpam-5398	265	29	(	(	PUNCT
ejpam-5398	265	30	b	b	NOUN
ejpam-5398	265	31	)	)	PUNCT
ejpam-5398	265	32	of	of	ADP
ejpam-5398	265	33	these	these	DET
ejpam-5398	265	34	figures	figure	NOUN
ejpam-5398	265	35	,	,	PUNCT
ejpam-5398	265	36	besides	besides	SCONJ
ejpam-5398	265	37	the	the	DET
ejpam-5398	265	38	part	part	NOUN
ejpam-5398	265	39	(	(	PUNCT
ejpam-5398	265	40	c	c	NOUN
ejpam-5398	265	41	)	)	PUNCT
ejpam-5398	265	42	of	of	ADP
ejpam-5398	265	43	fig	fig	NOUN
ejpam-5398	265	44	.	.	PUNCT
ejpam-5398	266	1	(	(	PUNCT
ejpam-5398	266	2	7	7	NUM
ejpam-5398	266	3	)	)	PUNCT
ejpam-5398	266	4	,	,	PUNCT
ejpam-5398	266	5	we	we	PRON
ejpam-5398	266	6	conclude	conclude	VERB
ejpam-5398	266	7	that	that	SCONJ
ejpam-5398	266	8	the	the	DET
ejpam-5398	266	9	stability	stability	NOUN
ejpam-5398	266	10	regions	region	NOUN
ejpam-5398	266	11	decrease	decrease	VERB
ejpam-5398	266	12	with	with	ADP
ejpam-5398	266	13	the	the	DET
ejpam-5398	266	14	increase	increase	NOUN
ejpam-5398	266	15	of	of	ADP
ejpam-5398	266	16	the	the	DET
ejpam-5398	266	17	values	value	NOUN
ejpam-5398	266	18	of	of	ADP
ejpam-5398	266	19	a.	a.	NOUN
ejpam-5398	266	20	this	this	PRON
ejpam-5398	266	21	means	mean	VERB
ejpam-5398	266	22	that	that	SCONJ
ejpam-5398	266	23	the	the	DET
ejpam-5398	266	24	stable	stable	ADJ
ejpam-5398	266	25	areas	area	NOUN
ejpam-5398	266	26	shrink	shrink	VERB
ejpam-5398	266	27	to	to	PART
ejpam-5398	266	28	account	account	VERB
ejpam-5398	266	29	for	for	ADP
ejpam-5398	266	30	the	the	DET
ejpam-5398	266	31	unstable	unstable	ADJ
ejpam-5398	266	32	areas	area	NOUN
ejpam-5398	266	33	.	.	PUNCT
ejpam-5398	267	1	the	the	DET
ejpam-5398	267	2	comparison	comparison	NOUN
ejpam-5398	267	3	of	of	ADP
ejpam-5398	267	4	fig	fig	NOUN
ejpam-5398	267	5	.	.	PUNCT
ejpam-5398	268	1	(	(	PUNCT
ejpam-5398	268	2	6	6	NUM
ejpam-5398	268	3	)	)	PUNCT
ejpam-5398	268	4	with	with	ADP
ejpam-5398	268	5	fig	fig	NOUN
ejpam-5398	268	6	.	.	PUNCT
ejpam-5398	269	1	(	(	PUNCT
ejpam-5398	269	2	7	7	NUM
ejpam-5398	269	3	)	)	PUNCT
ejpam-5398	269	4	,	,	PUNCT
ejpam-5398	269	5	shows	show	VERB
ejpam-5398	269	6	that	that	SCONJ
ejpam-5398	269	7	more	more	ADJ
ejpam-5398	269	8	deformation	deformation	NOUN
ejpam-5398	269	9	is	be	AUX
ejpam-5398	269	10	observed	observe	VERB
ejpam-5398	269	11	with	with	ADP
ejpam-5398	269	12	the	the	DET
ejpam-5398	269	13	increase	increase	NOUN
ejpam-5398	269	14	of	of	ADP
ejpam-5398	269	15	a	a	DET
ejpam-5398	269	16	and	and	CCONJ
ejpam-5398	269	17	b	b	NOUN
ejpam-5398	269	18	values	value	NOUN
ejpam-5398	269	19	.	.	PUNCT
ejpam-5398	270	1	the	the	DET
ejpam-5398	270	2	graphed	graph	VERB
ejpam-5398	270	3	areas	area	NOUN
ejpam-5398	270	4	in	in	ADP
ejpam-5398	270	5	the	the	DET
ejpam-5398	270	6	potions	potion	NOUN
ejpam-5398	270	7	of	of	ADP
ejpam-5398	270	8	fig	fig	NOUN
ejpam-5398	270	9	.	.	PUNCT
ejpam-5398	271	1	(	(	PUNCT
ejpam-5398	271	2	8)	8)	NUM
ejpam-5398	271	3	are	be	AUX
ejpam-5398	271	4	calculated	calculate	VERB
ejpam-5398	271	5	at	at	ADP
ejpam-5398	271	6	a	a	DET
ejpam-5398	271	7	=	=	SYM
ejpam-5398	271	8	b	b	NOUN
ejpam-5398	271	9	=	=	SYM
ejpam-5398	271	10	1	1	NUM
ejpam-5398	271	11	when	when	SCONJ
ejpam-5398	271	12	a	a	PRON
ejpam-5398	271	13	=	=	X
ejpam-5398	271	14	(	(	PUNCT
ejpam-5398	271	15	0.1	0.1	NUM
ejpam-5398	271	16	,	,	PUNCT
ejpam-5398	271	17	0.5	0.5	NUM
ejpam-5398	271	18	)	)	PUNCT
ejpam-5398	271	19	.	.	PUNCT
ejpam-5398	272	1	the	the	DET
ejpam-5398	272	2	increase	increase	NOUN
ejpam-5398	272	3	of	of	ADP
ejpam-5398	272	4	the	the	DET
ejpam-5398	272	5	values	value	NOUN
ejpam-5398	272	6	produces	produce	VERB
ejpam-5398	272	7	a	a	DET
ejpam-5398	272	8	decrease	decrease	NOUN
ejpam-5398	272	9	in	in	ADP
ejpam-5398	272	10	the	the	DET
ejpam-5398	272	11	stability	stability	NOUN
ejpam-5398	272	12	areas	area	NOUN
ejpam-5398	272	13	,	,	PUNCT
ejpam-5398	272	14	which	which	PRON
ejpam-5398	272	15	is	be	AUX
ejpam-5398	272	16	a.	a.	NOUN
ejpam-5398	272	17	a.	a.	NOUN
ejpam-5398	272	18	galal	galal	PROPN
ejpam-5398	272	19	et	et	PROPN
ejpam-5398	272	20	al	al	PROPN
ejpam-5398	272	21	.	.	PUNCT
ejpam-5398	272	22	/	/	SYM
ejpam-5398	272	23	eur	eur	PROPN
ejpam-5398	272	24	.	.	PUNCT
ejpam-5398	273	1	j.	j.	PROPN
ejpam-5398	273	2	pure	pure	PROPN
ejpam-5398	273	3	appl	appl	PROPN
ejpam-5398	273	4	.	.	PROPN
ejpam-5398	273	5	math	math	PROPN
ejpam-5398	273	6	,	,	PUNCT
ejpam-5398	273	7	17	17	NUM
ejpam-5398	273	8	(	(	PUNCT
ejpam-5398	273	9	4	4	NUM
ejpam-5398	273	10	)	)	PUNCT
ejpam-5398	273	11	(	(	PUNCT
ejpam-5398	273	12	2024	2024	NUM
ejpam-5398	273	13	)	)	PUNCT
ejpam-5398	273	14	,	,	PUNCT
ejpam-5398	273	15	2878	2878	NUM
ejpam-5398	273	16	-	-	SYM
ejpam-5398	273	17	2897	2897	NUM
ejpam-5398	273	18	2889	2889	NUM
ejpam-5398	273	19	figure	figure	NOUN
ejpam-5398	273	20	5	5	NUM
ejpam-5398	273	21	:	:	PUNCT
ejpam-5398	273	22	(	(	PUNCT
ejpam-5398	273	23	a	a	X
ejpam-5398	273	24	)	)	PUNCT
ejpam-5398	273	25	shows	show	VERB
ejpam-5398	273	26	curves	curve	NOUN
ejpam-5398	273	27	of	of	ADP
ejpam-5398	273	28	θ(t	θ(t	PROPN
ejpam-5398	273	29	)	)	PUNCT
ejpam-5398	273	30	at	at	ADP
ejpam-5398	273	31	different	different	ADJ
ejpam-5398	273	32	amounts	amount	NOUN
ejpam-5398	273	33	of	of	ADP
ejpam-5398	273	34	b	b	NOUN
ejpam-5398	273	35	,	,	PUNCT
ejpam-5398	273	36	and	and	CCONJ
ejpam-5398	273	37	(	(	PUNCT
ejpam-5398	273	38	b	b	NOUN
ejpam-5398	273	39	)	)	PUNCT
ejpam-5398	273	40	presents	present	VERB
ejpam-5398	273	41	the	the	DET
ejpam-5398	273	42	phase	phase	NOUN
ejpam-5398	273	43	plane	plane	NOUN
ejpam-5398	273	44	paths	path	NOUN
ejpam-5398	273	45	in	in	ADP
ejpam-5398	273	46	(	(	PUNCT
ejpam-5398	273	47	a	a	NOUN
ejpam-5398	273	48	)	)	PUNCT
ejpam-5398	273	49	.	.	PUNCT
ejpam-5398	274	1	figure	figure	VERB
ejpam-5398	274	2	6	6	NUM
ejpam-5398	274	3	:	:	PUNCT
ejpam-5398	274	4	show	show	VERB
ejpam-5398	274	5	the	the	DET
ejpam-5398	274	6	stability	stability	NOUN
ejpam-5398	274	7	/	/	SYM
ejpam-5398	274	8	instability	instability	NOUN
ejpam-5398	274	9	areas	area	NOUN
ejpam-5398	274	10	in	in	ADP
ejpam-5398	274	11	the	the	DET
ejpam-5398	274	12	plane	plane	NOUN
ejpam-5398	274	13	(	(	PUNCT
ejpam-5398	274	14	τ	τ	PROPN
ejpam-5398	274	15	−	−	PROPN
ejpam-5398	274	16	ω	ω	PROPN
ejpam-5398	274	17	)	)	PUNCT
ejpam-5398	274	18	at	at	ADP
ejpam-5398	274	19	a	a	DET
ejpam-5398	274	20	=	=	SYM
ejpam-5398	274	21	b	b	NOUN
ejpam-5398	274	22	=	=	NOUN
ejpam-5398	274	23	0.01	0.01	NUM
ejpam-5398	274	24	when	when	SCONJ
ejpam-5398	274	25	(	(	PUNCT
ejpam-5398	274	26	a	a	X
ejpam-5398	274	27	)	)	PUNCT
ejpam-5398	274	28	a	a	PRON
ejpam-5398	274	29	=	=	SYM
ejpam-5398	274	30	0.4	0.4	NUM
ejpam-5398	274	31	,	,	PUNCT
ejpam-5398	274	32	(	(	PUNCT
ejpam-5398	274	33	b	b	X
ejpam-5398	274	34	)	)	PUNCT
ejpam-5398	274	35	a	a	DET
ejpam-5398	274	36	=	=	NOUN
ejpam-5398	274	37	0.7	0.7	NUM
ejpam-5398	274	38	,	,	PUNCT
ejpam-5398	274	39	and	and	CCONJ
ejpam-5398	274	40	(	(	PUNCT
ejpam-5398	274	41	c	c	X
ejpam-5398	274	42	)	)	PUNCT
ejpam-5398	274	43	a	a	DET
ejpam-5398	274	44	=	=	ADJ
ejpam-5398	274	45	1	1	X
ejpam-5398	274	46	.	.	PUNCT
ejpam-5398	275	1	the	the	DET
ejpam-5398	275	2	reason	reason	NOUN
ejpam-5398	275	3	backs	back	VERB
ejpam-5398	275	4	to	to	ADP
ejpam-5398	275	5	the	the	DET
ejpam-5398	275	6	mathematical	mathematical	ADJ
ejpam-5398	275	7	form	form	NOUN
ejpam-5398	275	8	of	of	ADP
ejpam-5398	275	9	the	the	DET
ejpam-5398	275	10	first	first	ADJ
ejpam-5398	275	11	inequality	inequality	NOUN
ejpam-5398	275	12	in	in	ADP
ejpam-5398	275	13	eq	eq	ADP
ejpam-5398	275	14	.	.	PUNCT
ejpam-5398	276	1	(	(	PUNCT
ejpam-5398	276	2	15	15	NUM
ejpam-5398	276	3	)	)	PUNCT
ejpam-5398	276	4	,	,	PUNCT
ejpam-5398	276	5	where	where	SCONJ
ejpam-5398	276	6	the	the	DET
ejpam-5398	276	7	terms	term	NOUN
ejpam-5398	276	8	conclude	conclude	VERB
ejpam-5398	276	9	the	the	DET
ejpam-5398	276	10	parameter	parameter	NOUN
ejpam-5398	276	11	a	a	PRON
ejpam-5398	276	12	in	in	ADP
ejpam-5398	276	13	eq	eq	ADP
ejpam-5398	276	14	.	.	PUNCT
ejpam-5398	277	1	(	(	PUNCT
ejpam-5398	277	2	15	15	NUM
ejpam-5398	277	3	)	)	PUNCT
ejpam-5398	277	4	have	have	VERB
ejpam-5398	277	5	negative	negative	ADJ
ejpam-5398	277	6	signs	sign	NOUN
ejpam-5398	277	7	.	.	PUNCT
ejpam-5398	278	1	the	the	DET
ejpam-5398	278	2	inspection	inspection	NOUN
ejpam-5398	278	3	in	in	ADP
ejpam-5398	278	4	the	the	DET
ejpam-5398	278	5	drawn	draw	VERB
ejpam-5398	278	6	areas	area	NOUN
ejpam-5398	278	7	in	in	ADP
ejpam-5398	278	8	fig	fig	NOUN
ejpam-5398	278	9	.	.	PUNCT
ejpam-5398	279	1	(	(	PUNCT
ejpam-5398	279	2	9	9	X
ejpam-5398	279	3	)	)	PUNCT
ejpam-5398	279	4	shows	show	VERB
ejpam-5398	279	5	that	that	SCONJ
ejpam-5398	279	6	they	they	PRON
ejpam-5398	279	7	are	be	AUX
ejpam-5398	279	8	graphed	graph	VERB
ejpam-5398	279	9	at	at	ADP
ejpam-5398	279	10	a	a	DET
ejpam-5398	279	11	=	=	NOUN
ejpam-5398	279	12	a	a	PRON
ejpam-5398	279	13	=	=	SYM
ejpam-5398	279	14	1	1	NUM
ejpam-5398	279	15	when	when	SCONJ
ejpam-5398	279	16	b	b	X
ejpam-5398	279	17	=	=	SYM
ejpam-5398	279	18	(	(	PUNCT
ejpam-5398	279	19	0.01	0.01	NUM
ejpam-5398	279	20	,	,	PUNCT
ejpam-5398	279	21	0.1	0.1	NUM
ejpam-5398	279	22	)	)	PUNCT
ejpam-5398	279	23	.	.	PUNCT
ejpam-5398	280	1	a	a	DET
ejpam-5398	280	2	closer	close	ADJ
ejpam-5398	280	3	look	look	NOUN
ejpam-5398	280	4	at	at	ADP
ejpam-5398	280	5	the	the	DET
ejpam-5398	280	6	fig	fig	NOUN
ejpam-5398	280	7	.	.	PUNCT
ejpam-5398	281	1	(	(	PUNCT
ejpam-5398	281	2	9a	9a	NUM
ejpam-5398	281	3	)	)	PUNCT
ejpam-5398	281	4	and	and	CCONJ
ejpam-5398	281	5	fig	fig	NOUN
ejpam-5398	281	6	.	.	PUNCT
ejpam-5398	282	1	(	(	PUNCT
ejpam-5398	282	2	9b	9b	NOUN
ejpam-5398	282	3	)	)	PUNCT
ejpam-5398	282	4	,	,	PUNCT
ejpam-5398	282	5	shows	show	VERB
ejpam-5398	282	6	the	the	DET
ejpam-5398	282	7	positive	positive	ADJ
ejpam-5398	282	8	influence	influence	NOUN
ejpam-5398	282	9	of	of	ADP
ejpam-5398	282	10	the	the	DET
ejpam-5398	282	11	b	b	PROPN
ejpam-5398	282	12	values	value	NOUN
ejpam-5398	282	13	,	,	PUNCT
ejpam-5398	282	14	i.e.	i.e.	X
ejpam-5398	282	15	when	when	SCONJ
ejpam-5398	282	16	the	the	DET
ejpam-5398	282	17	values	value	NOUN
ejpam-5398	282	18	of	of	ADP
ejpam-5398	282	19	b	b	NOUN
ejpam-5398	282	20	grows	grow	NOUN
ejpam-5398	282	21	,	,	PUNCT
ejpam-5398	282	22	the	the	DET
ejpam-5398	282	23	stability	stability	NOUN
ejpam-5398	282	24	areas	area	NOUN
ejpam-5398	282	25	increases	increase	VERB
ejpam-5398	282	26	.	.	PUNCT
ejpam-5398	283	1	we	we	PRON
ejpam-5398	283	2	find	find	VERB
ejpam-5398	283	3	that	that	SCONJ
ejpam-5398	283	4	the	the	DET
ejpam-5398	283	5	reason	reason	NOUN
ejpam-5398	283	6	behind	behind	ADP
ejpam-5398	283	7	this	this	DET
ejpam-5398	283	8	increase	increase	NOUN
ejpam-5398	283	9	is	be	AUX
ejpam-5398	283	10	that	that	SCONJ
ejpam-5398	283	11	the	the	DET
ejpam-5398	283	12	term	term	NOUN
ejpam-5398	283	13	containing	contain	VERB
ejpam-5398	283	14	the	the	DET
ejpam-5398	283	15	parameter	parameter	NOUN
ejpam-5398	283	16	b	b	PROPN
ejpam-5398	283	17	in	in	ADP
ejpam-5398	283	18	the	the	DET
ejpam-5398	283	19	first	first	ADJ
ejpam-5398	283	20	inequalities	inequality	NOUN
ejpam-5398	283	21	eq	eq	ADP
ejpam-5398	283	22	.	.	PUNCT
ejpam-5398	284	1	(	(	PUNCT
ejpam-5398	284	2	15	15	NUM
ejpam-5398	284	3	)	)	PUNCT
ejpam-5398	284	4	has	have	VERB
ejpam-5398	284	5	a	a	DET
ejpam-5398	284	6	positive	positive	ADJ
ejpam-5398	284	7	sign	sign	NOUN
ejpam-5398	284	8	.	.	PUNCT
ejpam-5398	285	1	referring	refer	VERB
ejpam-5398	285	2	to	to	ADP
ejpam-5398	285	3	the	the	DET
ejpam-5398	285	4	previous	previous	ADJ
ejpam-5398	285	5	analysis	analysis	NOUN
ejpam-5398	285	6	,	,	PUNCT
ejpam-5398	285	7	one	one	PRON
ejpam-5398	285	8	can	can	AUX
ejpam-5398	285	9	say	say	VERB
ejpam-5398	285	10	that	that	SCONJ
ejpam-5398	285	11	periodic	periodic	ADJ
ejpam-5398	285	12	solutions	solution	NOUN
ejpam-5398	285	13	provide	provide	VERB
ejpam-5398	285	14	insights	insight	NOUN
ejpam-5398	285	15	into	into	ADP
ejpam-5398	285	16	the	the	DET
ejpam-5398	285	17	regular	regular	ADJ
ejpam-5398	285	18	and	and	CCONJ
ejpam-5398	285	19	predictable	predictable	ADJ
ejpam-5398	285	20	behavior	behavior	NOUN
ejpam-5398	285	21	of	of	ADP
ejpam-5398	285	22	systems	system	NOUN
ejpam-5398	285	23	.	.	PUNCT
ejpam-5398	286	1	the	the	DET
ejpam-5398	286	2	diagrams	diagram	NOUN
ejpam-5398	286	3	of	of	ADP
ejpam-5398	286	4	phase	phase	NOUN
ejpam-5398	286	5	plane	plane	NOUN
ejpam-5398	286	6	offer	offer	VERB
ejpam-5398	286	7	a	a	DET
ejpam-5398	286	8	visual	visual	ADJ
ejpam-5398	286	9	and	and	CCONJ
ejpam-5398	286	10	qualitative	qualitative	ADJ
ejpam-5398	286	11	understanding	understanding	NOUN
ejpam-5398	286	12	of	of	ADP
ejpam-5398	286	13	system	system	NOUN
ejpam-5398	286	14	dynamics	dynamic	NOUN
ejpam-5398	286	15	and	and	CCONJ
ejpam-5398	286	16	stability	stability	NOUN
ejpam-5398	286	17	,	,	PUNCT
ejpam-5398	286	18	while	while	SCONJ
ejpam-5398	286	19	stability	stability	NOUN
ejpam-5398	286	20	areas	area	NOUN
ejpam-5398	286	21	are	be	AUX
ejpam-5398	286	22	crucial	crucial	ADJ
ejpam-5398	286	23	for	for	ADP
ejpam-5398	286	24	ensuring	ensure	VERB
ejpam-5398	286	25	systems	system	NOUN
ejpam-5398	286	26	remain	remain	VERB
ejpam-5398	286	27	stable	stable	ADJ
ejpam-5398	286	28	and	and	CCONJ
ejpam-5398	286	29	operate	operate	VERB
ejpam-5398	286	30	safely	safely	ADV
ejpam-5398	286	31	under	under	ADP
ejpam-5398	286	32	different	different	ADJ
ejpam-5398	286	33	conditions	condition	NOUN
ejpam-5398	286	34	.	.	PUNCT
ejpam-5398	287	1	a.	a.	NOUN
ejpam-5398	287	2	a.	a.	PROPN
ejpam-5398	287	3	galal	galal	PROPN
ejpam-5398	287	4	et	et	PROPN
ejpam-5398	287	5	al	al	PROPN
ejpam-5398	287	6	.	.	PUNCT
ejpam-5398	287	7	/	/	SYM
ejpam-5398	287	8	eur	eur	PROPN
ejpam-5398	287	9	.	.	PUNCT
ejpam-5398	288	1	j.	j.	PROPN
ejpam-5398	288	2	pure	pure	PROPN
ejpam-5398	288	3	appl	appl	PROPN
ejpam-5398	288	4	.	.	PROPN
ejpam-5398	288	5	math	math	PROPN
ejpam-5398	288	6	,	,	PUNCT
ejpam-5398	288	7	17	17	NUM
ejpam-5398	288	8	(	(	PUNCT
ejpam-5398	288	9	4	4	NUM
ejpam-5398	288	10	)	)	PUNCT
ejpam-5398	288	11	(	(	PUNCT
ejpam-5398	288	12	2024	2024	NUM
ejpam-5398	288	13	)	)	PUNCT
ejpam-5398	288	14	,	,	PUNCT
ejpam-5398	288	15	2878	2878	NUM
ejpam-5398	288	16	-	-	SYM
ejpam-5398	288	17	2897	2897	NUM
ejpam-5398	288	18	2890	2890	NUM
ejpam-5398	288	19	figure	figure	NOUN
ejpam-5398	288	20	7	7	NUM
ejpam-5398	288	21	:	:	PUNCT
ejpam-5398	288	22	presents	present	VERB
ejpam-5398	288	23	the	the	DET
ejpam-5398	288	24	stability	stability	NOUN
ejpam-5398	288	25	/	/	SYM
ejpam-5398	288	26	instability	instability	NOUN
ejpam-5398	288	27	zones	zone	NOUN
ejpam-5398	288	28	in	in	ADP
ejpam-5398	288	29	the	the	DET
ejpam-5398	288	30	plane	plane	NOUN
ejpam-5398	288	31	(	(	PUNCT
ejpam-5398	288	32	τ	τ	PROPN
ejpam-5398	288	33	−	−	PROPN
ejpam-5398	288	34	ω	ω	PROPN
ejpam-5398	288	35	)	)	PUNCT
ejpam-5398	288	36	at	at	ADP
ejpam-5398	288	37	a	a	DET
ejpam-5398	288	38	=	=	SYM
ejpam-5398	288	39	b	b	NOUN
ejpam-5398	288	40	=	=	SYM
ejpam-5398	288	41	1	1	NUM
ejpam-5398	288	42	when	when	SCONJ
ejpam-5398	288	43	(	(	PUNCT
ejpam-5398	288	44	a	a	X
ejpam-5398	288	45	)	)	PUNCT
ejpam-5398	288	46	a	a	DET
ejpam-5398	288	47	=	=	SYM
ejpam-5398	288	48	0.4	0.4	NUM
ejpam-5398	288	49	,	,	PUNCT
ejpam-5398	288	50	and	and	CCONJ
ejpam-5398	288	51	(	(	PUNCT
ejpam-5398	288	52	b	b	X
ejpam-5398	288	53	)	)	PUNCT
ejpam-5398	288	54	a	a	DET
ejpam-5398	288	55	=	=	NOUN
ejpam-5398	288	56	0.7	0.7	NUM
ejpam-5398	288	57	.	.	NOUN
ejpam-5398	288	58	4	4	NUM
ejpam-5398	288	59	.	.	X
ejpam-5398	289	1	evaluation	evaluation	NOUN
ejpam-5398	289	2	of	of	ADP
ejpam-5398	289	3	the	the	DET
ejpam-5398	289	4	impact	impact	NOUN
ejpam-5398	289	5	of	of	ADP
ejpam-5398	289	6	outcomes	outcome	NOUN
ejpam-5398	289	7	assessing	assess	VERB
ejpam-5398	289	8	the	the	DET
ejpam-5398	289	9	impact	impact	NOUN
ejpam-5398	289	10	of	of	ADP
ejpam-5398	289	11	solving	solve	VERB
ejpam-5398	289	12	dynamical	dynamical	ADJ
ejpam-5398	289	13	systems	system	NOUN
ejpam-5398	289	14	with	with	ADP
ejpam-5398	289	15	periodic	periodic	ADJ
ejpam-5398	289	16	solutions	solution	NOUN
ejpam-5398	289	17	requires	require	VERB
ejpam-5398	289	18	a	a	DET
ejpam-5398	289	19	nuanced	nuanced	ADJ
ejpam-5398	289	20	understanding	understanding	NOUN
ejpam-5398	289	21	of	of	ADP
ejpam-5398	289	22	both	both	CCONJ
ejpam-5398	289	23	the	the	DET
ejpam-5398	289	24	theoretical	theoretical	ADJ
ejpam-5398	289	25	aspects	aspect	NOUN
ejpam-5398	289	26	and	and	CCONJ
ejpam-5398	289	27	practical	practical	ADJ
ejpam-5398	289	28	implications	implication	NOUN
ejpam-5398	289	29	.	.	PUNCT
ejpam-5398	290	1	the	the	DET
ejpam-5398	290	2	periodic	periodic	ADJ
ejpam-5398	290	3	nature	nature	NOUN
ejpam-5398	290	4	of	of	ADP
ejpam-5398	290	5	the	the	DET
ejpam-5398	290	6	solution	solution	NOUN
ejpam-5398	290	7	implies	imply	VERB
ejpam-5398	290	8	that	that	SCONJ
ejpam-5398	290	9	the	the	DET
ejpam-5398	290	10	system	system	NOUN
ejpam-5398	290	11	exhibits	exhibit	VERB
ejpam-5398	290	12	repeating	repeat	VERB
ejpam-5398	290	13	behavior	behavior	NOUN
ejpam-5398	290	14	over	over	ADP
ejpam-5398	290	15	time	time	NOUN
ejpam-5398	290	16	,	,	PUNCT
ejpam-5398	290	17	which	which	PRON
ejpam-5398	290	18	can	can	AUX
ejpam-5398	290	19	have	have	VERB
ejpam-5398	290	20	distinct	distinct	ADJ
ejpam-5398	290	21	short	short	ADJ
ejpam-5398	290	22	-	-	PUNCT
ejpam-5398	290	23	term	term	NOUN
ejpam-5398	290	24	and	and	CCONJ
ejpam-5398	290	25	long	long	ADJ
ejpam-5398	290	26	-	-	PUNCT
ejpam-5398	290	27	term	term	NOUN
ejpam-5398	290	28	effects	effect	NOUN
ejpam-5398	290	29	[	[	X
ejpam-5398	290	30	12	12	NUM
ejpam-5398	290	31	,	,	PUNCT
ejpam-5398	290	32	39	39	NUM
ejpam-5398	290	33	]	]	PUNCT
ejpam-5398	290	34	.	.	PUNCT
ejpam-5398	291	1	below	below	ADV
ejpam-5398	291	2	is	be	AUX
ejpam-5398	291	3	a	a	DET
ejpam-5398	291	4	comprehensive	comprehensive	ADJ
ejpam-5398	291	5	analysis	analysis	NOUN
ejpam-5398	291	6	of	of	ADP
ejpam-5398	291	7	the	the	DET
ejpam-5398	291	8	impact	impact	NOUN
ejpam-5398	291	9	assessment	assessment	NOUN
ejpam-5398	291	10	.	.	PUNCT
ejpam-5398	292	1	(	(	PUNCT
ejpam-5398	292	2	i	i	NOUN
ejpam-5398	292	3	)	)	PUNCT
ejpam-5398	292	4	short	short	ADJ
ejpam-5398	292	5	-	-	PUNCT
ejpam-5398	292	6	term	term	NOUN
ejpam-5398	292	7	effects	effect	NOUN
ejpam-5398	292	8	:	:	PUNCT
ejpam-5398	292	9	solving	solve	VERB
ejpam-5398	292	10	a	a	DET
ejpam-5398	292	11	dynamical	dynamical	ADJ
ejpam-5398	292	12	system	system	NOUN
ejpam-5398	292	13	with	with	ADP
ejpam-5398	292	14	periodic	periodic	ADJ
ejpam-5398	292	15	solutions	solution	NOUN
ejpam-5398	292	16	allows	allow	VERB
ejpam-5398	292	17	for	for	ADP
ejpam-5398	292	18	an	an	DET
ejpam-5398	292	19	immediate	immediate	ADJ
ejpam-5398	292	20	assessment	assessment	NOUN
ejpam-5398	292	21	of	of	ADP
ejpam-5398	292	22	system	system	NOUN
ejpam-5398	292	23	stability	stability	NOUN
ejpam-5398	292	24	.	.	PUNCT
ejpam-5398	293	1	in	in	ADP
ejpam-5398	293	2	the	the	DET
ejpam-5398	293	3	short	short	ADJ
ejpam-5398	293	4	term	term	NOUN
ejpam-5398	293	5	,	,	PUNCT
ejpam-5398	293	6	it	it	PRON
ejpam-5398	293	7	becomes	become	VERB
ejpam-5398	293	8	possible	possible	ADJ
ejpam-5398	293	9	to	to	PART
ejpam-5398	293	10	determine	determine	VERB
ejpam-5398	293	11	whether	whether	SCONJ
ejpam-5398	293	12	the	the	DET
ejpam-5398	293	13	system	system	NOUN
ejpam-5398	293	14	will	will	AUX
ejpam-5398	293	15	remain	remain	VERB
ejpam-5398	293	16	in	in	ADP
ejpam-5398	293	17	a	a	DET
ejpam-5398	293	18	stable	stable	ADJ
ejpam-5398	293	19	periodic	periodic	ADJ
ejpam-5398	293	20	orbit	orbit	NOUN
ejpam-5398	293	21	or	or	CCONJ
ejpam-5398	293	22	if	if	SCONJ
ejpam-5398	293	23	there	there	PRON
ejpam-5398	293	24	is	be	VERB
ejpam-5398	293	25	a	a	DET
ejpam-5398	293	26	risk	risk	NOUN
ejpam-5398	293	27	of	of	ADP
ejpam-5398	293	28	divergence	divergence	NOUN
ejpam-5398	293	29	.	.	PUNCT
ejpam-5398	294	1	this	this	PRON
ejpam-5398	294	2	is	be	AUX
ejpam-5398	294	3	crucial	crucial	ADJ
ejpam-5398	294	4	for	for	ADP
ejpam-5398	294	5	predicting	predict	VERB
ejpam-5398	294	6	short	short	ADJ
ejpam-5398	294	7	-	-	PUNCT
ejpam-5398	294	8	term	term	NOUN
ejpam-5398	294	9	behavior	behavior	NOUN
ejpam-5398	294	10	,	,	PUNCT
ejpam-5398	294	11	particularly	particularly	ADV
ejpam-5398	294	12	in	in	ADP
ejpam-5398	294	13	systems	system	NOUN
ejpam-5398	294	14	where	where	SCONJ
ejpam-5398	294	15	stability	stability	NOUN
ejpam-5398	294	16	is	be	AUX
ejpam-5398	294	17	paramount	paramount	ADJ
ejpam-5398	294	18	.	.	PUNCT
ejpam-5398	295	1	in	in	ADP
ejpam-5398	295	2	systems	system	NOUN
ejpam-5398	295	3	where	where	SCONJ
ejpam-5398	295	4	periodic	periodic	ADJ
ejpam-5398	295	5	motion	motion	NOUN
ejpam-5398	295	6	is	be	AUX
ejpam-5398	295	7	a	a	DET
ejpam-5398	295	8	factor	factor	NOUN
ejpam-5398	295	9	,	,	PUNCT
ejpam-5398	295	10	short	short	ADJ
ejpam-5398	295	11	-	-	PUNCT
ejpam-5398	295	12	term	term	NOUN
ejpam-5398	295	13	solutions	solution	NOUN
ejpam-5398	295	14	can	can	AUX
ejpam-5398	295	15	lead	lead	VERB
ejpam-5398	295	16	to	to	ADP
ejpam-5398	295	17	immediate	immediate	ADJ
ejpam-5398	295	18	gains	gain	NOUN
ejpam-5398	295	19	in	in	ADP
ejpam-5398	295	20	energy	energy	NOUN
ejpam-5398	295	21	efficiency	efficiency	NOUN
ejpam-5398	295	22	by	by	ADP
ejpam-5398	295	23	optimizing	optimize	VERB
ejpam-5398	295	24	the	the	DET
ejpam-5398	295	25	periodic	periodic	ADJ
ejpam-5398	295	26	cycles	cycle	NOUN
ejpam-5398	295	27	.	.	PUNCT
ejpam-5398	296	1	for	for	ADP
ejpam-5398	296	2	instance	instance	NOUN
ejpam-5398	296	3	,	,	PUNCT
ejpam-5398	296	4	in	in	ADP
ejpam-5398	296	5	resonancebased	resonancebase	VERB
ejpam-5398	296	6	systems	system	NOUN
ejpam-5398	296	7	,	,	PUNCT
ejpam-5398	296	8	ensuring	ensure	VERB
ejpam-5398	296	9	that	that	SCONJ
ejpam-5398	296	10	the	the	DET
ejpam-5398	296	11	system	system	NOUN
ejpam-5398	296	12	operates	operate	VERB
ejpam-5398	296	13	at	at	ADP
ejpam-5398	296	14	or	or	CCONJ
ejpam-5398	296	15	near	near	ADP
ejpam-5398	296	16	resonance	resonance	NOUN
ejpam-5398	296	17	can	can	AUX
ejpam-5398	296	18	minimize	minimize	VERB
ejpam-5398	296	19	energy	energy	NOUN
ejpam-5398	296	20	losses	loss	NOUN
ejpam-5398	296	21	.	.	PUNCT
ejpam-5398	297	1	(	(	PUNCT
ejpam-5398	297	2	ii	ii	NOUN
ejpam-5398	297	3	)	)	PUNCT
ejpam-5398	297	4	long	long	ADJ
ejpam-5398	297	5	-	-	PUNCT
ejpam-5398	297	6	term	term	NOUN
ejpam-5398	297	7	effects	effect	NOUN
ejpam-5398	297	8	:	:	PUNCT
ejpam-5398	297	9	periodic	periodic	ADJ
ejpam-5398	297	10	solutions	solution	NOUN
ejpam-5398	297	11	allow	allow	VERB
ejpam-5398	297	12	for	for	ADP
ejpam-5398	297	13	better	well	ADJ
ejpam-5398	297	14	prediction	prediction	NOUN
ejpam-5398	297	15	of	of	ADP
ejpam-5398	297	16	long	long	ADJ
ejpam-5398	297	17	-	-	PUNCT
ejpam-5398	297	18	term	term	NOUN
ejpam-5398	297	19	behavior	behavior	NOUN
ejpam-5398	297	20	,	,	PUNCT
ejpam-5398	297	21	including	include	VERB
ejpam-5398	297	22	the	the	DET
ejpam-5398	297	23	identification	identification	NOUN
ejpam-5398	297	24	of	of	ADP
ejpam-5398	297	25	potential	potential	ADJ
ejpam-5398	297	26	failure	failure	NOUN
ejpam-5398	297	27	points	point	NOUN
ejpam-5398	297	28	due	due	ADP
ejpam-5398	297	29	to	to	ADP
ejpam-5398	297	30	fatigue	fatigue	NOUN
ejpam-5398	297	31	in	in	ADP
ejpam-5398	297	32	mechanical	mechanical	ADJ
ejpam-5398	297	33	systems	system	NOUN
ejpam-5398	297	34	or	or	CCONJ
ejpam-5398	297	35	wear	wear	VERB
ejpam-5398	297	36	and	and	CCONJ
ejpam-5398	297	37	tear	tear	NOUN
ejpam-5398	297	38	in	in	ADP
ejpam-5398	297	39	repetitive	repetitive	ADJ
ejpam-5398	297	40	processes	process	NOUN
ejpam-5398	297	41	.	.	PUNCT
ejpam-5398	298	1	once	once	ADV
ejpam-5398	298	2	a	a	DET
ejpam-5398	298	3	periodic	periodic	ADJ
ejpam-5398	298	4	solution	solution	NOUN
ejpam-5398	298	5	is	be	AUX
ejpam-5398	298	6	established	establish	VERB
ejpam-5398	298	7	,	,	PUNCT
ejpam-5398	298	8	long	long	ADJ
ejpam-5398	298	9	-	-	PUNCT
ejpam-5398	298	10	term	term	NOUN
ejpam-5398	298	11	optimization	optimization	NOUN
ejpam-5398	298	12	strategies	strategy	NOUN
ejpam-5398	298	13	can	can	AUX
ejpam-5398	298	14	be	be	AUX
ejpam-5398	298	15	employed	employ	VERB
ejpam-5398	298	16	to	to	ADP
ejpam-5398	298	17	fine	fine	ADJ
ejpam-5398	298	18	-	-	PUNCT
ejpam-5398	298	19	tune	tune	NOUN
ejpam-5398	298	20	system	system	NOUN
ejpam-5398	298	21	performance	performance	NOUN
ejpam-5398	298	22	.	.	PUNCT
ejpam-5398	299	1	this	this	PRON
ejpam-5398	299	2	could	could	AUX
ejpam-5398	299	3	involve	involve	VERB
ejpam-5398	299	4	adjusting	adjust	VERB
ejpam-5398	299	5	system	system	NOUN
ejpam-5398	299	6	parameters	parameter	NOUN
ejpam-5398	299	7	to	to	PART
ejpam-5398	299	8	improve	improve	VERB
ejpam-5398	299	9	overall	overall	ADJ
ejpam-5398	299	10	system	system	NOUN
ejpam-5398	299	11	performance	performance	NOUN
ejpam-5398	299	12	.	.	PUNCT
ejpam-5398	300	1	over	over	ADP
ejpam-5398	300	2	time	time	NOUN
ejpam-5398	300	3	,	,	PUNCT
ejpam-5398	300	4	systems	system	NOUN
ejpam-5398	300	5	may	may	AUX
ejpam-5398	300	6	need	need	VERB
ejpam-5398	300	7	to	to	PART
ejpam-5398	300	8	adapt	adapt	VERB
ejpam-5398	300	9	to	to	ADP
ejpam-5398	300	10	changing	change	VERB
ejpam-5398	300	11	conditions	condition	NOUN
ejpam-5398	300	12	,	,	PUNCT
ejpam-5398	300	13	such	such	ADJ
ejpam-5398	300	14	as	as	ADP
ejpam-5398	300	15	varying	vary	VERB
ejpam-5398	300	16	external	external	ADJ
ejpam-5398	300	17	forces	force	NOUN
ejpam-5398	300	18	.	.	PUNCT
ejpam-5398	301	1	the	the	DET
ejpam-5398	301	2	periodic	periodic	ADJ
ejpam-5398	301	3	nature	nature	NOUN
ejpam-5398	301	4	of	of	ADP
ejpam-5398	301	5	the	the	DET
ejpam-5398	301	6	solution	solution	NOUN
ejpam-5398	301	7	can	can	AUX
ejpam-5398	301	8	guide	guide	VERB
ejpam-5398	301	9	the	the	DET
ejpam-5398	301	10	adaptation	adaptation	NOUN
ejpam-5398	301	11	process	process	NOUN
ejpam-5398	301	12	,	,	PUNCT
ejpam-5398	301	13	ensuring	ensure	VERB
ejpam-5398	301	14	that	that	SCONJ
ejpam-5398	301	15	the	the	DET
ejpam-5398	301	16	system	system	NOUN
ejpam-5398	301	17	remains	remain	VERB
ejpam-5398	301	18	in	in	ADP
ejpam-5398	301	19	a	a	DET
ejpam-5398	301	20	desirable	desirable	ADJ
ejpam-5398	301	21	state	state	NOUN
ejpam-5398	301	22	despite	despite	SCONJ
ejpam-5398	301	23	these	these	DET
ejpam-5398	301	24	changes	change	NOUN
ejpam-5398	301	25	.	.	PUNCT
ejpam-5398	302	1	a.	a.	NOUN
ejpam-5398	302	2	a.	a.	PROPN
ejpam-5398	302	3	galal	galal	PROPN
ejpam-5398	302	4	et	et	PROPN
ejpam-5398	302	5	al	al	PROPN
ejpam-5398	302	6	.	.	PUNCT
ejpam-5398	302	7	/	/	SYM
ejpam-5398	302	8	eur	eur	PROPN
ejpam-5398	302	9	.	.	PUNCT
ejpam-5398	303	1	j.	j.	PROPN
ejpam-5398	303	2	pure	pure	PROPN
ejpam-5398	303	3	appl	appl	PROPN
ejpam-5398	303	4	.	.	PROPN
ejpam-5398	303	5	math	math	PROPN
ejpam-5398	303	6	,	,	PUNCT
ejpam-5398	303	7	17	17	NUM
ejpam-5398	303	8	(	(	PUNCT
ejpam-5398	303	9	4	4	NUM
ejpam-5398	303	10	)	)	PUNCT
ejpam-5398	303	11	(	(	PUNCT
ejpam-5398	303	12	2024	2024	NUM
ejpam-5398	303	13	)	)	PUNCT
ejpam-5398	303	14	,	,	PUNCT
ejpam-5398	303	15	2878	2878	NUM
ejpam-5398	303	16	-	-	SYM
ejpam-5398	303	17	2897	2897	NUM
ejpam-5398	303	18	2891	2891	NUM
ejpam-5398	303	19	figure	figure	NOUN
ejpam-5398	303	20	8	8	NUM
ejpam-5398	303	21	:	:	PUNCT
ejpam-5398	303	22	presents	present	VERB
ejpam-5398	303	23	the	the	DET
ejpam-5398	303	24	time	time	NOUN
ejpam-5398	303	25	variation	variation	NOUN
ejpam-5398	303	26	ofω	ofω	NOUN
ejpam-5398	303	27	at	at	ADP
ejpam-5398	303	28	a	a	DET
ejpam-5398	303	29	=	=	SYM
ejpam-5398	303	30	b	b	NOUN
ejpam-5398	303	31	=	=	SYM
ejpam-5398	303	32	1	1	NUM
ejpam-5398	303	33	when	when	SCONJ
ejpam-5398	303	34	:	:	PUNCT
ejpam-5398	303	35	(	(	PUNCT
ejpam-5398	303	36	a)a	a)a	X
ejpam-5398	303	37	=	=	SYM
ejpam-5398	303	38	0.1	0.1	NUM
ejpam-5398	303	39	,	,	PUNCT
ejpam-5398	303	40	and	and	CCONJ
ejpam-5398	303	41	(	(	PUNCT
ejpam-5398	303	42	b	b	X
ejpam-5398	303	43	)	)	PUNCT
ejpam-5398	303	44	a	a	DET
ejpam-5398	303	45	=	=	SYM
ejpam-5398	303	46	0.5	0.5	NUM
ejpam-5398	303	47	.	.	NOUN
ejpam-5398	303	48	5	5	NUM
ejpam-5398	303	49	.	.	X
ejpam-5398	303	50	concluding	conclude	VERB
ejpam-5398	303	51	remarks	remark	VERB
ejpam-5398	303	52	the	the	DET
ejpam-5398	303	53	work	work	NOUN
ejpam-5398	303	54	investigates	investigate	VERB
ejpam-5398	303	55	the	the	DET
ejpam-5398	303	56	stability	stability	NOUN
ejpam-5398	303	57	of	of	ADP
ejpam-5398	303	58	a	a	DET
ejpam-5398	303	59	rolling	rolling	ADJ
ejpam-5398	303	60	rigid	rigid	ADJ
ejpam-5398	303	61	rod	rod	NOUN
ejpam-5398	303	62	with	with	ADP
ejpam-5398	303	63	square	square	ADJ
ejpam-5398	303	64	td	td	NOUN
ejpam-5398	303	65	position	position	NOUN
ejpam-5398	303	66	as	as	ADV
ejpam-5398	303	67	well	well	ADV
ejpam-5398	303	68	as	as	ADP
ejpam-5398	303	69	velocity	velocity	NOUN
ejpam-5398	303	70	.	.	PUNCT
ejpam-5398	304	1	the	the	DET
ejpam-5398	304	2	td	td	NOUN
ejpam-5398	304	3	and	and	CCONJ
ejpam-5398	304	4	other	other	ADJ
ejpam-5398	304	5	influential	influential	ADJ
ejpam-5398	304	6	aspects	aspect	NOUN
ejpam-5398	304	7	are	be	AUX
ejpam-5398	304	8	used	use	VERB
ejpam-5398	304	9	to	to	PART
ejpam-5398	304	10	evaluate	evaluate	VERB
ejpam-5398	304	11	the	the	DET
ejpam-5398	304	12	approximate	approximate	ADJ
ejpam-5398	304	13	analytical	analytical	ADJ
ejpam-5398	304	14	outcome	outcome	NOUN
ejpam-5398	304	15	technique	technique	NOUN
ejpam-5398	304	16	.	.	PUNCT
ejpam-5398	305	1	the	the	DET
ejpam-5398	305	2	investigation	investigation	NOUN
ejpam-5398	305	3	’s	’s	PART
ejpam-5398	305	4	motivation	motivation	NOUN
ejpam-5398	305	5	stems	stem	VERB
ejpam-5398	305	6	from	from	ADP
ejpam-5398	305	7	the	the	DET
ejpam-5398	305	8	fact	fact	NOUN
ejpam-5398	305	9	that	that	SCONJ
ejpam-5398	305	10	td	td	NOUN
ejpam-5398	305	11	technology	technology	NOUN
ejpam-5398	305	12	has	have	AUX
ejpam-5398	305	13	recently	recently	ADV
ejpam-5398	305	14	been	be	AUX
ejpam-5398	305	15	the	the	DET
ejpam-5398	305	16	subject	subject	NOUN
ejpam-5398	305	17	of	of	ADP
ejpam-5398	305	18	numerous	numerous	ADJ
ejpam-5398	305	19	technological	technological	ADJ
ejpam-5398	305	20	applications	application	NOUN
ejpam-5398	305	21	.	.	PUNCT
ejpam-5398	306	1	when	when	SCONJ
ejpam-5398	306	2	attempting	attempt	VERB
ejpam-5398	306	3	to	to	PART
ejpam-5398	306	4	solve	solve	VERB
ejpam-5398	306	5	an	an	DET
ejpam-5398	306	6	equivalent	equivalent	ADJ
ejpam-5398	306	7	linearized	linearize	VERB
ejpam-5398	306	8	ode	ode	NOUN
ejpam-5398	306	9	,	,	PUNCT
ejpam-5398	306	10	it	it	PRON
ejpam-5398	306	11	is	be	AUX
ejpam-5398	306	12	advised	advise	VERB
ejpam-5398	306	13	to	to	PART
ejpam-5398	306	14	utilize	utilize	VERB
ejpam-5398	306	15	the	the	DET
ejpam-5398	306	16	npa	npa	NOUN
ejpam-5398	306	17	.	.	PUNCT
ejpam-5398	307	1	this	this	DET
ejpam-5398	307	2	satisfactoriness	satisfactoriness	NOUN
ejpam-5398	307	3	is	be	AUX
ejpam-5398	307	4	compared	compare	VERB
ejpam-5398	307	5	and	and	CCONJ
ejpam-5398	307	6	evaluated	evaluate	VERB
ejpam-5398	307	7	using	use	VERB
ejpam-5398	307	8	the	the	DET
ejpam-5398	307	9	ms	ms	PROPN
ejpam-5398	307	10	.	.	PROPN
ejpam-5398	308	1	the	the	DET
ejpam-5398	308	2	stability	stability	NOUN
ejpam-5398	308	3	criterion	criterion	NOUN
ejpam-5398	308	4	is	be	AUX
ejpam-5398	308	5	illustrated	illustrate	VERB
ejpam-5398	308	6	physically	physically	ADV
ejpam-5398	308	7	and	and	CCONJ
ejpam-5398	308	8	explored	explore	VERB
ejpam-5398	308	9	conceptually	conceptually	ADV
ejpam-5398	308	10	.	.	PUNCT
ejpam-5398	309	1	a	a	DET
ejpam-5398	309	2	matching	matching	NOUN
ejpam-5398	309	3	between	between	ADP
ejpam-5398	309	4	the	the	DET
ejpam-5398	309	5	strong	strong	ADJ
ejpam-5398	309	6	nonlinear	nonlinear	ADJ
ejpam-5398	309	7	ode	ode	NOUN
ejpam-5398	309	8	and	and	CCONJ
ejpam-5398	309	9	the	the	DET
ejpam-5398	309	10	corresponding	corresponding	ADJ
ejpam-5398	309	11	analytical	analytical	ADJ
ejpam-5398	309	12	linear	linear	PROPN
ejpam-5398	309	13	ode	ode	NOUN
ejpam-5398	309	14	is	be	AUX
ejpam-5398	309	15	established	establish	VERB
ejpam-5398	309	16	by	by	ADP
ejpam-5398	309	17	using	use	VERB
ejpam-5398	309	18	the	the	DET
ejpam-5398	309	19	suitable	suitable	ADJ
ejpam-5398	309	20	nm	nm	NOUN
ejpam-5398	309	21	.	.	PUNCT
ejpam-5398	310	1	for	for	ADP
ejpam-5398	310	2	several	several	ADJ
ejpam-5398	310	3	criteria	criterion	NOUN
ejpam-5398	310	4	,	,	PUNCT
ejpam-5398	310	5	this	this	DET
ejpam-5398	310	6	matching	matching	NOUN
ejpam-5398	310	7	has	have	AUX
ejpam-5398	310	8	shown	show	VERB
ejpam-5398	310	9	a	a	DET
ejpam-5398	310	10	highly	highly	ADV
ejpam-5398	310	11	significant	significant	ADJ
ejpam-5398	310	12	agreement	agreement	NOUN
ejpam-5398	310	13	.	.	PUNCT
ejpam-5398	311	1	put	put	VERB
ejpam-5398	311	2	another	another	DET
ejpam-5398	311	3	way	way	NOUN
ejpam-5398	311	4	,	,	PUNCT
ejpam-5398	311	5	the	the	DET
ejpam-5398	311	6	new	new	ADJ
ejpam-5398	311	7	performance	performance	NOUN
ejpam-5398	311	8	is	be	AUX
ejpam-5398	311	9	robust	robust	ADJ
ejpam-5398	311	10	,	,	PUNCT
ejpam-5398	311	11	promising	promising	ADJ
ejpam-5398	311	12	,	,	PUNCT
ejpam-5398	311	13	and	and	CCONJ
ejpam-5398	311	14	practical	practical	ADJ
ejpam-5398	311	15	,	,	PUNCT
ejpam-5398	311	16	and	and	CCONJ
ejpam-5398	311	17	it	it	PRON
ejpam-5398	311	18	could	could	AUX
ejpam-5398	311	19	be	be	AUX
ejpam-5398	311	20	used	use	VERB
ejpam-5398	311	21	with	with	ADP
ejpam-5398	311	22	other	other	ADJ
ejpam-5398	311	23	types	type	NOUN
ejpam-5398	311	24	of	of	ADP
ejpam-5398	311	25	oscillators	oscillator	NOUN
ejpam-5398	311	26	with	with	ADP
ejpam-5398	311	27	high	high	ADJ
ejpam-5398	311	28	nonlinearity	nonlinearity	NOUN
ejpam-5398	311	29	.	.	PUNCT
ejpam-5398	312	1	it	it	PRON
ejpam-5398	312	2	is	be	AUX
ejpam-5398	312	3	accurate	accurate	ADJ
ejpam-5398	312	4	,	,	PUNCT
ejpam-5398	312	5	adaptable	adaptable	ADJ
ejpam-5398	312	6	,	,	PUNCT
ejpam-5398	312	7	and	and	CCONJ
ejpam-5398	312	8	practical	practical	ADJ
ejpam-5398	312	9	.	.	PUNCT
ejpam-5398	313	1	as	as	SCONJ
ejpam-5398	313	2	is	be	AUX
ejpam-5398	313	3	well	well	ADV
ejpam-5398	313	4	-	-	PUNCT
ejpam-5398	313	5	known	know	VERB
ejpam-5398	313	6	,	,	PUNCT
ejpam-5398	313	7	all	all	DET
ejpam-5398	313	8	traditional	traditional	ADJ
ejpam-5398	313	9	methods	method	NOUN
ejpam-5398	313	10	use	use	VERB
ejpam-5398	313	11	the	the	DET
ejpam-5398	313	12	taylor	taylor	PROPN
ejpam-5398	313	13	expansion	expansion	NOUN
ejpam-5398	313	14	to	to	PART
ejpam-5398	313	15	reduce	reduce	VERB
ejpam-5398	313	16	their	their	PRON
ejpam-5398	313	17	complexity	complexity	NOUN
ejpam-5398	313	18	when	when	SCONJ
ejpam-5398	313	19	the	the	DET
ejpam-5398	313	20	restoring	restore	VERB
ejpam-5398	313	21	forces	force	NOUN
ejpam-5398	313	22	are	be	AUX
ejpam-5398	313	23	present	present	ADJ
ejpam-5398	313	24	.	.	PUNCT
ejpam-5398	314	1	this	this	DET
ejpam-5398	314	2	flaw	flaw	NOUN
ejpam-5398	314	3	is	be	AUX
ejpam-5398	314	4	no	no	ADV
ejpam-5398	314	5	longer	long	ADV
ejpam-5398	314	6	included	include	VERB
ejpam-5398	314	7	in	in	ADP
ejpam-5398	314	8	the	the	DET
ejpam-5398	314	9	current	current	ADJ
ejpam-5398	314	10	development	development	NOUN
ejpam-5398	314	11	.	.	PUNCT
ejpam-5398	315	1	moreover	moreover	ADV
ejpam-5398	315	2	,	,	PUNCT
ejpam-5398	315	3	different	different	ADJ
ejpam-5398	315	4	stable	stable	ADJ
ejpam-5398	315	5	and	and	CCONJ
ejpam-5398	315	6	unstable	unstable	ADJ
ejpam-5398	315	7	zones	zone	NOUN
ejpam-5398	315	8	are	be	AUX
ejpam-5398	315	9	graphed	graph	VERB
ejpam-5398	315	10	according	accord	VERB
ejpam-5398	315	11	to	to	ADP
ejpam-5398	315	12	the	the	DET
ejpam-5398	315	13	various	various	ADJ
ejpam-5398	315	14	values	value	NOUN
ejpam-5398	315	15	of	of	ADP
ejpam-5398	315	16	the	the	DET
ejpam-5398	315	17	used	use	VERB
ejpam-5398	315	18	parameters	parameter	NOUN
ejpam-5398	315	19	.	.	PUNCT
ejpam-5398	316	1	these	these	DET
ejpam-5398	316	2	charts	chart	NOUN
ejpam-5398	316	3	confirm	confirm	VERB
ejpam-5398	316	4	the	the	DET
ejpam-5398	316	5	stability	stability	NOUN
ejpam-5398	316	6	performance	performance	NOUN
ejpam-5398	316	7	of	of	ADP
ejpam-5398	316	8	the	the	DET
ejpam-5398	316	9	stability	stability	NOUN
ejpam-5398	316	10	criteria	criterion	NOUN
ejpam-5398	316	11	as	as	SCONJ
ejpam-5398	316	12	given	give	VERB
ejpam-5398	316	13	in	in	ADP
ejpam-5398	316	14	eq(15	eq(15	NOUN
ejpam-5398	316	15	)	)	PUNCT
ejpam-5398	316	16	.	.	PUNCT
ejpam-5398	317	1	by	by	ADP
ejpam-5398	317	2	analyzing	analyze	VERB
ejpam-5398	317	3	the	the	DET
ejpam-5398	317	4	data	datum	NOUN
ejpam-5398	317	5	,	,	PUNCT
ejpam-5398	317	6	it	it	PRON
ejpam-5398	317	7	is	be	AUX
ejpam-5398	317	8	feasible	feasible	ADJ
ejpam-5398	317	9	to	to	PART
ejpam-5398	317	10	assess	assess	VERB
ejpam-5398	317	11	the	the	DET
ejpam-5398	317	12	applicability	applicability	NOUN
ejpam-5398	317	13	of	of	ADP
ejpam-5398	317	14	the	the	DET
ejpam-5398	317	15	used	use	VERB
ejpam-5398	317	16	parameter	parameter	NOUN
ejpam-5398	317	17	and	and	CCONJ
ejpam-5398	317	18	show	show	VERB
ejpam-5398	317	19	how	how	SCONJ
ejpam-5398	317	20	accurate	accurate	ADJ
ejpam-5398	317	21	the	the	DET
ejpam-5398	317	22	results	result	NOUN
ejpam-5398	317	23	are	be	AUX
ejpam-5398	317	24	.	.	PUNCT
ejpam-5398	318	1	this	this	DET
ejpam-5398	318	2	inquiry	inquiry	NOUN
ejpam-5398	318	3	scrutinizes	scrutinize	VERB
ejpam-5398	318	4	the	the	DET
ejpam-5398	318	5	problem	problem	NOUN
ejpam-5398	318	6	of	of	ADP
ejpam-5398	318	7	an	an	DET
ejpam-5398	318	8	inflexible	inflexible	ADJ
ejpam-5398	318	9	rotating	rotating	NOUN
ejpam-5398	318	10	rod	rod	NOUN
ejpam-5398	318	11	without	without	ADP
ejpam-5398	318	12	slipping	slip	VERB
ejpam-5398	318	13	on	on	ADP
ejpam-5398	318	14	a	a	DET
ejpam-5398	318	15	rigid	rigid	ADJ
ejpam-5398	318	16	circular	circular	ADJ
ejpam-5398	318	17	surface	surface	NOUN
ejpam-5398	318	18	.	.	PUNCT
ejpam-5398	319	1	the	the	DET
ejpam-5398	319	2	euler	euler	PROPN
ejpam-5398	319	3	-	-	PUNCT
ejpam-5398	319	4	lagrange	lagrange	NOUN
ejpam-5398	319	5	theorem	theorem	NOUN
ejpam-5398	319	6	worked	work	VERB
ejpam-5398	319	7	as	as	ADP
ejpam-5398	319	8	the	the	DET
ejpam-5398	319	9	foundation	foundation	NOUN
ejpam-5398	319	10	for	for	ADP
ejpam-5398	319	11	the	the	DET
ejpam-5398	319	12	development	development	NOUN
ejpam-5398	319	13	of	of	ADP
ejpam-5398	319	14	the	the	DET
ejpam-5398	319	15	governing	govern	VERB
ejpam-5398	319	16	equation	equation	NOUN
ejpam-5398	319	17	of	of	ADP
ejpam-5398	319	18	motion	motion	NOUN
ejpam-5398	319	19	in	in	ADP
ejpam-5398	319	20	our	our	PRON
ejpam-5398	319	21	earlier	early	ADJ
ejpam-5398	319	22	work	work	NOUN
ejpam-5398	319	23	[	[	X
ejpam-5398	319	24	17	17	NUM
ejpam-5398	319	25	]	]	PUNCT
ejpam-5398	319	26	.	.	PUNCT
ejpam-5398	320	1	the	the	DET
ejpam-5398	320	2	obtained	obtain	VERB
ejpam-5398	320	3	gaylord	gaylord	PROPN
ejpam-5398	320	4	’s	’s	PART
ejpam-5398	320	5	oscillator	oscillator	NOUN
ejpam-5398	320	6	has	have	VERB
ejpam-5398	320	7	a	a	DET
ejpam-5398	320	8	semi	semi	ADJ
ejpam-5398	320	9	-	-	ADJ
ejpam-5398	320	10	precise	precise	ADJ
ejpam-5398	320	11	periodic	periodic	ADJ
ejpam-5398	320	12	analytic	analytic	ADJ
ejpam-5398	320	13	solution	solution	NOUN
ejpam-5398	320	14	because	because	SCONJ
ejpam-5398	320	15	the	the	DET
ejpam-5398	320	16	expected	expect	VERB
ejpam-5398	320	17	non	non	ADJ
ejpam-5398	320	18	-	-	ADJ
ejpam-5398	320	19	linear	linear	ADJ
ejpam-5398	320	20	frequency	frequency	NOUN
ejpam-5398	320	21	was	be	AUX
ejpam-5398	320	22	anticipated	anticipate	VERB
ejpam-5398	320	23	based	base	VERB
ejpam-5398	320	24	on	on	ADP
ejpam-5398	320	25	the	the	DET
ejpam-5398	320	26	npa	npa	NOUN
ejpam-5398	320	27	.	.	PUNCT
ejpam-5398	321	1	the	the	DET
ejpam-5398	321	2	below	below	ADP
ejpam-5398	321	3	mentioned	mention	VERB
ejpam-5398	321	4	specifics	specific	NOUN
ejpam-5398	321	5	ought	ought	AUX
ejpam-5398	321	6	to	to	PART
ejpam-5398	321	7	be	be	AUX
ejpam-5398	321	8	highlighted	highlight	VERB
ejpam-5398	321	9	pertaining	pertain	VERB
ejpam-5398	321	10	to	to	ADP
ejpam-5398	321	11	the	the	DET
ejpam-5398	321	12	innovative	innovative	ADJ
ejpam-5398	321	13	method	method	NOUN
ejpam-5398	321	14	or	or	CCONJ
ejpam-5398	321	15	results	result	NOUN
ejpam-5398	321	16	that	that	PRON
ejpam-5398	321	17	are	be	AUX
ejpam-5398	321	18	important	important	ADJ
ejpam-5398	321	19	:	:	PUNCT
ejpam-5398	321	20	a.	a.	NOUN
ejpam-5398	321	21	a.	a.	PROPN
ejpam-5398	321	22	galal	galal	PROPN
ejpam-5398	321	23	et	et	PROPN
ejpam-5398	321	24	al	al	PROPN
ejpam-5398	321	25	.	.	PUNCT
ejpam-5398	321	26	/	/	SYM
ejpam-5398	321	27	eur	eur	PROPN
ejpam-5398	321	28	.	.	PUNCT
ejpam-5398	322	1	j.	j.	PROPN
ejpam-5398	322	2	pure	pure	PROPN
ejpam-5398	322	3	appl	appl	PROPN
ejpam-5398	322	4	.	.	PROPN
ejpam-5398	322	5	math	math	PROPN
ejpam-5398	322	6	,	,	PUNCT
ejpam-5398	322	7	17	17	NUM
ejpam-5398	322	8	(	(	PUNCT
ejpam-5398	322	9	4	4	NUM
ejpam-5398	322	10	)	)	PUNCT
ejpam-5398	322	11	(	(	PUNCT
ejpam-5398	322	12	2024	2024	NUM
ejpam-5398	322	13	)	)	PUNCT
ejpam-5398	322	14	,	,	PUNCT
ejpam-5398	322	15	2878	2878	NUM
ejpam-5398	322	16	-	-	SYM
ejpam-5398	322	17	2897	2897	NUM
ejpam-5398	322	18	2892	2892	NUM
ejpam-5398	322	19	figure	figure	NOUN
ejpam-5398	322	20	9	9	NUM
ejpam-5398	322	21	:	:	PUNCT
ejpam-5398	322	22	describes	describe	VERB
ejpam-5398	322	23	the	the	DET
ejpam-5398	322	24	time	time	NOUN
ejpam-5398	322	25	variation	variation	NOUN
ejpam-5398	322	26	of	of	ADP
ejpam-5398	322	27	ω	ω	NUM
ejpam-5398	322	28	at	at	ADP
ejpam-5398	322	29	a	a	DET
ejpam-5398	322	30	=	=	NOUN
ejpam-5398	322	31	a	a	PRON
ejpam-5398	322	32	=	=	NOUN
ejpam-5398	322	33	1	1	NUM
ejpam-5398	322	34	when	when	SCONJ
ejpam-5398	322	35	:	:	PUNCT
ejpam-5398	322	36	(	(	PUNCT
ejpam-5398	322	37	a	a	X
ejpam-5398	322	38	)	)	PUNCT
ejpam-5398	322	39	b	b	NOUN
ejpam-5398	322	40	=	=	NOUN
ejpam-5398	322	41	0.01	0.01	NUM
ejpam-5398	322	42	,	,	PUNCT
ejpam-5398	322	43	and	and	CCONJ
ejpam-5398	322	44	(	(	PUNCT
ejpam-5398	322	45	b	b	X
ejpam-5398	322	46	)	)	PUNCT
ejpam-5398	322	47	b	b	NOUN
ejpam-5398	322	48	=	=	SYM
ejpam-5398	322	49	0.1	0.1	NUM
ejpam-5398	322	50	.	.	PUNCT
ejpam-5398	322	51	•	•	NOUN
ejpam-5398	322	52	in	in	ADP
ejpam-5398	322	53	essence	essence	NOUN
ejpam-5398	322	54	,	,	PUNCT
ejpam-5398	322	55	the	the	DET
ejpam-5398	322	56	novel	novel	ADJ
ejpam-5398	322	57	approach	approach	NOUN
ejpam-5398	322	58	creates	create	VERB
ejpam-5398	322	59	a	a	DET
ejpam-5398	322	60	parallel	parallel	ADJ
ejpam-5398	322	61	linear	linear	ADJ
ejpam-5398	322	62	ode	ode	NOUN
ejpam-5398	322	63	that	that	PRON
ejpam-5398	322	64	corresponds	correspond	VERB
ejpam-5398	322	65	to	to	ADP
ejpam-5398	322	66	the	the	DET
ejpam-5398	322	67	existing	exist	VERB
ejpam-5398	322	68	nonlinear	nonlinear	ADJ
ejpam-5398	322	69	one	one	NUM
ejpam-5398	322	70	.	.	PUNCT
ejpam-5398	323	1	•	•	NUM
ejpam-5398	323	2	a	a	DET
ejpam-5398	323	3	good	good	ADJ
ejpam-5398	323	4	match	match	NOUN
ejpam-5398	323	5	between	between	ADP
ejpam-5398	323	6	these	these	DET
ejpam-5398	323	7	two	two	NUM
ejpam-5398	323	8	equations	equation	NOUN
ejpam-5398	323	9	is	be	AUX
ejpam-5398	323	10	achieved	achieve	VERB
ejpam-5398	323	11	to	to	PART
ejpam-5398	323	12	ensure	ensure	VERB
ejpam-5398	323	13	the	the	DET
ejpam-5398	323	14	effectiveness	effectiveness	NOUN
ejpam-5398	323	15	of	of	ADP
ejpam-5398	323	16	the	the	DET
ejpam-5398	323	17	novel	novel	ADJ
ejpam-5398	323	18	method	method	NOUN
ejpam-5398	323	19	.	.	PUNCT
ejpam-5398	324	1	•	•	NOUN
ejpam-5398	324	2	every	every	DET
ejpam-5398	324	3	traditional	traditional	ADJ
ejpam-5398	324	4	approach	approach	NOUN
ejpam-5398	324	5	employed	employ	VERB
ejpam-5398	324	6	the	the	DET
ejpam-5398	324	7	taylor	taylor	PROPN
ejpam-5398	324	8	expansion	expansion	NOUN
ejpam-5398	324	9	to	to	PART
ejpam-5398	324	10	simplify	simplify	VERB
ejpam-5398	324	11	the	the	DET
ejpam-5398	324	12	given	give	VERB
ejpam-5398	324	13	problem	problem	NOUN
ejpam-5398	324	14	in	in	ADP
ejpam-5398	324	15	the	the	DET
ejpam-5398	324	16	case	case	NOUN
ejpam-5398	324	17	of	of	ADP
ejpam-5398	324	18	existence	existence	NOUN
ejpam-5398	324	19	of	of	ADP
ejpam-5398	324	20	the	the	DET
ejpam-5398	324	21	restoring	restore	VERB
ejpam-5398	324	22	forces	force	NOUN
ejpam-5398	324	23	.	.	PUNCT
ejpam-5398	325	1	the	the	DET
ejpam-5398	325	2	current	current	ADJ
ejpam-5398	325	3	strategy	strategy	NOUN
ejpam-5398	325	4	has	have	AUX
ejpam-5398	325	5	eliminated	eliminate	VERB
ejpam-5398	325	6	this	this	DET
ejpam-5398	325	7	shortcoming	shortcoming	NOUN
ejpam-5398	325	8	.	.	PUNCT
ejpam-5398	325	9	•	•	NUM
ejpam-5398	325	10	away	away	ADV
ejpam-5398	325	11	from	from	ADP
ejpam-5398	325	12	the	the	DET
ejpam-5398	325	13	traditional	traditional	ADJ
ejpam-5398	325	14	perturbations	perturbation	NOUN
ejpam-5398	325	15	,	,	PUNCT
ejpam-5398	325	16	the	the	DET
ejpam-5398	325	17	current	current	ADJ
ejpam-5398	325	18	methodology	methodology	NOUN
ejpam-5398	325	19	enables	enable	VERB
ejpam-5398	325	20	us	we	PRON
ejpam-5398	325	21	to	to	PART
ejpam-5398	325	22	investigate	investigate	VERB
ejpam-5398	325	23	the	the	DET
ejpam-5398	325	24	stability	stability	NOUN
ejpam-5398	325	25	analysis	analysis	NOUN
ejpam-5398	325	26	of	of	ADP
ejpam-5398	325	27	the	the	DET
ejpam-5398	325	28	problem	problem	NOUN
ejpam-5398	325	29	.	.	PUNCT
ejpam-5398	326	1	•	•	ADV
ejpam-5398	326	2	finally	finally	ADV
ejpam-5398	326	3	,	,	PUNCT
ejpam-5398	326	4	npa	npa	PROPN
ejpam-5398	326	5	appears	appear	VERB
ejpam-5398	326	6	to	to	PART
ejpam-5398	326	7	be	be	AUX
ejpam-5398	326	8	a	a	DET
ejpam-5398	326	9	straightforward	straightforward	ADJ
ejpam-5398	326	10	,	,	PUNCT
ejpam-5398	326	11	effective	effective	ADJ
ejpam-5398	326	12	,	,	PUNCT
ejpam-5398	326	13	and	and	CCONJ
ejpam-5398	326	14	promising	promise	VERB
ejpam-5398	326	15	tool	tool	NOUN
ejpam-5398	326	16	.	.	PUNCT
ejpam-5398	327	1	this	this	PRON
ejpam-5398	327	2	can	can	AUX
ejpam-5398	327	3	be	be	AUX
ejpam-5398	327	4	utilized	utilize	VERB
ejpam-5398	327	5	to	to	PART
ejpam-5398	327	6	examine	examine	VERB
ejpam-5398	327	7	different	different	ADJ
ejpam-5398	327	8	nonlinear	nonlinear	ADJ
ejpam-5398	327	9	oscillator	oscillator	NOUN
ejpam-5398	327	10	classes	class	NOUN
ejpam-5398	327	11	.	.	PUNCT
ejpam-5398	328	1	the	the	DET
ejpam-5398	328	2	implications	implication	NOUN
ejpam-5398	328	3	of	of	ADP
ejpam-5398	328	4	the	the	DET
ejpam-5398	328	5	original	original	ADJ
ejpam-5398	328	6	nonlinear	nonlinear	PROPN
ejpam-5398	328	7	gaylord	gaylord	PROPN
ejpam-5398	328	8	oscillator	oscillator	NOUN
ejpam-5398	328	9	led	lead	VERB
ejpam-5398	328	10	to	to	ADP
ejpam-5398	328	11	the	the	DET
ejpam-5398	328	12	establishing	establishing	NOUN
ejpam-5398	328	13	of	of	ADP
ejpam-5398	328	14	the	the	DET
ejpam-5398	328	15	equivalent	equivalent	ADJ
ejpam-5398	328	16	frequency	frequency	NOUN
ejpam-5398	328	17	.	.	PUNCT
ejpam-5398	329	1	consequently	consequently	ADV
ejpam-5398	329	2	,	,	PUNCT
ejpam-5398	329	3	this	this	DET
ejpam-5398	329	4	strategy	strategy	NOUN
ejpam-5398	329	5	enables	enable	VERB
ejpam-5398	329	6	us	we	PRON
ejpam-5398	329	7	to	to	PART
ejpam-5398	329	8	tackle	tackle	VERB
ejpam-5398	329	9	a	a	DET
ejpam-5398	329	10	wide	wide	ADJ
ejpam-5398	329	11	range	range	NOUN
ejpam-5398	329	12	of	of	ADP
ejpam-5398	329	13	issues	issue	NOUN
ejpam-5398	329	14	related	relate	VERB
ejpam-5398	329	15	to	to	ADP
ejpam-5398	329	16	the	the	DET
ejpam-5398	329	17	use	use	NOUN
ejpam-5398	329	18	of	of	ADP
ejpam-5398	329	19	various	various	ADJ
ejpam-5398	329	20	oscillators	oscillator	NOUN
ejpam-5398	329	21	in	in	ADP
ejpam-5398	329	22	mechanical	mechanical	ADJ
ejpam-5398	329	23	systems	system	NOUN
ejpam-5398	329	24	.	.	PUNCT
ejpam-5398	330	1	to	to	PART
ejpam-5398	330	2	analyze	analyze	VERB
ejpam-5398	330	3	the	the	DET
ejpam-5398	330	4	stability	stability	NOUN
ejpam-5398	330	5	analysis	analysis	NOUN
ejpam-5398	330	6	in	in	ADP
ejpam-5398	330	7	the	the	DET
ejpam-5398	330	8	current	current	ADJ
ejpam-5398	330	9	work	work	NOUN
ejpam-5398	330	10	,	,	PUNCT
ejpam-5398	330	11	a	a	DET
ejpam-5398	330	12	td	td	NOUN
ejpam-5398	330	13	square	square	ADJ
ejpam-5398	330	14	position	position	NOUN
ejpam-5398	330	15	and	and	CCONJ
ejpam-5398	330	16	velocity	velocity	NOUN
ejpam-5398	330	17	are	be	AUX
ejpam-5398	330	18	used	use	VERB
ejpam-5398	330	19	.	.	PUNCT
ejpam-5398	331	1	to	to	PART
ejpam-5398	331	2	achieve	achieve	VERB
ejpam-5398	331	3	an	an	DET
ejpam-5398	331	4	analogous	analogous	ADJ
ejpam-5398	331	5	frequency	frequency	NOUN
ejpam-5398	331	6	and	and	CCONJ
ejpam-5398	331	7	subsequently	subsequently	ADV
ejpam-5398	331	8	an	an	DET
ejpam-5398	331	9	equivalent	equivalent	ADJ
ejpam-5398	331	10	linear	linear	ADJ
ejpam-5398	331	11	ode	ode	PROPN
ejpam-5398	331	12	,	,	PUNCT
ejpam-5398	331	13	the	the	DET
ejpam-5398	331	14	new	new	ADJ
ejpam-5398	331	15	npa	npa	NOUN
ejpam-5398	331	16	has	have	AUX
ejpam-5398	331	17	been	be	AUX
ejpam-5398	331	18	used	use	VERB
ejpam-5398	331	19	.	.	PUNCT
ejpam-5398	332	1	it	it	PRON
ejpam-5398	332	2	becomes	become	VERB
ejpam-5398	332	3	clear	clear	ADJ
ejpam-5398	332	4	that	that	SCONJ
ejpam-5398	332	5	the	the	DET
ejpam-5398	332	6	total	total	ADJ
ejpam-5398	332	7	frequency	frequency	NOUN
ejpam-5398	332	8	includes	include	VERB
ejpam-5398	332	9	every	every	DET
ejpam-5398	332	10	physical	physical	ADJ
ejpam-5398	332	11	variable	variable	NOUN
ejpam-5398	332	12	in	in	ADP
ejpam-5398	332	13	the	the	DET
ejpam-5398	332	14	fundamental	fundamental	ADJ
ejpam-5398	332	15	governing	govern	VERB
ejpam-5398	332	16	equation	equation	NOUN
ejpam-5398	332	17	of	of	ADP
ejpam-5398	332	18	motion	motion	NOUN
ejpam-5398	332	19	.	.	PUNCT
ejpam-5398	333	1	the	the	DET
ejpam-5398	333	2	equivalent	equivalent	ADJ
ejpam-5398	333	3	frequency	frequency	NOUN
ejpam-5398	333	4	of	of	ADP
ejpam-5398	333	5	the	the	DET
ejpam-5398	333	6	alternative	alternative	ADJ
ejpam-5398	333	7	linear	linear	ADJ
ejpam-5398	333	8	ode	ode	NOUN
ejpam-5398	333	9	that	that	PRON
ejpam-5398	333	10	includes	include	VERB
ejpam-5398	333	11	trigonometric	trigonometric	ADJ
ejpam-5398	333	12	and	and	CCONJ
ejpam-5398	333	13	bessel	bessel	ADJ
ejpam-5398	333	14	functions	function	NOUN
ejpam-5398	333	15	is	be	AUX
ejpam-5398	333	16	expressed	express	VERB
ejpam-5398	333	17	as	as	ADP
ejpam-5398	333	18	a	a	DET
ejpam-5398	333	19	transcendental	transcendental	ADJ
ejpam-5398	333	20	relationship	relationship	NOUN
ejpam-5398	333	21	.	.	PUNCT
ejpam-5398	334	1	a	a	DET
ejpam-5398	334	2	comparison	comparison	NOUN
ejpam-5398	334	3	between	between	ADP
ejpam-5398	334	4	the	the	DET
ejpam-5398	334	5	numerical	numerical	ADJ
ejpam-5398	334	6	and	and	CCONJ
ejpam-5398	334	7	the	the	DET
ejpam-5398	334	8	theoretical	theoretical	ADJ
ejpam-5398	334	9	outcomes	outcome	NOUN
ejpam-5398	334	10	reveals	reveal	VERB
ejpam-5398	334	11	a	a	DET
ejpam-5398	334	12	precise	precise	ADJ
ejpam-5398	334	13	accuracy	accuracy	NOUN
ejpam-5398	334	14	.	.	PUNCT
ejpam-5398	335	1	the	the	DET
ejpam-5398	335	2	study	study	NOUN
ejpam-5398	335	3	purposes	purpose	VERB
ejpam-5398	335	4	a	a	DET
ejpam-5398	335	5	careful	careful	ADJ
ejpam-5398	335	6	analysis	analysis	NOUN
ejpam-5398	335	7	of	of	ADP
ejpam-5398	335	8	the	the	DET
ejpam-5398	335	9	conclusions	conclusion	NOUN
ejpam-5398	335	10	reached	reach	VERB
ejpam-5398	335	11	utilizing	utilize	VERB
ejpam-5398	335	12	the	the	DET
ejpam-5398	335	13	analytical	analytical	ADJ
ejpam-5398	335	14	strategy	strategy	NOUN
ejpam-5398	335	15	of	of	ADP
ejpam-5398	335	16	practical	practical	ADJ
ejpam-5398	335	17	approximation	approximation	NOUN
ejpam-5398	335	18	.	.	PUNCT
ejpam-5398	336	1	a	a	DET
ejpam-5398	336	2	secondary	secondary	ADJ
ejpam-5398	336	3	argument	argument	NOUN
ejpam-5398	336	4	together	together	ADV
ejpam-5398	336	5	with	with	ADP
ejpam-5398	336	6	the	the	DET
ejpam-5398	336	7	system	system	NOUN
ejpam-5398	336	8	potential	potential	NOUN
ejpam-5398	336	9	for	for	ADP
ejpam-5398	336	10	nonlinear	nonlinear	ADJ
ejpam-5398	336	11	vibration	vibration	NOUN
ejpam-5398	336	12	is	be	AUX
ejpam-5398	336	13	provided	provide	VERB
ejpam-5398	336	14	by	by	ADP
ejpam-5398	336	15	the	the	DET
ejpam-5398	336	16	references	reference	NOUN
ejpam-5398	336	17	2893	2893	NUM
ejpam-5398	336	18	td	td	NOUN
ejpam-5398	336	19	.	.	PUNCT
ejpam-5398	337	1	additionally	additionally	ADV
ejpam-5398	337	2	,	,	PUNCT
ejpam-5398	337	3	the	the	DET
ejpam-5398	337	4	time	time	NOUN
ejpam-5398	337	5	history	history	NOUN
ejpam-5398	337	6	of	of	ADP
ejpam-5398	337	7	the	the	DET
ejpam-5398	337	8	achieved	achieve	VERB
ejpam-5398	337	9	results	result	NOUN
ejpam-5398	337	10	and	and	CCONJ
ejpam-5398	337	11	their	their	PRON
ejpam-5398	337	12	stabilities	stability	NOUN
ejpam-5398	337	13	are	be	AUX
ejpam-5398	337	14	plotted	plot	VERB
ejpam-5398	337	15	to	to	PART
ejpam-5398	337	16	show	show	VERB
ejpam-5398	337	17	the	the	DET
ejpam-5398	337	18	positive	positive	ADJ
ejpam-5398	337	19	effect	effect	NOUN
ejpam-5398	337	20	of	of	ADP
ejpam-5398	337	21	the	the	DET
ejpam-5398	337	22	used	use	VERB
ejpam-5398	337	23	parameter	parameter	NOUN
ejpam-5398	337	24	.	.	PUNCT
ejpam-5398	338	1	coupled	couple	VERB
ejpam-5398	338	2	dynamical	dynamical	ADJ
ejpam-5398	338	3	systems	system	NOUN
ejpam-5398	338	4	constitute	constitute	VERB
ejpam-5398	338	5	interrelated	interrelated	ADJ
ejpam-5398	338	6	systems	system	NOUN
ejpam-5398	338	7	that	that	PRON
ejpam-5398	338	8	mutually	mutually	ADV
ejpam-5398	338	9	affect	affect	VERB
ejpam-5398	338	10	one	one	NUM
ejpam-5398	338	11	other	other	ADJ
ejpam-5398	338	12	’s	’s	PART
ejpam-5398	338	13	behavior	behavior	NOUN
ejpam-5398	338	14	,	,	PUNCT
ejpam-5398	338	15	offering	offer	VERB
ejpam-5398	338	16	valuable	valuable	ADJ
ejpam-5398	338	17	insights	insight	NOUN
ejpam-5398	338	18	into	into	ADP
ejpam-5398	338	19	intricate	intricate	ADJ
ejpam-5398	338	20	phenomena	phenomenon	NOUN
ejpam-5398	338	21	like	like	ADP
ejpam-5398	338	22	as	as	ADP
ejpam-5398	338	23	biological	biological	ADJ
ejpam-5398	338	24	rhythms	rhythm	NOUN
ejpam-5398	338	25	,	,	PUNCT
ejpam-5398	338	26	disease	disease	NOUN
ejpam-5398	338	27	transmission	transmission	NOUN
ejpam-5398	338	28	,	,	PUNCT
ejpam-5398	338	29	brain	brain	NOUN
ejpam-5398	338	30	activity	activity	NOUN
ejpam-5398	338	31	,	,	PUNCT
ejpam-5398	338	32	and	and	CCONJ
ejpam-5398	338	33	social	social	ADJ
ejpam-5398	338	34	dynamics	dynamic	NOUN
ejpam-5398	338	35	.	.	PUNCT
ejpam-5398	339	1	these	these	DET
ejpam-5398	339	2	systems	system	NOUN
ejpam-5398	339	3	have	have	VERB
ejpam-5398	339	4	the	the	DET
ejpam-5398	339	5	potential	potential	NOUN
ejpam-5398	339	6	to	to	PART
ejpam-5398	339	7	exhibit	exhibit	VERB
ejpam-5398	339	8	emergent	emergent	ADJ
ejpam-5398	339	9	behavior	behavior	NOUN
ejpam-5398	339	10	,	,	PUNCT
ejpam-5398	339	11	which	which	PRON
ejpam-5398	339	12	can	can	AUX
ejpam-5398	339	13	offer	offer	VERB
ejpam-5398	339	14	valuable	valuable	ADJ
ejpam-5398	339	15	insights	insight	NOUN
ejpam-5398	339	16	into	into	ADP
ejpam-5398	339	17	their	their	PRON
ejpam-5398	339	18	functioning	functioning	NOUN
ejpam-5398	339	19	,	,	PUNCT
ejpam-5398	339	20	enable	enable	ADJ
ejpam-5398	339	21	predictions	prediction	NOUN
ejpam-5398	339	22	of	of	ADP
ejpam-5398	339	23	future	future	ADJ
ejpam-5398	339	24	behavior	behavior	NOUN
ejpam-5398	339	25	,	,	PUNCT
ejpam-5398	339	26	and	and	CCONJ
ejpam-5398	339	27	provide	provide	VERB
ejpam-5398	339	28	suggestions	suggestion	NOUN
ejpam-5398	339	29	for	for	ADP
ejpam-5398	339	30	controlling	control	VERB
ejpam-5398	339	31	or	or	CCONJ
ejpam-5398	339	32	optimizing	optimize	VERB
ejpam-5398	339	33	them	they	PRON
ejpam-5398	339	34	in	in	ADP
ejpam-5398	339	35	practical	practical	ADJ
ejpam-5398	339	36	applications	application	NOUN
ejpam-5398	339	37	.	.	PUNCT
ejpam-5398	340	1	therefore	therefore	ADV
ejpam-5398	340	2	,	,	PUNCT
ejpam-5398	340	3	in	in	ADP
ejpam-5398	340	4	subsequent	subsequent	ADJ
ejpam-5398	340	5	papers	paper	NOUN
ejpam-5398	340	6	,	,	PUNCT
ejpam-5398	340	7	the	the	DET
ejpam-5398	340	8	npa	npa	NOUN
ejpam-5398	340	9	will	will	AUX
ejpam-5398	340	10	be	be	AUX
ejpam-5398	340	11	developed	develop	VERB
ejpam-5398	340	12	to	to	PART
ejpam-5398	340	13	analyze	analyze	VERB
ejpam-5398	340	14	such	such	ADJ
ejpam-5398	340	15	systems	system	NOUN
ejpam-5398	340	16	.	.	PUNCT
ejpam-5398	341	1	authors	author	NOUN
ejpam-5398	341	2	statements	statement	VERB
ejpam-5398	341	3	khalid	khalid	PROPN
ejpam-5398	341	4	alluhydan	alluhydan	PROPN
ejpam-5398	341	5	:	:	PUNCT
ejpam-5398	341	6	resources	resource	NOUN
ejpam-5398	341	7	,	,	PUNCT
ejpam-5398	341	8	methodology	methodology	NOUN
ejpam-5398	341	9	,	,	PUNCT
ejpam-5398	341	10	formal	formal	ADJ
ejpam-5398	341	11	analysis	analysis	NOUN
ejpam-5398	341	12	,	,	PUNCT
ejpam-5398	341	13	validation	validation	NOUN
ejpam-5398	341	14	,	,	PUNCT
ejpam-5398	341	15	visualization	visualization	NOUN
ejpam-5398	341	16	and	and	CCONJ
ejpam-5398	341	17	reviewing	reviewing	NOUN
ejpam-5398	341	18	.	.	PUNCT
ejpam-5398	342	1	galal	galal	PROPN
ejpam-5398	342	2	m.	m.	PROPN
ejpam-5398	342	3	moatimid	moatimid	PROPN
ejpam-5398	342	4	:	:	PUNCT
ejpam-5398	342	5	conceptualization	conceptualization	NOUN
ejpam-5398	342	6	,	,	PUNCT
ejpam-5398	342	7	resources	resource	NOUN
ejpam-5398	342	8	,	,	PUNCT
ejpam-5398	342	9	methodology	methodology	NOUN
ejpam-5398	342	10	,	,	PUNCT
ejpam-5398	342	11	formal	formal	ADJ
ejpam-5398	342	12	analysis	analysis	NOUN
ejpam-5398	342	13	,	,	PUNCT
ejpam-5398	342	14	validation	validation	NOUN
ejpam-5398	342	15	,	,	PUNCT
ejpam-5398	342	16	writingoriginal	writingoriginal	ADJ
ejpam-5398	342	17	draft	draft	NOUN
ejpam-5398	342	18	preparation	preparation	NOUN
ejpam-5398	342	19	,	,	PUNCT
ejpam-5398	342	20	visualization	visualization	NOUN
ejpam-5398	342	21	and	and	CCONJ
ejpam-5398	342	22	reviewing	reviewing	NOUN
ejpam-5398	342	23	.	.	PUNCT
ejpam-5398	343	1	t.	t.	PROPN
ejpam-5398	343	2	s.	s.	PROPN
ejpam-5398	343	3	amer	amer	PROPN
ejpam-5398	343	4	:	:	PUNCT
ejpam-5398	343	5	investigation	investigation	NOUN
ejpam-5398	343	6	,	,	PUNCT
ejpam-5398	343	7	methodology	methodology	NOUN
ejpam-5398	343	8	,	,	PUNCT
ejpam-5398	343	9	data	data	NOUN
ejpam-5398	343	10	duration	duration	NOUN
ejpam-5398	343	11	,	,	PUNCT
ejpam-5398	343	12	conceptualization	conceptualization	NOUN
ejpam-5398	343	13	,	,	PUNCT
ejpam-5398	343	14	validation	validation	NOUN
ejpam-5398	343	15	,	,	PUNCT
ejpam-5398	343	16	reviewing	reviewing	NOUN
ejpam-5398	343	17	and	and	CCONJ
ejpam-5398	343	18	editing	editing	NOUN
ejpam-5398	343	19	.	.	PUNCT
ejpam-5398	344	1	a.	a.	NOUN
ejpam-5398	344	2	a.	a.	PROPN
ejpam-5398	344	3	galal	galal	PROPN
ejpam-5398	344	4	:	:	PUNCT
ejpam-5398	344	5	examination	examination	NOUN
ejpam-5398	344	6	,	,	PUNCT
ejpam-5398	344	7	organization	organization	NOUN
ejpam-5398	344	8	,	,	PUNCT
ejpam-5398	344	9	data	data	NOUN
ejpam-5398	344	10	duration	duration	NOUN
ejpam-5398	344	11	,	,	PUNCT
ejpam-5398	344	12	validation	validation	NOUN
ejpam-5398	344	13	,	,	PUNCT
ejpam-5398	344	14	corroboration	corroboration	NOUN
ejpam-5398	344	15	,	,	PUNCT
ejpam-5398	344	16	rereading	reread	VERB
ejpam-5398	344	17	and	and	CCONJ
ejpam-5398	344	18	editing	editing	NOUN
ejpam-5398	344	19	.	.	PUNCT
ejpam-5398	345	1	conflict	conflict	NOUN
ejpam-5398	345	2	of	of	ADP
ejpam-5398	345	3	interest	interest	NOUN
ejpam-5398	345	4	there	there	PRON
ejpam-5398	345	5	are	be	VERB
ejpam-5398	345	6	no	no	DET
ejpam-5398	345	7	conflicts	conflict	NOUN
ejpam-5398	345	8	of	of	ADP
ejpam-5398	345	9	interest	interest	NOUN
ejpam-5398	345	10	declared	declare	VERB
ejpam-5398	345	11	by	by	ADP
ejpam-5398	345	12	the	the	DET
ejpam-5398	345	13	authors	author	NOUN
ejpam-5398	345	14	.	.	PUNCT
ejpam-5398	346	1	data	datum	NOUN
ejpam-5398	346	2	availability	availability	NOUN
ejpam-5398	346	3	all	all	DET
ejpam-5398	346	4	data	datum	NOUN
ejpam-5398	346	5	generated	generate	VERB
ejpam-5398	346	6	or	or	CCONJ
ejpam-5398	346	7	analysed	analyse	VERB
ejpam-5398	346	8	during	during	ADP
ejpam-5398	346	9	this	this	DET
ejpam-5398	346	10	study	study	NOUN
ejpam-5398	346	11	are	be	AUX
ejpam-5398	346	12	included	include	VERB
ejpam-5398	346	13	in	in	ADP
ejpam-5398	346	14	this	this	DET
ejpam-5398	346	15	published	publish	VERB
ejpam-5398	346	16	article	article	NOUN
ejpam-5398	346	17	.	.	PUNCT
ejpam-5398	347	1	references	reference	NOUN
ejpam-5398	347	2	[	[	X
ejpam-5398	347	3	1	1	X
ejpam-5398	347	4	]	]	PUNCT
ejpam-5398	347	5	ata	ata	NOUN
ejpam-5398	347	6	abu	abu	NOUN
ejpam-5398	347	7	-	-	PUNCT
ejpam-5398	347	8	as	as	ADP
ejpam-5398	347	9	’	'	PUNCT
ejpam-5398	347	10	ad	ad	NOUN
ejpam-5398	347	11	and	and	CCONJ
ejpam-5398	347	12	jihad	jihad	PROPN
ejpam-5398	347	13	asad	asad	PROPN
ejpam-5398	347	14	.	.	PUNCT
ejpam-5398	348	1	exact	exact	ADJ
ejpam-5398	348	2	solution	solution	NOUN
ejpam-5398	348	3	for	for	ADP
ejpam-5398	348	4	nonlinear	nonlinear	ADJ
ejpam-5398	348	5	oscillators	oscillator	NOUN
ejpam-5398	348	6	with	with	ADP
ejpam-5398	348	7	coordinate	coordinate	NOUN
ejpam-5398	348	8	-	-	PUNCT
ejpam-5398	348	9	dependent	dependent	ADJ
ejpam-5398	348	10	mass	mass	NOUN
ejpam-5398	348	11	.	.	PUNCT
ejpam-5398	349	1	european	european	PROPN
ejpam-5398	349	2	journal	journal	PROPN
ejpam-5398	349	3	of	of	ADP
ejpam-5398	349	4	pure	pure	ADJ
ejpam-5398	349	5	and	and	CCONJ
ejpam-5398	349	6	applied	applied	ADJ
ejpam-5398	349	7	mathematics	mathematic	NOUN
ejpam-5398	349	8	,	,	PUNCT
ejpam-5398	349	9	15(2):496–510	15(2):496–510	NUM
ejpam-5398	349	10	,	,	PUNCT
ejpam-5398	349	11	2022	2022	NUM
ejpam-5398	349	12	.	.	PUNCT
ejpam-5398	350	1	[	[	X
ejpam-5398	350	2	2	2	NUM
ejpam-5398	350	3	]	]	PUNCT
ejpam-5398	350	4	ts	ts	ADP
ejpam-5398	350	5	amer	amer	PROPN
ejpam-5398	350	6	,	,	PUNCT
ejpam-5398	350	7	galal	galal	PROPN
ejpam-5398	350	8	m	m	PROPN
ejpam-5398	350	9	moatimid	moatimid	PROPN
ejpam-5398	350	10	,	,	PUNCT
ejpam-5398	350	11	and	and	CCONJ
ejpam-5398	350	12	ws	ws	PROPN
ejpam-5398	350	13	amer	amer	PROPN
ejpam-5398	350	14	.	.	PUNCT
ejpam-5398	351	1	dynamical	dynamical	ADJ
ejpam-5398	351	2	stability	stability	NOUN
ejpam-5398	351	3	of	of	ADP
ejpam-5398	351	4	a	a	DET
ejpam-5398	351	5	3	3	NUM
ejpam-5398	351	6	-	-	PUNCT
ejpam-5398	351	7	dof	dof	NOUN
ejpam-5398	351	8	autoparametric	autoparametric	ADJ
ejpam-5398	351	9	vibrating	vibrating	NOUN
ejpam-5398	351	10	system	system	NOUN
ejpam-5398	351	11	.	.	PUNCT
ejpam-5398	352	1	journal	journal	NOUN
ejpam-5398	352	2	of	of	ADP
ejpam-5398	352	3	vibration	vibration	NOUN
ejpam-5398	352	4	engineering	engineering	NOUN
ejpam-5398	352	5	&	&	CCONJ
ejpam-5398	352	6	technologies	technology	NOUN
ejpam-5398	352	7	,	,	PUNCT
ejpam-5398	352	8	11(8):4151–4186	11(8):4151–4186	NUM
ejpam-5398	352	9	,	,	PUNCT
ejpam-5398	352	10	2023	2023	NUM
ejpam-5398	352	11	.	.	PUNCT
ejpam-5398	353	1	[	[	X
ejpam-5398	353	2	3	3	X
ejpam-5398	353	3	]	]	PUNCT
ejpam-5398	353	4	vs	vs	ADP
ejpam-5398	353	5	erturk	erturk	PROPN
ejpam-5398	353	6	,	,	PUNCT
ejpam-5398	353	7	b	b	PROPN
ejpam-5398	353	8	rath	rath	PROPN
ejpam-5398	353	9	,	,	PUNCT
ejpam-5398	353	10	taqwa	taqwa	PROPN
ejpam-5398	353	11	m	m	PROPN
ejpam-5398	353	12	al	al	PROPN
ejpam-5398	353	13	-	-	PUNCT
ejpam-5398	353	14	khader	khader	PROPN
ejpam-5398	353	15	,	,	PUNCT
ejpam-5398	353	16	noorhan	noorhan	PROPN
ejpam-5398	353	17	alshaikh	alshaikh	PROPN
ejpam-5398	353	18	,	,	PUNCT
ejpam-5398	353	19	p	p	PROPN
ejpam-5398	353	20	mallick	mallick	NOUN
ejpam-5398	353	21	,	,	PUNCT
ejpam-5398	353	22	and	and	CCONJ
ejpam-5398	353	23	jihad	jihad	PROPN
ejpam-5398	353	24	asad	asad	PROPN
ejpam-5398	353	25	.	.	PUNCT
ejpam-5398	354	1	two	two	NUM
ejpam-5398	354	2	-	-	PUNCT
ejpam-5398	354	3	dimensional	dimensional	ADJ
ejpam-5398	354	4	coupled	couple	VERB
ejpam-5398	354	5	asymmetric	asymmetric	ADJ
ejpam-5398	354	6	van	van	PROPN
ejpam-5398	354	7	der	der	PROPN
ejpam-5398	354	8	pol	pol	PROPN
ejpam-5398	354	9	oscillator	oscillator	NOUN
ejpam-5398	354	10	.	.	PUNCT
ejpam-5398	355	1	european	european	PROPN
ejpam-5398	355	2	journal	journal	PROPN
ejpam-5398	355	3	of	of	ADP
ejpam-5398	355	4	pure	pure	ADJ
ejpam-5398	355	5	and	and	CCONJ
ejpam-5398	355	6	applied	applied	ADJ
ejpam-5398	355	7	mathematics	mathematic	NOUN
ejpam-5398	355	8	,	,	PUNCT
ejpam-5398	355	9	17(2):1254–1264	17(2):1254–1264	NUM
ejpam-5398	355	10	,	,	PUNCT
ejpam-5398	355	11	2024	2024	NUM
ejpam-5398	355	12	.	.	PUNCT
ejpam-5398	356	1	[	[	X
ejpam-5398	356	2	4	4	NUM
ejpam-5398	356	3	]	]	X
ejpam-5398	356	4	bawar	bawar	ADJ
ejpam-5398	356	5	mohammed	mohammed	PROPN
ejpam-5398	356	6	faraj	faraj	PROPN
ejpam-5398	356	7	,	,	PUNCT
ejpam-5398	356	8	shnyar	shnyar	NOUN
ejpam-5398	356	9	karim	karim	PROPN
ejpam-5398	356	10	rahman	rahman	PROPN
ejpam-5398	356	11	,	,	PUNCT
ejpam-5398	356	12	deni	deni	PROPN
ejpam-5398	356	13	adnan	adnan	PROPN
ejpam-5398	356	14	mohammed	mohammed	PROPN
ejpam-5398	356	15	,	,	PUNCT
ejpam-5398	356	16	hozan	hozan	PROPN
ejpam-5398	356	17	dlshad	dlshad	VERB
ejpam-5398	356	18	hilmi	hilmi	PROPN
ejpam-5398	356	19	,	,	PUNCT
ejpam-5398	356	20	and	and	CCONJ
ejpam-5398	356	21	ali	ali	PROPN
ejpam-5398	356	22	akgul	akgul	PROPN
ejpam-5398	356	23	.	.	PUNCT
ejpam-5398	357	1	efficient	efficient	ADJ
ejpam-5398	357	2	finite	finite	ADJ
ejpam-5398	357	3	difference	difference	NOUN
ejpam-5398	357	4	approaches	approach	NOUN
ejpam-5398	357	5	for	for	ADP
ejpam-5398	357	6	solving	solve	VERB
ejpam-5398	357	7	references	reference	NOUN
ejpam-5398	357	8	2894	2894	NUM
ejpam-5398	357	9	initial	initial	ADJ
ejpam-5398	357	10	boundary	boundary	ADJ
ejpam-5398	357	11	value	value	NOUN
ejpam-5398	357	12	problems	problem	NOUN
ejpam-5398	357	13	in	in	ADP
ejpam-5398	357	14	helmholtz	helmholtz	NOUN
ejpam-5398	357	15	partial	partial	ADJ
ejpam-5398	357	16	differential	differential	NOUN
ejpam-5398	357	17	equations	equation	NOUN
ejpam-5398	357	18	.	.	PUNCT
ejpam-5398	358	1	contemporary	contemporary	ADJ
ejpam-5398	358	2	mathematics	mathematic	NOUN
ejpam-5398	358	3	,	,	PUNCT
ejpam-5398	358	4	pages	page	NOUN
ejpam-5398	358	5	569–580	569–580	NUM
ejpam-5398	358	6	,	,	PUNCT
ejpam-5398	358	7	2023	2023	NUM
ejpam-5398	358	8	.	.	PUNCT
ejpam-5398	359	1	[	[	X
ejpam-5398	359	2	5	5	NUM
ejpam-5398	359	3	]	]	X
ejpam-5398	359	4	bawar	bawar	ADJ
ejpam-5398	359	5	mohammed	mohammed	PROPN
ejpam-5398	359	6	faraj	faraj	PROPN
ejpam-5398	359	7	,	,	PUNCT
ejpam-5398	359	8	dana	dana	PROPN
ejpam-5398	359	9	taha	taha	PROPN
ejpam-5398	359	10	mohammed	mohammed	PROPN
ejpam-5398	359	11	salih	salih	PROPN
ejpam-5398	359	12	,	,	PUNCT
ejpam-5398	359	13	bnar	bnar	ADJ
ejpam-5398	359	14	hama	hama	PROPN
ejpam-5398	359	15	zaman	zaman	PROPN
ejpam-5398	359	16	hama	hama	PROPN
ejpam-5398	359	17	ali	ali	PROPN
ejpam-5398	359	18	,	,	PUNCT
ejpam-5398	359	19	bahadin	bahadin	PROPN
ejpam-5398	359	20	muhammad	muhammad	PROPN
ejpam-5398	359	21	hussien	hussien	PROPN
ejpam-5398	359	22	,	,	PUNCT
ejpam-5398	359	23	sarkhel	sarkhel	PROPN
ejpam-5398	359	24	akbar	akbar	PROPN
ejpam-5398	359	25	mahmood	mahmood	PROPN
ejpam-5398	359	26	,	,	PUNCT
ejpam-5398	359	27	and	and	CCONJ
ejpam-5398	359	28	shewa	shewa	PROPN
ejpam-5398	359	29	abid	abid	PROPN
ejpam-5398	359	30	hama	hama	PROPN
ejpam-5398	359	31	.	.	PUNCT
ejpam-5398	360	1	on	on	ADP
ejpam-5398	360	2	the	the	DET
ejpam-5398	360	3	numerical	numerical	ADJ
ejpam-5398	360	4	solution	solution	NOUN
ejpam-5398	360	5	for	for	ADP
ejpam-5398	360	6	two	two	NUM
ejpam-5398	360	7	dimensional	dimensional	ADJ
ejpam-5398	360	8	laplace	laplace	NOUN
ejpam-5398	360	9	equation	equation	NOUN
ejpam-5398	360	10	with	with	ADP
ejpam-5398	360	11	initial	initial	ADJ
ejpam-5398	360	12	boundary	boundary	ADJ
ejpam-5398	360	13	conditions	condition	NOUN
ejpam-5398	360	14	by	by	ADP
ejpam-5398	360	15	using	use	VERB
ejpam-5398	360	16	finite	finite	ADJ
ejpam-5398	360	17	difference	difference	NOUN
ejpam-5398	360	18	methods	method	NOUN
ejpam-5398	360	19	.	.	PUNCT
ejpam-5398	361	1	journal	journal	NOUN
ejpam-5398	361	2	of	of	ADP
ejpam-5398	361	3	studies	study	NOUN
ejpam-5398	361	4	in	in	ADP
ejpam-5398	361	5	science	science	NOUN
ejpam-5398	361	6	and	and	CCONJ
ejpam-5398	361	7	engineering	engineering	NOUN
ejpam-5398	361	8	,	,	PUNCT
ejpam-5398	361	9	2(4):50–59	2(4):50–59	NUM
ejpam-5398	361	10	,	,	PUNCT
ejpam-5398	361	11	2022	2022	NUM
ejpam-5398	361	12	.	.	PUNCT
ejpam-5398	362	1	[	[	X
ejpam-5398	362	2	6	6	NUM
ejpam-5398	362	3	]	]	PUNCT
ejpam-5398	362	4	seyed	seyed	PROPN
ejpam-5398	362	5	s	s	PROPN
ejpam-5398	362	6	ganji	ganji	X
ejpam-5398	362	7	,	,	PUNCT
ejpam-5398	362	8	amin	amin	NOUN
ejpam-5398	362	9	barari	barari	PROPN
ejpam-5398	362	10	,	,	PUNCT
ejpam-5398	362	11	s	s	PART
ejpam-5398	362	12	karimpour	karimpour	NOUN
ejpam-5398	362	13	,	,	PUNCT
ejpam-5398	362	14	and	and	CCONJ
ejpam-5398	362	15	g	g	PROPN
ejpam-5398	362	16	domairry	domairry	NOUN
ejpam-5398	362	17	.	.	PUNCT
ejpam-5398	363	1	motion	motion	NOUN
ejpam-5398	363	2	of	of	ADP
ejpam-5398	363	3	a	a	DET
ejpam-5398	363	4	rigid	rigid	ADJ
ejpam-5398	363	5	rod	rod	NOUN
ejpam-5398	363	6	rocking	rock	VERB
ejpam-5398	363	7	back	back	ADV
ejpam-5398	363	8	and	and	CCONJ
ejpam-5398	363	9	forth	forth	ADV
ejpam-5398	363	10	and	and	CCONJ
ejpam-5398	363	11	cubic	cubic	ADJ
ejpam-5398	363	12	-	-	PUNCT
ejpam-5398	363	13	quintic	quintic	ADJ
ejpam-5398	363	14	duffing	duffing	NOUN
ejpam-5398	363	15	oscillators	oscillator	NOUN
ejpam-5398	363	16	.	.	PUNCT
ejpam-5398	364	1	journal	journal	NOUN
ejpam-5398	364	2	of	of	ADP
ejpam-5398	364	3	theoretical	theoretical	ADJ
ejpam-5398	364	4	and	and	CCONJ
ejpam-5398	364	5	applied	applied	ADJ
ejpam-5398	364	6	mechanics	mechanic	NOUN
ejpam-5398	364	7	,	,	PUNCT
ejpam-5398	364	8	50(1):215–229	50(1):215–229	PROPN
ejpam-5398	364	9	,	,	PUNCT
ejpam-5398	364	10	2012	2012	NUM
ejpam-5398	364	11	.	.	PUNCT
ejpam-5398	365	1	[	[	X
ejpam-5398	365	2	7	7	X
ejpam-5398	365	3	]	]	X
ejpam-5398	365	4	ji	ji	PROPN
ejpam-5398	365	5	-	-	PROPN
ejpam-5398	365	6	huan	huan	PROPN
ejpam-5398	365	7	he	he	PROPN
ejpam-5398	365	8	.	.	PUNCT
ejpam-5398	366	1	amplitude	amplitude	NOUN
ejpam-5398	366	2	-	-	PUNCT
ejpam-5398	366	3	frequency	frequency	NOUN
ejpam-5398	366	4	relationship	relationship	NOUN
ejpam-5398	366	5	for	for	ADP
ejpam-5398	366	6	conservative	conservative	ADJ
ejpam-5398	366	7	nonlinear	nonlinear	ADJ
ejpam-5398	366	8	oscillators	oscillator	NOUN
ejpam-5398	366	9	with	with	ADP
ejpam-5398	366	10	odd	odd	ADJ
ejpam-5398	366	11	nonlinearities	nonlinearitie	NOUN
ejpam-5398	366	12	.	.	PUNCT
ejpam-5398	367	1	international	international	ADJ
ejpam-5398	367	2	journal	journal	PROPN
ejpam-5398	367	3	of	of	ADP
ejpam-5398	367	4	applied	applied	ADJ
ejpam-5398	367	5	and	and	CCONJ
ejpam-5398	367	6	computational	computational	ADJ
ejpam-5398	367	7	mathematics	mathematic	NOUN
ejpam-5398	367	8	,	,	PUNCT
ejpam-5398	367	9	3:1557–1560	3:1557–1560	PROPN
ejpam-5398	367	10	,	,	PUNCT
ejpam-5398	367	11	2017	2017	NUM
ejpam-5398	367	12	.	.	PUNCT
ejpam-5398	368	1	[	[	X
ejpam-5398	368	2	8	8	NUM
ejpam-5398	368	3	]	]	X
ejpam-5398	368	4	gamal	gamal	PROPN
ejpam-5398	368	5	ismail	ismail	PROPN
ejpam-5398	368	6	,	,	PUNCT
ejpam-5398	368	7	galal	galal	PROPN
ejpam-5398	368	8	moatimid	moatimid	PROPN
ejpam-5398	368	9	,	,	PUNCT
ejpam-5398	368	10	and	and	CCONJ
ejpam-5398	368	11	mohammed	mohammed	PROPN
ejpam-5398	368	12	yamani	yamani	PROPN
ejpam-5398	368	13	.	.	PUNCT
ejpam-5398	369	1	periodic	periodic	ADJ
ejpam-5398	369	2	solutions	solution	NOUN
ejpam-5398	369	3	of	of	ADP
ejpam-5398	369	4	strongly	strongly	ADV
ejpam-5398	369	5	nonlinear	nonlinear	ADJ
ejpam-5398	369	6	oscillators	oscillator	NOUN
ejpam-5398	369	7	using	use	VERB
ejpam-5398	369	8	he	he	PRON
ejpam-5398	369	9	’s	’s	PART
ejpam-5398	369	10	frequency	frequency	NOUN
ejpam-5398	369	11	formulation	formulation	NOUN
ejpam-5398	369	12	.	.	PUNCT
ejpam-5398	370	1	european	european	ADJ
ejpam-5398	370	2	journal	journal	PROPN
ejpam-5398	370	3	of	of	ADP
ejpam-5398	370	4	pure	pure	ADJ
ejpam-5398	370	5	and	and	CCONJ
ejpam-5398	370	6	applied	applied	ADJ
ejpam-5398	370	7	mathematics	mathematic	NOUN
ejpam-5398	370	8	,	,	PUNCT
ejpam-5398	370	9	17(3):2155–2172	17(3):2155–2172	NUM
ejpam-5398	370	10	,	,	PUNCT
ejpam-5398	370	11	2024	2024	NUM
ejpam-5398	370	12	.	.	PUNCT
ejpam-5398	371	1	[	[	X
ejpam-5398	371	2	9	9	NUM
ejpam-5398	371	3	]	]	X
ejpam-5398	371	4	goran	goran	NOUN
ejpam-5398	371	5	janevski	janevski	PROPN
ejpam-5398	371	6	,	,	PUNCT
ejpam-5398	371	7	predrag	predrag	PROPN
ejpam-5398	371	8	kozić	kozić	PROPN
ejpam-5398	371	9	,	,	PUNCT
ejpam-5398	371	10	ratko	ratko	PROPN
ejpam-5398	371	11	pavlović	pavlović	NOUN
ejpam-5398	371	12	,	,	PUNCT
ejpam-5398	371	13	and	and	CCONJ
ejpam-5398	371	14	strain	strain	VERB
ejpam-5398	371	15	posavljak	posavljak	ADV
ejpam-5398	371	16	.	.	PUNCT
ejpam-5398	372	1	moment	moment	NOUN
ejpam-5398	372	2	lyapunov	lyapunov	PROPN
ejpam-5398	372	3	exponents	exponent	NOUN
ejpam-5398	372	4	and	and	CCONJ
ejpam-5398	372	5	stochastic	stochastic	ADJ
ejpam-5398	372	6	stability	stability	NOUN
ejpam-5398	372	7	of	of	ADP
ejpam-5398	372	8	a	a	DET
ejpam-5398	372	9	thin	thin	ADJ
ejpam-5398	372	10	-	-	PUNCT
ejpam-5398	372	11	walled	walled	ADJ
ejpam-5398	372	12	beam	beam	NOUN
ejpam-5398	372	13	subjected	subject	VERB
ejpam-5398	372	14	to	to	ADP
ejpam-5398	372	15	axial	axial	ADJ
ejpam-5398	372	16	loads	load	NOUN
ejpam-5398	372	17	and	and	CCONJ
ejpam-5398	372	18	end	end	VERB
ejpam-5398	372	19	moments	moment	NOUN
ejpam-5398	372	20	.	.	PUNCT
ejpam-5398	373	1	facta	facta	PROPN
ejpam-5398	373	2	universitatis	universitatis	PROPN
ejpam-5398	373	3	,	,	PUNCT
ejpam-5398	373	4	series	series	NOUN
ejpam-5398	373	5	:	:	PUNCT
ejpam-5398	373	6	mechanical	mechanical	ADJ
ejpam-5398	373	7	engineering	engineering	NOUN
ejpam-5398	373	8	,	,	PUNCT
ejpam-5398	373	9	19(2):209–228	19(2):209–228	PROPN
ejpam-5398	373	10	,	,	PUNCT
ejpam-5398	373	11	2021	2021	NUM
ejpam-5398	373	12	.	.	PUNCT
ejpam-5398	374	1	[	[	X
ejpam-5398	374	2	10	10	NUM
ejpam-5398	374	3	]	]	X
ejpam-5398	374	4	weiming	weime	VERB
ejpam-5398	374	5	ji	ji	PROPN
ejpam-5398	374	6	,	,	PUNCT
ejpam-5398	374	7	hui	hui	PROPN
ejpam-5398	374	8	wang	wang	PROPN
ejpam-5398	374	9	,	,	PUNCT
ejpam-5398	374	10	and	and	CCONJ
ejpam-5398	374	11	meng	meng	PROPN
ejpam-5398	374	12	liu	liu	PROPN
ejpam-5398	374	13	.	.	PUNCT
ejpam-5398	375	1	dynamics	dynamic	VERB
ejpam-5398	375	2	analysis	analysis	NOUN
ejpam-5398	375	3	of	of	ADP
ejpam-5398	375	4	an	an	DET
ejpam-5398	375	5	impulsive	impulsive	ADJ
ejpam-5398	375	6	stochastic	stochastic	ADJ
ejpam-5398	375	7	model	model	NOUN
ejpam-5398	375	8	for	for	ADP
ejpam-5398	375	9	spruce	spruce	NOUN
ejpam-5398	375	10	budworm	budworm	NOUN
ejpam-5398	375	11	growth	growth	NOUN
ejpam-5398	375	12	.	.	PUNCT
ejpam-5398	376	1	applied	apply	VERB
ejpam-5398	376	2	and	and	CCONJ
ejpam-5398	376	3	computational	computational	ADJ
ejpam-5398	376	4	mathematics	mathematic	NOUN
ejpam-5398	376	5	,	,	PUNCT
ejpam-5398	376	6	19(3):336–359	19(3):336–359	NUM
ejpam-5398	376	7	,	,	PUNCT
ejpam-5398	376	8	2020	2020	NUM
ejpam-5398	376	9	.	.	PUNCT
ejpam-5398	377	1	[	[	X
ejpam-5398	377	2	11	11	NUM
ejpam-5398	377	3	]	]	PUNCT
ejpam-5398	377	4	h	h	NOUN
ejpam-5398	377	5	ebrahimi	ebrahimi	PROPN
ejpam-5398	377	6	khah	khah	PROPN
ejpam-5398	377	7	and	and	CCONJ
ejpam-5398	377	8	dd	dd	VERB
ejpam-5398	377	9	ganji	ganji	NOUN
ejpam-5398	377	10	.	.	PUNCT
ejpam-5398	378	1	a	a	DET
ejpam-5398	378	2	study	study	NOUN
ejpam-5398	378	3	on	on	ADP
ejpam-5398	378	4	the	the	DET
ejpam-5398	378	5	motion	motion	NOUN
ejpam-5398	378	6	of	of	ADP
ejpam-5398	378	7	a	a	DET
ejpam-5398	378	8	rigid	rigid	ADJ
ejpam-5398	378	9	rod	rod	NOUN
ejpam-5398	378	10	rocking	rock	VERB
ejpam-5398	378	11	back	back	ADV
ejpam-5398	378	12	and	and	CCONJ
ejpam-5398	378	13	cubic	cubic	ADJ
ejpam-5398	378	14	-	-	PUNCT
ejpam-5398	378	15	quintic	quintic	ADJ
ejpam-5398	378	16	duffing	duffing	NOUN
ejpam-5398	378	17	oscillators	oscillator	NOUN
ejpam-5398	378	18	by	by	ADP
ejpam-5398	378	19	using	use	VERB
ejpam-5398	378	20	he	he	PRON
ejpam-5398	378	21	’s	’s	PART
ejpam-5398	378	22	energy	energy	NOUN
ejpam-5398	378	23	balance	balance	NOUN
ejpam-5398	378	24	method	method	NOUN
ejpam-5398	378	25	.	.	PUNCT
ejpam-5398	379	1	international	international	ADJ
ejpam-5398	379	2	journal	journal	PROPN
ejpam-5398	379	3	of	of	ADP
ejpam-5398	379	4	nonlinear	nonlinear	ADJ
ejpam-5398	379	5	science	science	NOUN
ejpam-5398	379	6	,	,	PUNCT
ejpam-5398	379	7	10(4):447–451	10(4):447–451	PROPN
ejpam-5398	379	8	,	,	PUNCT
ejpam-5398	379	9	2010	2010	NUM
ejpam-5398	379	10	.	.	PUNCT
ejpam-5398	380	1	[	[	X
ejpam-5398	380	2	12	12	NUM
ejpam-5398	380	3	]	]	X
ejpam-5398	380	4	craig	craig	PROPN
ejpam-5398	380	5	a	a	PRON
ejpam-5398	380	6	kluever	kluever	ADV
ejpam-5398	380	7	.	.	PUNCT
ejpam-5398	381	1	dynamic	dynamic	ADJ
ejpam-5398	381	2	systems	system	NOUN
ejpam-5398	381	3	:	:	PUNCT
ejpam-5398	381	4	modeling	modeling	NOUN
ejpam-5398	381	5	,	,	PUNCT
ejpam-5398	381	6	simulation	simulation	NOUN
ejpam-5398	381	7	,	,	PUNCT
ejpam-5398	381	8	and	and	CCONJ
ejpam-5398	381	9	control	control	NOUN
ejpam-5398	381	10	.	.	PUNCT
ejpam-5398	382	1	john	john	PROPN
ejpam-5398	382	2	wiley	wiley	PROPN
ejpam-5398	382	3	&	&	CCONJ
ejpam-5398	382	4	sons	son	NOUN
ejpam-5398	382	5	,	,	PUNCT
ejpam-5398	382	6	2020	2020	NUM
ejpam-5398	382	7	.	.	PUNCT
ejpam-5398	383	1	[	[	X
ejpam-5398	383	2	13	13	NUM
ejpam-5398	383	3	]	]	X
ejpam-5398	383	4	jw	jw	PROPN
ejpam-5398	383	5	meek	meek	PROPN
ejpam-5398	383	6	.	.	PUNCT
ejpam-5398	384	1	dynamic	dynamic	ADJ
ejpam-5398	384	2	response	response	NOUN
ejpam-5398	384	3	of	of	ADP
ejpam-5398	384	4	tipping	tip	VERB
ejpam-5398	384	5	core	core	NOUN
ejpam-5398	384	6	buildings	building	NOUN
ejpam-5398	384	7	.	.	PUNCT
ejpam-5398	385	1	earthquake	earthquake	NOUN
ejpam-5398	385	2	engineering	engineering	PROPN
ejpam-5398	385	3	&	&	CCONJ
ejpam-5398	385	4	structural	structural	ADJ
ejpam-5398	385	5	dynamics	dynamic	NOUN
ejpam-5398	385	6	,	,	PUNCT
ejpam-5398	385	7	6(5):437–454	6(5):437–454	NOUN
ejpam-5398	385	8	,	,	PUNCT
ejpam-5398	385	9	1978	1978	NUM
ejpam-5398	385	10	.	.	PUNCT
ejpam-5398	386	1	[	[	X
ejpam-5398	386	2	14	14	NUM
ejpam-5398	386	3	]	]	PUNCT
ejpam-5398	386	4	galal	galal	PROPN
ejpam-5398	386	5	m	m	PROPN
ejpam-5398	386	6	moatimid	moatimid	NOUN
ejpam-5398	386	7	and	and	CCONJ
ejpam-5398	386	8	ts	ts	ADP
ejpam-5398	386	9	amer	amer	PROPN
ejpam-5398	386	10	.	.	PUNCT
ejpam-5398	387	1	analytical	analytical	ADJ
ejpam-5398	387	2	solution	solution	NOUN
ejpam-5398	387	3	for	for	ADP
ejpam-5398	387	4	the	the	DET
ejpam-5398	387	5	motion	motion	NOUN
ejpam-5398	387	6	of	of	ADP
ejpam-5398	387	7	a	a	DET
ejpam-5398	387	8	pendulum	pendulum	NOUN
ejpam-5398	387	9	with	with	ADP
ejpam-5398	387	10	rolling	rolling	ADJ
ejpam-5398	387	11	wheel	wheel	NOUN
ejpam-5398	387	12	:	:	PUNCT
ejpam-5398	387	13	stability	stability	NOUN
ejpam-5398	387	14	analysis	analysis	NOUN
ejpam-5398	387	15	.	.	PUNCT
ejpam-5398	388	1	scientific	scientific	ADJ
ejpam-5398	388	2	reports	report	NOUN
ejpam-5398	388	3	,	,	PUNCT
ejpam-5398	388	4	12(1):12628	12(1):12628	NUM
ejpam-5398	388	5	,	,	PUNCT
ejpam-5398	388	6	2022	2022	NUM
ejpam-5398	388	7	.	.	PUNCT
ejpam-5398	389	1	[	[	X
ejpam-5398	389	2	15	15	NUM
ejpam-5398	389	3	]	]	AUX
ejpam-5398	389	4	galal	galal	PROPN
ejpam-5398	389	5	m	m	PROPN
ejpam-5398	389	6	moatimid	moatimid	NOUN
ejpam-5398	389	7	and	and	CCONJ
ejpam-5398	389	8	ts	ts	ADP
ejpam-5398	389	9	amer	amer	PROPN
ejpam-5398	389	10	.	.	PUNCT
ejpam-5398	390	1	nonlinear	nonlinear	ADJ
ejpam-5398	390	2	suppression	suppression	NOUN
ejpam-5398	390	3	using	use	VERB
ejpam-5398	390	4	time	time	NOUN
ejpam-5398	390	5	-	-	PUNCT
ejpam-5398	390	6	delayed	delay	VERB
ejpam-5398	390	7	controller	controller	NOUN
ejpam-5398	390	8	to	to	ADP
ejpam-5398	390	9	excited	excited	ADJ
ejpam-5398	390	10	van	van	PROPN
ejpam-5398	390	11	der	der	ADJ
ejpam-5398	390	12	pol	pol	PROPN
ejpam-5398	390	13	–	–	PUNCT
ejpam-5398	390	14	duffing	duffe	VERB
ejpam-5398	390	15	oscillator	oscillator	NOUN
ejpam-5398	390	16	:	:	PUNCT
ejpam-5398	390	17	analytical	analytical	ADJ
ejpam-5398	390	18	solution	solution	NOUN
ejpam-5398	390	19	techniques	technique	NOUN
ejpam-5398	390	20	.	.	PUNCT
ejpam-5398	391	1	archive	archive	NOUN
ejpam-5398	391	2	of	of	ADP
ejpam-5398	391	3	applied	apply	VERB
ejpam-5398	391	4	mechanics	mechanic	NOUN
ejpam-5398	391	5	,	,	PUNCT
ejpam-5398	391	6	92(12):3515–3531	92(12):3515–3531	NUM
ejpam-5398	391	7	,	,	PUNCT
ejpam-5398	391	8	2022	2022	NUM
ejpam-5398	391	9	.	.	PUNCT
ejpam-5398	392	1	references	reference	NOUN
ejpam-5398	392	2	2895	2895	NUM
ejpam-5398	393	1	[	[	X
ejpam-5398	393	2	16	16	NUM
ejpam-5398	393	3	]	]	PUNCT
ejpam-5398	393	4	galal	galal	PROPN
ejpam-5398	393	5	m	m	PROPN
ejpam-5398	393	6	moatimid	moatimid	NOUN
ejpam-5398	393	7	and	and	CCONJ
ejpam-5398	393	8	ts	ts	ADP
ejpam-5398	393	9	amer	amer	PROPN
ejpam-5398	393	10	.	.	PROPN
ejpam-5398	394	1	analytical	analytical	ADJ
ejpam-5398	394	2	approximate	approximate	ADJ
ejpam-5398	394	3	solutions	solution	NOUN
ejpam-5398	394	4	of	of	ADP
ejpam-5398	394	5	a	a	DET
ejpam-5398	394	6	magnetic	magnetic	ADJ
ejpam-5398	394	7	spherical	spherical	ADJ
ejpam-5398	394	8	pendulum	pendulum	NOUN
ejpam-5398	394	9	:	:	PUNCT
ejpam-5398	394	10	stability	stability	NOUN
ejpam-5398	394	11	analysis	analysis	NOUN
ejpam-5398	394	12	.	.	PUNCT
ejpam-5398	395	1	journal	journal	NOUN
ejpam-5398	395	2	of	of	ADP
ejpam-5398	395	3	vibration	vibration	NOUN
ejpam-5398	395	4	engineering	engineering	NOUN
ejpam-5398	395	5	&	&	CCONJ
ejpam-5398	395	6	technologies	technology	NOUN
ejpam-5398	395	7	,	,	PUNCT
ejpam-5398	395	8	11(5):2155–2165	11(5):2155–2165	NUM
ejpam-5398	395	9	,	,	PUNCT
ejpam-5398	395	10	2023	2023	NUM
ejpam-5398	395	11	.	.	PUNCT
ejpam-5398	396	1	[	[	X
ejpam-5398	396	2	17	17	NUM
ejpam-5398	396	3	]	]	PUNCT
ejpam-5398	396	4	galal	galal	PROPN
ejpam-5398	396	5	m	m	PROPN
ejpam-5398	396	6	moatimid	moatimid	NOUN
ejpam-5398	396	7	and	and	CCONJ
ejpam-5398	396	8	ts	ts	ADP
ejpam-5398	396	9	amer	amer	PROPN
ejpam-5398	396	10	.	.	PUNCT
ejpam-5398	397	1	dynamical	dynamical	ADJ
ejpam-5398	397	2	system	system	NOUN
ejpam-5398	397	3	of	of	ADP
ejpam-5398	397	4	a	a	DET
ejpam-5398	397	5	time	time	NOUN
ejpam-5398	397	6	-	-	PUNCT
ejpam-5398	397	7	delayed	delay	VERB
ejpam-5398	397	8	of	of	ADP
ejpam-5398	397	9	rigid	rigid	ADJ
ejpam-5398	397	10	rocking	rocking	NOUN
ejpam-5398	397	11	rod	rod	NOUN
ejpam-5398	397	12	:	:	PUNCT
ejpam-5398	397	13	analytical	analytical	ADJ
ejpam-5398	397	14	approximate	approximate	ADJ
ejpam-5398	397	15	solution	solution	NOUN
ejpam-5398	397	16	.	.	PUNCT
ejpam-5398	398	1	scientific	scientific	ADJ
ejpam-5398	398	2	reports	report	NOUN
ejpam-5398	398	3	,	,	PUNCT
ejpam-5398	398	4	13(1):5570	13(1):5570	NUM
ejpam-5398	398	5	,	,	PUNCT
ejpam-5398	398	6	2023	2023	NUM
ejpam-5398	398	7	.	.	PUNCT
ejpam-5398	399	1	[	[	X
ejpam-5398	399	2	18	18	NUM
ejpam-5398	399	3	]	]	PUNCT
ejpam-5398	399	4	galal	galal	PROPN
ejpam-5398	399	5	m	m	PROPN
ejpam-5398	399	6	moatimid	moatimid	NOUN
ejpam-5398	399	7	and	and	CCONJ
ejpam-5398	399	8	ts	ts	ADP
ejpam-5398	399	9	amer	amer	PROPN
ejpam-5398	399	10	.	.	PUNCT
ejpam-5398	400	1	dynamical	dynamical	ADJ
ejpam-5398	400	2	system	system	NOUN
ejpam-5398	400	3	of	of	ADP
ejpam-5398	400	4	a	a	DET
ejpam-5398	400	5	time	time	NOUN
ejpam-5398	400	6	-	-	PUNCT
ejpam-5398	400	7	delayed	delay	VERB
ejpam-5398	400	8	ϕ	ϕ	NOUN
ejpam-5398	400	9	6	6	NUM
ejpam-5398	400	10	-	-	PUNCT
ejpam-5398	400	11	van	van	PROPN
ejpam-5398	400	12	der	der	ADJ
ejpam-5398	400	13	pol	pol	PROPN
ejpam-5398	400	14	oscillator	oscillator	NOUN
ejpam-5398	400	15	:	:	PUNCT
ejpam-5398	400	16	a	a	DET
ejpam-5398	400	17	non	non	ADJ
ejpam-5398	400	18	-	-	ADJ
ejpam-5398	400	19	perturbative	perturbative	ADJ
ejpam-5398	400	20	approach	approach	NOUN
ejpam-5398	400	21	.	.	PUNCT
ejpam-5398	401	1	scientific	scientific	ADJ
ejpam-5398	401	2	reports	report	NOUN
ejpam-5398	401	3	,	,	PUNCT
ejpam-5398	401	4	13(1):11942	13(1):11942	NUM
ejpam-5398	401	5	,	,	PUNCT
ejpam-5398	401	6	2023	2023	NUM
ejpam-5398	401	7	.	.	PUNCT
ejpam-5398	402	1	[	[	X
ejpam-5398	402	2	19	19	NUM
ejpam-5398	402	3	]	]	PUNCT
ejpam-5398	402	4	galal	galal	PROPN
ejpam-5398	402	5	m	m	PROPN
ejpam-5398	402	6	moatimid	moatimid	PROPN
ejpam-5398	402	7	,	,	PUNCT
ejpam-5398	402	8	ts	ts	ADP
ejpam-5398	402	9	amer	amer	PROPN
ejpam-5398	402	10	,	,	PUNCT
ejpam-5398	402	11	and	and	CCONJ
ejpam-5398	402	12	ws	ws	PROPN
ejpam-5398	402	13	amer	amer	PROPN
ejpam-5398	402	14	.	.	PUNCT
ejpam-5398	403	1	dynamical	dynamical	ADJ
ejpam-5398	403	2	analysis	analysis	NOUN
ejpam-5398	403	3	of	of	ADP
ejpam-5398	403	4	a	a	DET
ejpam-5398	403	5	damped	damped	ADJ
ejpam-5398	403	6	harmonic	harmonic	NOUN
ejpam-5398	403	7	forced	force	VERB
ejpam-5398	403	8	duffing	duffe	VERB
ejpam-5398	403	9	oscillator	oscillator	NOUN
ejpam-5398	403	10	with	with	ADP
ejpam-5398	403	11	time	time	NOUN
ejpam-5398	403	12	delay	delay	NOUN
ejpam-5398	403	13	.	.	PUNCT
ejpam-5398	404	1	scientific	scientific	ADJ
ejpam-5398	404	2	reports	report	NOUN
ejpam-5398	404	3	,	,	PUNCT
ejpam-5398	404	4	13(1):6507	13(1):6507	NUM
ejpam-5398	404	5	,	,	PUNCT
ejpam-5398	404	6	2023	2023	NUM
ejpam-5398	404	7	.	.	PUNCT
ejpam-5398	405	1	[	[	X
ejpam-5398	405	2	20	20	NUM
ejpam-5398	405	3	]	]	PUNCT
ejpam-5398	405	4	galal	galal	PROPN
ejpam-5398	405	5	m	m	PROPN
ejpam-5398	405	6	moatimid	moatimid	PROPN
ejpam-5398	405	7	,	,	PUNCT
ejpam-5398	405	8	ts	ts	ADP
ejpam-5398	405	9	amer	amer	PROPN
ejpam-5398	405	10	,	,	PUNCT
ejpam-5398	405	11	and	and	CCONJ
ejpam-5398	405	12	yy	yy	PROPN
ejpam-5398	405	13	ellabban	ellabban	VERB
ejpam-5398	405	14	.	.	PUNCT
ejpam-5398	406	1	a	a	DET
ejpam-5398	406	2	novel	novel	ADJ
ejpam-5398	406	3	methodology	methodology	NOUN
ejpam-5398	406	4	for	for	ADP
ejpam-5398	406	5	a	a	DET
ejpam-5398	406	6	timedelayed	timedelayed	ADJ
ejpam-5398	406	7	controller	controller	NOUN
ejpam-5398	406	8	to	to	PART
ejpam-5398	406	9	prevent	prevent	VERB
ejpam-5398	406	10	nonlinear	nonlinear	ADJ
ejpam-5398	406	11	system	system	NOUN
ejpam-5398	406	12	oscillations	oscillation	NOUN
ejpam-5398	406	13	.	.	PUNCT
ejpam-5398	407	1	journal	journal	NOUN
ejpam-5398	407	2	of	of	ADP
ejpam-5398	407	3	low	low	ADJ
ejpam-5398	407	4	frequency	frequency	NOUN
ejpam-5398	407	5	noise	noise	NOUN
ejpam-5398	407	6	,	,	PUNCT
ejpam-5398	407	7	vibration	vibration	NOUN
ejpam-5398	407	8	and	and	CCONJ
ejpam-5398	407	9	active	active	ADJ
ejpam-5398	407	10	control	control	NOUN
ejpam-5398	407	11	,	,	PUNCT
ejpam-5398	407	12	43(1):525–542	43(1):525–542	PROPN
ejpam-5398	407	13	,	,	PUNCT
ejpam-5398	407	14	2024	2024	NUM
ejpam-5398	407	15	.	.	PUNCT
ejpam-5398	408	1	[	[	X
ejpam-5398	408	2	21	21	NUM
ejpam-5398	408	3	]	]	AUX
ejpam-5398	408	4	galal	galal	PROPN
ejpam-5398	408	5	m	m	PROPN
ejpam-5398	408	6	moatimid	moatimid	PROPN
ejpam-5398	408	7	,	,	PUNCT
ejpam-5398	408	8	ts	ts	ADP
ejpam-5398	408	9	amer	amer	PROPN
ejpam-5398	408	10	,	,	PUNCT
ejpam-5398	408	11	and	and	CCONJ
ejpam-5398	408	12	aa	aa	PROPN
ejpam-5398	408	13	galal	galal	PROPN
ejpam-5398	408	14	.	.	PUNCT
ejpam-5398	409	1	studying	study	VERB
ejpam-5398	409	2	highly	highly	ADV
ejpam-5398	409	3	nonlinear	nonlinear	ADJ
ejpam-5398	409	4	oscillators	oscillator	NOUN
ejpam-5398	409	5	using	use	VERB
ejpam-5398	409	6	the	the	DET
ejpam-5398	409	7	non	non	ADJ
ejpam-5398	409	8	-	-	ADJ
ejpam-5398	409	9	perturbative	perturbative	ADJ
ejpam-5398	409	10	methodology	methodology	NOUN
ejpam-5398	409	11	.	.	PUNCT
ejpam-5398	410	1	scientific	scientific	ADJ
ejpam-5398	410	2	reports	report	NOUN
ejpam-5398	410	3	,	,	PUNCT
ejpam-5398	410	4	13(1):20288	13(1):20288	NUM
ejpam-5398	410	5	,	,	PUNCT
ejpam-5398	410	6	2023	2023	NUM
ejpam-5398	410	7	.	.	PUNCT
ejpam-5398	411	1	[	[	X
ejpam-5398	411	2	22	22	NUM
ejpam-5398	411	3	]	]	PUNCT
ejpam-5398	411	4	galal	galal	PROPN
ejpam-5398	411	5	m	m	PROPN
ejpam-5398	411	6	moatimid	moatimid	PROPN
ejpam-5398	411	7	,	,	PUNCT
ejpam-5398	411	8	ts	ts	ADP
ejpam-5398	411	9	amer	amer	PROPN
ejpam-5398	411	10	,	,	PUNCT
ejpam-5398	411	11	and	and	CCONJ
ejpam-5398	411	12	aa	aa	PROPN
ejpam-5398	411	13	galal	galal	PROPN
ejpam-5398	411	14	.	.	PUNCT
ejpam-5398	412	1	studying	study	VERB
ejpam-5398	412	2	highly	highly	ADV
ejpam-5398	412	3	nonlinear	nonlinear	ADJ
ejpam-5398	412	4	oscillators	oscillator	NOUN
ejpam-5398	412	5	using	use	VERB
ejpam-5398	412	6	the	the	DET
ejpam-5398	412	7	non	non	ADJ
ejpam-5398	412	8	-	-	ADJ
ejpam-5398	412	9	perturbative	perturbative	ADJ
ejpam-5398	412	10	methodology	methodology	NOUN
ejpam-5398	412	11	.	.	PUNCT
ejpam-5398	413	1	scientific	scientific	ADJ
ejpam-5398	413	2	reports	report	NOUN
ejpam-5398	413	3	,	,	PUNCT
ejpam-5398	413	4	13(1):20288	13(1):20288	NUM
ejpam-5398	413	5	,	,	PUNCT
ejpam-5398	413	6	2023	2023	NUM
ejpam-5398	413	7	.	.	PUNCT
ejpam-5398	414	1	[	[	X
ejpam-5398	414	2	23	23	NUM
ejpam-5398	414	3	]	]	PUNCT
ejpam-5398	414	4	galal	galal	PROPN
ejpam-5398	414	5	m	m	PROPN
ejpam-5398	414	6	moatimid	moatimid	PROPN
ejpam-5398	414	7	,	,	PUNCT
ejpam-5398	414	8	ts	ts	ADP
ejpam-5398	414	9	amer	amer	PROPN
ejpam-5398	414	10	,	,	PUNCT
ejpam-5398	414	11	and	and	CCONJ
ejpam-5398	414	12	aa	aa	PROPN
ejpam-5398	414	13	galal	galal	PROPN
ejpam-5398	414	14	.	.	PUNCT
ejpam-5398	415	1	inspection	inspection	NOUN
ejpam-5398	415	2	of	of	ADP
ejpam-5398	415	3	some	some	DET
ejpam-5398	415	4	extremely	extremely	ADV
ejpam-5398	415	5	nonlinear	nonlinear	ADJ
ejpam-5398	415	6	oscillators	oscillator	NOUN
ejpam-5398	415	7	using	use	VERB
ejpam-5398	415	8	an	an	DET
ejpam-5398	415	9	inventive	inventive	ADJ
ejpam-5398	415	10	approach	approach	NOUN
ejpam-5398	415	11	.	.	PUNCT
ejpam-5398	416	1	journal	journal	NOUN
ejpam-5398	416	2	of	of	ADP
ejpam-5398	416	3	vibration	vibration	NOUN
ejpam-5398	416	4	engineering	engineering	NOUN
ejpam-5398	416	5	&	&	CCONJ
ejpam-5398	416	6	technologies	technology	NOUN
ejpam-5398	416	7	,	,	PUNCT
ejpam-5398	416	8	pages	page	NOUN
ejpam-5398	416	9	1–11	1–11	PROPN
ejpam-5398	416	10	,	,	PUNCT
ejpam-5398	416	11	2024	2024	NUM
ejpam-5398	416	12	.	.	PUNCT
ejpam-5398	417	1	[	[	X
ejpam-5398	417	2	24	24	NUM
ejpam-5398	417	3	]	]	PUNCT
ejpam-5398	417	4	galal	galal	PROPN
ejpam-5398	417	5	m	m	PROPN
ejpam-5398	417	6	moatimid	moatimid	PROPN
ejpam-5398	417	7	,	,	PUNCT
ejpam-5398	417	8	ts	ts	ADP
ejpam-5398	417	9	amer	amer	PROPN
ejpam-5398	417	10	,	,	PUNCT
ejpam-5398	417	11	and	and	CCONJ
ejpam-5398	417	12	marwa	marwa	PROPN
ejpam-5398	417	13	h	h	PROPN
ejpam-5398	417	14	zekry	zekry	PROPN
ejpam-5398	417	15	.	.	PROPN
ejpam-5398	418	1	analytical	analytical	ADJ
ejpam-5398	418	2	and	and	CCONJ
ejpam-5398	418	3	numerical	numerical	ADJ
ejpam-5398	418	4	study	study	NOUN
ejpam-5398	418	5	of	of	ADP
ejpam-5398	418	6	a	a	DET
ejpam-5398	418	7	vibrating	vibrate	VERB
ejpam-5398	418	8	magnetic	magnetic	ADJ
ejpam-5398	418	9	inverted	invert	VERB
ejpam-5398	418	10	pendulum	pendulum	NOUN
ejpam-5398	418	11	.	.	PUNCT
ejpam-5398	419	1	archive	archive	NOUN
ejpam-5398	419	2	of	of	ADP
ejpam-5398	419	3	applied	apply	VERB
ejpam-5398	419	4	mechanics	mechanic	NOUN
ejpam-5398	419	5	,	,	PUNCT
ejpam-5398	419	6	93(6):2533	93(6):2533	NUM
ejpam-5398	419	7	–	–	PUNCT
ejpam-5398	419	8	2547	2547	NUM
ejpam-5398	419	9	,	,	PUNCT
ejpam-5398	419	10	2023	2023	NUM
ejpam-5398	419	11	.	.	PUNCT
ejpam-5398	420	1	[	[	X
ejpam-5398	420	2	25	25	NUM
ejpam-5398	420	3	]	]	AUX
ejpam-5398	420	4	galal	galal	PROPN
ejpam-5398	420	5	m	m	PROPN
ejpam-5398	420	6	moatimid	moatimid	PROPN
ejpam-5398	420	7	,	,	PUNCT
ejpam-5398	420	8	at	at	ADP
ejpam-5398	420	9	el	el	PROPN
ejpam-5398	420	10	-	-	PUNCT
ejpam-5398	420	11	sayed	say	VERB
ejpam-5398	420	12	,	,	PUNCT
ejpam-5398	420	13	and	and	CCONJ
ejpam-5398	420	14	hala	hala	PROPN
ejpam-5398	420	15	f	f	PROPN
ejpam-5398	420	16	salman	salman	PROPN
ejpam-5398	420	17	.	.	PUNCT
ejpam-5398	421	1	different	different	ADJ
ejpam-5398	421	2	controllers	controller	NOUN
ejpam-5398	421	3	for	for	ADP
ejpam-5398	421	4	suppressing	suppress	VERB
ejpam-5398	421	5	oscillations	oscillation	NOUN
ejpam-5398	421	6	of	of	ADP
ejpam-5398	421	7	a	a	DET
ejpam-5398	421	8	hybrid	hybrid	ADJ
ejpam-5398	421	9	oscillator	oscillator	NOUN
ejpam-5398	421	10	via	via	ADP
ejpam-5398	421	11	non	non	ADJ
ejpam-5398	421	12	-	-	ADJ
ejpam-5398	421	13	perturbative	perturbative	ADJ
ejpam-5398	421	14	analysis	analysis	NOUN
ejpam-5398	421	15	.	.	PUNCT
ejpam-5398	422	1	scientific	scientific	ADJ
ejpam-5398	422	2	reports	report	NOUN
ejpam-5398	422	3	,	,	PUNCT
ejpam-5398	422	4	14(1):307	14(1):307	NUM
ejpam-5398	422	5	,	,	PUNCT
ejpam-5398	422	6	2024	2024	NUM
ejpam-5398	422	7	.	.	PUNCT
ejpam-5398	423	1	[	[	X
ejpam-5398	423	2	26	26	NUM
ejpam-5398	423	3	]	]	PUNCT
ejpam-5398	423	4	galal	galal	PROPN
ejpam-5398	423	5	m	m	PROPN
ejpam-5398	423	6	moatimid	moatimid	PROPN
ejpam-5398	423	7	,	,	PUNCT
ejpam-5398	423	8	mona	mona	PROPN
ejpam-5398	423	9	aa	aa	PROPN
ejpam-5398	423	10	mohamed	mohamed	PROPN
ejpam-5398	423	11	,	,	PUNCT
ejpam-5398	423	12	and	and	CCONJ
ejpam-5398	423	13	khaled	khaled	PROPN
ejpam-5398	423	14	elagamy	elagamy	PROPN
ejpam-5398	423	15	.	.	PUNCT
ejpam-5398	424	1	nonlinear	nonlinear	ADJ
ejpam-5398	424	2	kelvinhelmholtz	kelvinhelmholtz	NOUN
ejpam-5398	424	3	instability	instability	NOUN
ejpam-5398	424	4	of	of	ADP
ejpam-5398	424	5	a	a	DET
ejpam-5398	424	6	horizontal	horizontal	ADJ
ejpam-5398	424	7	interface	interface	NOUN
ejpam-5398	424	8	separating	separate	VERB
ejpam-5398	424	9	two	two	NUM
ejpam-5398	424	10	electrified	electrify	VERB
ejpam-5398	424	11	walters	walter	NOUN
ejpam-5398	424	12	’	'	PUNCT
ejpam-5398	424	13	b	b	PROPN
ejpam-5398	424	14	liquids	liquid	NOUN
ejpam-5398	424	15	:	:	PUNCT
ejpam-5398	424	16	a	a	DET
ejpam-5398	424	17	new	new	ADJ
ejpam-5398	424	18	approach	approach	NOUN
ejpam-5398	424	19	.	.	PUNCT
ejpam-5398	425	1	chinese	chinese	ADJ
ejpam-5398	425	2	journal	journal	PROPN
ejpam-5398	425	3	of	of	ADP
ejpam-5398	425	4	physics	physics	PROPN
ejpam-5398	425	5	,	,	PUNCT
ejpam-5398	425	6	85:629–648	85:629–648	PROPN
ejpam-5398	425	7	,	,	PUNCT
ejpam-5398	425	8	2023	2023	NUM
ejpam-5398	425	9	.	.	PUNCT
ejpam-5398	426	1	[	[	X
ejpam-5398	426	2	27	27	NUM
ejpam-5398	426	3	]	]	PUNCT
ejpam-5398	426	4	galal	galal	PROPN
ejpam-5398	426	5	m	m	PROPN
ejpam-5398	426	6	moatimid	moatimid	PROPN
ejpam-5398	426	7	,	,	PUNCT
ejpam-5398	426	8	mona	mona	PROPN
ejpam-5398	426	9	aa	aa	PROPN
ejpam-5398	426	10	mohamed	mohamed	PROPN
ejpam-5398	426	11	,	,	PUNCT
ejpam-5398	426	12	and	and	CCONJ
ejpam-5398	426	13	khaled	khaled	PROPN
ejpam-5398	426	14	elagamy	elagamy	NOUN
ejpam-5398	426	15	.	.	PUNCT
ejpam-5398	427	1	an	an	DET
ejpam-5398	427	2	innovative	innovative	ADJ
ejpam-5398	427	3	approach	approach	NOUN
ejpam-5398	427	4	in	in	ADP
ejpam-5398	427	5	inspecting	inspect	VERB
ejpam-5398	427	6	a	a	DET
ejpam-5398	427	7	damped	damp	VERB
ejpam-5398	427	8	mathieu	mathieu	PROPN
ejpam-5398	427	9	cubic	cubic	ADJ
ejpam-5398	427	10	–	–	PUNCT
ejpam-5398	427	11	quintic	quintic	ADJ
ejpam-5398	427	12	duffing	duffing	NOUN
ejpam-5398	427	13	oscillator	oscillator	NOUN
ejpam-5398	427	14	.	.	PUNCT
ejpam-5398	428	1	journal	journal	NOUN
ejpam-5398	428	2	of	of	ADP
ejpam-5398	428	3	vibration	vibration	NOUN
ejpam-5398	428	4	engineering	engineering	NOUN
ejpam-5398	428	5	&	&	CCONJ
ejpam-5398	428	6	technologies	technology	NOUN
ejpam-5398	428	7	,	,	PUNCT
ejpam-5398	428	8	pages	page	NOUN
ejpam-5398	428	9	1–18	1–18	NUM
ejpam-5398	428	10	,	,	PUNCT
ejpam-5398	428	11	2024	2024	NUM
ejpam-5398	428	12	.	.	PUNCT
ejpam-5398	429	1	[	[	X
ejpam-5398	429	2	28	28	NUM
ejpam-5398	429	3	]	]	X
ejpam-5398	429	4	galal	galal	PROPN
ejpam-5398	429	5	m	m	PROPN
ejpam-5398	429	6	moatimid	moatimid	PROPN
ejpam-5398	429	7	,	,	PUNCT
ejpam-5398	429	8	mona	mona	PROPN
ejpam-5398	429	9	aa	aa	PROPN
ejpam-5398	429	10	mohamed	mohamed	PROPN
ejpam-5398	429	11	,	,	PUNCT
ejpam-5398	429	12	and	and	CCONJ
ejpam-5398	429	13	khaled	khaled	PROPN
ejpam-5398	429	14	elagamy	elagamy	NOUN
ejpam-5398	429	15	.	.	PUNCT
ejpam-5398	430	1	insightful	insightful	ADJ
ejpam-5398	430	2	inspection	inspection	NOUN
ejpam-5398	430	3	of	of	ADP
ejpam-5398	430	4	the	the	DET
ejpam-5398	430	5	nonlinear	nonlinear	ADJ
ejpam-5398	430	6	instability	instability	NOUN
ejpam-5398	430	7	of	of	ADP
ejpam-5398	430	8	an	an	DET
ejpam-5398	430	9	azimuthal	azimuthal	ADJ
ejpam-5398	430	10	disturbance	disturbance	NOUN
ejpam-5398	430	11	separating	separate	VERB
ejpam-5398	430	12	two	two	NUM
ejpam-5398	430	13	rotating	rotate	VERB
ejpam-5398	430	14	magnetic	magnetic	ADJ
ejpam-5398	430	15	liquid	liquid	ADJ
ejpam-5398	430	16	columns	column	NOUN
ejpam-5398	430	17	.	.	PUNCT
ejpam-5398	431	1	the	the	DET
ejpam-5398	431	2	european	european	PROPN
ejpam-5398	431	3	physical	physical	PROPN
ejpam-5398	431	4	journal	journal	PROPN
ejpam-5398	431	5	plus	plus	CCONJ
ejpam-5398	431	6	,	,	PUNCT
ejpam-5398	431	7	139(7):1–23	139(7):1–23	PROPN
ejpam-5398	431	8	,	,	PUNCT
ejpam-5398	431	9	2024	2024	NUM
ejpam-5398	431	10	.	.	PUNCT
ejpam-5398	432	1	references	reference	NOUN
ejpam-5398	432	2	2896	2896	NUM
ejpam-5398	433	1	[	[	X
ejpam-5398	433	2	29	29	NUM
ejpam-5398	433	3	]	]	PUNCT
ejpam-5398	433	4	galal	galal	PROPN
ejpam-5398	433	5	m	m	PROPN
ejpam-5398	433	6	moatimid	moatimid	PROPN
ejpam-5398	433	7	,	,	PUNCT
ejpam-5398	433	8	mona	mona	PROPN
ejpam-5398	433	9	aa	aa	PROPN
ejpam-5398	433	10	mohamed	mohamed	PROPN
ejpam-5398	433	11	,	,	PUNCT
ejpam-5398	433	12	and	and	CCONJ
ejpam-5398	433	13	khaled	khaled	PROPN
ejpam-5398	433	14	elagamy	elagamy	NOUN
ejpam-5398	433	15	.	.	PUNCT
ejpam-5398	434	1	inspection	inspection	NOUN
ejpam-5398	434	2	of	of	ADP
ejpam-5398	434	3	the	the	DET
ejpam-5398	434	4	nonlinear	nonlinear	ADJ
ejpam-5398	434	5	instability	instability	NOUN
ejpam-5398	434	6	of	of	ADP
ejpam-5398	434	7	electrified	electrified	ADJ
ejpam-5398	434	8	casson	casson	PROPN
ejpam-5398	434	9	fluids	fluid	NOUN
ejpam-5398	434	10	:	:	PUNCT
ejpam-5398	434	11	a	a	DET
ejpam-5398	434	12	novel	novel	ADJ
ejpam-5398	434	13	approach	approach	NOUN
ejpam-5398	434	14	.	.	PUNCT
ejpam-5398	435	1	waves	wave	NOUN
ejpam-5398	435	2	in	in	ADP
ejpam-5398	435	3	random	random	ADJ
ejpam-5398	435	4	and	and	CCONJ
ejpam-5398	435	5	complex	complex	ADJ
ejpam-5398	435	6	media	medium	NOUN
ejpam-5398	435	7	,	,	PUNCT
ejpam-5398	435	8	pages	page	NOUN
ejpam-5398	435	9	1–31	1–31	PROPN
ejpam-5398	435	10	,	,	PUNCT
ejpam-5398	435	11	2024	2024	NUM
ejpam-5398	435	12	.	.	PUNCT
ejpam-5398	436	1	[	[	X
ejpam-5398	436	2	30	30	NUM
ejpam-5398	436	3	]	]	PUNCT
ejpam-5398	436	4	galal	galal	PROPN
ejpam-5398	436	5	m	m	PROPN
ejpam-5398	436	6	moatimid	moatimid	PROPN
ejpam-5398	436	7	and	and	CCONJ
ejpam-5398	436	8	yasmeen	yasmeen	PROPN
ejpam-5398	436	9	m	m	PROPN
ejpam-5398	436	10	mohamed	mohamed	PROPN
ejpam-5398	436	11	.	.	PUNCT
ejpam-5398	437	1	nonlinear	nonlinear	ADJ
ejpam-5398	437	2	electro	electro	ADJ
ejpam-5398	437	3	-	-	PUNCT
ejpam-5398	437	4	rheological	rheological	ADJ
ejpam-5398	437	5	instability	instability	NOUN
ejpam-5398	437	6	of	of	ADP
ejpam-5398	437	7	two	two	NUM
ejpam-5398	437	8	moving	move	VERB
ejpam-5398	437	9	cylindrical	cylindrical	ADJ
ejpam-5398	437	10	fluids	fluid	NOUN
ejpam-5398	437	11	:	:	PUNCT
ejpam-5398	437	12	an	an	DET
ejpam-5398	437	13	innovative	innovative	ADJ
ejpam-5398	437	14	approach	approach	NOUN
ejpam-5398	437	15	.	.	PUNCT
ejpam-5398	438	1	physics	physics	NOUN
ejpam-5398	438	2	of	of	ADP
ejpam-5398	438	3	fluids	fluid	NOUN
ejpam-5398	438	4	,	,	PUNCT
ejpam-5398	438	5	36(2	36(2	NUM
ejpam-5398	438	6	)	)	PUNCT
ejpam-5398	438	7	,	,	PUNCT
ejpam-5398	438	8	2024	2024	NUM
ejpam-5398	438	9	.	.	PUNCT
ejpam-5398	439	1	[	[	X
ejpam-5398	439	2	31	31	NUM
ejpam-5398	439	3	]	]	PUNCT
ejpam-5398	439	4	galal	galal	PROPN
ejpam-5398	439	5	m	m	PROPN
ejpam-5398	439	6	moatimid	moatimid	PROPN
ejpam-5398	439	7	and	and	CCONJ
ejpam-5398	439	8	yasmeen	yasmeen	PROPN
ejpam-5398	439	9	m	m	PROPN
ejpam-5398	439	10	mohamed	mohame	VERB
ejpam-5398	439	11	.	.	PUNCT
ejpam-5398	440	1	a	a	DET
ejpam-5398	440	2	novel	novel	ADJ
ejpam-5398	440	3	methodology	methodology	NOUN
ejpam-5398	440	4	in	in	ADP
ejpam-5398	440	5	analyzing	analyze	VERB
ejpam-5398	440	6	nonlinear	nonlinear	ADJ
ejpam-5398	440	7	stability	stability	NOUN
ejpam-5398	440	8	of	of	ADP
ejpam-5398	440	9	two	two	NUM
ejpam-5398	440	10	electrified	electrify	VERB
ejpam-5398	440	11	viscoelastic	viscoelastic	ADJ
ejpam-5398	440	12	liquids	liquid	NOUN
ejpam-5398	440	13	.	.	PUNCT
ejpam-5398	441	1	chinese	chinese	ADJ
ejpam-5398	441	2	journal	journal	PROPN
ejpam-5398	441	3	of	of	ADP
ejpam-5398	441	4	physics	physics	PROPN
ejpam-5398	441	5	,	,	PUNCT
ejpam-5398	441	6	89:679–706	89:679–706	PROPN
ejpam-5398	441	7	,	,	PUNCT
ejpam-5398	441	8	2024	2024	NUM
ejpam-5398	441	9	.	.	PUNCT
ejpam-5398	442	1	[	[	X
ejpam-5398	442	2	32	32	NUM
ejpam-5398	442	3	]	]	PUNCT
ejpam-5398	442	4	galal	galal	PROPN
ejpam-5398	442	5	m	m	PROPN
ejpam-5398	442	6	moatimid	moatimid	PROPN
ejpam-5398	442	7	and	and	CCONJ
ejpam-5398	442	8	dm	dm	PROPN
ejpam-5398	442	9	mostafa	mostafa	PROPN
ejpam-5398	442	10	.	.	PUNCT
ejpam-5398	443	1	nonlinear	nonlinear	ADJ
ejpam-5398	443	2	stability	stability	NOUN
ejpam-5398	443	3	of	of	ADP
ejpam-5398	443	4	two	two	NUM
ejpam-5398	443	5	superimposed	superimpose	VERB
ejpam-5398	443	6	electrified	electrified	ADJ
ejpam-5398	443	7	dusty	dusty	ADJ
ejpam-5398	443	8	fluids	fluid	NOUN
ejpam-5398	443	9	of	of	ADP
ejpam-5398	443	10	type	type	NOUN
ejpam-5398	443	11	rivlin	rivlin	PROPN
ejpam-5398	443	12	-	-	PUNCT
ejpam-5398	443	13	ericksen	ericksen	ADJ
ejpam-5398	443	14	:	:	PUNCT
ejpam-5398	443	15	non	non	ADJ
ejpam-5398	443	16	-	-	ADJ
ejpam-5398	443	17	perturbative	perturbative	ADJ
ejpam-5398	443	18	approach	approach	NOUN
ejpam-5398	443	19	.	.	PUNCT
ejpam-5398	444	1	partial	partial	ADJ
ejpam-5398	444	2	differential	differential	ADJ
ejpam-5398	444	3	equations	equation	NOUN
ejpam-5398	444	4	in	in	ADP
ejpam-5398	444	5	applied	applied	ADJ
ejpam-5398	444	6	mathematics	mathematic	NOUN
ejpam-5398	444	7	,	,	PUNCT
ejpam-5398	444	8	page	page	NOUN
ejpam-5398	444	9	100745	100745	NUM
ejpam-5398	444	10	,	,	PUNCT
ejpam-5398	444	11	2024	2024	NUM
ejpam-5398	444	12	.	.	PUNCT
ejpam-5398	445	1	[	[	X
ejpam-5398	445	2	33	33	NUM
ejpam-5398	445	3	]	]	PUNCT
ejpam-5398	445	4	galal	galal	PROPN
ejpam-5398	445	5	m	m	PROPN
ejpam-5398	445	6	moatimid	moatimid	PROPN
ejpam-5398	445	7	,	,	PUNCT
ejpam-5398	445	8	dm	dm	PROPN
ejpam-5398	445	9	mostafa	mostafa	PROPN
ejpam-5398	445	10	,	,	PUNCT
ejpam-5398	445	11	and	and	CCONJ
ejpam-5398	445	12	marwa	marwa	PROPN
ejpam-5398	445	13	h	h	PROPN
ejpam-5398	445	14	zekry	zekry	PROPN
ejpam-5398	445	15	.	.	PUNCT
ejpam-5398	446	1	a	a	DET
ejpam-5398	446	2	new	new	ADJ
ejpam-5398	446	3	methodology	methodology	NOUN
ejpam-5398	446	4	in	in	ADP
ejpam-5398	446	5	evaluating	evaluate	VERB
ejpam-5398	446	6	nonlinear	nonlinear	ADJ
ejpam-5398	446	7	electrohydrodynamic	electrohydrodynamic	ADJ
ejpam-5398	446	8	azimuthal	azimuthal	NOUN
ejpam-5398	446	9	stability	stability	NOUN
ejpam-5398	446	10	between	between	ADP
ejpam-5398	446	11	two	two	NUM
ejpam-5398	446	12	dusty	dusty	ADJ
ejpam-5398	446	13	viscous	viscous	ADJ
ejpam-5398	446	14	fluids	fluid	NOUN
ejpam-5398	446	15	.	.	PUNCT
ejpam-5398	447	1	chinese	chinese	ADJ
ejpam-5398	447	2	journal	journal	PROPN
ejpam-5398	447	3	of	of	ADP
ejpam-5398	447	4	physics	physics	PROPN
ejpam-5398	447	5	,	,	PUNCT
ejpam-5398	447	6	90:134–154	90:134–154	NUM
ejpam-5398	447	7	,	,	PUNCT
ejpam-5398	447	8	2024	2024	NUM
ejpam-5398	447	9	.	.	PUNCT
ejpam-5398	448	1	[	[	X
ejpam-5398	448	2	34	34	NUM
ejpam-5398	448	3	]	]	PUNCT
ejpam-5398	448	4	galal	galal	PROPN
ejpam-5398	448	5	m	m	PROPN
ejpam-5398	448	6	moatimid	moatimid	PROPN
ejpam-5398	448	7	and	and	CCONJ
ejpam-5398	448	8	aya	aya	PROPN
ejpam-5398	448	9	sayed	say	VERB
ejpam-5398	448	10	.	.	PUNCT
ejpam-5398	449	1	nonlinear	nonlinear	ADJ
ejpam-5398	449	2	ehd	ehd	NOUN
ejpam-5398	449	3	stability	stability	NOUN
ejpam-5398	449	4	of	of	ADP
ejpam-5398	449	5	a	a	DET
ejpam-5398	449	6	cylindrical	cylindrical	ADJ
ejpam-5398	449	7	interface	interface	NOUN
ejpam-5398	449	8	separating	separate	VERB
ejpam-5398	449	9	two	two	NUM
ejpam-5398	449	10	rivlin	rivlin	ADJ
ejpam-5398	449	11	-	-	PUNCT
ejpam-5398	449	12	ericksen	ericksen	ADJ
ejpam-5398	449	13	fluids	fluid	NOUN
ejpam-5398	449	14	:	:	PUNCT
ejpam-5398	449	15	a	a	DET
ejpam-5398	449	16	novel	novel	ADJ
ejpam-5398	449	17	analysis	analysis	NOUN
ejpam-5398	449	18	.	.	PUNCT
ejpam-5398	450	1	chinese	chinese	ADJ
ejpam-5398	450	2	journal	journal	PROPN
ejpam-5398	450	3	of	of	ADP
ejpam-5398	450	4	physics	physics	PROPN
ejpam-5398	450	5	,	,	PUNCT
ejpam-5398	450	6	87:379–397	87:379–397	NUM
ejpam-5398	450	7	,	,	PUNCT
ejpam-5398	450	8	2024	2024	NUM
ejpam-5398	450	9	.	.	PUNCT
ejpam-5398	451	1	[	[	X
ejpam-5398	451	2	35	35	NUM
ejpam-5398	451	3	]	]	X
ejpam-5398	451	4	ivan	ivan	PROPN
ejpam-5398	451	5	r	r	PROPN
ejpam-5398	451	6	pavlović	pavlović	NOUN
ejpam-5398	451	7	,	,	PUNCT
ejpam-5398	451	8	ratko	ratko	PROPN
ejpam-5398	451	9	pavlović	pavlović	NOUN
ejpam-5398	451	10	,	,	PUNCT
ejpam-5398	451	11	goran	goran	PROPN
ejpam-5398	451	12	janevski	janevski	PROPN
ejpam-5398	451	13	,	,	PUNCT
ejpam-5398	451	14	nikola	nikola	PROPN
ejpam-5398	451	15	despenić	despenić	PROPN
ejpam-5398	451	16	,	,	PUNCT
ejpam-5398	451	17	and	and	CCONJ
ejpam-5398	451	18	vladimir	vladimir	PROPN
ejpam-5398	451	19	pajković.	pajković.	PROPN
ejpam-5398	451	20	dynamic	dynamic	ADJ
ejpam-5398	451	21	behavior	behavior	NOUN
ejpam-5398	451	22	of	of	ADP
ejpam-5398	451	23	two	two	NUM
ejpam-5398	451	24	elastically	elastically	ADV
ejpam-5398	451	25	connected	connect	VERB
ejpam-5398	451	26	nanobeams	nanobeam	NOUN
ejpam-5398	451	27	under	under	ADP
ejpam-5398	451	28	a	a	DET
ejpam-5398	451	29	white	white	ADJ
ejpam-5398	451	30	noise	noise	NOUN
ejpam-5398	451	31	process	process	NOUN
ejpam-5398	451	32	.	.	PUNCT
ejpam-5398	452	1	facta	facta	PROPN
ejpam-5398	452	2	universitatis	universitatis	PROPN
ejpam-5398	452	3	,	,	PUNCT
ejpam-5398	452	4	series	series	NOUN
ejpam-5398	452	5	:	:	PUNCT
ejpam-5398	452	6	mechanical	mechanical	ADJ
ejpam-5398	452	7	engineering	engineering	NOUN
ejpam-5398	452	8	,	,	PUNCT
ejpam-5398	452	9	18(2):219–227	18(2):219–227	PROPN
ejpam-5398	452	10	,	,	PUNCT
ejpam-5398	452	11	2020	2020	NUM
ejpam-5398	452	12	.	.	PUNCT
ejpam-5398	453	1	[	[	X
ejpam-5398	453	2	36	36	NUM
ejpam-5398	453	3	]	]	PUNCT
ejpam-5398	453	4	na	na	PART
ejpam-5398	453	5	qie	qie	PROPN
ejpam-5398	453	6	,	,	PUNCT
ejpam-5398	453	7	wei	wei	PROPN
ejpam-5398	453	8	-	-	PUNCT
ejpam-5398	453	9	fan	fan	PROPN
ejpam-5398	453	10	houa	houa	NOUN
ejpam-5398	453	11	,	,	PUNCT
ejpam-5398	453	12	and	and	CCONJ
ejpam-5398	453	13	ji	ji	PROPN
ejpam-5398	453	14	-	-	PROPN
ejpam-5398	453	15	huan	huan	PROPN
ejpam-5398	453	16	he	he	PROPN
ejpam-5398	453	17	.	.	PUNCT
ejpam-5398	454	1	the	the	DET
ejpam-5398	454	2	fastest	fast	ADJ
ejpam-5398	454	3	insight	insight	NOUN
ejpam-5398	454	4	into	into	ADP
ejpam-5398	454	5	the	the	DET
ejpam-5398	454	6	large	large	ADJ
ejpam-5398	454	7	amplitude	amplitude	NOUN
ejpam-5398	454	8	vibration	vibration	NOUN
ejpam-5398	454	9	of	of	ADP
ejpam-5398	454	10	a	a	DET
ejpam-5398	454	11	string	string	NOUN
ejpam-5398	454	12	.	.	PUNCT
ejpam-5398	455	1	reports	report	NOUN
ejpam-5398	455	2	in	in	ADP
ejpam-5398	455	3	mechanical	mechanical	ADJ
ejpam-5398	455	4	engineering	engineering	NOUN
ejpam-5398	455	5	,	,	PUNCT
ejpam-5398	455	6	2(1):1–5	2(1):1–5	NUM
ejpam-5398	455	7	,	,	PUNCT
ejpam-5398	455	8	2021	2021	NUM
ejpam-5398	455	9	.	.	PUNCT
ejpam-5398	456	1	[	[	X
ejpam-5398	456	2	37	37	NUM
ejpam-5398	456	3	]	]	X
ejpam-5398	456	4	zhong	zhong	PROPN
ejpam-5398	456	5	-	-	PUNCT
ejpam-5398	456	6	fu	fu	PROPN
ejpam-5398	456	7	ren	ren	PROPN
ejpam-5398	456	8	and	and	CCONJ
ejpam-5398	456	9	gui	gui	NOUN
ejpam-5398	456	10	-	-	PUNCT
ejpam-5398	456	11	fang	fang	X
ejpam-5398	456	12	hu	hu	PROPN
ejpam-5398	456	13	.	.	PUNCT
ejpam-5398	457	1	he	he	PRON
ejpam-5398	457	2	’s	’	VERB
ejpam-5398	457	3	frequency	frequency	NOUN
ejpam-5398	457	4	–	–	PUNCT
ejpam-5398	457	5	amplitude	amplitude	NOUN
ejpam-5398	457	6	formulation	formulation	NOUN
ejpam-5398	457	7	with	with	ADP
ejpam-5398	457	8	average	average	ADJ
ejpam-5398	457	9	residuals	residual	NOUN
ejpam-5398	457	10	for	for	ADP
ejpam-5398	457	11	nonlinear	nonlinear	ADJ
ejpam-5398	457	12	oscillators	oscillator	NOUN
ejpam-5398	457	13	.	.	PUNCT
ejpam-5398	458	1	journal	journal	NOUN
ejpam-5398	458	2	of	of	ADP
ejpam-5398	458	3	low	low	ADJ
ejpam-5398	458	4	frequency	frequency	NOUN
ejpam-5398	458	5	noise	noise	NOUN
ejpam-5398	458	6	,	,	PUNCT
ejpam-5398	458	7	vibration	vibration	NOUN
ejpam-5398	458	8	and	and	CCONJ
ejpam-5398	458	9	active	active	ADJ
ejpam-5398	458	10	control	control	NOUN
ejpam-5398	458	11	,	,	PUNCT
ejpam-5398	458	12	38(3	38(3	PROPN
ejpam-5398	458	13	-	-	SYM
ejpam-5398	458	14	4):1050–1059	4):1050–1059	NOUN
ejpam-5398	458	15	,	,	PUNCT
ejpam-5398	458	16	2019	2019	NUM
ejpam-5398	458	17	.	.	PUNCT
ejpam-5398	459	1	[	[	X
ejpam-5398	459	2	38	38	NUM
ejpam-5398	459	3	]	]	X
ejpam-5398	459	4	nasser	nasser	PROPN
ejpam-5398	459	5	a	a	DET
ejpam-5398	459	6	saeed	saeed	PROPN
ejpam-5398	459	7	,	,	PUNCT
ejpam-5398	459	8	galal	galal	PROPN
ejpam-5398	459	9	m	m	PROPN
ejpam-5398	459	10	moatimid	moatimid	PROPN
ejpam-5398	459	11	,	,	PUNCT
ejpam-5398	459	12	fawzy	fawzy	PROPN
ejpam-5398	459	13	m	m	PROPN
ejpam-5398	459	14	elsabaa	elsabaa	ADJ
ejpam-5398	459	15	,	,	PUNCT
ejpam-5398	459	16	yomna	yomna	PROPN
ejpam-5398	459	17	y	y	PROPN
ejpam-5398	459	18	ellabban	ellabban	PROPN
ejpam-5398	459	19	,	,	PUNCT
ejpam-5398	459	20	mohammed	mohammed	PROPN
ejpam-5398	459	21	a	a	DET
ejpam-5398	459	22	el	el	PROPN
ejpam-5398	459	23	-	-	PUNCT
ejpam-5398	459	24	meligy	meligy	PROPN
ejpam-5398	459	25	,	,	PUNCT
ejpam-5398	459	26	and	and	CCONJ
ejpam-5398	459	27	mohamed	mohamed	PROPN
ejpam-5398	459	28	sharaf	sharaf	PROPN
ejpam-5398	459	29	.	.	PUNCT
ejpam-5398	460	1	time	time	NOUN
ejpam-5398	460	2	-	-	PUNCT
ejpam-5398	460	3	delayed	delay	VERB
ejpam-5398	460	4	nonlinear	nonlinear	ADJ
ejpam-5398	460	5	feedback	feedback	NOUN
ejpam-5398	460	6	controllers	controller	NOUN
ejpam-5398	460	7	to	to	PART
ejpam-5398	460	8	suppress	suppress	VERB
ejpam-5398	460	9	the	the	DET
ejpam-5398	460	10	principal	principal	ADJ
ejpam-5398	460	11	parameter	parameter	NOUN
ejpam-5398	460	12	excitation	excitation	NOUN
ejpam-5398	460	13	.	.	PUNCT
ejpam-5398	461	1	ieee	ieee	NOUN
ejpam-5398	461	2	access	access	NOUN
ejpam-5398	461	3	,	,	PUNCT
ejpam-5398	461	4	8:226151	8:226151	NUM
ejpam-5398	461	5	–	–	PUNCT
ejpam-5398	461	6	226166	226166	NUM
ejpam-5398	461	7	,	,	PUNCT
ejpam-5398	461	8	2020	2020	NUM
ejpam-5398	461	9	.	.	PUNCT
ejpam-5398	462	1	[	[	X
ejpam-5398	462	2	39	39	NUM
ejpam-5398	462	3	]	]	PUNCT
ejpam-5398	462	4	steven	steven	PROPN
ejpam-5398	462	5	h	h	PROPN
ejpam-5398	462	6	strogatz	strogatz	PROPN
ejpam-5398	462	7	.	.	PUNCT
ejpam-5398	463	1	nonlinear	nonlinear	ADJ
ejpam-5398	463	2	dynamics	dynamic	NOUN
ejpam-5398	463	3	and	and	CCONJ
ejpam-5398	463	4	chaos	chaos	NOUN
ejpam-5398	463	5	:	:	PUNCT
ejpam-5398	463	6	with	with	ADP
ejpam-5398	463	7	applications	application	NOUN
ejpam-5398	463	8	to	to	ADP
ejpam-5398	463	9	physics	physics	NOUN
ejpam-5398	463	10	,	,	PUNCT
ejpam-5398	463	11	biology	biology	NOUN
ejpam-5398	463	12	,	,	PUNCT
ejpam-5398	463	13	chemistry	chemistry	NOUN
ejpam-5398	463	14	,	,	PUNCT
ejpam-5398	463	15	and	and	CCONJ
ejpam-5398	463	16	engineering	engineering	NOUN
ejpam-5398	463	17	.	.	PUNCT
ejpam-5398	464	1	crc	crc	PROPN
ejpam-5398	464	2	press	press	PROPN
ejpam-5398	464	3	,	,	PUNCT
ejpam-5398	464	4	2018	2018	NUM
ejpam-5398	464	5	.	.	PUNCT
ejpam-5398	465	1	[	[	X
ejpam-5398	465	2	40	40	NUM
ejpam-5398	465	3	]	]	X
ejpam-5398	465	4	yue	yue	PROPN
ejpam-5398	465	5	wu	wu	PROPN
ejpam-5398	465	6	and	and	CCONJ
ejpam-5398	465	7	yan	yan	PROPN
ejpam-5398	465	8	-	-	PUNCT
ejpam-5398	465	9	ping	ping	PROPN
ejpam-5398	465	10	liu	liu	PROPN
ejpam-5398	465	11	.	.	PUNCT
ejpam-5398	466	1	residual	residual	ADJ
ejpam-5398	466	2	calculation	calculation	NOUN
ejpam-5398	466	3	in	in	ADP
ejpam-5398	466	4	he	he	PRON
ejpam-5398	466	5	’s	’s	PART
ejpam-5398	466	6	frequency	frequency	NOUN
ejpam-5398	466	7	–	–	PUNCT
ejpam-5398	466	8	amplitude	amplitude	NOUN
ejpam-5398	466	9	formulation	formulation	NOUN
ejpam-5398	466	10	.	.	PUNCT
ejpam-5398	467	1	journal	journal	NOUN
ejpam-5398	467	2	of	of	ADP
ejpam-5398	467	3	low	low	ADJ
ejpam-5398	467	4	frequency	frequency	NOUN
ejpam-5398	467	5	noise	noise	NOUN
ejpam-5398	467	6	,	,	PUNCT
ejpam-5398	467	7	vibration	vibration	NOUN
ejpam-5398	467	8	and	and	CCONJ
ejpam-5398	467	9	active	active	ADJ
ejpam-5398	467	10	control	control	NOUN
ejpam-5398	467	11	,	,	PUNCT
ejpam-5398	467	12	40(2):1040–1047	40(2):1040–1047	NUM
ejpam-5398	467	13	,	,	PUNCT
ejpam-5398	467	14	2021	2021	NUM
ejpam-5398	467	15	.	.	PUNCT
ejpam-5398	468	1	references	reference	NOUN
ejpam-5398	468	2	2897	2897	NUM
ejpam-5398	469	1	[	[	X
ejpam-5398	469	2	41	41	NUM
ejpam-5398	469	3	]	]	PUNCT
ejpam-5398	469	4	chik	chik	NOUN
ejpam-5398	469	5	-	-	PUNCT
ejpam-5398	469	6	sing	sing	VERB
ejpam-5398	469	7	yim	yim	PROPN
ejpam-5398	469	8	and	and	CCONJ
ejpam-5398	469	9	anil	anil	PROPN
ejpam-5398	469	10	k	k	PROPN
ejpam-5398	469	11	chopra	chopra	PROPN
ejpam-5398	469	12	.	.	PUNCT
ejpam-5398	470	1	earthquake	earthquake	NOUN
ejpam-5398	470	2	response	response	NOUN
ejpam-5398	470	3	of	of	ADP
ejpam-5398	470	4	structures	structure	NOUN
ejpam-5398	470	5	with	with	ADP
ejpam-5398	470	6	partial	partial	ADJ
ejpam-5398	470	7	uplift	uplift	NOUN
ejpam-5398	470	8	on	on	ADP
ejpam-5398	470	9	winkler	winkler	PROPN
ejpam-5398	470	10	foundation	foundation	PROPN
ejpam-5398	470	11	.	.	PUNCT
ejpam-5398	471	1	earthquake	earthquake	NOUN
ejpam-5398	471	2	engineering	engineering	PROPN
ejpam-5398	471	3	&	&	CCONJ
ejpam-5398	471	4	structural	structural	ADJ
ejpam-5398	471	5	dynamics	dynamic	NOUN
ejpam-5398	471	6	,	,	PUNCT
ejpam-5398	471	7	12(2):263–281	12(2):263–281	NUM
ejpam-5398	471	8	,	,	PUNCT
ejpam-5398	471	9	1984	1984	NUM
ejpam-5398	471	10	.	.	PUNCT
ejpam-5398	472	1	[	[	X
ejpam-5398	472	2	42	42	NUM
ejpam-5398	472	3	]	]	PUNCT
ejpam-5398	472	4	yuting	yute	VERB
ejpam-5398	472	5	zuo	zuo	PROPN
ejpam-5398	472	6	.	.	PUNCT
ejpam-5398	473	1	a	a	DET
ejpam-5398	473	2	gecko	gecko	NOUN
ejpam-5398	473	3	-	-	PUNCT
ejpam-5398	473	4	like	like	ADJ
ejpam-5398	473	5	fractal	fractal	ADJ
ejpam-5398	473	6	receptor	receptor	NOUN
ejpam-5398	473	7	of	of	ADP
ejpam-5398	473	8	a	a	DET
ejpam-5398	473	9	three	three	NUM
ejpam-5398	473	10	-	-	PUNCT
ejpam-5398	473	11	dimensional	dimensional	ADJ
ejpam-5398	473	12	printing	printing	NOUN
ejpam-5398	473	13	technology	technology	NOUN
ejpam-5398	473	14	:	:	PUNCT
ejpam-5398	473	15	a	a	DET
ejpam-5398	473	16	fractal	fractal	ADJ
ejpam-5398	473	17	oscillator	oscillator	NOUN
ejpam-5398	473	18	.	.	PUNCT
ejpam-5398	474	1	journal	journal	PROPN
ejpam-5398	474	2	of	of	ADP
ejpam-5398	474	3	mathematical	mathematical	ADJ
ejpam-5398	474	4	chemistry	chemistry	NOUN
ejpam-5398	474	5	,	,	PUNCT
ejpam-5398	474	6	59(3):735–744	59(3):735–744	NUM
ejpam-5398	474	7	,	,	PUNCT
ejpam-5398	474	8	2021	2021	NUM
ejpam-5398	474	9	.	.	PUNCT