id	sid	tid	token	lemma	pos
ejpam-6091	1	1	european	european	PROPN
ejpam-6091	1	2	journal	journal	PROPN
ejpam-6091	1	3	of	of	ADP
ejpam-6091	1	4	pure	pure	ADJ
ejpam-6091	1	5	and	and	CCONJ
ejpam-6091	1	6	applied	applied	ADJ
ejpam-6091	1	7	mathematics	mathematic	NOUN
ejpam-6091	1	8	2025	2025	NUM
ejpam-6091	1	9	,	,	PUNCT
ejpam-6091	1	10	vol	vol	NOUN
ejpam-6091	1	11	.	.	PROPN
ejpam-6091	1	12	18	18	NUM
ejpam-6091	1	13	,	,	PUNCT
ejpam-6091	1	14	issue	issue	NOUN
ejpam-6091	1	15	3	3	NUM
ejpam-6091	1	16	,	,	PUNCT
ejpam-6091	1	17	article	article	NOUN
ejpam-6091	1	18	number	number	NOUN
ejpam-6091	1	19	6091	6091	NUM
ejpam-6091	1	20	issn	issn	PROPN
ejpam-6091	1	21	1307	1307	NUM
ejpam-6091	1	22	-	-	SYM
ejpam-6091	1	23	5543	5543	NUM
ejpam-6091	1	24	–	–	PUNCT
ejpam-6091	1	25	ejpam.com	ejpam.com	X
ejpam-6091	1	26	published	publish	VERB
ejpam-6091	1	27	by	by	ADP
ejpam-6091	1	28	new	new	PROPN
ejpam-6091	1	29	york	york	PROPN
ejpam-6091	1	30	business	business	PROPN
ejpam-6091	1	31	global	global	PROPN
ejpam-6091	1	32	hamilton	hamilton	PROPN
ejpam-6091	1	33	-	-	PUNCT
ejpam-6091	1	34	jacobi	jacobi	PROPN
ejpam-6091	1	35	framework	framework	NOUN
ejpam-6091	1	36	for	for	ADP
ejpam-6091	1	37	nonholonomic	nonholonomic	ADJ
ejpam-6091	1	38	dynamics	dynamic	NOUN
ejpam-6091	1	39	k.	k.	PROPN
ejpam-6091	1	40	i.	i.	PROPN
ejpam-6091	1	41	nawafleh	nawafleh	PROPN
ejpam-6091	1	42	physics	physics	PROPN
ejpam-6091	1	43	department	department	PROPN
ejpam-6091	1	44	,	,	PUNCT
ejpam-6091	1	45	mu’tah	mu’tah	PROPN
ejpam-6091	1	46	university	university	PROPN
ejpam-6091	1	47	,	,	PUNCT
ejpam-6091	1	48	al	al	PROPN
ejpam-6091	1	49	-	-	PUNCT
ejpam-6091	1	50	karak	karak	PROPN
ejpam-6091	1	51	,	,	PUNCT
ejpam-6091	1	52	jordan	jordan	PROPN
ejpam-6091	1	53	abstract	abstract	PROPN
ejpam-6091	1	54	.	.	PUNCT
ejpam-6091	2	1	we	we	PRON
ejpam-6091	2	2	derive	derive	VERB
ejpam-6091	2	3	generalized	generalized	ADJ
ejpam-6091	2	4	hamilton	hamilton	PROPN
ejpam-6091	2	5	–	–	PUNCT
ejpam-6091	2	6	jacobi	jacobi	PROPN
ejpam-6091	2	7	equations	equation	NOUN
ejpam-6091	2	8	for	for	ADP
ejpam-6091	2	9	dynamical	dynamical	ADJ
ejpam-6091	2	10	systems	system	NOUN
ejpam-6091	2	11	subject	subject	ADJ
ejpam-6091	2	12	to	to	ADP
ejpam-6091	2	13	nonholonomic	nonholonomic	ADJ
ejpam-6091	2	14	constraints	constraint	NOUN
ejpam-6091	2	15	.	.	PUNCT
ejpam-6091	3	1	the	the	DET
ejpam-6091	3	2	geometric	geometric	ADJ
ejpam-6091	3	3	formulation	formulation	NOUN
ejpam-6091	3	4	of	of	ADP
ejpam-6091	3	5	hamilton	hamilton	PROPN
ejpam-6091	3	6	-	-	PUNCT
ejpam-6091	3	7	jacobi	jacobi	PROPN
ejpam-6091	3	8	theory	theory	NOUN
ejpam-6091	3	9	for	for	ADP
ejpam-6091	3	10	nonholonomic	nonholonomic	ADJ
ejpam-6091	3	11	constraints	constraint	NOUN
ejpam-6091	3	12	is	be	AUX
ejpam-6091	3	13	developed	develop	VERB
ejpam-6091	3	14	,	,	PUNCT
ejpam-6091	3	15	following	follow	VERB
ejpam-6091	3	16	the	the	DET
ejpam-6091	3	17	ideas	idea	NOUN
ejpam-6091	3	18	of	of	ADP
ejpam-6091	3	19	the	the	DET
ejpam-6091	3	20	authors	author	NOUN
ejpam-6091	3	21	in	in	ADP
ejpam-6091	3	22	previous	previous	ADJ
ejpam-6091	3	23	papers	paper	NOUN
ejpam-6091	3	24	.	.	PUNCT
ejpam-6091	4	1	it	it	PRON
ejpam-6091	4	2	is	be	AUX
ejpam-6091	4	3	shown	show	VERB
ejpam-6091	4	4	that	that	SCONJ
ejpam-6091	4	5	the	the	DET
ejpam-6091	4	6	equations	equation	NOUN
ejpam-6091	4	7	of	of	ADP
ejpam-6091	4	8	motion	motion	NOUN
ejpam-6091	4	9	which	which	PRON
ejpam-6091	4	10	follow	follow	VERB
ejpam-6091	4	11	from	from	ADP
ejpam-6091	4	12	the	the	DET
ejpam-6091	4	13	principle	principle	NOUN
ejpam-6091	4	14	of	of	ADP
ejpam-6091	4	15	d’alembert	d’alembert	NOUN
ejpam-6091	4	16	are	be	AUX
ejpam-6091	4	17	identical	identical	ADJ
ejpam-6091	4	18	to	to	ADP
ejpam-6091	4	19	the	the	DET
ejpam-6091	4	20	equations	equation	NOUN
ejpam-6091	4	21	which	which	PRON
ejpam-6091	4	22	follow	follow	VERB
ejpam-6091	4	23	from	from	ADP
ejpam-6091	4	24	the	the	DET
ejpam-6091	4	25	variational	variational	ADJ
ejpam-6091	4	26	action	action	NOUN
ejpam-6091	4	27	principle	principle	NOUN
ejpam-6091	4	28	.	.	PUNCT
ejpam-6091	5	1	to	to	PART
ejpam-6091	5	2	illustrate	illustrate	VERB
ejpam-6091	5	3	the	the	DET
ejpam-6091	5	4	effectiveness	effectiveness	NOUN
ejpam-6091	5	5	of	of	ADP
ejpam-6091	5	6	the	the	DET
ejpam-6091	5	7	proposed	propose	VERB
ejpam-6091	5	8	framework	framework	NOUN
ejpam-6091	5	9	,	,	PUNCT
ejpam-6091	5	10	we	we	PRON
ejpam-6091	5	11	present	present	VERB
ejpam-6091	5	12	and	and	CCONJ
ejpam-6091	5	13	analyze	analyze	VERB
ejpam-6091	5	14	two	two	NUM
ejpam-6091	5	15	illustrative	illustrative	ADJ
ejpam-6091	5	16	examples	example	NOUN
ejpam-6091	5	17	:	:	PUNCT
ejpam-6091	5	18	the	the	DET
ejpam-6091	5	19	motion	motion	NOUN
ejpam-6091	5	20	of	of	ADP
ejpam-6091	5	21	a	a	DET
ejpam-6091	5	22	rolling	rolling	ADJ
ejpam-6091	5	23	disk	disk	NOUN
ejpam-6091	5	24	on	on	ADP
ejpam-6091	5	25	a	a	DET
ejpam-6091	5	26	horizontal	horizontal	ADJ
ejpam-6091	5	27	plane	plane	NOUN
ejpam-6091	5	28	and	and	CCONJ
ejpam-6091	5	29	the	the	DET
ejpam-6091	5	30	motion	motion	NOUN
ejpam-6091	5	31	of	of	ADP
ejpam-6091	5	32	a	a	DET
ejpam-6091	5	33	knife	knife	NOUN
ejpam-6091	5	34	edge	edge	NOUN
ejpam-6091	5	35	on	on	ADP
ejpam-6091	5	36	an	an	DET
ejpam-6091	5	37	inclined	inclined	ADJ
ejpam-6091	5	38	plane	plane	NOUN
ejpam-6091	5	39	.	.	PUNCT
ejpam-6091	6	1	2020	2020	NUM
ejpam-6091	6	2	mathematics	mathematic	NOUN
ejpam-6091	6	3	subject	subject	NOUN
ejpam-6091	6	4	classifications	classification	NOUN
ejpam-6091	6	5	:	:	PUNCT
ejpam-6091	6	6	70h20	70h20	NUM
ejpam-6091	6	7	,	,	PUNCT
ejpam-6091	6	8	70f25	70f25	NUM
ejpam-6091	6	9	,	,	PUNCT
ejpam-6091	6	10	49s05	49s05	NUM
ejpam-6091	6	11	key	key	ADJ
ejpam-6091	6	12	words	word	NOUN
ejpam-6091	6	13	and	and	CCONJ
ejpam-6091	6	14	phrases	phrase	NOUN
ejpam-6091	6	15	:	:	PUNCT
ejpam-6091	6	16	lagrange	lagrange	ADJ
ejpam-6091	6	17	-	-	PUNCT
ejpam-6091	6	18	d’alembert	d’alembert	NOUN
ejpam-6091	6	19	principle	principle	NOUN
ejpam-6091	6	20	,	,	PUNCT
ejpam-6091	6	21	nonholonomic	nonholonomic	ADJ
ejpam-6091	6	22	constraints	constraint	NOUN
ejpam-6091	6	23	1	1	NUM
ejpam-6091	6	24	.	.	PUNCT
ejpam-6091	7	1	introduction	introduction	NOUN
ejpam-6091	7	2	the	the	DET
ejpam-6091	7	3	theory	theory	NOUN
ejpam-6091	7	4	of	of	ADP
ejpam-6091	7	5	systems	system	NOUN
ejpam-6091	7	6	with	with	ADP
ejpam-6091	7	7	nonholonomic	nonholonomic	ADJ
ejpam-6091	7	8	constrains	constrain	NOUN
ejpam-6091	7	9	goes	go	VERB
ejpam-6091	7	10	back	back	ADV
ejpam-6091	7	11	to	to	ADP
ejpam-6091	7	12	the	the	DET
ejpam-6091	7	13	19th	19th	ADJ
ejpam-6091	7	14	century	century	NOUN
ejpam-6091	8	1	[	[	X
ejpam-6091	8	2	1	1	NUM
ejpam-6091	8	3	–	–	PUNCT
ejpam-6091	8	4	4	4	NUM
ejpam-6091	8	5	]	]	PUNCT
ejpam-6091	8	6	nonholonomic	nonholonomic	ADJ
ejpam-6091	8	7	constraints	constraint	NOUN
ejpam-6091	8	8	arise	arise	VERB
ejpam-6091	8	9	naturally	naturally	ADV
ejpam-6091	8	10	in	in	ADP
ejpam-6091	8	11	the	the	DET
ejpam-6091	8	12	context	context	NOUN
ejpam-6091	8	13	of	of	ADP
ejpam-6091	8	14	mechanical	mechanical	ADJ
ejpam-6091	8	15	systems	system	NOUN
ejpam-6091	8	16	with	with	ADP
ejpam-6091	8	17	rigid	rigid	ADJ
ejpam-6091	8	18	bodies	body	NOUN
ejpam-6091	8	19	rolling	roll	VERB
ejpam-6091	8	20	without	without	ADP
ejpam-6091	8	21	slipping	slip	VERB
ejpam-6091	8	22	over	over	ADP
ejpam-6091	8	23	a	a	DET
ejpam-6091	8	24	surface	surface	NOUN
ejpam-6091	8	25	.	.	PUNCT
ejpam-6091	9	1	another	another	DET
ejpam-6091	9	2	typical	typical	ADJ
ejpam-6091	9	3	example	example	NOUN
ejpam-6091	9	4	is	be	AUX
ejpam-6091	9	5	the	the	DET
ejpam-6091	9	6	chaplygin	chaplygin	ADJ
ejpam-6091	9	7	sleigh	sleigh	NOUN
ejpam-6091	9	8	.	.	PUNCT
ejpam-6091	10	1	this	this	PRON
ejpam-6091	10	2	is	be	AUX
ejpam-6091	10	3	a	a	DET
ejpam-6091	10	4	rigid	rigid	ADJ
ejpam-6091	10	5	body	body	NOUN
ejpam-6091	10	6	where	where	SCONJ
ejpam-6091	10	7	one	one	NUM
ejpam-6091	10	8	of	of	ADP
ejpam-6091	10	9	the	the	DET
ejpam-6091	10	10	contact	contact	NOUN
ejpam-6091	10	11	points	point	VERB
ejpam-6091	10	12	with	with	ADP
ejpam-6091	10	13	the	the	DET
ejpam-6091	10	14	surface	surface	NOUN
ejpam-6091	10	15	forms	form	VERB
ejpam-6091	10	16	a	a	DET
ejpam-6091	10	17	knife	knife	NOUN
ejpam-6091	10	18	edge	edge	NOUN
ejpam-6091	10	19	.	.	PUNCT
ejpam-6091	11	1	the	the	DET
ejpam-6091	11	2	nonholonomic	nonholonomic	ADJ
ejpam-6091	11	3	constraint	constraint	NOUN
ejpam-6091	11	4	assumed	assume	VERB
ejpam-6091	11	5	that	that	SCONJ
ejpam-6091	11	6	there	there	PRON
ejpam-6091	11	7	is	be	VERB
ejpam-6091	11	8	no	no	DET
ejpam-6091	11	9	motion	motion	NOUN
ejpam-6091	11	10	perpendicular	perpendicular	NOUN
ejpam-6091	11	11	to	to	ADP
ejpam-6091	11	12	the	the	DET
ejpam-6091	11	13	knife	knife	NOUN
ejpam-6091	11	14	edge	edge	NOUN
ejpam-6091	11	15	[	[	X
ejpam-6091	11	16	5–10	5–10	ADJ
ejpam-6091	11	17	]	]	PUNCT
ejpam-6091	11	18	or	or	CCONJ
ejpam-6091	11	19	that	that	SCONJ
ejpam-6091	11	20	the	the	DET
ejpam-6091	11	21	velocity	velocity	NOUN
ejpam-6091	11	22	of	of	ADP
ejpam-6091	11	23	the	the	DET
ejpam-6091	11	24	contact	contact	NOUN
ejpam-6091	11	25	point	point	NOUN
ejpam-6091	11	26	remains	remain	VERB
ejpam-6091	11	27	in	in	ADP
ejpam-6091	11	28	the	the	DET
ejpam-6091	11	29	direction	direction	NOUN
ejpam-6091	11	30	of	of	ADP
ejpam-6091	11	31	x	x	SYM
ejpam-6091	11	32	axis	axis	NOUN
ejpam-6091	11	33	of	of	ADP
ejpam-6091	11	34	the	the	DET
ejpam-6091	11	35	body	body	NOUN
ejpam-6091	11	36	.	.	PUNCT
ejpam-6091	12	1	the	the	DET
ejpam-6091	12	2	equations	equation	NOUN
ejpam-6091	12	3	of	of	ADP
ejpam-6091	12	4	constraints	constraint	NOUN
ejpam-6091	12	5	in	in	ADP
ejpam-6091	12	6	nonholonomic	nonholonomic	ADJ
ejpam-6091	12	7	dynamics	dynamic	NOUN
ejpam-6091	12	8	,	,	PUNCT
ejpam-6091	12	9	written	write	VERB
ejpam-6091	12	10	in	in	ADP
ejpam-6091	12	11	terms	term	NOUN
ejpam-6091	12	12	of	of	ADP
ejpam-6091	12	13	generalized	generalized	ADJ
ejpam-6091	12	14	coordinates	coordinate	NOUN
ejpam-6091	12	15	qi	qi	PROPN
ejpam-6091	12	16	and	and	CCONJ
ejpam-6091	12	17	generalized	generalized	ADJ
ejpam-6091	12	18	velocities	velocity	NOUN
ejpam-6091	12	19	q̇i	q̇i	NOUN
ejpam-6091	12	20	.	.	PUNCT
ejpam-6091	13	1	typical	typical	ADJ
ejpam-6091	13	2	engineering	engineering	NOUN
ejpam-6091	13	3	problems	problem	NOUN
ejpam-6091	13	4	that	that	PRON
ejpam-6091	13	5	involve	involve	VERB
ejpam-6091	13	6	such	such	ADJ
ejpam-6091	13	7	constraints	constraint	NOUN
ejpam-6091	13	8	arise	arise	VERB
ejpam-6091	13	9	for	for	ADP
ejpam-6091	13	10	example	example	NOUN
ejpam-6091	13	11	in	in	ADP
ejpam-6091	13	12	robotics	robotic	NOUN
ejpam-6091	13	13	,	,	PUNCT
ejpam-6091	13	14	where	where	SCONJ
ejpam-6091	13	15	the	the	DET
ejpam-6091	13	16	wheels	wheel	NOUN
ejpam-6091	13	17	of	of	ADP
ejpam-6091	13	18	a	a	DET
ejpam-6091	13	19	mobile	mobile	ADJ
ejpam-6091	13	20	robot	robot	NOUN
ejpam-6091	13	21	are	be	AUX
ejpam-6091	13	22	often	often	ADV
ejpam-6091	13	23	required	require	VERB
ejpam-6091	13	24	to	to	PART
ejpam-6091	13	25	roll	roll	VERB
ejpam-6091	13	26	without	without	ADP
ejpam-6091	13	27	slipping	slip	VERB
ejpam-6091	13	28	,	,	PUNCT
ejpam-6091	13	29	or	or	CCONJ
ejpam-6091	13	30	if	if	SCONJ
ejpam-6091	13	31	one	one	NUM
ejpam-6091	13	32	interested	interested	ADJ
ejpam-6091	13	33	in	in	ADP
ejpam-6091	13	34	guiding	guide	VERB
ejpam-6091	13	35	the	the	DET
ejpam-6091	13	36	motion	motion	NOUN
ejpam-6091	13	37	of	of	ADP
ejpam-6091	13	38	a	a	DET
ejpam-6091	13	39	cutting	cut	VERB
ejpam-6091	13	40	tool	tool	NOUN
ejpam-6091	13	41	.	.	PUNCT
ejpam-6091	14	1	ghori	ghori	PROPN
ejpam-6091	15	1	[	[	X
ejpam-6091	15	2	11]developed	11]developed	NUM
ejpam-6091	15	3	a	a	DET
ejpam-6091	15	4	generalization	generalization	NOUN
ejpam-6091	15	5	of	of	ADP
ejpam-6091	15	6	the	the	DET
ejpam-6091	15	7	classical	classical	ADJ
ejpam-6091	15	8	hamilton	hamilton	PROPN
ejpam-6091	15	9	-	-	PUNCT
ejpam-6091	15	10	jacobi	jacobi	PROPN
ejpam-6091	15	11	method	method	NOUN
ejpam-6091	15	12	in	in	ADP
ejpam-6091	15	13	order	order	NOUN
ejpam-6091	15	14	to	to	PART
ejpam-6091	15	15	cover	cover	VERB
ejpam-6091	15	16	mechanical	mechanical	ADJ
ejpam-6091	15	17	systems	system	NOUN
ejpam-6091	15	18	subject	subject	ADJ
ejpam-6091	15	19	to	to	ADP
ejpam-6091	15	20	nonholonomic	nonholonomic	ADJ
ejpam-6091	15	21	constraints	constraint	NOUN
ejpam-6091	15	22	.	.	PUNCT
ejpam-6091	16	1	the	the	DET
ejpam-6091	16	2	method	method	NOUN
ejpam-6091	16	3	was	be	AUX
ejpam-6091	16	4	based	base	VERB
ejpam-6091	16	5	on	on	ADP
ejpam-6091	16	6	a	a	DET
ejpam-6091	16	7	modification	modification	NOUN
ejpam-6091	16	8	of	of	ADP
ejpam-6091	16	9	the	the	DET
ejpam-6091	16	10	classical	classical	ADJ
ejpam-6091	16	11	hamilton	hamilton	PROPN
ejpam-6091	16	12	-	-	PUNCT
ejpam-6091	16	13	jacobi	jacobi	PROPN
ejpam-6091	16	14	equation	equation	NOUN
ejpam-6091	16	15	by	by	ADP
ejpam-6091	16	16	supplementing	supplement	VERB
ejpam-6091	16	17	a	a	DET
ejpam-6091	16	18	modifying	modify	VERB
ejpam-6091	16	19	function	function	NOUN
ejpam-6091	16	20	.	.	PUNCT
ejpam-6091	17	1	however	however	ADV
ejpam-6091	17	2	,	,	PUNCT
ejpam-6091	17	3	nzaziev	nzaziev	NOUN
ejpam-6091	17	4	[	[	X
ejpam-6091	17	5	12	12	NUM
ejpam-6091	17	6	]	]	PUNCT
ejpam-6091	17	7	proved	prove	VERB
ejpam-6091	17	8	that	that	SCONJ
ejpam-6091	17	9	ghori	ghori	PROPN
ejpam-6091	17	10	’s	’s	PART
ejpam-6091	17	11	theorem	theorem	NOUN
ejpam-6091	17	12	is	be	AUX
ejpam-6091	17	13	incorrect	incorrect	ADJ
ejpam-6091	17	14	.	.	PUNCT
ejpam-6091	18	1	recently	recently	ADV
ejpam-6091	18	2	,	,	PUNCT
ejpam-6091	18	3	the	the	DET
ejpam-6091	18	4	authors	author	NOUN
ejpam-6091	18	5	[	[	X
ejpam-6091	18	6	13	13	NUM
ejpam-6091	18	7	,	,	PUNCT
ejpam-6091	18	8	14	14	NUM
ejpam-6091	18	9	]	]	PUNCT
ejpam-6091	18	10	introduced	introduce	VERB
ejpam-6091	18	11	a	a	DET
ejpam-6091	18	12	new	new	ADJ
ejpam-6091	18	13	generalized	generalized	ADJ
ejpam-6091	18	14	hamilton	hamilton	PROPN
ejpam-6091	18	15	-	-	PUNCT
ejpam-6091	18	16	jacobi	jacobi	PROPN
ejpam-6091	18	17	method	method	NOUN
ejpam-6091	18	18	for	for	ADP
ejpam-6091	18	19	such	such	ADJ
ejpam-6091	18	20	systems	system	NOUN
ejpam-6091	18	21	.	.	PUNCT
ejpam-6091	19	1	doi	doi	NOUN
ejpam-6091	19	2	:	:	PUNCT
ejpam-6091	19	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6091	https://doi.org/10.29020/nybg.ejpam.v18i3.6091	NOUN
ejpam-6091	19	4	email	email	NOUN
ejpam-6091	19	5	address	address	NOUN
ejpam-6091	19	6	:	:	PUNCT
ejpam-6091	19	7	knawafleh@mutah.edu.jo	knawafleh@mutah.edu.jo	NOUN
ejpam-6091	19	8	(	(	PUNCT
ejpam-6091	19	9	k.	k.	PROPN
ejpam-6091	19	10	i.	i.	PROPN
ejpam-6091	19	11	nawafleh	nawafleh	PROPN
ejpam-6091	19	12	)	)	PUNCT
ejpam-6091	19	13	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6091	20	1	1	1	NUM
ejpam-6091	20	2	copyright	copyright	NOUN
ejpam-6091	20	3	:	:	PUNCT
ejpam-6091	20	4	©	©	PROPN
ejpam-6091	20	5	2025	2025	NUM
ejpam-6091	20	6	the	the	DET
ejpam-6091	20	7	author(s	author(s	NOUN
ejpam-6091	20	8	)	)	PUNCT
ejpam-6091	20	9	.	.	PUNCT
ejpam-6091	21	1	(	(	PUNCT
ejpam-6091	21	2	cc	cc	NOUN
ejpam-6091	21	3	by	by	ADP
ejpam-6091	21	4	-	-	PUNCT
ejpam-6091	21	5	nc	nc	PROPN
ejpam-6091	21	6	4.0	4.0	NUM
ejpam-6091	21	7	)	)	PUNCT
ejpam-6091	21	8	k.	k.	PROPN
ejpam-6091	21	9	i.	i.	PROPN
ejpam-6091	21	10	nawafleh	nawafleh	PROPN
ejpam-6091	21	11	/	/	SYM
ejpam-6091	21	12	eur	eur	PROPN
ejpam-6091	21	13	.	.	PUNCT
ejpam-6091	22	1	j.	j.	PROPN
ejpam-6091	22	2	pure	pure	PROPN
ejpam-6091	22	3	appl	appl	PROPN
ejpam-6091	22	4	.	.	PROPN
ejpam-6091	22	5	math	math	PROPN
ejpam-6091	22	6	,	,	PUNCT
ejpam-6091	22	7	18	18	NUM
ejpam-6091	22	8	(	(	PUNCT
ejpam-6091	22	9	3	3	NUM
ejpam-6091	22	10	)	)	PUNCT
ejpam-6091	22	11	(	(	PUNCT
ejpam-6091	22	12	2025	2025	NUM
ejpam-6091	22	13	)	)	PUNCT
ejpam-6091	22	14	,	,	PUNCT
ejpam-6091	22	15	6091	6091	NUM
ejpam-6091	22	16	2	2	NUM
ejpam-6091	22	17	of	of	ADP
ejpam-6091	22	18	15	15	NUM
ejpam-6091	22	19	this	this	DET
ejpam-6091	22	20	method	method	NOUN
ejpam-6091	22	21	used	use	VERB
ejpam-6091	22	22	a	a	DET
ejpam-6091	22	23	variational	variational	ADJ
ejpam-6091	22	24	principle	principle	NOUN
ejpam-6091	22	25	for	for	ADP
ejpam-6091	22	26	the	the	DET
ejpam-6091	22	27	integral	integral	ADJ
ejpam-6091	22	28	of	of	ADP
ejpam-6091	22	29	action	action	NOUN
ejpam-6091	22	30	in	in	ADP
ejpam-6091	22	31	connection	connection	NOUN
ejpam-6091	22	32	with	with	ADP
ejpam-6091	22	33	the	the	DET
ejpam-6091	22	34	introduction	introduction	NOUN
ejpam-6091	22	35	of	of	ADP
ejpam-6091	22	36	unknown	unknown	ADJ
ejpam-6091	22	37	multipliers	multiplier	NOUN
ejpam-6091	22	38	.	.	PUNCT
ejpam-6091	23	1	we	we	PRON
ejpam-6091	23	2	will	will	AUX
ejpam-6091	23	3	start	start	VERB
ejpam-6091	23	4	from	from	ADP
ejpam-6091	23	5	the	the	DET
ejpam-6091	23	6	actual	actual	ADJ
ejpam-6091	23	7	solutions	solution	NOUN
ejpam-6091	23	8	of	of	ADP
ejpam-6091	23	9	the	the	DET
ejpam-6091	23	10	nonholonomic	nonholonomic	ADJ
ejpam-6091	23	11	system	system	NOUN
ejpam-6091	23	12	,	,	PUNCT
ejpam-6091	23	13	and	and	CCONJ
ejpam-6091	23	14	apply	apply	VERB
ejpam-6091	23	15	a	a	DET
ejpam-6091	23	16	sort	sort	NOUN
ejpam-6091	23	17	of	of	ADP
ejpam-6091	23	18	hamilton	hamilton	PROPN
ejpam-6091	23	19	-	-	PUNCT
ejpam-6091	23	20	jacobi	jacobi	PROPN
ejpam-6091	23	21	theory	theory	NOUN
ejpam-6091	23	22	to	to	PART
ejpam-6091	23	23	arrive	arrive	VERB
ejpam-6091	23	24	to	to	ADP
ejpam-6091	23	25	the	the	DET
ejpam-6091	23	26	generating	generate	VERB
ejpam-6091	23	27	function	function	NOUN
ejpam-6091	23	28	,	,	PUNCT
ejpam-6091	23	29	subsequently	subsequently	ADV
ejpam-6091	23	30	we	we	PRON
ejpam-6091	23	31	will	will	AUX
ejpam-6091	23	32	derive	derive	VERB
ejpam-6091	23	33	hamilton	hamilton	PROPN
ejpam-6091	23	34	’s	’s	PART
ejpam-6091	23	35	equations	equation	NOUN
ejpam-6091	23	36	of	of	ADP
ejpam-6091	23	37	motion	motion	NOUN
ejpam-6091	23	38	.	.	PUNCT
ejpam-6091	24	1	this	this	DET
ejpam-6091	24	2	method	method	NOUN
ejpam-6091	24	3	was	be	AUX
ejpam-6091	24	4	governed	govern	VERB
ejpam-6091	24	5	by	by	ADP
ejpam-6091	24	6	a	a	DET
ejpam-6091	24	7	variational	variational	ADJ
ejpam-6091	24	8	principle	principle	NOUN
ejpam-6091	24	9	applied	apply	VERB
ejpam-6091	24	10	to	to	ADP
ejpam-6091	24	11	a	a	DET
ejpam-6091	24	12	certain	certain	ADJ
ejpam-6091	24	13	function	function	NOUN
ejpam-6091	24	14	.	.	PUNCT
ejpam-6091	25	1	the	the	DET
ejpam-6091	25	2	resulting	result	VERB
ejpam-6091	25	3	variational	variational	ADJ
ejpam-6091	25	4	relation	relation	NOUN
ejpam-6091	25	5	was	be	AUX
ejpam-6091	25	6	then	then	ADV
ejpam-6091	25	7	treated	treat	VERB
ejpam-6091	25	8	by	by	ADP
ejpam-6091	25	9	introducing	introduce	VERB
ejpam-6091	25	10	some	some	DET
ejpam-6091	25	11	unknown	unknown	ADJ
ejpam-6091	25	12	multipliers	multiplier	NOUN
ejpam-6091	25	13	in	in	ADP
ejpam-6091	25	14	connection	connection	NOUN
ejpam-6091	25	15	with	with	ADP
ejpam-6091	25	16	constraint	constraint	NOUN
ejpam-6091	25	17	relations	relation	NOUN
ejpam-6091	25	18	.	.	PUNCT
ejpam-6091	26	1	after	after	ADP
ejpam-6091	26	2	the	the	DET
ejpam-6091	26	3	elimination	elimination	NOUN
ejpam-6091	26	4	of	of	ADP
ejpam-6091	26	5	these	these	DET
ejpam-6091	26	6	multipliers	multiplier	NOUN
ejpam-6091	26	7	the	the	DET
ejpam-6091	26	8	generalized	generalized	ADJ
ejpam-6091	26	9	momenta	momenta	NOUN
ejpam-6091	26	10	were	be	AUX
ejpam-6091	26	11	found	find	VERB
ejpam-6091	26	12	to	to	PART
ejpam-6091	26	13	be	be	AUX
ejpam-6091	26	14	certain	certain	ADJ
ejpam-6091	26	15	functions	function	NOUN
ejpam-6091	26	16	of	of	ADP
ejpam-6091	26	17	the	the	DET
ejpam-6091	26	18	partial	partial	ADJ
ejpam-6091	26	19	derivatives	derivative	NOUN
ejpam-6091	26	20	of	of	ADP
ejpam-6091	26	21	the	the	DET
ejpam-6091	26	22	hamilton	hamilton	PROPN
ejpam-6091	26	23	jacobi	jacobi	PROPN
ejpam-6091	26	24	function	function	VERB
ejpam-6091	26	25	with	with	ADP
ejpam-6091	26	26	respect	respect	NOUN
ejpam-6091	26	27	to	to	ADP
ejpam-6091	26	28	the	the	DET
ejpam-6091	26	29	generalized	generalized	ADJ
ejpam-6091	26	30	coordinates	coordinate	NOUN
ejpam-6091	26	31	and	and	CCONJ
ejpam-6091	26	32	the	the	DET
ejpam-6091	26	33	time	time	NOUN
ejpam-6091	26	34	.	.	PUNCT
ejpam-6091	27	1	then	then	ADV
ejpam-6091	27	2	the	the	DET
ejpam-6091	27	3	partial	partial	ADJ
ejpam-6091	27	4	differential	differential	ADJ
ejpam-6091	27	5	equation	equation	NOUN
ejpam-6091	27	6	of	of	ADP
ejpam-6091	27	7	the	the	DET
ejpam-6091	27	8	classical	classical	ADJ
ejpam-6091	27	9	hamilton	hamilton	PROPN
ejpam-6091	27	10	-	-	PUNCT
ejpam-6091	27	11	jacobi	jacobi	PROPN
ejpam-6091	27	12	method	method	NOUN
ejpam-6091	27	13	was	be	AUX
ejpam-6091	27	14	modified	modify	VERB
ejpam-6091	27	15	by	by	ADP
ejpam-6091	27	16	inserting	insert	VERB
ejpam-6091	27	17	these	these	DET
ejpam-6091	27	18	functions	function	NOUN
ejpam-6091	27	19	for	for	ADP
ejpam-6091	27	20	the	the	DET
ejpam-6091	27	21	generalized	generalize	VERB
ejpam-6091	27	22	momenta	momenta	NOUN
ejpam-6091	27	23	in	in	ADP
ejpam-6091	27	24	the	the	DET
ejpam-6091	27	25	hamiltonian	hamiltonian	NOUN
ejpam-6091	27	26	of	of	ADP
ejpam-6091	27	27	the	the	DET
ejpam-6091	27	28	system	system	NOUN
ejpam-6091	27	29	.	.	PUNCT
ejpam-6091	28	1	unlike	unlike	ADP
ejpam-6091	28	2	previous	previous	ADJ
ejpam-6091	28	3	methods	method	NOUN
ejpam-6091	28	4	that	that	PRON
ejpam-6091	28	5	changed	change	VERB
ejpam-6091	28	6	the	the	DET
ejpam-6091	28	7	classical	classical	ADJ
ejpam-6091	28	8	hamilton	hamilton	PROPN
ejpam-6091	28	9	-	-	PUNCT
ejpam-6091	28	10	jacobi	jacobi	PROPN
ejpam-6091	28	11	equation	equation	NOUN
ejpam-6091	28	12	using	use	VERB
ejpam-6091	28	13	extra	extra	ADJ
ejpam-6091	28	14	assumptions	assumption	NOUN
ejpam-6091	28	15	or	or	CCONJ
ejpam-6091	28	16	added	add	VERB
ejpam-6091	28	17	functions	function	NOUN
ejpam-6091	28	18	,	,	PUNCT
ejpam-6091	28	19	this	this	DET
ejpam-6091	28	20	work	work	NOUN
ejpam-6091	28	21	develops	develop	VERB
ejpam-6091	28	22	the	the	DET
ejpam-6091	28	23	hamilton	hamilton	PROPN
ejpam-6091	28	24	-	-	PUNCT
ejpam-6091	28	25	jacobi	jacobi	PROPN
ejpam-6091	28	26	approach	approach	NOUN
ejpam-6091	28	27	in	in	ADP
ejpam-6091	28	28	a	a	DET
ejpam-6091	28	29	clear	clear	ADJ
ejpam-6091	28	30	and	and	CCONJ
ejpam-6091	28	31	organized	organized	ADJ
ejpam-6091	28	32	way	way	NOUN
ejpam-6091	28	33	,	,	PUNCT
ejpam-6091	28	34	starting	start	VERB
ejpam-6091	28	35	directly	directly	ADV
ejpam-6091	28	36	from	from	ADP
ejpam-6091	28	37	a	a	DET
ejpam-6091	28	38	variational	variational	ADJ
ejpam-6091	28	39	principle	principle	NOUN
ejpam-6091	28	40	.	.	PUNCT
ejpam-6091	29	1	it	it	PRON
ejpam-6091	29	2	includes	include	VERB
ejpam-6091	29	3	nonholonomic	nonholonomic	ADJ
ejpam-6091	29	4	constraints	constraint	NOUN
ejpam-6091	29	5	by	by	ADP
ejpam-6091	29	6	using	use	VERB
ejpam-6091	29	7	lagrange	lagrange	NOUN
ejpam-6091	29	8	multipliers	multiplier	NOUN
ejpam-6091	29	9	and	and	CCONJ
ejpam-6091	29	10	shows	show	VERB
ejpam-6091	29	11	that	that	SCONJ
ejpam-6091	29	12	the	the	DET
ejpam-6091	29	13	resulting	result	VERB
ejpam-6091	29	14	equations	equation	NOUN
ejpam-6091	29	15	match	match	VERB
ejpam-6091	29	16	those	those	PRON
ejpam-6091	29	17	from	from	ADP
ejpam-6091	29	18	the	the	DET
ejpam-6091	29	19	well	well	ADV
ejpam-6091	29	20	-	-	PUNCT
ejpam-6091	29	21	known	know	VERB
ejpam-6091	29	22	lagrange	lagrange	NOUN
ejpam-6091	29	23	-	-	PUNCT
ejpam-6091	29	24	d’alembert	d’alembert	NOUN
ejpam-6091	29	25	principle	principle	NOUN
ejpam-6091	29	26	.	.	PUNCT
ejpam-6091	30	1	the	the	DET
ejpam-6091	30	2	main	main	ADJ
ejpam-6091	30	3	contribution	contribution	NOUN
ejpam-6091	30	4	of	of	ADP
ejpam-6091	30	5	this	this	DET
ejpam-6091	30	6	work	work	NOUN
ejpam-6091	30	7	is	be	AUX
ejpam-6091	30	8	applying	apply	VERB
ejpam-6091	30	9	this	this	DET
ejpam-6091	30	10	method	method	NOUN
ejpam-6091	30	11	to	to	PART
ejpam-6091	30	12	find	find	VERB
ejpam-6091	30	13	exact	exact	ADJ
ejpam-6091	30	14	solutions	solution	NOUN
ejpam-6091	30	15	and	and	CCONJ
ejpam-6091	30	16	hamiltonjacobi	hamiltonjacobi	NOUN
ejpam-6091	30	17	functions	function	NOUN
ejpam-6091	30	18	for	for	ADP
ejpam-6091	30	19	real	real	ADJ
ejpam-6091	30	20	-	-	PUNCT
ejpam-6091	30	21	world	world	NOUN
ejpam-6091	30	22	systems	system	NOUN
ejpam-6091	30	23	,	,	PUNCT
ejpam-6091	30	24	making	make	VERB
ejpam-6091	30	25	it	it	PRON
ejpam-6091	30	26	easier	easy	ADJ
ejpam-6091	30	27	and	and	CCONJ
ejpam-6091	30	28	more	more	ADV
ejpam-6091	30	29	understandable	understandable	ADJ
ejpam-6091	30	30	to	to	PART
ejpam-6091	30	31	solve	solve	VERB
ejpam-6091	30	32	problems	problem	NOUN
ejpam-6091	30	33	involving	involve	VERB
ejpam-6091	30	34	constrained	constrain	VERB
ejpam-6091	30	35	motion	motion	NOUN
ejpam-6091	30	36	.	.	PUNCT
ejpam-6091	31	1	2	2	X
ejpam-6091	31	2	.	.	X
ejpam-6091	31	3	formalism	formalism	NOUN
ejpam-6091	31	4	hamiltonian	hamiltonian	ADJ
ejpam-6091	31	5	approaches	approach	NOUN
ejpam-6091	31	6	to	to	ADP
ejpam-6091	31	7	nonholonomic	nonholonomic	ADJ
ejpam-6091	31	8	mechanical	mechanical	ADJ
ejpam-6091	31	9	systems	system	NOUN
ejpam-6091	31	10	are	be	AUX
ejpam-6091	31	11	developed	develop	VERB
ejpam-6091	31	12	by	by	ADP
ejpam-6091	31	13	,	,	PUNCT
ejpam-6091	31	14	for	for	ADP
ejpam-6091	31	15	example	example	NOUN
ejpam-6091	32	1	[	[	X
ejpam-6091	32	2	3,4,6,8	3,4,6,8	NUM
ejpam-6091	32	3	]	]	X
ejpam-6091	32	4	.	.	PUNCT
ejpam-6091	33	1	the	the	DET
ejpam-6091	33	2	standard	standard	ADJ
ejpam-6091	33	3	way	way	NOUN
ejpam-6091	33	4	to	to	PART
ejpam-6091	33	5	derive	derive	VERB
ejpam-6091	33	6	the	the	DET
ejpam-6091	33	7	equations	equation	NOUN
ejpam-6091	33	8	of	of	ADP
ejpam-6091	33	9	motion	motion	NOUN
ejpam-6091	33	10	of	of	ADP
ejpam-6091	33	11	a	a	DET
ejpam-6091	33	12	nonholonomic	nonholonomic	ADJ
ejpam-6091	33	13	mechanical	mechanical	ADJ
ejpam-6091	33	14	systems	system	NOUN
ejpam-6091	33	15	starts	start	VERB
ejpam-6091	33	16	from	from	ADP
ejpam-6091	33	17	lagrange	lagrange	PROPN
ejpam-6091	33	18	’s	’s	PART
ejpam-6091	33	19	equations	equation	NOUN
ejpam-6091	33	20	and	and	CCONJ
ejpam-6091	33	21	the	the	DET
ejpam-6091	33	22	addition	addition	NOUN
ejpam-6091	33	23	of	of	ADP
ejpam-6091	33	24	some	some	DET
ejpam-6091	33	25	unknown	unknown	ADJ
ejpam-6091	33	26	force	force	NOUN
ejpam-6091	33	27	that	that	PRON
ejpam-6091	33	28	have	have	VERB
ejpam-6091	33	29	to	to	PART
ejpam-6091	33	30	be	be	AUX
ejpam-6091	33	31	exerted	exert	VERB
ejpam-6091	33	32	by	by	ADP
ejpam-6091	33	33	the	the	DET
ejpam-6091	33	34	constraint	constraint	NOUN
ejpam-6091	33	35	in	in	ADP
ejpam-6091	33	36	order	order	NOUN
ejpam-6091	33	37	to	to	PART
ejpam-6091	33	38	satisfy	satisfy	VERB
ejpam-6091	33	39	the	the	DET
ejpam-6091	33	40	nonholonomic	nonholonomic	ADJ
ejpam-6091	33	41	constraint	constraint	NOUN
ejpam-6091	33	42	.	.	PUNCT
ejpam-6091	34	1	consider	consider	VERB
ejpam-6091	34	2	a	a	DET
ejpam-6091	34	3	lagrangian	lagrangian	ADJ
ejpam-6091	34	4	function	function	NOUN
ejpam-6091	34	5	l	l	NOUN
ejpam-6091	34	6	=	=	SYM
ejpam-6091	34	7	l(qi	l(qi	PROPN
ejpam-6091	34	8	,	,	PUNCT
ejpam-6091	34	9	q̇i	q̇i	PROPN
ejpam-6091	34	10	,	,	PUNCT
ejpam-6091	34	11	t	t	PROPN
ejpam-6091	34	12	)	)	PUNCT
ejpam-6091	34	13	(	(	PUNCT
ejpam-6091	34	14	1	1	X
ejpam-6091	34	15	)	)	PUNCT
ejpam-6091	34	16	along	along	ADP
ejpam-6091	34	17	with	with	ADP
ejpam-6091	34	18	a	a	DET
ejpam-6091	34	19	set	set	NOUN
ejpam-6091	34	20	of	of	ADP
ejpam-6091	34	21	nonholonomic	nonholonomic	ADJ
ejpam-6091	34	22	constraints	constraint	NOUN
ejpam-6091	34	23	that	that	PRON
ejpam-6091	34	24	are	be	AUX
ejpam-6091	34	25	linear	linear	ADJ
ejpam-6091	34	26	functions	function	NOUN
ejpam-6091	34	27	of	of	ADP
ejpam-6091	34	28	the	the	DET
ejpam-6091	34	29	velocities	velocity	NOUN
ejpam-6091	34	30	:	:	PUNCT
ejpam-6091	34	31	fα(qi	fα(qi	NUM
ejpam-6091	34	32	,	,	PUNCT
ejpam-6091	34	33	q̇i	q̇i	NOUN
ejpam-6091	34	34	)	)	PUNCT
ejpam-6091	34	35	=	=	SYM
ejpam-6091	34	36	0	0	NUM
ejpam-6091	34	37	,	,	PUNCT
ejpam-6091	34	38	α	α	X
ejpam-6091	34	39	=	=	PUNCT
ejpam-6091	34	40	n+	n+	PUNCT
ejpam-6091	34	41	1	1	NUM
ejpam-6091	34	42	,	,	PUNCT
ejpam-6091	34	43	n+	n+	X
ejpam-6091	34	44	2	2	NUM
ejpam-6091	34	45	,	,	PUNCT
ejpam-6091	34	46	.	.	PUNCT
ejpam-6091	34	47	.	.	PUNCT
ejpam-6091	35	1	.	.	PUNCT
ejpam-6091	36	1	,	,	PUNCT
ejpam-6091	36	2	n+m	n+m	NUM
ejpam-6091	36	3	(	(	PUNCT
ejpam-6091	36	4	2	2	X
ejpam-6091	36	5	)	)	PUNCT
ejpam-6091	36	6	the	the	DET
ejpam-6091	36	7	generalized	generalized	ADJ
ejpam-6091	36	8	momenta	momenta	NOUN
ejpam-6091	36	9	and	and	CCONJ
ejpam-6091	36	10	the	the	DET
ejpam-6091	36	11	hamiltonian	hamiltonian	NOUN
ejpam-6091	36	12	of	of	ADP
ejpam-6091	36	13	the	the	DET
ejpam-6091	36	14	system	system	NOUN
ejpam-6091	36	15	are	be	AUX
ejpam-6091	36	16	defined	define	VERB
ejpam-6091	36	17	by	by	ADP
ejpam-6091	36	18	the	the	DET
ejpam-6091	36	19	relations	relation	NOUN
ejpam-6091	36	20	:	:	PUNCT
ejpam-6091	36	21	pi	pi	NOUN
ejpam-6091	36	22	=	=	PUNCT
ejpam-6091	36	23	∂l	∂l	PROPN
ejpam-6091	36	24	∂q̇i	∂q̇i	VERB
ejpam-6091	36	25	(	(	PUNCT
ejpam-6091	36	26	3	3	NUM
ejpam-6091	36	27	)	)	PUNCT
ejpam-6091	36	28	h(qi	h(qi	PROPN
ejpam-6091	36	29	,	,	PUNCT
ejpam-6091	36	30	pi	pi	NOUN
ejpam-6091	36	31	,	,	PUNCT
ejpam-6091	36	32	t	t	PROPN
ejpam-6091	36	33	)	)	PUNCT
ejpam-6091	36	34	=	=	PUNCT
ejpam-6091	36	35	piq̇i	piq̇i	NUM
ejpam-6091	36	36	−	−	NOUN
ejpam-6091	36	37	l(qi	l(qi	PROPN
ejpam-6091	36	38	,	,	PUNCT
ejpam-6091	36	39	q̇i	q̇i	PROPN
ejpam-6091	36	40	,	,	PUNCT
ejpam-6091	36	41	t	t	PROPN
ejpam-6091	36	42	)	)	PUNCT
ejpam-6091	36	43	(	(	PUNCT
ejpam-6091	36	44	4	4	X
ejpam-6091	36	45	)	)	PUNCT
ejpam-6091	36	46	when	when	SCONJ
ejpam-6091	36	47	the	the	DET
ejpam-6091	36	48	system	system	NOUN
ejpam-6091	36	49	is	be	AUX
ejpam-6091	36	50	nonholonomic	nonholonomic	ADJ
ejpam-6091	36	51	,	,	PUNCT
ejpam-6091	36	52	hamilton	hamilton	PROPN
ejpam-6091	36	53	’s	’s	PART
ejpam-6091	36	54	variational	variational	ADJ
ejpam-6091	36	55	principle	principle	NOUN
ejpam-6091	36	56	has	have	VERB
ejpam-6091	36	57	to	to	PART
ejpam-6091	36	58	be	be	AUX
ejpam-6091	36	59	expressed	express	VERB
ejpam-6091	36	60	in	in	ADP
ejpam-6091	36	61	the	the	DET
ejpam-6091	36	62	form	form	NOUN
ejpam-6091	36	63	[	[	X
ejpam-6091	36	64	14	14	NUM
ejpam-6091	36	65	]	]	PUNCT
ejpam-6091	36	66	δ	δ	PROPN
ejpam-6091	36	67	∫	∫	PROPN
ejpam-6091	36	68	ldt	ldt	PROPN
ejpam-6091	36	69	=	=	PROPN
ejpam-6091	36	70	0	0	PROPN
ejpam-6091	36	71	.	.	PUNCT
ejpam-6091	37	1	(	(	PUNCT
ejpam-6091	37	2	5	5	NUM
ejpam-6091	37	3	)	)	PUNCT
ejpam-6091	37	4	k.	k.	PROPN
ejpam-6091	37	5	i.	i.	PROPN
ejpam-6091	37	6	nawafleh	nawafleh	PROPN
ejpam-6091	37	7	/	/	SYM
ejpam-6091	37	8	eur	eur	PROPN
ejpam-6091	37	9	.	.	PUNCT
ejpam-6091	38	1	j.	j.	PROPN
ejpam-6091	38	2	pure	pure	PROPN
ejpam-6091	38	3	appl	appl	PROPN
ejpam-6091	38	4	.	.	PROPN
ejpam-6091	38	5	math	math	PROPN
ejpam-6091	38	6	,	,	PUNCT
ejpam-6091	38	7	18	18	NUM
ejpam-6091	38	8	(	(	PUNCT
ejpam-6091	38	9	3	3	NUM
ejpam-6091	38	10	)	)	PUNCT
ejpam-6091	38	11	(	(	PUNCT
ejpam-6091	38	12	2025	2025	NUM
ejpam-6091	38	13	)	)	PUNCT
ejpam-6091	38	14	,	,	PUNCT
ejpam-6091	38	15	6091	6091	NUM
ejpam-6091	38	16	3	3	NUM
ejpam-6091	38	17	of	of	ADP
ejpam-6091	38	18	15	15	NUM
ejpam-6091	38	19	the	the	DET
ejpam-6091	38	20	lagrangian	lagrangian	ADJ
ejpam-6091	38	21	formulation	formulation	NOUN
ejpam-6091	38	22	of	of	ADP
ejpam-6091	38	23	these	these	DET
ejpam-6091	38	24	theories	theory	NOUN
ejpam-6091	38	25	requires	require	VERB
ejpam-6091	38	26	the	the	DET
ejpam-6091	38	27	configuration	configuration	NOUN
ejpam-6091	38	28	space	space	NOUN
ejpam-6091	38	29	formed	form	VERB
ejpam-6091	38	30	by	by	ADP
ejpam-6091	38	31	n	n	CCONJ
ejpam-6091	38	32	generalized	generalized	ADJ
ejpam-6091	38	33	coordinates	coordinate	NOUN
ejpam-6091	38	34	qi	qi	PROPN
ejpam-6091	38	35	and	and	CCONJ
ejpam-6091	38	36	n	n	CCONJ
ejpam-6091	38	37	generalized	generalized	ADJ
ejpam-6091	38	38	velocities	velocity	NOUN
ejpam-6091	38	39	q̇i	q̇i	NOUN
ejpam-6091	38	40	.	.	PUNCT
ejpam-6091	39	1	according	accord	VERB
ejpam-6091	39	2	to	to	ADP
ejpam-6091	39	3	the	the	DET
ejpam-6091	39	4	usual	usual	ADJ
ejpam-6091	39	5	approach	approach	NOUN
ejpam-6091	39	6	of	of	ADP
ejpam-6091	39	7	the	the	DET
ejpam-6091	39	8	calculus	calculus	NOUN
ejpam-6091	39	9	of	of	ADP
ejpam-6091	39	10	variations	variation	NOUN
ejpam-6091	39	11	,	,	PUNCT
ejpam-6091	39	12	it	it	PRON
ejpam-6091	39	13	is	be	AUX
ejpam-6091	39	14	found	find	VERB
ejpam-6091	39	15	that	that	SCONJ
ejpam-6091	39	16	the	the	DET
ejpam-6091	39	17	generalized	generalize	VERB
ejpam-6091	39	18	lagrange	lagrange	NOUN
ejpam-6091	39	19	equations	equation	NOUN
ejpam-6091	39	20	for	for	ADP
ejpam-6091	39	21	such	such	ADJ
ejpam-6091	39	22	nonholonomic	nonholonomic	ADJ
ejpam-6091	39	23	systems	system	NOUN
ejpam-6091	39	24	are	be	AUX
ejpam-6091	39	25	given	give	VERB
ejpam-6091	39	26	by	by	ADP
ejpam-6091	39	27	[	[	X
ejpam-6091	39	28	15	15	NUM
ejpam-6091	39	29	,	,	PUNCT
ejpam-6091	39	30	16	16	NUM
ejpam-6091	39	31	]	]	PUNCT
ejpam-6091	39	32	by	by	ADP
ejpam-6091	39	33	using	use	VERB
ejpam-6091	39	34	the	the	DET
ejpam-6091	39	35	hamilton	hamilton	PROPN
ejpam-6091	39	36	’s	’s	PART
ejpam-6091	39	37	principle	principle	NOUN
ejpam-6091	39	38	:	:	PUNCT
ejpam-6091	39	39	d	d	X
ejpam-6091	39	40	dt	dt	X
ejpam-6091	39	41	(	(	PUNCT
ejpam-6091	39	42	∂l	∂l	PROPN
ejpam-6091	39	43	∂q̇i	∂q̇i	VERB
ejpam-6091	39	44	)	)	PUNCT
ejpam-6091	40	1	−	−	PROPN
ejpam-6091	40	2	∂l	∂l	NOUN
ejpam-6091	41	1	∂qi	∂qi	NOUN
ejpam-6091	41	2	=	=	PUNCT
ejpam-6091	41	3	λα	λα	NOUN
ejpam-6091	41	4	∂fα	∂fα	NOUN
ejpam-6091	41	5	∂q̇i	∂q̇i	NOUN
ejpam-6091	41	6	,	,	PUNCT
ejpam-6091	41	7	(	(	PUNCT
ejpam-6091	41	8	6	6	X
ejpam-6091	41	9	)	)	PUNCT
ejpam-6091	41	10	these	these	DET
ejpam-6091	41	11	dynamic	dynamic	ADJ
ejpam-6091	41	12	nonholonomic	nonholonomic	ADJ
ejpam-6091	41	13	equations	equation	NOUN
ejpam-6091	41	14	of	of	ADP
ejpam-6091	41	15	motion	motion	NOUN
ejpam-6091	41	16	are	be	AUX
ejpam-6091	41	17	known	know	VERB
ejpam-6091	41	18	as	as	ADP
ejpam-6091	41	19	lagrange	lagrange	NOUN
ejpam-6091	41	20	-	-	PUNCT
ejpam-6091	41	21	d’alembert	d’alembert	NOUN
ejpam-6091	41	22	principle	principle	NOUN
ejpam-6091	41	23	and	and	CCONJ
ejpam-6091	41	24	are	be	AUX
ejpam-6091	41	25	the	the	DET
ejpam-6091	41	26	correct	correct	ADJ
ejpam-6091	41	27	equations	equation	NOUN
ejpam-6091	41	28	to	to	PART
ejpam-6091	41	29	describe	describe	VERB
ejpam-6091	41	30	the	the	DET
ejpam-6091	41	31	time	time	NOUN
ejpam-6091	41	32	evolution	evolution	NOUN
ejpam-6091	41	33	a	a	DET
ejpam-6091	41	34	mechanical	mechanical	ADJ
ejpam-6091	41	35	system	system	NOUN
ejpam-6091	41	36	under	under	ADP
ejpam-6091	41	37	velocity	velocity	NOUN
ejpam-6091	41	38	dependent	dependent	ADJ
ejpam-6091	41	39	constraints	constraint	NOUN
ejpam-6091	41	40	.	.	PUNCT
ejpam-6091	42	1	where	where	SCONJ
ejpam-6091	42	2	λ	λ	PROPN
ejpam-6091	42	3	is	be	AUX
ejpam-6091	42	4	lagrange	lagrange	NOUN
ejpam-6091	42	5	multiplier	multipli	ADJ
ejpam-6091	42	6	,	,	PUNCT
ejpam-6091	42	7	to	to	PART
ejpam-6091	42	8	be	be	AUX
ejpam-6091	42	9	determined	determine	VERB
ejpam-6091	42	10	that	that	SCONJ
ejpam-6091	42	11	representing	represent	VERB
ejpam-6091	42	12	the	the	DET
ejpam-6091	42	13	force	force	NOUN
ejpam-6091	42	14	of	of	ADP
ejpam-6091	42	15	constraint	constraint	NOUN
ejpam-6091	42	16	.	.	PUNCT
ejpam-6091	43	1	this	this	DET
ejpam-6091	43	2	equation	equation	NOUN
ejpam-6091	43	3	represents	represent	VERB
ejpam-6091	43	4	a	a	DET
ejpam-6091	43	5	system	system	NOUN
ejpam-6091	43	6	of	of	ADP
ejpam-6091	43	7	n	n	DET
ejpam-6091	43	8	+	+	NOUN
ejpam-6091	43	9	m	m	PROPN
ejpam-6091	43	10	differential	differential	ADJ
ejpam-6091	43	11	equations	equation	NOUN
ejpam-6091	43	12	that	that	PRON
ejpam-6091	43	13	can	can	AUX
ejpam-6091	43	14	be	be	AUX
ejpam-6091	43	15	solved	solve	VERB
ejpam-6091	43	16	for	for	ADP
ejpam-6091	43	17	the	the	DET
ejpam-6091	43	18	n+m	n+m	NUM
ejpam-6091	43	19	unknown	unknown	ADJ
ejpam-6091	43	20	functions	function	NOUN
ejpam-6091	43	21	qi(t	qi(t	NOUN
ejpam-6091	43	22	)	)	PUNCT
ejpam-6091	43	23	,	,	PUNCT
ejpam-6091	43	24	λi(t	λi(t	NUM
ejpam-6091	43	25	)	)	PUNCT
ejpam-6091	43	26	.	.	PUNCT
ejpam-6091	44	1	we	we	PRON
ejpam-6091	44	2	will	will	AUX
ejpam-6091	44	3	consider	consider	VERB
ejpam-6091	44	4	a	a	DET
ejpam-6091	44	5	lagrangian	lagrangian	ADJ
ejpam-6091	44	6	system	system	NOUN
ejpam-6091	44	7	with	with	ADP
ejpam-6091	44	8	nonholonomic	nonholonomic	ADJ
ejpam-6091	44	9	constraints	constraint	NOUN
ejpam-6091	44	10	whose	whose	DET
ejpam-6091	44	11	motion	motion	NOUN
ejpam-6091	44	12	obeys	obey	VERB
ejpam-6091	44	13	the	the	DET
ejpam-6091	44	14	lagrange	lagrange	NOUN
ejpam-6091	44	15	-	-	PUNCT
ejpam-6091	44	16	d’alembert	d’alembert	NOUN
ejpam-6091	44	17	principle	principle	NOUN
ejpam-6091	44	18	in	in	ADP
ejpam-6091	44	19	the	the	DET
ejpam-6091	44	20	case	case	NOUN
ejpam-6091	44	21	of	of	ADP
ejpam-6091	44	22	completely	completely	ADV
ejpam-6091	44	23	integrable	integrable	ADJ
ejpam-6091	44	24	constraints	constraint	NOUN
ejpam-6091	44	25	.	.	PUNCT
ejpam-6091	45	1	the	the	DET
ejpam-6091	45	2	standard	standard	ADJ
ejpam-6091	45	3	formulation	formulation	NOUN
ejpam-6091	45	4	of	of	ADP
ejpam-6091	45	5	the	the	DET
ejpam-6091	45	6	hamilton	hamilton	PROPN
ejpam-6091	45	7	–	–	PUNCT
ejpam-6091	45	8	jacobi	jacobi	PROPN
ejpam-6091	45	9	problem	problem	NOUN
ejpam-6091	45	10	for	for	ADP
ejpam-6091	45	11	a	a	DET
ejpam-6091	45	12	hamiltonian	hamiltonian	ADJ
ejpam-6091	45	13	system	system	NOUN
ejpam-6091	45	14	is	be	AUX
ejpam-6091	45	15	based	base	VERB
ejpam-6091	45	16	on	on	ADP
ejpam-6091	45	17	the	the	DET
ejpam-6091	45	18	generating	generate	VERB
ejpam-6091	45	19	function	function	NOUN
ejpam-6091	45	20	s(q	s(q	NOUN
ejpam-6091	45	21	,	,	PUNCT
ejpam-6091	45	22	t	t	PROPN
ejpam-6091	45	23	)	)	PUNCT
ejpam-6091	45	24	which	which	PRON
ejpam-6091	45	25	is	be	AUX
ejpam-6091	45	26	called	call	VERB
ejpam-6091	45	27	the	the	DET
ejpam-6091	45	28	hamilton	hamilton	PROPN
ejpam-6091	45	29	-	-	PUNCT
ejpam-6091	45	30	jacobi	jacobi	PROPN
ejpam-6091	45	31	function	function	PROPN
ejpam-6091	45	32	:	:	PUNCT
ejpam-6091	45	33	the	the	DET
ejpam-6091	45	34	set	set	NOUN
ejpam-6091	45	35	of	of	ADP
ejpam-6091	45	36	the	the	DET
ejpam-6091	45	37	hamilton	hamilton	PROPN
ejpam-6091	45	38	-	-	PUNCT
ejpam-6091	45	39	jacobi	jacobi	PROPN
ejpam-6091	45	40	partial	partial	ADJ
ejpam-6091	45	41	differential	differential	NOUN
ejpam-6091	45	42	equation	equation	NOUN
ejpam-6091	45	43	can	can	AUX
ejpam-6091	45	44	be	be	AUX
ejpam-6091	45	45	written	write	VERB
ejpam-6091	45	46	in	in	ADP
ejpam-6091	45	47	compact	compact	ADJ
ejpam-6091	45	48	form	form	NOUN
ejpam-6091	45	49	as	as	ADP
ejpam-6091	45	50	[	[	X
ejpam-6091	45	51	17–24	17–24	NUM
ejpam-6091	45	52	]	]	X
ejpam-6091	45	53	:	:	PUNCT
ejpam-6091	46	1	∂s	∂s	PROPN
ejpam-6091	46	2	∂t	∂t	PROPN
ejpam-6091	47	1	+	+	ADV
ejpam-6091	47	2	h(pi	h(pi	X
ejpam-6091	47	3	,	,	PUNCT
ejpam-6091	47	4	qi	qi	PROPN
ejpam-6091	47	5	,	,	PUNCT
ejpam-6091	47	6	t	t	PROPN
ejpam-6091	47	7	)	)	PUNCT
ejpam-6091	47	8	=	=	SYM
ejpam-6091	48	1	0	0	PROPN
ejpam-6091	48	2	.	.	PUNCT
ejpam-6091	49	1	(	(	PUNCT
ejpam-6091	49	2	7	7	X
ejpam-6091	49	3	)	)	PUNCT
ejpam-6091	49	4	we	we	PRON
ejpam-6091	49	5	find	find	VERB
ejpam-6091	49	6	the	the	DET
ejpam-6091	49	7	solution	solution	NOUN
ejpam-6091	49	8	of	of	ADP
ejpam-6091	49	9	constraint	constraint	NOUN
ejpam-6091	49	10	equations	equation	NOUN
ejpam-6091	49	11	by	by	ADP
ejpam-6091	49	12	integration	integration	NOUN
ejpam-6091	49	13	whose	whose	DET
ejpam-6091	49	14	solution	solution	NOUN
ejpam-6091	49	15	has	have	VERB
ejpam-6091	49	16	the	the	DET
ejpam-6091	49	17	following	follow	VERB
ejpam-6091	49	18	form	form	NOUN
ejpam-6091	49	19	:	:	PUNCT
ejpam-6091	49	20	qi	qi	NOUN
ejpam-6091	49	21	=	=	SYM
ejpam-6091	49	22	qi(α1	qi(α1	NOUN
ejpam-6091	49	23	,	,	PUNCT
ejpam-6091	49	24	α2	α2	ADJ
ejpam-6091	49	25	,	,	PUNCT
ejpam-6091	49	26	.	.	PUNCT
ejpam-6091	49	27	.	.	PUNCT
ejpam-6091	49	28	.	.	PUNCT
ejpam-6091	50	1	,	,	PUNCT
ejpam-6091	50	2	αn−m	αn−m	NOUN
ejpam-6091	50	3	,	,	PUNCT
ejpam-6091	50	4	β1	β1	PROPN
ejpam-6091	50	5	,	,	PUNCT
ejpam-6091	50	6	β2	β2	NOUN
ejpam-6091	50	7	,	,	PUNCT
ejpam-6091	50	8	.	.	PUNCT
ejpam-6091	50	9	.	.	PUNCT
ejpam-6091	50	10	.	.	PUNCT
ejpam-6091	51	1	,	,	PUNCT
ejpam-6091	51	2	βn	βn	NOUN
ejpam-6091	51	3	,	,	PUNCT
ejpam-6091	51	4	t	t	PROPN
ejpam-6091	51	5	)	)	PUNCT
ejpam-6091	51	6	.	.	PUNCT
ejpam-6091	52	1	(	(	PUNCT
ejpam-6091	52	2	8)	8)	NUM
ejpam-6091	52	3	where	where	SCONJ
ejpam-6091	52	4	n	n	PRON
ejpam-6091	52	5	is	be	AUX
ejpam-6091	52	6	dimensional	dimensional	ADJ
ejpam-6091	52	7	configuration	configuration	NOUN
ejpam-6091	52	8	space	space	NOUN
ejpam-6091	52	9	,	,	PUNCT
ejpam-6091	52	10	subject	subject	ADJ
ejpam-6091	52	11	to	to	ADP
ejpam-6091	52	12	m	m	PROPN
ejpam-6091	52	13	nonholonomic	nonholonomic	ADJ
ejpam-6091	52	14	constraints	constraint	NOUN
ejpam-6091	52	15	.	.	PUNCT
ejpam-6091	53	1	m	m	VERB
ejpam-6091	53	2	<	<	X
ejpam-6091	53	3	n−	n−	NOUN
ejpam-6091	53	4	1	1	NUM
ejpam-6091	53	5	we	we	PRON
ejpam-6091	53	6	may	may	AUX
ejpam-6091	53	7	rewrite	rewrite	VERB
ejpam-6091	53	8	the	the	DET
ejpam-6091	53	9	above	above	ADJ
ejpam-6091	53	10	equations	equation	NOUN
ejpam-6091	53	11	as	as	ADP
ejpam-6091	53	12	:	:	PUNCT
ejpam-6091	53	13	xi(α1	xi(α1	NOUN
ejpam-6091	53	14	,	,	PUNCT
ejpam-6091	53	15	α2	α2	ADJ
ejpam-6091	53	16	,	,	PUNCT
ejpam-6091	53	17	.	.	PUNCT
ejpam-6091	53	18	.	.	PUNCT
ejpam-6091	54	1	.	.	PUNCT
ejpam-6091	55	1	,	,	PUNCT
ejpam-6091	55	2	αn−m	αn−m	NOUN
ejpam-6091	55	3	,	,	PUNCT
ejpam-6091	55	4	qi	qi	PROPN
ejpam-6091	55	5	,	,	PUNCT
ejpam-6091	55	6	t	t	PROPN
ejpam-6091	55	7	)	)	PUNCT
ejpam-6091	55	8	=	=	SYM
ejpam-6091	56	1	βi	βi	PROPN
ejpam-6091	56	2	.	.	PUNCT
ejpam-6091	57	1	(	(	PUNCT
ejpam-6091	57	2	9	9	X
ejpam-6091	57	3	)	)	PUNCT
ejpam-6091	57	4	where	where	SCONJ
ejpam-6091	57	5	αi	αi	PRON
ejpam-6091	57	6	and	and	CCONJ
ejpam-6091	57	7	βi	βi	PRON
ejpam-6091	57	8	are	be	AUX
ejpam-6091	57	9	initial	initial	ADJ
ejpam-6091	57	10	constants	constant	NOUN
ejpam-6091	57	11	of	of	ADP
ejpam-6091	57	12	motion	motion	NOUN
ejpam-6091	57	13	respectively	respectively	ADV
ejpam-6091	57	14	related	relate	VERB
ejpam-6091	57	15	to	to	ADP
ejpam-6091	57	16	the	the	DET
ejpam-6091	57	17	initial	initial	ADJ
ejpam-6091	57	18	velocity	velocity	NOUN
ejpam-6091	57	19	and	and	CCONJ
ejpam-6091	57	20	position	position	NOUN
ejpam-6091	57	21	of	of	ADP
ejpam-6091	57	22	the	the	DET
ejpam-6091	57	23	particle	particle	NOUN
ejpam-6091	57	24	.	.	PUNCT
ejpam-6091	58	1	the	the	DET
ejpam-6091	58	2	central	central	ADJ
ejpam-6091	58	3	issue	issue	NOUN
ejpam-6091	58	4	in	in	ADP
ejpam-6091	58	5	the	the	DET
ejpam-6091	58	6	procedure	procedure	NOUN
ejpam-6091	58	7	is	be	AUX
ejpam-6091	58	8	to	to	PART
ejpam-6091	58	9	assume	assume	VERB
ejpam-6091	58	10	the	the	DET
ejpam-6091	58	11	existence	existence	NOUN
ejpam-6091	58	12	of	of	ADP
ejpam-6091	58	13	hamilton	hamilton	PROPN
ejpam-6091	58	14	’s	’s	PART
ejpam-6091	58	15	principal	principal	ADJ
ejpam-6091	58	16	function	function	NOUN
ejpam-6091	58	17	from	from	ADP
ejpam-6091	58	18	which	which	PRON
ejpam-6091	58	19	the	the	DET
ejpam-6091	58	20	relations	relation	NOUN
ejpam-6091	58	21	are	be	AUX
ejpam-6091	58	22	obtained	obtain	VERB
ejpam-6091	58	23	[	[	PUNCT
ejpam-6091	58	24	13	13	NUM
ejpam-6091	58	25	-	-	SYM
ejpam-6091	58	26	14	14	NUM
ejpam-6091	58	27	]	]	PUNCT
ejpam-6091	58	28	we	we	PRON
ejpam-6091	58	29	can	can	AUX
ejpam-6091	58	30	set	set	VERB
ejpam-6091	58	31	:	:	PUNCT
ejpam-6091	58	32	∂s	∂s	PROPN
ejpam-6091	58	33	∂αi	∂αi	VERB
ejpam-6091	58	34	=	=	PUNCT
ejpam-6091	58	35	βi	βi	X
ejpam-6091	58	36	.	.	PUNCT
ejpam-6091	59	1	(	(	PUNCT
ejpam-6091	59	2	10	10	NUM
ejpam-6091	59	3	)	)	PUNCT
ejpam-6091	59	4	from	from	ADP
ejpam-6091	59	5	the	the	DET
ejpam-6091	59	6	above	above	ADJ
ejpam-6091	59	7	equations	equation	NOUN
ejpam-6091	59	8	we	we	PRON
ejpam-6091	59	9	can	can	AUX
ejpam-6091	59	10	find	find	VERB
ejpam-6091	59	11	the	the	DET
ejpam-6091	59	12	hamilton	hamilton	PROPN
ejpam-6091	59	13	-	-	PUNCT
ejpam-6091	59	14	jacobi	jacobi	PROPN
ejpam-6091	59	15	function	function	NOUN
ejpam-6091	59	16	,	,	PUNCT
ejpam-6091	59	17	we	we	PRON
ejpam-6091	59	18	will	will	AUX
ejpam-6091	59	19	see	see	VERB
ejpam-6091	59	20	that	that	SCONJ
ejpam-6091	59	21	the	the	DET
ejpam-6091	59	22	separation	separation	NOUN
ejpam-6091	59	23	of	of	ADP
ejpam-6091	59	24	variables	variable	NOUN
ejpam-6091	59	25	is	be	AUX
ejpam-6091	59	26	done	do	VERB
ejpam-6091	59	27	in	in	ADP
ejpam-6091	59	28	the	the	DET
ejpam-6091	59	29	following	follow	VERB
ejpam-6091	59	30	simple	simple	ADJ
ejpam-6091	59	31	manner	manner	NOUN
ejpam-6091	59	32	:	:	PUNCT
ejpam-6091	59	33	s(q1	s(q1	NOUN
ejpam-6091	59	34	,	,	PUNCT
ejpam-6091	59	35	q2	q2	NOUN
ejpam-6091	59	36	,	,	PUNCT
ejpam-6091	59	37	.	.	PUNCT
ejpam-6091	59	38	.	.	PUNCT
ejpam-6091	60	1	.	.	PUNCT
ejpam-6091	61	1	,	,	PUNCT
ejpam-6091	61	2	qn;α1	qn;α1	X
ejpam-6091	61	3	,	,	PUNCT
ejpam-6091	61	4	α2	α2	ADJ
ejpam-6091	61	5	,	,	PUNCT
ejpam-6091	61	6	.	.	PUNCT
ejpam-6091	61	7	.	.	PUNCT
ejpam-6091	62	1	.	.	PUNCT
ejpam-6091	63	1	,	,	PUNCT
ejpam-6091	63	2	αn	αn	NOUN
ejpam-6091	63	3	,	,	PUNCT
ejpam-6091	63	4	t	t	PROPN
ejpam-6091	63	5	)	)	PUNCT
ejpam-6091	64	1	=	=	SYM
ejpam-6091	64	2	s1(q1	s1(q1	PROPN
ejpam-6091	64	3	,	,	PUNCT
ejpam-6091	64	4	α1	α1	PROPN
ejpam-6091	64	5	)	)	PUNCT
ejpam-6091	64	6	+	+	SYM
ejpam-6091	64	7	s2(q2	s2(q2	NOUN
ejpam-6091	64	8	,	,	PUNCT
ejpam-6091	64	9	α2	α2	ADJ
ejpam-6091	64	10	)	)	PUNCT
ejpam-6091	64	11	+	+	CCONJ
ejpam-6091	64	12	·	·	PUNCT
ejpam-6091	64	13	·	·	PUNCT
ejpam-6091	64	14	·	·	PUNCT
ejpam-6091	64	15	+	+	NUM
ejpam-6091	64	16	sn(qn	sn(qn	PROPN
ejpam-6091	64	17	,	,	PUNCT
ejpam-6091	64	18	αn	αn	NOUN
ejpam-6091	64	19	)	)	PUNCT
ejpam-6091	64	20	.	.	PUNCT
ejpam-6091	65	1	(	(	PUNCT
ejpam-6091	65	2	11	11	NUM
ejpam-6091	65	3	)	)	PUNCT
ejpam-6091	65	4	k.	k.	PROPN
ejpam-6091	65	5	i.	i.	PROPN
ejpam-6091	65	6	nawafleh	nawafleh	PROPN
ejpam-6091	65	7	/	/	SYM
ejpam-6091	65	8	eur	eur	PROPN
ejpam-6091	65	9	.	.	PUNCT
ejpam-6091	66	1	j.	j.	PROPN
ejpam-6091	66	2	pure	pure	PROPN
ejpam-6091	66	3	appl	appl	PROPN
ejpam-6091	66	4	.	.	PROPN
ejpam-6091	66	5	math	math	PROPN
ejpam-6091	66	6	,	,	PUNCT
ejpam-6091	66	7	18	18	NUM
ejpam-6091	66	8	(	(	PUNCT
ejpam-6091	66	9	3	3	NUM
ejpam-6091	66	10	)	)	PUNCT
ejpam-6091	66	11	(	(	PUNCT
ejpam-6091	66	12	2025	2025	NUM
ejpam-6091	66	13	)	)	PUNCT
ejpam-6091	66	14	,	,	PUNCT
ejpam-6091	66	15	6091	6091	NUM
ejpam-6091	66	16	4	4	NUM
ejpam-6091	66	17	of	of	ADP
ejpam-6091	66	18	15	15	NUM
ejpam-6091	66	19	the	the	DET
ejpam-6091	66	20	generalized	generalized	ADJ
ejpam-6091	66	21	momenta	momenta	NOUN
ejpam-6091	66	22	are	be	AUX
ejpam-6091	66	23	determined	determine	VERB
ejpam-6091	66	24	by	by	ADP
ejpam-6091	66	25	:	:	PUNCT
ejpam-6091	66	26	pi	pi	NOUN
ejpam-6091	66	27	=	=	PUNCT
ejpam-6091	66	28	∂s	∂s	PROPN
ejpam-6091	66	29	∂qi	∂qi	PROPN
ejpam-6091	66	30	.	.	PUNCT
ejpam-6091	67	1	(	(	PUNCT
ejpam-6091	67	2	12	12	NUM
ejpam-6091	67	3	)	)	PUNCT
ejpam-6091	67	4	we	we	PRON
ejpam-6091	67	5	further	far	ADV
ejpam-6091	67	6	have	have	VERB
ejpam-6091	67	7	:	:	PUNCT
ejpam-6091	67	8	α	α	X
ejpam-6091	67	9	=	=	SYM
ejpam-6091	67	10	α(qi	α(qi	PROPN
ejpam-6091	67	11	,	,	PUNCT
ejpam-6091	67	12	pi	pi	NOUN
ejpam-6091	67	13	,	,	PUNCT
ejpam-6091	67	14	t	t	PROPN
ejpam-6091	67	15	)	)	PUNCT
ejpam-6091	67	16	.	.	PUNCT
ejpam-6091	68	1	(	(	PUNCT
ejpam-6091	68	2	13	13	NUM
ejpam-6091	68	3	)	)	PUNCT
ejpam-6091	68	4	where	where	SCONJ
ejpam-6091	68	5	we	we	PRON
ejpam-6091	68	6	substitute	substitute	VERB
ejpam-6091	68	7	α	α	NOUN
ejpam-6091	68	8	by	by	ADP
ejpam-6091	68	9	their	their	PRON
ejpam-6091	68	10	expression	expression	NOUN
ejpam-6091	68	11	in	in	ADP
ejpam-6091	68	12	terms	term	NOUN
ejpam-6091	68	13	of	of	ADP
ejpam-6091	68	14	qi	qi	PROPN
ejpam-6091	68	15	and	and	CCONJ
ejpam-6091	68	16	pi	pi	NOUN
ejpam-6091	68	17	.	.	PUNCT
ejpam-6091	69	1	the	the	DET
ejpam-6091	69	2	hamiltonian	hamiltonian	NOUN
ejpam-6091	69	3	is	be	AUX
ejpam-6091	69	4	obtained	obtain	VERB
ejpam-6091	69	5	as	as	ADP
ejpam-6091	69	6	:	:	PUNCT
ejpam-6091	69	7	h	h	NOUN
ejpam-6091	69	8	=	=	PUNCT
ejpam-6091	69	9	−∂s	−∂s	NUM
ejpam-6091	69	10	∂t	∂t	PROPN
ejpam-6091	69	11	.	.	PUNCT
ejpam-6091	70	1	(	(	PUNCT
ejpam-6091	70	2	14	14	NUM
ejpam-6091	70	3	)	)	PUNCT
ejpam-6091	70	4	following	follow	VERB
ejpam-6091	70	5	[	[	X
ejpam-6091	70	6	7	7	NUM
ejpam-6091	70	7	]	]	PUNCT
ejpam-6091	70	8	,	,	PUNCT
ejpam-6091	70	9	the	the	DET
ejpam-6091	70	10	hamilton	hamilton	PROPN
ejpam-6091	70	11	’s	’s	PART
ejpam-6091	70	12	equations	equation	NOUN
ejpam-6091	70	13	of	of	ADP
ejpam-6091	70	14	motion	motion	NOUN
ejpam-6091	70	15	are	be	AUX
ejpam-6091	70	16	given	give	VERB
ejpam-6091	70	17	by	by	ADP
ejpam-6091	70	18	[	[	PUNCT
ejpam-6091	70	19	14	14	NUM
ejpam-6091	70	20	-	-	SYM
ejpam-6091	70	21	16	16	NUM
ejpam-6091	70	22	]	]	PUNCT
ejpam-6091	70	23	:	:	PUNCT
ejpam-6091	70	24	q̇i	q̇i	PROPN
ejpam-6091	70	25	=	=	SYM
ejpam-6091	70	26	∂h	∂h	PROPN
ejpam-6091	70	27	∂pi	∂pi	NOUN
ejpam-6091	70	28	;	;	PUNCT
ejpam-6091	70	29	ṗi	ṗi	PROPN
ejpam-6091	70	30	=	=	PUNCT
ejpam-6091	70	31	−∂h	−∂h	PROPN
ejpam-6091	70	32	∂qi	∂qi	PROPN
ejpam-6091	70	33	+	+	CCONJ
ejpam-6091	70	34	λα	λα	PRON
ejpam-6091	70	35	∂fα	∂fα	VERB
ejpam-6091	70	36	∂q̇i	∂q̇i	NOUN
ejpam-6091	70	37	(	(	PUNCT
ejpam-6091	70	38	15	15	NUM
ejpam-6091	70	39	)	)	PUNCT
ejpam-6091	70	40	this	this	PRON
ejpam-6091	70	41	represents	represent	VERB
ejpam-6091	70	42	the	the	DET
ejpam-6091	70	43	equations	equation	NOUN
ejpam-6091	70	44	of	of	ADP
ejpam-6091	70	45	motion	motion	NOUN
ejpam-6091	70	46	for	for	ADP
ejpam-6091	70	47	nonholonmic	nonholonmic	ADJ
ejpam-6091	70	48	constraints	constraint	NOUN
ejpam-6091	70	49	.	.	PUNCT
ejpam-6091	71	1	it	it	PRON
ejpam-6091	71	2	is	be	AUX
ejpam-6091	71	3	worth	worth	ADJ
ejpam-6091	71	4	to	to	PART
ejpam-6091	71	5	mention	mention	VERB
ejpam-6091	71	6	that	that	SCONJ
ejpam-6091	71	7	the	the	DET
ejpam-6091	71	8	advantage	advantage	NOUN
ejpam-6091	71	9	of	of	ADP
ejpam-6091	71	10	this	this	DET
ejpam-6091	71	11	method	method	NOUN
ejpam-6091	71	12	is	be	AUX
ejpam-6091	71	13	that	that	SCONJ
ejpam-6091	71	14	,	,	PUNCT
ejpam-6091	71	15	in	in	ADP
ejpam-6091	71	16	spite	spite	NOUN
ejpam-6091	71	17	of	of	ADP
ejpam-6091	71	18	the	the	DET
ejpam-6091	71	19	difficulties	difficulty	NOUN
ejpam-6091	71	20	to	to	PART
ejpam-6091	71	21	solve	solve	VERB
ejpam-6091	71	22	a	a	DET
ejpam-6091	71	23	partial	partial	ADJ
ejpam-6091	71	24	differential	differential	NOUN
ejpam-6091	71	25	equation	equation	NOUN
ejpam-6091	71	26	instead	instead	ADV
ejpam-6091	71	27	of	of	ADP
ejpam-6091	71	28	an	an	DET
ejpam-6091	71	29	ordinary	ordinary	ADJ
ejpam-6091	71	30	differential	differential	NOUN
ejpam-6091	71	31	one	one	NOUN
ejpam-6091	71	32	,	,	PUNCT
ejpam-6091	71	33	in	in	ADP
ejpam-6091	71	34	many	many	ADJ
ejpam-6091	71	35	cases	case	NOUN
ejpam-6091	71	36	it	it	PRON
ejpam-6091	71	37	works	work	VERB
ejpam-6091	71	38	,	,	PUNCT
ejpam-6091	71	39	being	be	AUX
ejpam-6091	71	40	an	an	DET
ejpam-6091	71	41	extremely	extremely	ADV
ejpam-6091	71	42	useful	useful	ADJ
ejpam-6091	71	43	tool	tool	NOUN
ejpam-6091	71	44	,	,	PUNCT
ejpam-6091	71	45	indeed	indeed	ADV
ejpam-6091	71	46	,	,	PUNCT
ejpam-6091	71	47	in	in	ADP
ejpam-6091	71	48	these	these	DET
ejpam-6091	71	49	cases	case	NOUN
ejpam-6091	71	50	the	the	DET
ejpam-6091	71	51	method	method	NOUN
ejpam-6091	71	52	provides	provide	VERB
ejpam-6091	71	53	an	an	DET
ejpam-6091	71	54	immediate	immediate	ADJ
ejpam-6091	71	55	way	way	NOUN
ejpam-6091	71	56	to	to	PART
ejpam-6091	71	57	integrate	integrate	VERB
ejpam-6091	71	58	the	the	DET
ejpam-6091	71	59	equations	equation	NOUN
ejpam-6091	71	60	of	of	ADP
ejpam-6091	71	61	motion	motion	NOUN
ejpam-6091	71	62	.	.	PUNCT
ejpam-6091	72	1	to	to	PART
ejpam-6091	72	2	demonstrate	demonstrate	VERB
ejpam-6091	72	3	how	how	SCONJ
ejpam-6091	72	4	the	the	DET
ejpam-6091	72	5	proposed	propose	VERB
ejpam-6091	72	6	scheme	scheme	NOUN
ejpam-6091	72	7	works	work	NOUN
ejpam-6091	72	8	,	,	PUNCT
ejpam-6091	72	9	we	we	PRON
ejpam-6091	72	10	will	will	AUX
ejpam-6091	72	11	consider	consider	VERB
ejpam-6091	72	12	two	two	NUM
ejpam-6091	72	13	examples	example	NOUN
ejpam-6091	72	14	.	.	PUNCT
ejpam-6091	73	1	3	3	X
ejpam-6091	73	2	.	.	X
ejpam-6091	73	3	examples	example	NOUN
ejpam-6091	73	4	in	in	ADP
ejpam-6091	73	5	order	order	NOUN
ejpam-6091	73	6	to	to	PART
ejpam-6091	73	7	illustrate	illustrate	VERB
ejpam-6091	73	8	the	the	DET
ejpam-6091	73	9	general	general	ADJ
ejpam-6091	73	10	discussion	discussion	NOUN
ejpam-6091	73	11	we	we	PRON
ejpam-6091	73	12	will	will	AUX
ejpam-6091	73	13	examine	examine	VERB
ejpam-6091	73	14	two	two	NUM
ejpam-6091	73	15	examples	example	NOUN
ejpam-6091	73	16	subject	subject	ADJ
ejpam-6091	73	17	to	to	ADP
ejpam-6091	73	18	nonholonmic	nonholonmic	ADJ
ejpam-6091	73	19	constrains	constrain	NOUN
ejpam-6091	73	20	.	.	PUNCT
ejpam-6091	74	1	example	example	NOUN
ejpam-6091	74	2	1	1	NUM
ejpam-6091	74	3	as	as	ADP
ejpam-6091	74	4	a	a	DET
ejpam-6091	74	5	first	first	ADJ
ejpam-6091	74	6	example	example	NOUN
ejpam-6091	74	7	of	of	ADP
ejpam-6091	74	8	nonholonomic	nonholonomic	ADJ
ejpam-6091	74	9	constraints	constraint	NOUN
ejpam-6091	74	10	consider	consider	VERB
ejpam-6091	74	11	the	the	DET
ejpam-6091	74	12	motion	motion	NOUN
ejpam-6091	74	13	of	of	ADP
ejpam-6091	74	14	a	a	DET
ejpam-6091	74	15	flat	flat	ADJ
ejpam-6091	74	16	uniform	uniform	NOUN
ejpam-6091	74	17	disk	disk	NOUN
ejpam-6091	74	18	rolls	roll	NOUN
ejpam-6091	74	19	upright	upright	ADJ
ejpam-6091	74	20	without	without	ADP
ejpam-6091	74	21	slipping	slip	VERB
ejpam-6091	74	22	on	on	ADP
ejpam-6091	74	23	horizontal	horizontal	ADJ
ejpam-6091	74	24	plane	plane	NOUN
ejpam-6091	74	25	;	;	PUNCT
ejpam-6091	74	26	we	we	PRON
ejpam-6091	74	27	assume	assume	VERB
ejpam-6091	74	28	that	that	SCONJ
ejpam-6091	74	29	the	the	DET
ejpam-6091	74	30	mass	mass	NOUN
ejpam-6091	74	31	,	,	PUNCT
ejpam-6091	74	32	the	the	DET
ejpam-6091	74	33	moments	moment	NOUN
ejpam-6091	74	34	of	of	ADP
ejpam-6091	74	35	inertia	inertia	NOUN
ejpam-6091	74	36	and	and	CCONJ
ejpam-6091	74	37	the	the	DET
ejpam-6091	74	38	radius	radius	NOUN
ejpam-6091	74	39	of	of	ADP
ejpam-6091	74	40	the	the	DET
ejpam-6091	74	41	disk	disk	NOUN
ejpam-6091	74	42	are	be	AUX
ejpam-6091	74	43	all	all	ADV
ejpam-6091	74	44	equal	equal	ADJ
ejpam-6091	74	45	to	to	ADP
ejpam-6091	74	46	unity	unity	NOUN
ejpam-6091	74	47	.	.	PUNCT
ejpam-6091	75	1	the	the	DET
ejpam-6091	75	2	lagrangian	lagrangian	ADJ
ejpam-6091	75	3	describing	describe	VERB
ejpam-6091	75	4	the	the	DET
ejpam-6091	75	5	system	system	NOUN
ejpam-6091	75	6	is	be	AUX
ejpam-6091	75	7	l	l	NOUN
ejpam-6091	75	8	=	=	SYM
ejpam-6091	75	9	1	1	NUM
ejpam-6091	75	10	2	2	NUM
ejpam-6091	75	11	(	(	PUNCT
ejpam-6091	75	12	ẋ2	ẋ2	PROPN
ejpam-6091	76	1	+	+	PUNCT
ejpam-6091	76	2	ẏ2	ẏ2	PROPN
ejpam-6091	76	3	+	+	CCONJ
ejpam-6091	76	4	θ̇2	θ̇2	PROPN
ejpam-6091	76	5	+	+	CCONJ
ejpam-6091	76	6	φ̇2	φ̇2	PROPN
ejpam-6091	76	7	)	)	PUNCT
ejpam-6091	76	8	(	(	PUNCT
ejpam-6091	76	9	16	16	NUM
ejpam-6091	76	10	)	)	PUNCT
ejpam-6091	76	11	where	where	SCONJ
ejpam-6091	76	12	θ	θ	PROPN
ejpam-6091	76	13	is	be	AUX
ejpam-6091	76	14	the	the	DET
ejpam-6091	76	15	coordinate	coordinate	NOUN
ejpam-6091	76	16	associated	associate	VERB
ejpam-6091	76	17	to	to	ADP
ejpam-6091	76	18	rolling	roll	VERB
ejpam-6091	76	19	,	,	PUNCT
ejpam-6091	76	20	φ	φ	PROPN
ejpam-6091	76	21	to	to	ADP
ejpam-6091	76	22	pivoting	pivot	VERB
ejpam-6091	76	23	,	,	PUNCT
ejpam-6091	76	24	x	x	SYM
ejpam-6091	76	25	and	and	CCONJ
ejpam-6091	76	26	y	y	PROPN
ejpam-6091	76	27	to	to	PART
ejpam-6091	76	28	point	point	VERB
ejpam-6091	76	29	of	of	ADP
ejpam-6091	76	30	contact	contact	NOUN
ejpam-6091	76	31	of	of	ADP
ejpam-6091	76	32	the	the	DET
ejpam-6091	76	33	disk	disk	NOUN
ejpam-6091	76	34	with	with	ADP
ejpam-6091	76	35	the	the	DET
ejpam-6091	76	36	horizontal	horizontal	ADJ
ejpam-6091	76	37	plane	plane	NOUN
ejpam-6091	76	38	.	.	PUNCT
ejpam-6091	77	1	the	the	DET
ejpam-6091	77	2	system	system	NOUN
ejpam-6091	77	3	has	have	VERB
ejpam-6091	77	4	two	two	NUM
ejpam-6091	77	5	nonholonomic	nonholonomic	ADJ
ejpam-6091	77	6	constraints	constraint	NOUN
ejpam-6091	77	7	:	:	PUNCT
ejpam-6091	77	8	f1	f1	NOUN
ejpam-6091	77	9	=	=	SYM
ejpam-6091	77	10	ẋ−	ẋ−	VERB
ejpam-6091	77	11	θ̇	θ̇	DET
ejpam-6091	77	12	cosφ	cosφ	NOUN
ejpam-6091	77	13	=	=	SYM
ejpam-6091	78	1	0	0	NUM
ejpam-6091	78	2	(	(	PUNCT
ejpam-6091	78	3	17	17	NUM
ejpam-6091	78	4	)	)	PUNCT
ejpam-6091	78	5	f2	f2	PROPN
ejpam-6091	78	6	=	=	NOUN
ejpam-6091	78	7	ẏ	ẏ	PROPN
ejpam-6091	78	8	−	−	ADP
ejpam-6091	78	9	θ̇	θ̇	DET
ejpam-6091	78	10	sinφ	sinφ	NOUN
ejpam-6091	78	11	=	=	SYM
ejpam-6091	78	12	0	0	PUNCT
ejpam-6091	79	1	(	(	PUNCT
ejpam-6091	79	2	18	18	NUM
ejpam-6091	79	3	)	)	PUNCT
ejpam-6091	79	4	k.	k.	PROPN
ejpam-6091	79	5	i.	i.	PROPN
ejpam-6091	79	6	nawafleh	nawafleh	PROPN
ejpam-6091	79	7	/	/	SYM
ejpam-6091	79	8	eur	eur	PROPN
ejpam-6091	79	9	.	.	PUNCT
ejpam-6091	80	1	j.	j.	PROPN
ejpam-6091	80	2	pure	pure	PROPN
ejpam-6091	80	3	appl	appl	PROPN
ejpam-6091	80	4	.	.	PROPN
ejpam-6091	80	5	math	math	PROPN
ejpam-6091	80	6	,	,	PUNCT
ejpam-6091	80	7	18	18	NUM
ejpam-6091	80	8	(	(	PUNCT
ejpam-6091	80	9	3	3	NUM
ejpam-6091	80	10	)	)	PUNCT
ejpam-6091	80	11	(	(	PUNCT
ejpam-6091	80	12	2025	2025	NUM
ejpam-6091	80	13	)	)	PUNCT
ejpam-6091	80	14	,	,	PUNCT
ejpam-6091	80	15	6091	6091	NUM
ejpam-6091	80	16	5	5	NUM
ejpam-6091	80	17	of	of	ADP
ejpam-6091	80	18	15	15	NUM
ejpam-6091	80	19	the	the	DET
ejpam-6091	80	20	constraint	constraint	NOUN
ejpam-6091	80	21	equations	equation	NOUN
ejpam-6091	80	22	(	(	PUNCT
ejpam-6091	80	23	17	17	NUM
ejpam-6091	80	24	)	)	PUNCT
ejpam-6091	80	25	and	and	CCONJ
ejpam-6091	80	26	(	(	PUNCT
ejpam-6091	80	27	18	18	NUM
ejpam-6091	80	28	)	)	PUNCT
ejpam-6091	80	29	can	can	AUX
ejpam-6091	80	30	be	be	AUX
ejpam-6091	80	31	rewritten	rewrite	VERB
ejpam-6091	80	32	as	as	ADP
ejpam-6091	80	33	ẋ	ẋ	PROPN
ejpam-6091	80	34	=	=	PUNCT
ejpam-6091	81	1	θ̇	θ̇	ADJ
ejpam-6091	81	2	cosφ	cosφ	NOUN
ejpam-6091	81	3	,	,	PUNCT
ejpam-6091	81	4	(	(	PUNCT
ejpam-6091	81	5	19	19	NUM
ejpam-6091	81	6	)	)	PUNCT
ejpam-6091	81	7	ẏ	ẏ	NOUN
ejpam-6091	81	8	=	=	NOUN
ejpam-6091	82	1	θ̇	θ̇	DET
ejpam-6091	82	2	sinφ	sinφ	NOUN
ejpam-6091	82	3	.	.	PUNCT
ejpam-6091	83	1	(	(	PUNCT
ejpam-6091	83	2	20	20	NUM
ejpam-6091	83	3	)	)	PUNCT
ejpam-6091	83	4	first	first	ADV
ejpam-6091	83	5	we	we	PRON
ejpam-6091	83	6	derive	derive	VERB
ejpam-6091	83	7	the	the	DET
ejpam-6091	83	8	equations	equation	NOUN
ejpam-6091	83	9	of	of	ADP
ejpam-6091	83	10	motion	motion	NOUN
ejpam-6091	83	11	as	as	ADP
ejpam-6091	83	12	a	a	DET
ejpam-6091	83	13	result	result	NOUN
ejpam-6091	83	14	of	of	ADP
ejpam-6091	83	15	varying	vary	VERB
ejpam-6091	83	16	the	the	DET
ejpam-6091	83	17	coordinates	coordinate	NOUN
ejpam-6091	83	18	of	of	ADP
ejpam-6091	83	19	the	the	DET
ejpam-6091	83	20	extended	extend	VERB
ejpam-6091	83	21	phase	phase	NOUN
ejpam-6091	83	22	space	space	NOUN
ejpam-6091	83	23	including	include	VERB
ejpam-6091	83	24	the	the	DET
ejpam-6091	83	25	multipliers	multiplier	NOUN
ejpam-6091	83	26	qi	qi	PROPN
ejpam-6091	83	27	and	and	CCONJ
ejpam-6091	83	28	λα	λα	X
ejpam-6091	83	29	according	accord	VERB
ejpam-6091	83	30	to	to	ADP
ejpam-6091	83	31	equation	equation	NOUN
ejpam-6091	83	32	(	(	PUNCT
ejpam-6091	83	33	6	6	NUM
ejpam-6091	83	34	)	)	PUNCT
ejpam-6091	83	35	,	,	PUNCT
ejpam-6091	83	36	we	we	PRON
ejpam-6091	83	37	obtain	obtain	VERB
ejpam-6091	84	1	d	d	X
ejpam-6091	84	2	dt	dt	X
ejpam-6091	85	1	(	(	PUNCT
ejpam-6091	85	2	∂l	∂l	PROPN
ejpam-6091	85	3	∂ẋ	∂ẋ	ADJ
ejpam-6091	85	4	)	)	PUNCT
ejpam-6091	86	1	−	−	PROPN
ejpam-6091	86	2	∂l	∂l	NOUN
ejpam-6091	86	3	∂x	∂x	NOUN
ejpam-6091	86	4	=	=	SYM
ejpam-6091	86	5	λ1	λ1	PROPN
ejpam-6091	86	6	∂f1	∂f1	PROPN
ejpam-6091	86	7	∂ẋ	∂ẋ	PROPN
ejpam-6091	86	8	,	,	PUNCT
ejpam-6091	86	9	(	(	PUNCT
ejpam-6091	86	10	21	21	NUM
ejpam-6091	86	11	)	)	PUNCT
ejpam-6091	86	12	d	d	NOUN
ejpam-6091	86	13	dt	dt	X
ejpam-6091	86	14	(	(	PUNCT
ejpam-6091	86	15	∂l	∂l	X
ejpam-6091	86	16	∂ẏ	∂ẏ	X
ejpam-6091	86	17	)	)	PUNCT
ejpam-6091	87	1	−	−	PUNCT
ejpam-6091	87	2	∂l	∂l	NOUN
ejpam-6091	87	3	∂y	∂y	SYM
ejpam-6091	87	4	=	=	SYM
ejpam-6091	87	5	λ2	λ2	NOUN
ejpam-6091	87	6	∂f2	∂f2	VERB
ejpam-6091	87	7	∂ẏ	∂ẏ	ADJ
ejpam-6091	87	8	,	,	PUNCT
ejpam-6091	87	9	(	(	PUNCT
ejpam-6091	87	10	22	22	NUM
ejpam-6091	87	11	)	)	PUNCT
ejpam-6091	88	1	d	d	NOUN
ejpam-6091	88	2	dt	dt	X
ejpam-6091	89	1	(	(	PUNCT
ejpam-6091	89	2	∂l	∂l	PROPN
ejpam-6091	89	3	∂θ̇	∂θ̇	NUM
ejpam-6091	89	4	)	)	PUNCT
ejpam-6091	90	1	−	−	PROPN
ejpam-6091	91	1	∂l	∂l	NOUN
ejpam-6091	91	2	∂θ	∂θ	NOUN
ejpam-6091	92	1	=	=	PUNCT
ejpam-6091	92	2	λ1	λ1	ADJ
ejpam-6091	92	3	∂f1	∂f1	PROPN
ejpam-6091	92	4	∂θ̇	∂θ̇	VERB
ejpam-6091	92	5	+	+	CCONJ
ejpam-6091	92	6	λ2	λ2	NOUN
ejpam-6091	92	7	∂f2	∂f2	VERB
ejpam-6091	92	8	∂θ̇	∂θ̇	VERB
ejpam-6091	92	9	,	,	PUNCT
ejpam-6091	92	10	(	(	PUNCT
ejpam-6091	92	11	23	23	NUM
ejpam-6091	92	12	)	)	PUNCT
ejpam-6091	93	1	d	d	NOUN
ejpam-6091	93	2	dt	dt	X
ejpam-6091	93	3	(	(	PUNCT
ejpam-6091	93	4	∂l	∂l	INTJ
ejpam-6091	93	5	∂φ̇	∂φ̇	ADV
ejpam-6091	93	6	)	)	PUNCT
ejpam-6091	93	7	−	−	PROPN
ejpam-6091	94	1	∂l	∂l	NOUN
ejpam-6091	94	2	∂φ	∂φ	PUNCT
ejpam-6091	95	1	=	=	PUNCT
ejpam-6091	95	2	0	0	PROPN
ejpam-6091	95	3	.	.	PUNCT
ejpam-6091	96	1	(	(	PUNCT
ejpam-6091	96	2	24	24	NUM
ejpam-6091	96	3	)	)	PUNCT
ejpam-6091	96	4	these	these	PRON
ejpam-6091	96	5	give	give	VERB
ejpam-6091	96	6	:	:	PUNCT
ejpam-6091	96	7	ẍ	ẍ	X
ejpam-6091	97	1	=	=	PROPN
ejpam-6091	97	2	λ1	λ1	PROPN
ejpam-6091	97	3	,	,	PUNCT
ejpam-6091	97	4	(	(	PUNCT
ejpam-6091	97	5	25	25	NUM
ejpam-6091	97	6	)	)	PUNCT
ejpam-6091	97	7	ÿ	ÿ	NOUN
ejpam-6091	97	8	=	=	SYM
ejpam-6091	97	9	λ2	λ2	PROPN
ejpam-6091	97	10	,	,	PUNCT
ejpam-6091	97	11	(	(	PUNCT
ejpam-6091	97	12	26	26	NUM
ejpam-6091	97	13	)	)	PUNCT
ejpam-6091	97	14	θ̈	θ̈	NOUN
ejpam-6091	97	15	=	=	SYM
ejpam-6091	98	1	−λ1	−λ1	PROPN
ejpam-6091	98	2	cosφ−	cosφ−	NOUN
ejpam-6091	98	3	λ2	λ2	NOUN
ejpam-6091	98	4	sinφ	sinφ	NOUN
ejpam-6091	98	5	,	,	PUNCT
ejpam-6091	98	6	(	(	PUNCT
ejpam-6091	98	7	27	27	NUM
ejpam-6091	98	8	)	)	PUNCT
ejpam-6091	98	9	φ̈	φ̈	X
ejpam-6091	99	1	=	=	NOUN
ejpam-6091	99	2	0	0	X
ejpam-6091	99	3	.	.	PUNCT
ejpam-6091	100	1	(	(	PUNCT
ejpam-6091	100	2	28	28	NUM
ejpam-6091	100	3	)	)	PUNCT
ejpam-6091	100	4	according	accord	VERB
ejpam-6091	100	5	to	to	ADP
ejpam-6091	100	6	equations	equation	NOUN
ejpam-6091	100	7	(	(	PUNCT
ejpam-6091	100	8	25	25	NUM
ejpam-6091	100	9	)	)	PUNCT
ejpam-6091	100	10	and	and	CCONJ
ejpam-6091	100	11	(	(	PUNCT
ejpam-6091	100	12	26	26	NUM
ejpam-6091	100	13	)	)	PUNCT
ejpam-6091	100	14	,	,	PUNCT
ejpam-6091	100	15	equation	equation	NOUN
ejpam-6091	100	16	(	(	PUNCT
ejpam-6091	100	17	27	27	NUM
ejpam-6091	100	18	)	)	PUNCT
ejpam-6091	100	19	can	can	AUX
ejpam-6091	100	20	be	be	AUX
ejpam-6091	100	21	expressed	express	VERB
ejpam-6091	100	22	as	as	ADP
ejpam-6091	100	23	:	:	PUNCT
ejpam-6091	100	24	θ̈	θ̈	NOUN
ejpam-6091	100	25	=	=	SYM
ejpam-6091	100	26	−ẍ	−ẍ	ADJ
ejpam-6091	100	27	cosφ−	cosφ−	NOUN
ejpam-6091	100	28	ÿ	ÿ	NUM
ejpam-6091	100	29	sinφ	sinφ	NOUN
ejpam-6091	100	30	.	.	PUNCT
ejpam-6091	101	1	(	(	PUNCT
ejpam-6091	101	2	29	29	NUM
ejpam-6091	101	3	)	)	PUNCT
ejpam-6091	101	4	differentiating	differentiate	VERB
ejpam-6091	101	5	constraint	constraint	NOUN
ejpam-6091	101	6	functions	function	NOUN
ejpam-6091	101	7	in	in	ADP
ejpam-6091	101	8	equations	equation	NOUN
ejpam-6091	101	9	(	(	PUNCT
ejpam-6091	101	10	19	19	NUM
ejpam-6091	101	11	)	)	PUNCT
ejpam-6091	101	12	and	and	CCONJ
ejpam-6091	101	13	(	(	PUNCT
ejpam-6091	101	14	20	20	NUM
ejpam-6091	101	15	)	)	PUNCT
ejpam-6091	101	16	with	with	ADP
ejpam-6091	101	17	respect	respect	NOUN
ejpam-6091	101	18	to	to	ADP
ejpam-6091	101	19	time	time	NOUN
ejpam-6091	101	20	,	,	PUNCT
ejpam-6091	101	21	we	we	PRON
ejpam-6091	101	22	find	find	VERB
ejpam-6091	101	23	ẍ	ẍ	X
ejpam-6091	102	1	=	=	PUNCT
ejpam-6091	102	2	θ̈	θ̈	NOUN
ejpam-6091	102	3	cosφ−	cosφ−	NOUN
ejpam-6091	102	4	φ̇θ̇	φ̇θ̇	NOUN
ejpam-6091	102	5	sinφ	sinφ	NOUN
ejpam-6091	102	6	,	,	PUNCT
ejpam-6091	102	7	(	(	PUNCT
ejpam-6091	102	8	30	30	NUM
ejpam-6091	102	9	)	)	PUNCT
ejpam-6091	102	10	ÿ	ÿ	NOUN
ejpam-6091	102	11	=	=	SYM
ejpam-6091	102	12	θ̈	θ̈	ADP
ejpam-6091	102	13	sinφ+	sinφ+	NOUN
ejpam-6091	102	14	φ̇θ̇	φ̇θ̇	NOUN
ejpam-6091	102	15	cosφ	cosφ	NOUN
ejpam-6091	102	16	,	,	PUNCT
ejpam-6091	102	17	(	(	PUNCT
ejpam-6091	102	18	31	31	NUM
ejpam-6091	102	19	)	)	PUNCT
ejpam-6091	102	20	by	by	ADP
ejpam-6091	102	21	inserting	insert	VERB
ejpam-6091	102	22	equations	equation	NOUN
ejpam-6091	102	23	(	(	PUNCT
ejpam-6091	102	24	30	30	NUM
ejpam-6091	102	25	)	)	PUNCT
ejpam-6091	102	26	and	and	CCONJ
ejpam-6091	102	27	(	(	PUNCT
ejpam-6091	102	28	31	31	NUM
ejpam-6091	102	29	)	)	PUNCT
ejpam-6091	102	30	in	in	ADP
ejpam-6091	102	31	equation	equation	NOUN
ejpam-6091	102	32	(	(	PUNCT
ejpam-6091	102	33	29	29	NUM
ejpam-6091	102	34	)	)	PUNCT
ejpam-6091	102	35	,	,	PUNCT
ejpam-6091	102	36	we	we	PRON
ejpam-6091	102	37	arrive	arrive	VERB
ejpam-6091	102	38	at	at	ADP
ejpam-6091	102	39	the	the	DET
ejpam-6091	102	40	following	follow	VERB
ejpam-6091	102	41	equation	equation	NOUN
ejpam-6091	102	42	θ̈	θ̈	NOUN
ejpam-6091	103	1	=	=	SYM
ejpam-6091	104	1	0	0	PROPN
ejpam-6091	104	2	.	.	PUNCT
ejpam-6091	105	1	(	(	PUNCT
ejpam-6091	105	2	32	32	NUM
ejpam-6091	105	3	)	)	PUNCT
ejpam-6091	105	4	so	so	SCONJ
ejpam-6091	105	5	we	we	PRON
ejpam-6091	105	6	obtain	obtain	VERB
ejpam-6091	105	7	the	the	DET
ejpam-6091	105	8	constrained	constrain	VERB
ejpam-6091	105	9	equations	equation	NOUN
ejpam-6091	105	10	:	:	PUNCT
ejpam-6091	105	11	θ̈	θ̈	NOUN
ejpam-6091	105	12	=	=	SYM
ejpam-6091	105	13	0	0	NUM
ejpam-6091	105	14	,	,	PUNCT
ejpam-6091	105	15	φ̈	φ̈	X
ejpam-6091	105	16	=	=	SYM
ejpam-6091	105	17	0	0	NUM
ejpam-6091	105	18	,	,	PUNCT
ejpam-6091	105	19	ẋ	ẋ	PUNCT
ejpam-6091	105	20	=	=	PUNCT
ejpam-6091	105	21	cosφθ̇	cosφθ̇	PROPN
ejpam-6091	105	22	,	,	PUNCT
ejpam-6091	105	23	ẏ	ẏ	PROPN
ejpam-6091	105	24	=	=	SYM
ejpam-6091	105	25	sinφθ̇.	sinφθ̇.	PROPN
ejpam-6091	105	26	(	(	PUNCT
ejpam-6091	105	27	33	33	NUM
ejpam-6091	105	28	)	)	PUNCT
ejpam-6091	105	29	this	this	PRON
ejpam-6091	105	30	is	be	AUX
ejpam-6091	105	31	a	a	DET
ejpam-6091	105	32	mixed	mixed	ADJ
ejpam-6091	105	33	set	set	NOUN
ejpam-6091	105	34	of	of	ADP
ejpam-6091	105	35	first	first	ADJ
ejpam-6091	105	36	and	and	CCONJ
ejpam-6091	105	37	second	second	ADJ
ejpam-6091	105	38	-	-	PUNCT
ejpam-6091	105	39	order	order	NOUN
ejpam-6091	105	40	differential	differential	ADJ
ejpam-6091	105	41	equations	equation	NOUN
ejpam-6091	105	42	.	.	PUNCT
ejpam-6091	106	1	from	from	ADP
ejpam-6091	106	2	these	these	DET
ejpam-6091	106	3	equations	equation	NOUN
ejpam-6091	106	4	,	,	PUNCT
ejpam-6091	106	5	we	we	PRON
ejpam-6091	106	6	can	can	AUX
ejpam-6091	106	7	solve	solve	VERB
ejpam-6091	106	8	θ(t	θ(t	NOUN
ejpam-6091	106	9	)	)	PUNCT
ejpam-6091	106	10	,	,	PUNCT
ejpam-6091	106	11	φ(t	φ(t	PROPN
ejpam-6091	106	12	)	)	PUNCT
ejpam-6091	106	13	,	,	PUNCT
ejpam-6091	106	14	x(t	x(t	PROPN
ejpam-6091	106	15	)	)	PUNCT
ejpam-6091	106	16	,	,	PUNCT
ejpam-6091	106	17	y(t	y(t	NUM
ejpam-6091	106	18	)	)	PUNCT
ejpam-6091	106	19	as	as	SCONJ
ejpam-6091	106	20	follows	follow	VERB
ejpam-6091	106	21	:	:	PUNCT
ejpam-6091	106	22	k.	k.	PROPN
ejpam-6091	106	23	i.	i.	PROPN
ejpam-6091	106	24	nawafleh	nawafleh	PROPN
ejpam-6091	106	25	/	/	SYM
ejpam-6091	106	26	eur	eur	PROPN
ejpam-6091	106	27	.	.	PUNCT
ejpam-6091	107	1	j.	j.	PROPN
ejpam-6091	107	2	pure	pure	PROPN
ejpam-6091	107	3	appl	appl	PROPN
ejpam-6091	107	4	.	.	PROPN
ejpam-6091	107	5	math	math	PROPN
ejpam-6091	107	6	,	,	PUNCT
ejpam-6091	107	7	18	18	NUM
ejpam-6091	107	8	(	(	PUNCT
ejpam-6091	107	9	3	3	NUM
ejpam-6091	107	10	)	)	PUNCT
ejpam-6091	107	11	(	(	PUNCT
ejpam-6091	107	12	2025	2025	NUM
ejpam-6091	107	13	)	)	PUNCT
ejpam-6091	107	14	,	,	PUNCT
ejpam-6091	107	15	6091	6091	NUM
ejpam-6091	107	16	6	6	NUM
ejpam-6091	107	17	of	of	ADP
ejpam-6091	107	18	15	15	NUM
ejpam-6091	107	19	the	the	DET
ejpam-6091	107	20	first	first	ADJ
ejpam-6091	107	21	two	two	NUM
ejpam-6091	107	22	equations	equation	NOUN
ejpam-6091	107	23	can	can	AUX
ejpam-6091	107	24	be	be	AUX
ejpam-6091	107	25	easily	easily	ADV
ejpam-6091	107	26	integrated	integrate	VERB
ejpam-6091	107	27	to	to	PART
ejpam-6091	107	28	give	give	VERB
ejpam-6091	107	29	:	:	PUNCT
ejpam-6091	107	30	θ(t	θ(t	NUM
ejpam-6091	107	31	)	)	PUNCT
ejpam-6091	107	32	=	=	PUNCT
ejpam-6091	108	1	α1t+	α1t+	NOUN
ejpam-6091	108	2	β1	β1	PROPN
ejpam-6091	108	3	,	,	PUNCT
ejpam-6091	108	4	(	(	PUNCT
ejpam-6091	108	5	34	34	NUM
ejpam-6091	108	6	)	)	PUNCT
ejpam-6091	108	7	φ(t	φ(t	PROPN
ejpam-6091	108	8	)	)	PUNCT
ejpam-6091	108	9	=	=	SYM
ejpam-6091	108	10	α2t+	α2t+	NOUN
ejpam-6091	108	11	β2	β2	NOUN
ejpam-6091	108	12	.	.	PUNCT
ejpam-6091	109	1	(	(	PUNCT
ejpam-6091	109	2	35	35	NUM
ejpam-6091	109	3	)	)	PUNCT
ejpam-6091	109	4	differentiating	differentiate	VERB
ejpam-6091	109	5	equations	equation	NOUN
ejpam-6091	109	6	(	(	PUNCT
ejpam-6091	109	7	34	34	NUM
ejpam-6091	109	8	)	)	PUNCT
ejpam-6091	109	9	and	and	CCONJ
ejpam-6091	109	10	(	(	PUNCT
ejpam-6091	109	11	35	35	NUM
ejpam-6091	109	12	)	)	PUNCT
ejpam-6091	109	13	with	with	ADP
ejpam-6091	109	14	respect	respect	NOUN
ejpam-6091	109	15	to	to	ADP
ejpam-6091	109	16	time	time	NOUN
ejpam-6091	109	17	,	,	PUNCT
ejpam-6091	109	18	we	we	PRON
ejpam-6091	109	19	get	get	VERB
ejpam-6091	109	20	θ̇	θ̇	ADJ
ejpam-6091	109	21	=	=	SYM
ejpam-6091	109	22	α1	α1	NOUN
ejpam-6091	109	23	,	,	PUNCT
ejpam-6091	109	24	(	(	PUNCT
ejpam-6091	109	25	36	36	NUM
ejpam-6091	109	26	)	)	PUNCT
ejpam-6091	109	27	φ̇	φ̇	NOUN
ejpam-6091	109	28	=	=	PUNCT
ejpam-6091	109	29	α2	α2	PROPN
ejpam-6091	109	30	.	.	PUNCT
ejpam-6091	110	1	(	(	PUNCT
ejpam-6091	110	2	37	37	NUM
ejpam-6091	110	3	)	)	PUNCT
ejpam-6091	110	4	substituting	substitute	VERB
ejpam-6091	110	5	equations	equation	NOUN
ejpam-6091	110	6	(	(	PUNCT
ejpam-6091	110	7	35	35	NUM
ejpam-6091	110	8	)	)	PUNCT
ejpam-6091	110	9	and	and	CCONJ
ejpam-6091	110	10	(	(	PUNCT
ejpam-6091	110	11	36	36	NUM
ejpam-6091	110	12	)	)	PUNCT
ejpam-6091	110	13	into	into	ADP
ejpam-6091	110	14	equation	equation	NOUN
ejpam-6091	110	15	(	(	PUNCT
ejpam-6091	110	16	19	19	NUM
ejpam-6091	110	17	)	)	PUNCT
ejpam-6091	110	18	and	and	CCONJ
ejpam-6091	110	19	integrating	integrate	VERB
ejpam-6091	110	20	the	the	DET
ejpam-6091	110	21	result	result	NOUN
ejpam-6091	110	22	equation	equation	NOUN
ejpam-6091	110	23	,	,	PUNCT
ejpam-6091	110	24	we	we	PRON
ejpam-6091	110	25	obtain	obtain	VERB
ejpam-6091	110	26	∫	∫	PROPN
ejpam-6091	110	27	ẋdt	ẋdt	PUNCT
ejpam-6091	111	1	=	=	SYM
ejpam-6091	111	2	∫	∫	PROPN
ejpam-6091	111	3	α1	α1	PROPN
ejpam-6091	111	4	cos(α2t+	cos(α2t+	NOUN
ejpam-6091	111	5	β2)dt	β2)dt	NOUN
ejpam-6091	111	6	,	,	PUNCT
ejpam-6091	111	7	(	(	PUNCT
ejpam-6091	111	8	38	38	NUM
ejpam-6091	111	9	)	)	PUNCT
ejpam-6091	111	10	and	and	CCONJ
ejpam-6091	111	11	this	this	PRON
ejpam-6091	111	12	gives	give	VERB
ejpam-6091	111	13	:	:	PUNCT
ejpam-6091	111	14	x(t	x(t	PROPN
ejpam-6091	111	15	)	)	PUNCT
ejpam-6091	111	16	=	=	SYM
ejpam-6091	112	1	α3	α3	NOUN
ejpam-6091	112	2	sinφ+	sinφ+	NOUN
ejpam-6091	112	3	β3	β3	ADJ
ejpam-6091	112	4	,	,	PUNCT
ejpam-6091	112	5	(	(	PUNCT
ejpam-6091	112	6	39	39	NUM
ejpam-6091	112	7	)	)	PUNCT
ejpam-6091	112	8	where	where	SCONJ
ejpam-6091	112	9	α3	α3	NOUN
ejpam-6091	112	10	=	=	SYM
ejpam-6091	112	11	α1	α1	PROPN
ejpam-6091	112	12	α2	α2	NOUN
ejpam-6091	112	13	.	.	PUNCT
ejpam-6091	113	1	also	also	ADV
ejpam-6091	113	2	substituting	substitute	VERB
ejpam-6091	113	3	equations	equation	NOUN
ejpam-6091	113	4	(	(	PUNCT
ejpam-6091	113	5	35	35	NUM
ejpam-6091	113	6	)	)	PUNCT
ejpam-6091	113	7	,	,	PUNCT
ejpam-6091	113	8	(	(	PUNCT
ejpam-6091	113	9	36	36	NUM
ejpam-6091	113	10	)	)	PUNCT
ejpam-6091	113	11	into	into	ADP
ejpam-6091	113	12	equation	equation	NOUN
ejpam-6091	113	13	(	(	PUNCT
ejpam-6091	113	14	20	20	NUM
ejpam-6091	113	15	)	)	PUNCT
ejpam-6091	113	16	and	and	CCONJ
ejpam-6091	113	17	integrating	integrate	VERB
ejpam-6091	113	18	the	the	DET
ejpam-6091	113	19	result	result	NOUN
ejpam-6091	113	20	equation	equation	NOUN
ejpam-6091	113	21	,	,	PUNCT
ejpam-6091	113	22	we	we	PRON
ejpam-6091	113	23	have	have	VERB
ejpam-6091	113	24	:	:	PUNCT
ejpam-6091	114	1	∫	∫	PROPN
ejpam-6091	114	2	ẏdt	ẏdt	PART
ejpam-6091	115	1	=	=	SYM
ejpam-6091	115	2	∫	∫	PROPN
ejpam-6091	115	3	α1	α1	PROPN
ejpam-6091	115	4	sin(α2t+	sin(α2t+	PROPN
ejpam-6091	115	5	β2)dt	β2)dt	PROPN
ejpam-6091	115	6	,	,	PUNCT
ejpam-6091	115	7	(	(	PUNCT
ejpam-6091	115	8	40	40	NUM
ejpam-6091	115	9	)	)	PUNCT
ejpam-6091	115	10	which	which	PRON
ejpam-6091	115	11	leads	lead	VERB
ejpam-6091	115	12	to	to	ADP
ejpam-6091	115	13	y(t	y(t	NUM
ejpam-6091	115	14	)	)	PUNCT
ejpam-6091	116	1	=	=	SYM
ejpam-6091	116	2	α4	α4	NOUN
ejpam-6091	116	3	cosφ+	cosφ+	X
ejpam-6091	116	4	β4	β4	PROPN
ejpam-6091	116	5	,	,	PUNCT
ejpam-6091	116	6	(	(	PUNCT
ejpam-6091	116	7	41	41	NUM
ejpam-6091	116	8	)	)	PUNCT
ejpam-6091	116	9	where	where	SCONJ
ejpam-6091	116	10	α4	α4	NOUN
ejpam-6091	116	11	=	=	SYM
ejpam-6091	116	12	−α1	−α1	VERB
ejpam-6091	116	13	α2	α2	ADV
ejpam-6091	116	14	.	.	PUNCT
ejpam-6091	117	1	here	here	ADV
ejpam-6091	117	2	β1	β1	PROPN
ejpam-6091	117	3	,	,	PUNCT
ejpam-6091	117	4	β2	β2	NOUN
ejpam-6091	117	5	,	,	PUNCT
ejpam-6091	117	6	β3	β3	VERB
ejpam-6091	117	7	and	and	CCONJ
ejpam-6091	117	8	β4	β4	PROPN
ejpam-6091	117	9	are	be	AUX
ejpam-6091	117	10	constants	constant	NOUN
ejpam-6091	117	11	of	of	ADP
ejpam-6091	117	12	integration	integration	NOUN
ejpam-6091	117	13	related	relate	VERB
ejpam-6091	117	14	to	to	ADP
ejpam-6091	117	15	the	the	DET
ejpam-6091	117	16	initial	initial	ADJ
ejpam-6091	117	17	values	value	NOUN
ejpam-6091	117	18	of	of	ADP
ejpam-6091	117	19	θ	θ	PROPN
ejpam-6091	117	20	,	,	PUNCT
ejpam-6091	117	21	φ	φ	PROPN
ejpam-6091	117	22	,	,	PUNCT
ejpam-6091	117	23	x	x	PRON
ejpam-6091	117	24	,	,	PUNCT
ejpam-6091	117	25	y	y	PROPN
ejpam-6091	117	26	respectively	respectively	ADV
ejpam-6091	117	27	while	while	SCONJ
ejpam-6091	117	28	α1	α1	PROPN
ejpam-6091	117	29	,	,	PUNCT
ejpam-6091	117	30	α2	α2	ADJ
ejpam-6091	117	31	,	,	PUNCT
ejpam-6091	117	32	α3	α3	NOUN
ejpam-6091	117	33	and	and	CCONJ
ejpam-6091	117	34	α4	α4	NOUN
ejpam-6091	117	35	are	be	AUX
ejpam-6091	117	36	the	the	DET
ejpam-6091	117	37	initial	initial	ADJ
ejpam-6091	117	38	values	value	NOUN
ejpam-6091	117	39	of	of	ADP
ejpam-6091	117	40	velocities	velocity	NOUN
ejpam-6091	117	41	.	.	PUNCT
ejpam-6091	118	1	the	the	DET
ejpam-6091	118	2	essential	essential	ADJ
ejpam-6091	118	3	point	point	NOUN
ejpam-6091	118	4	of	of	ADP
ejpam-6091	118	5	our	our	PRON
ejpam-6091	118	6	procedure	procedure	NOUN
ejpam-6091	118	7	for	for	ADP
ejpam-6091	118	8	obtaining	obtain	VERB
ejpam-6091	118	9	the	the	DET
ejpam-6091	118	10	hamiltonian	hamiltonian	ADJ
ejpam-6091	118	11	formalism	formalism	NOUN
ejpam-6091	118	12	for	for	ADP
ejpam-6091	118	13	nonholonomic	nonholonomic	ADJ
ejpam-6091	118	14	systems	system	NOUN
ejpam-6091	118	15	is	be	AUX
ejpam-6091	118	16	to	to	PART
ejpam-6091	118	17	recognize	recognize	VERB
ejpam-6091	118	18	that	that	SCONJ
ejpam-6091	118	19	the	the	DET
ejpam-6091	118	20	above	above	ADJ
ejpam-6091	118	21	equations	equation	NOUN
ejpam-6091	118	22	(	(	PUNCT
ejpam-6091	118	23	34	34	NUM
ejpam-6091	118	24	)	)	PUNCT
ejpam-6091	118	25	,	,	PUNCT
ejpam-6091	118	26	(	(	PUNCT
ejpam-6091	118	27	35	35	NUM
ejpam-6091	118	28	)	)	PUNCT
ejpam-6091	118	29	,	,	PUNCT
ejpam-6091	118	30	(	(	PUNCT
ejpam-6091	118	31	39	39	NUM
ejpam-6091	118	32	)	)	PUNCT
ejpam-6091	118	33	,	,	PUNCT
ejpam-6091	118	34	(	(	PUNCT
ejpam-6091	118	35	41	41	NUM
ejpam-6091	118	36	)	)	PUNCT
ejpam-6091	118	37	can	can	AUX
ejpam-6091	118	38	be	be	AUX
ejpam-6091	118	39	obtained	obtain	VERB
ejpam-6091	118	40	in	in	ADP
ejpam-6091	118	41	the	the	DET
ejpam-6091	118	42	hamilton	hamilton	PROPN
ejpam-6091	118	43	-	-	PUNCT
ejpam-6091	118	44	jacobi	jacobi	PROPN
ejpam-6091	118	45	formalism	formalism	NOUN
ejpam-6091	118	46	.	.	PUNCT
ejpam-6091	119	1	we	we	PRON
ejpam-6091	119	2	may	may	AUX
ejpam-6091	119	3	rewrite	rewrite	VERB
ejpam-6091	119	4	these	these	DET
ejpam-6091	119	5	equations	equation	NOUN
ejpam-6091	119	6	respectively	respectively	ADV
ejpam-6091	119	7	as	as	ADP
ejpam-6091	119	8	:	:	PUNCT
ejpam-6091	119	9	β1	β1	PROPN
ejpam-6091	119	10	=	=	PUNCT
ejpam-6091	119	11	θ	θ	PROPN
ejpam-6091	119	12	−	−	PROPN
ejpam-6091	119	13	α1	α1	PROPN
ejpam-6091	119	14	t	t	NOUN
ejpam-6091	119	15	=	=	SYM
ejpam-6091	119	16	∂s1	∂s1	PROPN
ejpam-6091	119	17	∂α1	∂α1	PROPN
ejpam-6091	119	18	,	,	PUNCT
ejpam-6091	119	19	(	(	PUNCT
ejpam-6091	119	20	42	42	X
ejpam-6091	119	21	)	)	PUNCT
ejpam-6091	119	22	β2	β2	NOUN
ejpam-6091	119	23	=	=	SYM
ejpam-6091	119	24	φ−	φ−	PROPN
ejpam-6091	119	25	α2	α2	PROPN
ejpam-6091	119	26	t	t	NOUN
ejpam-6091	119	27	=	=	PUNCT
ejpam-6091	119	28	∂s2	∂s2	NOUN
ejpam-6091	119	29	∂α2	∂α2	NOUN
ejpam-6091	119	30	,	,	PUNCT
ejpam-6091	119	31	(	(	PUNCT
ejpam-6091	119	32	43	43	NUM
ejpam-6091	119	33	)	)	PUNCT
ejpam-6091	119	34	β3	β3	PROPN
ejpam-6091	119	35	=	=	SYM
ejpam-6091	120	1	x−	x−	PROPN
ejpam-6091	120	2	α3	α3	PROPN
ejpam-6091	120	3	sinφ	sinφ	NOUN
ejpam-6091	120	4	=	=	PROPN
ejpam-6091	120	5	∂s3	∂s3	PROPN
ejpam-6091	120	6	∂α3	∂α3	PROPN
ejpam-6091	120	7	,	,	PUNCT
ejpam-6091	120	8	(	(	PUNCT
ejpam-6091	120	9	44	44	NUM
ejpam-6091	120	10	)	)	PUNCT
ejpam-6091	120	11	β4	β4	PROPN
ejpam-6091	121	1	=	=	SYM
ejpam-6091	121	2	y	y	PROPN
ejpam-6091	121	3	−	−	PROPN
ejpam-6091	121	4	α4	α4	NOUN
ejpam-6091	121	5	cosφ	cosφ	NOUN
ejpam-6091	121	6	=	=	SYM
ejpam-6091	121	7	∂s4	∂s4	NOUN
ejpam-6091	121	8	∂α4	∂α4	NOUN
ejpam-6091	121	9	.	.	PUNCT
ejpam-6091	122	1	(	(	PUNCT
ejpam-6091	122	2	45	45	NUM
ejpam-6091	122	3	)	)	PUNCT
ejpam-6091	122	4	k.	k.	PROPN
ejpam-6091	122	5	i.	i.	PROPN
ejpam-6091	122	6	nawafleh	nawafleh	PROPN
ejpam-6091	122	7	/	/	SYM
ejpam-6091	122	8	eur	eur	PROPN
ejpam-6091	122	9	.	.	PUNCT
ejpam-6091	123	1	j.	j.	PROPN
ejpam-6091	123	2	pure	pure	PROPN
ejpam-6091	123	3	appl	appl	PROPN
ejpam-6091	123	4	.	.	PROPN
ejpam-6091	123	5	math	math	PROPN
ejpam-6091	123	6	,	,	PUNCT
ejpam-6091	123	7	18	18	NUM
ejpam-6091	123	8	(	(	PUNCT
ejpam-6091	123	9	3	3	NUM
ejpam-6091	123	10	)	)	PUNCT
ejpam-6091	123	11	(	(	PUNCT
ejpam-6091	123	12	2025	2025	NUM
ejpam-6091	123	13	)	)	PUNCT
ejpam-6091	123	14	,	,	PUNCT
ejpam-6091	123	15	6091	6091	NUM
ejpam-6091	123	16	7	7	NUM
ejpam-6091	123	17	of	of	ADP
ejpam-6091	123	18	15	15	NUM
ejpam-6091	123	19	solving	solving	NOUN
ejpam-6091	123	20	equations	equation	NOUN
ejpam-6091	123	21	(	(	PUNCT
ejpam-6091	123	22	42	42	NUM
ejpam-6091	123	23	-	-	SYM
ejpam-6091	123	24	45	45	NUM
ejpam-6091	123	25	)	)	PUNCT
ejpam-6091	123	26	simultaneously	simultaneously	ADV
ejpam-6091	123	27	,	,	PUNCT
ejpam-6091	123	28	we	we	PRON
ejpam-6091	123	29	obtain	obtain	VERB
ejpam-6091	123	30	:	:	PUNCT
ejpam-6091	123	31	s1(θ	s1(θ	NOUN
ejpam-6091	123	32	,	,	PUNCT
ejpam-6091	123	33	α1	α1	PROPN
ejpam-6091	123	34	)	)	PUNCT
ejpam-6091	123	35	=	=	SYM
ejpam-6091	123	36	θα1	θα1	NOUN
ejpam-6091	123	37	−	−	NOUN
ejpam-6091	123	38	1	1	NUM
ejpam-6091	123	39	2	2	NUM
ejpam-6091	123	40	α2	α2	ADJ
ejpam-6091	123	41	1	1	NUM
ejpam-6091	123	42	t	t	NOUN
ejpam-6091	123	43	,	,	PUNCT
ejpam-6091	123	44	(	(	PUNCT
ejpam-6091	123	45	46	46	NUM
ejpam-6091	123	46	)	)	PUNCT
ejpam-6091	123	47	s2(φ	s2(φ	PROPN
ejpam-6091	123	48	,	,	PUNCT
ejpam-6091	123	49	α2	α2	ADJ
ejpam-6091	123	50	)	)	PUNCT
ejpam-6091	123	51	=	=	SYM
ejpam-6091	124	1	φα2	φα2	NOUN
ejpam-6091	125	1	−	−	NUM
ejpam-6091	125	2	1	1	NUM
ejpam-6091	125	3	2	2	NUM
ejpam-6091	125	4	α2	α2	NOUN
ejpam-6091	125	5	2	2	NUM
ejpam-6091	125	6	t	t	NOUN
ejpam-6091	125	7	,	,	PUNCT
ejpam-6091	125	8	(	(	PUNCT
ejpam-6091	125	9	47	47	NUM
ejpam-6091	125	10	)	)	PUNCT
ejpam-6091	125	11	s3(x	s3(x	PROPN
ejpam-6091	125	12	,	,	PUNCT
ejpam-6091	125	13	α3	α3	NOUN
ejpam-6091	125	14	)	)	PUNCT
ejpam-6091	125	15	=	=	PUNCT
ejpam-6091	126	1	xα3	xα3	X
ejpam-6091	127	1	−	−	NOUN
ejpam-6091	127	2	1	1	NUM
ejpam-6091	127	3	2	2	NUM
ejpam-6091	127	4	α2	α2	NOUN
ejpam-6091	127	5	3	3	NUM
ejpam-6091	127	6	sinφ	sinφ	NOUN
ejpam-6091	127	7	,	,	PUNCT
ejpam-6091	127	8	(	(	PUNCT
ejpam-6091	127	9	48	48	NUM
ejpam-6091	127	10	)	)	PUNCT
ejpam-6091	127	11	s4(y	s4(y	PROPN
ejpam-6091	127	12	,	,	PUNCT
ejpam-6091	127	13	α4	α4	NOUN
ejpam-6091	127	14	)	)	PUNCT
ejpam-6091	127	15	=	=	SYM
ejpam-6091	127	16	yα4	yα4	NOUN
ejpam-6091	127	17	−	−	NOUN
ejpam-6091	127	18	1	1	NUM
ejpam-6091	127	19	2	2	NUM
ejpam-6091	127	20	α2	α2	ADJ
ejpam-6091	127	21	4	4	NUM
ejpam-6091	127	22	cosφ	cosφ	NOUN
ejpam-6091	127	23	.	.	PUNCT
ejpam-6091	128	1	(	(	PUNCT
ejpam-6091	128	2	49	49	NUM
ejpam-6091	128	3	)	)	PUNCT
ejpam-6091	128	4	we	we	PRON
ejpam-6091	128	5	saw	see	VERB
ejpam-6091	128	6	that	that	SCONJ
ejpam-6091	128	7	it	it	PRON
ejpam-6091	128	8	is	be	AUX
ejpam-6091	128	9	possible	possible	ADJ
ejpam-6091	128	10	to	to	PART
ejpam-6091	128	11	separate	separate	VERB
ejpam-6091	128	12	the	the	DET
ejpam-6091	128	13	variables	variable	NOUN
ejpam-6091	128	14	in	in	ADP
ejpam-6091	128	15	the	the	DET
ejpam-6091	128	16	hamilton	hamilton	PROPN
ejpam-6091	128	17	-	-	PUNCT
ejpam-6091	128	18	jacobi	jacobi	PROPN
ejpam-6091	128	19	equations	equation	NOUN
ejpam-6091	128	20	.	.	PUNCT
ejpam-6091	129	1	with	with	ADP
ejpam-6091	129	2	these	these	DET
ejpam-6091	129	3	results	result	NOUN
ejpam-6091	129	4	,	,	PUNCT
ejpam-6091	129	5	the	the	DET
ejpam-6091	129	6	hamilton	hamilton	PROPN
ejpam-6091	129	7	-	-	PUNCT
ejpam-6091	129	8	jacobi	jacobi	PROPN
ejpam-6091	129	9	function	function	NOUN
ejpam-6091	129	10	s	s	PART
ejpam-6091	129	11	becomes	become	VERB
ejpam-6091	129	12	s	s	PART
ejpam-6091	129	13	=	=	X
ejpam-6091	129	14	θα1	θα1	NOUN
ejpam-6091	129	15	+	+	CCONJ
ejpam-6091	129	16	φα2	φα2	PROPN
ejpam-6091	130	1	+	+	CCONJ
ejpam-6091	130	2	xα3	xα3	PROPN
ejpam-6091	131	1	+	+	CCONJ
ejpam-6091	131	2	yα4	yα4	NOUN
ejpam-6091	131	3	−	−	NOUN
ejpam-6091	131	4	1	1	NUM
ejpam-6091	131	5	2	2	NUM
ejpam-6091	131	6	t(α2	t(α2	NOUN
ejpam-6091	131	7	1	1	NUM
ejpam-6091	132	1	+	+	CCONJ
ejpam-6091	132	2	α2	α2	ADJ
ejpam-6091	132	3	2)−	2)−	NUM
ejpam-6091	132	4	1	1	NUM
ejpam-6091	132	5	2	2	NUM
ejpam-6091	132	6	α2	α2	NOUN
ejpam-6091	132	7	3	3	NUM
ejpam-6091	132	8	sinφ−	sinφ−	NOUN
ejpam-6091	132	9	1	1	NUM
ejpam-6091	132	10	2	2	NUM
ejpam-6091	132	11	α2	α2	ADJ
ejpam-6091	132	12	4	4	NUM
ejpam-6091	132	13	cosφ	cosφ	NOUN
ejpam-6091	132	14	.	.	PUNCT
ejpam-6091	133	1	(	(	PUNCT
ejpam-6091	133	2	50	50	NUM
ejpam-6091	133	3	)	)	PUNCT
ejpam-6091	133	4	we	we	PRON
ejpam-6091	133	5	interpret	interpret	VERB
ejpam-6091	133	6	s(θ	s(θ	PROPN
ejpam-6091	133	7	,	,	PUNCT
ejpam-6091	133	8	φ	φ	NUM
ejpam-6091	133	9	,	,	PUNCT
ejpam-6091	133	10	x	x	PROPN
ejpam-6091	133	11	,	,	PUNCT
ejpam-6091	133	12	y	y	PROPN
ejpam-6091	133	13	,	,	PUNCT
ejpam-6091	133	14	α1	α1	PROPN
ejpam-6091	133	15	,	,	PUNCT
ejpam-6091	133	16	α2	α2	ADJ
ejpam-6091	133	17	,	,	PUNCT
ejpam-6091	133	18	α3	α3	PROPN
ejpam-6091	133	19	,	,	PUNCT
ejpam-6091	133	20	α4	α4	PROPN
ejpam-6091	133	21	,	,	PUNCT
ejpam-6091	133	22	t	t	PROPN
ejpam-6091	133	23	)	)	PUNCT
ejpam-6091	133	24	as	as	ADP
ejpam-6091	133	25	the	the	DET
ejpam-6091	133	26	solution	solution	NOUN
ejpam-6091	133	27	of	of	ADP
ejpam-6091	133	28	hamilton	hamilton	PROPN
ejpam-6091	133	29	-	-	PUNCT
ejpam-6091	133	30	jacobi	jacobi	PROPN
ejpam-6091	133	31	equation	equation	NOUN
ejpam-6091	133	32	.	.	PUNCT
ejpam-6091	134	1	the	the	DET
ejpam-6091	134	2	generalized	generalized	ADJ
ejpam-6091	134	3	momenta	momenta	NOUN
ejpam-6091	134	4	are	be	AUX
ejpam-6091	134	5	derived	derive	VERB
ejpam-6091	134	6	as	as	ADP
ejpam-6091	134	7	pθ	pθ	ADV
ejpam-6091	134	8	=	=	SYM
ejpam-6091	134	9	∂s	∂s	PROPN
ejpam-6091	134	10	∂θ	∂θ	PROPN
ejpam-6091	134	11	=	=	SYM
ejpam-6091	134	12	α1	α1	PROPN
ejpam-6091	134	13	,	,	PUNCT
ejpam-6091	134	14	(	(	PUNCT
ejpam-6091	134	15	51	51	NUM
ejpam-6091	134	16	)	)	PUNCT
ejpam-6091	134	17	pφ	pφ	ADP
ejpam-6091	134	18	=	=	PUNCT
ejpam-6091	134	19	∂s	∂s	PROPN
ejpam-6091	134	20	∂φ	∂φ	PROPN
ejpam-6091	135	1	=	=	PUNCT
ejpam-6091	136	1	α2	α2	ADJ
ejpam-6091	136	2	−	−	NOUN
ejpam-6091	136	3	1	1	NUM
ejpam-6091	136	4	2	2	NUM
ejpam-6091	136	5	α2	α2	NOUN
ejpam-6091	136	6	3	3	NUM
ejpam-6091	136	7	cosφ+	cosφ+	SYM
ejpam-6091	136	8	1	1	NUM
ejpam-6091	136	9	2	2	NUM
ejpam-6091	136	10	α2	α2	ADJ
ejpam-6091	136	11	4	4	NUM
ejpam-6091	136	12	sinφ	sinφ	NOUN
ejpam-6091	136	13	,	,	PUNCT
ejpam-6091	136	14	(	(	PUNCT
ejpam-6091	136	15	52	52	NUM
ejpam-6091	136	16	)	)	PUNCT
ejpam-6091	136	17	px	px	NOUN
ejpam-6091	136	18	=	=	PUNCT
ejpam-6091	136	19	∂s	∂s	PROPN
ejpam-6091	136	20	∂x	∂x	PROPN
ejpam-6091	136	21	=	=	SYM
ejpam-6091	136	22	α3	α3	PROPN
ejpam-6091	136	23	,	,	PUNCT
ejpam-6091	136	24	(	(	PUNCT
ejpam-6091	136	25	53	53	NUM
ejpam-6091	136	26	)	)	PUNCT
ejpam-6091	136	27	py	py	NOUN
ejpam-6091	137	1	=	=	PUNCT
ejpam-6091	137	2	∂s	∂s	PROPN
ejpam-6091	137	3	∂y	∂y	SYM
ejpam-6091	137	4	=	=	SYM
ejpam-6091	137	5	α4	α4	PROPN
ejpam-6091	137	6	.	.	PUNCT
ejpam-6091	138	1	(	(	PUNCT
ejpam-6091	138	2	54	54	NUM
ejpam-6091	138	3	)	)	PUNCT
ejpam-6091	138	4	from	from	ADP
ejpam-6091	138	5	the	the	DET
ejpam-6091	138	6	above	above	ADJ
ejpam-6091	138	7	equations	equation	NOUN
ejpam-6091	138	8	we	we	PRON
ejpam-6091	138	9	can	can	AUX
ejpam-6091	138	10	obtain	obtain	VERB
ejpam-6091	138	11	α1	α1	NOUN
ejpam-6091	138	12	,	,	PUNCT
ejpam-6091	138	13	α2	α2	ADJ
ejpam-6091	138	14	,	,	PUNCT
ejpam-6091	138	15	α3	α3	NOUN
ejpam-6091	138	16	,	,	PUNCT
ejpam-6091	138	17	α4	α4	NOUN
ejpam-6091	138	18	as	as	ADP
ejpam-6091	138	19	functions	function	NOUN
ejpam-6091	138	20	of	of	ADP
ejpam-6091	138	21	pi	pi	NOUN
ejpam-6091	138	22	and	and	CCONJ
ejpam-6091	138	23	qi	qi	PROPN
ejpam-6091	138	24	:	:	PUNCT
ejpam-6091	138	25	α1	α1	PROPN
ejpam-6091	138	26	=	=	SYM
ejpam-6091	138	27	pθ	pθ	PROPN
ejpam-6091	138	28	,	,	PUNCT
ejpam-6091	138	29	(	(	PUNCT
ejpam-6091	138	30	55	55	NUM
ejpam-6091	138	31	)	)	PUNCT
ejpam-6091	138	32	α2	α2	NOUN
ejpam-6091	138	33	=	=	SYM
ejpam-6091	139	1	pφ	pφ	ADP
ejpam-6091	139	2	+	+	NOUN
ejpam-6091	139	3	1	1	NUM
ejpam-6091	139	4	2	2	NUM
ejpam-6091	139	5	α2	α2	NOUN
ejpam-6091	139	6	3	3	NUM
ejpam-6091	139	7	cosφ−	cosφ−	NOUN
ejpam-6091	139	8	1	1	NUM
ejpam-6091	139	9	2	2	NUM
ejpam-6091	139	10	α2	α2	NOUN
ejpam-6091	139	11	4	4	NUM
ejpam-6091	139	12	sinφ	sinφ	NOUN
ejpam-6091	139	13	,	,	PUNCT
ejpam-6091	139	14	(	(	PUNCT
ejpam-6091	139	15	56	56	NUM
ejpam-6091	139	16	)	)	PUNCT
ejpam-6091	139	17	α3	α3	NOUN
ejpam-6091	139	18	=	=	SYM
ejpam-6091	139	19	px	px	PROPN
ejpam-6091	139	20	,	,	PUNCT
ejpam-6091	139	21	(	(	PUNCT
ejpam-6091	139	22	57	57	NUM
ejpam-6091	139	23	)	)	PUNCT
ejpam-6091	139	24	α4	α4	NOUN
ejpam-6091	139	25	=	=	SYM
ejpam-6091	139	26	py	py	PROPN
ejpam-6091	139	27	.	.	PUNCT
ejpam-6091	140	1	(	(	PUNCT
ejpam-6091	140	2	58	58	NUM
ejpam-6091	140	3	)	)	PUNCT
ejpam-6091	140	4	following	follow	VERB
ejpam-6091	140	5	the	the	DET
ejpam-6091	140	6	equation	equation	NOUN
ejpam-6091	140	7	(	(	PUNCT
ejpam-6091	140	8	14	14	NUM
ejpam-6091	140	9	)	)	PUNCT
ejpam-6091	140	10	,	,	PUNCT
ejpam-6091	140	11	the	the	DET
ejpam-6091	140	12	hamiltonian	hamiltonian	NOUN
ejpam-6091	140	13	is	be	AUX
ejpam-6091	140	14	defined	define	VERB
ejpam-6091	140	15	as	as	ADP
ejpam-6091	140	16	:	:	PUNCT
ejpam-6091	140	17	h	h	NOUN
ejpam-6091	140	18	=	=	PUNCT
ejpam-6091	140	19	−∂s	−∂s	NUM
ejpam-6091	140	20	∂t	∂t	PROPN
ejpam-6091	140	21	=	=	SYM
ejpam-6091	140	22	1	1	NUM
ejpam-6091	140	23	2	2	NUM
ejpam-6091	140	24	(	(	PUNCT
ejpam-6091	140	25	α2	α2	NOUN
ejpam-6091	140	26	1	1	NUM
ejpam-6091	140	27	+	+	CCONJ
ejpam-6091	140	28	α2	α2	ADJ
ejpam-6091	140	29	2	2	NUM
ejpam-6091	140	30	)	)	PUNCT
ejpam-6091	140	31	.	.	PUNCT
ejpam-6091	141	1	(	(	PUNCT
ejpam-6091	141	2	59	59	NUM
ejpam-6091	141	3	)	)	PUNCT
ejpam-6091	141	4	substituting	substitute	VERB
ejpam-6091	141	5	equation	equation	NOUN
ejpam-6091	141	6	(	(	PUNCT
ejpam-6091	141	7	55	55	NUM
ejpam-6091	141	8	)	)	PUNCT
ejpam-6091	141	9	and	and	CCONJ
ejpam-6091	141	10	(	(	PUNCT
ejpam-6091	141	11	56	56	NUM
ejpam-6091	141	12	)	)	PUNCT
ejpam-6091	141	13	into	into	ADP
ejpam-6091	141	14	equation	equation	NOUN
ejpam-6091	141	15	(	(	PUNCT
ejpam-6091	141	16	59	59	NUM
ejpam-6091	141	17	)	)	PUNCT
ejpam-6091	141	18	,	,	PUNCT
ejpam-6091	141	19	this	this	PRON
ejpam-6091	141	20	leads	lead	VERB
ejpam-6091	141	21	the	the	DET
ejpam-6091	141	22	following	follow	VERB
ejpam-6091	141	23	expression	expression	NOUN
ejpam-6091	141	24	for	for	ADP
ejpam-6091	141	25	the	the	DET
ejpam-6091	141	26	hamiltonian	hamiltonian	NOUN
ejpam-6091	141	27	:	:	PUNCT
ejpam-6091	142	1	h	h	NOUN
ejpam-6091	142	2	=	=	NOUN
ejpam-6091	142	3	1	1	NUM
ejpam-6091	142	4	2	2	NUM
ejpam-6091	142	5	[	[	PUNCT
ejpam-6091	142	6	p	p	NOUN
ejpam-6091	142	7	2	2	NUM
ejpam-6091	142	8	θ	θ	NOUN
ejpam-6091	142	9	+	+	CCONJ
ejpam-6091	142	10	(	(	PUNCT
ejpam-6091	142	11	pφ	pφ	ADP
ejpam-6091	142	12	+	+	NOUN
ejpam-6091	142	13	1	1	NUM
ejpam-6091	142	14	2	2	NUM
ejpam-6091	142	15	p	p	NOUN
ejpam-6091	142	16	2	2	NUM
ejpam-6091	142	17	x	x	SYM
ejpam-6091	142	18	cosφ−	cosφ−	NOUN
ejpam-6091	142	19	1	1	NUM
ejpam-6091	142	20	2	2	NUM
ejpam-6091	142	21	p2y	p2y	NOUN
ejpam-6091	142	22	sinφ	sinφ	NOUN
ejpam-6091	142	23	)	)	PUNCT
ejpam-6091	142	24	2	2	NUM
ejpam-6091	142	25	]	]	PUNCT
ejpam-6091	142	26	.	.	PUNCT
ejpam-6091	143	1	(	(	PUNCT
ejpam-6091	143	2	60	60	NUM
ejpam-6091	143	3	)	)	PUNCT
ejpam-6091	143	4	k.	k.	PROPN
ejpam-6091	143	5	i.	i.	PROPN
ejpam-6091	143	6	nawafleh	nawafleh	PROPN
ejpam-6091	143	7	/	/	SYM
ejpam-6091	143	8	eur	eur	PROPN
ejpam-6091	143	9	.	.	PUNCT
ejpam-6091	144	1	j.	j.	PROPN
ejpam-6091	144	2	pure	pure	PROPN
ejpam-6091	144	3	appl	appl	PROPN
ejpam-6091	144	4	.	.	PROPN
ejpam-6091	144	5	math	math	PROPN
ejpam-6091	144	6	,	,	PUNCT
ejpam-6091	144	7	18	18	NUM
ejpam-6091	144	8	(	(	PUNCT
ejpam-6091	144	9	3	3	NUM
ejpam-6091	144	10	)	)	PUNCT
ejpam-6091	144	11	(	(	PUNCT
ejpam-6091	144	12	2025	2025	NUM
ejpam-6091	144	13	)	)	PUNCT
ejpam-6091	144	14	,	,	PUNCT
ejpam-6091	144	15	6091	6091	NUM
ejpam-6091	144	16	8	8	NUM
ejpam-6091	144	17	of	of	ADP
ejpam-6091	144	18	15	15	NUM
ejpam-6091	144	19	the	the	DET
ejpam-6091	144	20	hamilton	hamilton	PROPN
ejpam-6091	144	21	’s	’s	PART
ejpam-6091	144	22	equations	equation	NOUN
ejpam-6091	144	23	of	of	ADP
ejpam-6091	144	24	motion	motion	NOUN
ejpam-6091	144	25	can	can	AUX
ejpam-6091	144	26	be	be	AUX
ejpam-6091	144	27	found	find	VERB
ejpam-6091	144	28	from	from	ADP
ejpam-6091	144	29	equation	equation	NOUN
ejpam-6091	144	30	(	(	PUNCT
ejpam-6091	144	31	15	15	NUM
ejpam-6091	144	32	)	)	PUNCT
ejpam-6091	144	33	.	.	PUNCT
ejpam-6091	145	1	so	so	ADV
ejpam-6091	145	2	the	the	DET
ejpam-6091	145	3	generalized	generalized	ADJ
ejpam-6091	145	4	velocities	velocity	NOUN
ejpam-6091	145	5	corresponding	correspond	VERB
ejpam-6091	145	6	to	to	ADP
ejpam-6091	145	7	this	this	DET
ejpam-6091	145	8	hamiltonian	hamiltonian	NOUN
ejpam-6091	145	9	are	be	AUX
ejpam-6091	145	10	:	:	PUNCT
ejpam-6091	145	11	θ̇	θ̇	ADJ
ejpam-6091	145	12	=	=	SYM
ejpam-6091	145	13	∂h	∂h	VERB
ejpam-6091	145	14	∂pθ	∂pθ	NOUN
ejpam-6091	145	15	=	=	SYM
ejpam-6091	145	16	pθ	pθ	PROPN
ejpam-6091	145	17	,	,	PUNCT
ejpam-6091	145	18	(	(	PUNCT
ejpam-6091	145	19	61	61	NUM
ejpam-6091	145	20	)	)	PUNCT
ejpam-6091	145	21	φ̇	φ̇	NOUN
ejpam-6091	146	1	=	=	PUNCT
ejpam-6091	146	2	∂h	∂h	VERB
ejpam-6091	146	3	∂pφ	∂pφ	PROPN
ejpam-6091	146	4	=	=	PUNCT
ejpam-6091	146	5	(	(	PUNCT
ejpam-6091	146	6	pφ	pφ	ADP
ejpam-6091	146	7	+	+	NOUN
ejpam-6091	146	8	1	1	NUM
ejpam-6091	146	9	2	2	NUM
ejpam-6091	146	10	p	p	NOUN
ejpam-6091	146	11	2	2	NUM
ejpam-6091	146	12	x	x	SYM
ejpam-6091	146	13	cosφ−	cosφ−	NOUN
ejpam-6091	146	14	1	1	NUM
ejpam-6091	146	15	2	2	NUM
ejpam-6091	146	16	p2y	p2y	NOUN
ejpam-6091	146	17	sinφ	sinφ	NOUN
ejpam-6091	146	18	)	)	PUNCT
ejpam-6091	146	19	,	,	PUNCT
ejpam-6091	146	20	(	(	PUNCT
ejpam-6091	146	21	62	62	NUM
ejpam-6091	146	22	)	)	PUNCT
ejpam-6091	146	23	ẋ	ẋ	PUNCT
ejpam-6091	147	1	=	=	SYM
ejpam-6091	147	2	∂h	∂h	PROPN
ejpam-6091	147	3	∂px	∂px	NOUN
ejpam-6091	147	4	=	=	PUNCT
ejpam-6091	147	5	(	(	PUNCT
ejpam-6091	147	6	pφ	pφ	ADP
ejpam-6091	147	7	+	+	NOUN
ejpam-6091	147	8	1	1	NUM
ejpam-6091	147	9	2	2	NUM
ejpam-6091	147	10	p	p	NOUN
ejpam-6091	147	11	2	2	NUM
ejpam-6091	147	12	x	x	SYM
ejpam-6091	147	13	cosφ−	cosφ−	NOUN
ejpam-6091	147	14	1	1	NUM
ejpam-6091	147	15	2	2	NUM
ejpam-6091	147	16	p2y	p2y	NOUN
ejpam-6091	147	17	sinφ	sinφ	NOUN
ejpam-6091	147	18	)	)	PUNCT
ejpam-6091	148	1	(	(	PUNCT
ejpam-6091	148	2	px	px	NOUN
ejpam-6091	148	3	cosφ	cosφ	NOUN
ejpam-6091	148	4	)	)	PUNCT
ejpam-6091	148	5	,	,	PUNCT
ejpam-6091	148	6	(	(	PUNCT
ejpam-6091	148	7	63	63	NUM
ejpam-6091	148	8	)	)	PUNCT
ejpam-6091	148	9	ẏ	ẏ	PROPN
ejpam-6091	148	10	=	=	SYM
ejpam-6091	149	1	∂h	∂h	PROPN
ejpam-6091	149	2	∂py	∂py	PROPN
ejpam-6091	149	3	=	=	PUNCT
ejpam-6091	149	4	(	(	PUNCT
ejpam-6091	149	5	pφ	pφ	ADP
ejpam-6091	149	6	+	+	NOUN
ejpam-6091	149	7	1	1	NUM
ejpam-6091	149	8	2	2	NUM
ejpam-6091	149	9	p	p	NOUN
ejpam-6091	149	10	2	2	NUM
ejpam-6091	149	11	x	x	SYM
ejpam-6091	149	12	cosφ−	cosφ−	NOUN
ejpam-6091	149	13	1	1	NUM
ejpam-6091	149	14	2	2	NUM
ejpam-6091	149	15	p2y	p2y	NOUN
ejpam-6091	149	16	sinφ	sinφ	NOUN
ejpam-6091	149	17	)	)	PUNCT
ejpam-6091	149	18	(	(	PUNCT
ejpam-6091	149	19	−py	−py	NOUN
ejpam-6091	149	20	sinφ	sinφ	NOUN
ejpam-6091	149	21	)	)	PUNCT
ejpam-6091	149	22	.	.	PUNCT
ejpam-6091	150	1	(	(	PUNCT
ejpam-6091	150	2	64	64	NUM
ejpam-6091	150	3	)	)	PUNCT
ejpam-6091	150	4	substituting	substitute	VERB
ejpam-6091	150	5	equations	equation	NOUN
ejpam-6091	150	6	(	(	PUNCT
ejpam-6091	150	7	52–54	52–54	NUM
ejpam-6091	150	8	)	)	PUNCT
ejpam-6091	150	9	into	into	ADP
ejpam-6091	150	10	equation	equation	NOUN
ejpam-6091	150	11	(	(	PUNCT
ejpam-6091	150	12	62	62	NUM
ejpam-6091	150	13	)	)	PUNCT
ejpam-6091	150	14	,	,	PUNCT
ejpam-6091	150	15	we	we	PRON
ejpam-6091	150	16	find	find	VERB
ejpam-6091	150	17	φ̇	φ̇	ADV
ejpam-6091	150	18	=	=	SYM
ejpam-6091	150	19	(	(	PUNCT
ejpam-6091	150	20	α2	α2	ADV
ejpam-6091	150	21	−	−	PROPN
ejpam-6091	150	22	1	1	NUM
ejpam-6091	150	23	2	2	NUM
ejpam-6091	150	24	α2	α2	NOUN
ejpam-6091	150	25	3	3	NUM
ejpam-6091	150	26	cosφ+	cosφ+	SYM
ejpam-6091	150	27	1	1	NUM
ejpam-6091	150	28	2	2	NUM
ejpam-6091	150	29	α2	α2	ADJ
ejpam-6091	150	30	4	4	NUM
ejpam-6091	150	31	sinφ+	sinφ+	NOUN
ejpam-6091	150	32	1	1	NUM
ejpam-6091	150	33	2	2	NUM
ejpam-6091	150	34	α2	α2	NOUN
ejpam-6091	150	35	3	3	NUM
ejpam-6091	150	36	cosφ−	cosφ−	NOUN
ejpam-6091	150	37	1	1	NUM
ejpam-6091	150	38	2	2	NUM
ejpam-6091	150	39	α2	α2	ADJ
ejpam-6091	150	40	4	4	NUM
ejpam-6091	150	41	sinφ	sinφ	NOUN
ejpam-6091	150	42	)	)	PUNCT
ejpam-6091	150	43	,	,	PUNCT
ejpam-6091	150	44	or	or	CCONJ
ejpam-6091	150	45	,	,	PUNCT
ejpam-6091	150	46	φ̇	φ̇	ADV
ejpam-6091	150	47	=	=	PUNCT
ejpam-6091	150	48	α2	α2	ADJ
ejpam-6091	150	49	.	.	PUNCT
ejpam-6091	151	1	(	(	PUNCT
ejpam-6091	151	2	65	65	X
ejpam-6091	151	3	)	)	PUNCT
ejpam-6091	151	4	substituting	substitute	VERB
ejpam-6091	151	5	equations	equation	NOUN
ejpam-6091	151	6	(	(	PUNCT
ejpam-6091	151	7	52–54	52–54	NUM
ejpam-6091	151	8	)	)	PUNCT
ejpam-6091	151	9	into	into	ADP
ejpam-6091	151	10	equation	equation	NOUN
ejpam-6091	151	11	(	(	PUNCT
ejpam-6091	151	12	63	63	NUM
ejpam-6091	151	13	)	)	PUNCT
ejpam-6091	151	14	,	,	PUNCT
ejpam-6091	151	15	and	and	CCONJ
ejpam-6091	151	16	using	use	VERB
ejpam-6091	151	17	α2	α2	PROPN
ejpam-6091	151	18	for	for	ADP
ejpam-6091	151	19	the	the	DET
ejpam-6091	151	20	bracket	bracket	ADJ
ejpam-6091	151	21	term	term	NOUN
ejpam-6091	151	22	(	(	PUNCT
ejpam-6091	151	23	from	from	ADP
ejpam-6091	151	24	eq	eq	ADP
ejpam-6091	151	25	.	.	PROPN
ejpam-6091	151	26	65	65	NUM
ejpam-6091	151	27	)	)	PUNCT
ejpam-6091	151	28	and	and	CCONJ
ejpam-6091	151	29	px	px	X
ejpam-6091	151	30	=	=	PROPN
ejpam-6091	151	31	α3	α3	PROPN
ejpam-6091	151	32	(	(	PUNCT
ejpam-6091	151	33	from	from	ADP
ejpam-6091	151	34	eq	eq	ADP
ejpam-6091	151	35	.	.	PROPN
ejpam-6091	151	36	57	57	NUM
ejpam-6091	151	37	,	,	PUNCT
ejpam-6091	151	38	assuming	assume	VERB
ejpam-6091	151	39	px	px	PROPN
ejpam-6091	151	40	=	=	PROPN
ejpam-6091	151	41	px	px	PROPN
ejpam-6091	151	42	):	):	PUNCT
ejpam-6091	151	43	ẋ	ẋ	PROPN
ejpam-6091	151	44	=	=	SYM
ejpam-6091	151	45	α2α3	α2α3	PRON
ejpam-6091	151	46	cosφ	cosφ	NOUN
ejpam-6091	151	47	.	.	PUNCT
ejpam-6091	152	1	using	use	VERB
ejpam-6091	152	2	the	the	DET
ejpam-6091	152	3	definition	definition	NOUN
ejpam-6091	152	4	α3	α3	NOUN
ejpam-6091	152	5	=	=	PROPN
ejpam-6091	152	6	α1	α1	PROPN
ejpam-6091	152	7	/	/	SYM
ejpam-6091	152	8	α2	α2	PROPN
ejpam-6091	152	9	(	(	PUNCT
ejpam-6091	152	10	from	from	ADP
ejpam-6091	152	11	the	the	DET
ejpam-6091	152	12	context	context	NOUN
ejpam-6091	152	13	of	of	ADP
ejpam-6091	152	14	eq	eq	PROPN
ejpam-6091	152	15	.	.	PROPN
ejpam-6091	152	16	39	39	NUM
ejpam-6091	152	17	)	)	PUNCT
ejpam-6091	152	18	,	,	PUNCT
ejpam-6091	152	19	this	this	DET
ejpam-6091	152	20	simplifies	simplifie	NOUN
ejpam-6091	152	21	to	to	PART
ejpam-6091	152	22	:	:	PUNCT
ejpam-6091	152	23	ẋ	ẋ	PROPN
ejpam-6091	153	1	=	=	SYM
ejpam-6091	154	1	α1	α1	PROPN
ejpam-6091	154	2	cosφ	cosφ	NOUN
ejpam-6091	154	3	.	.	PUNCT
ejpam-6091	155	1	(	(	PUNCT
ejpam-6091	155	2	66	66	NUM
ejpam-6091	155	3	)	)	PUNCT
ejpam-6091	155	4	according	accord	VERB
ejpam-6091	155	5	to	to	ADP
ejpam-6091	155	6	equation	equation	NOUN
ejpam-6091	155	7	(	(	PUNCT
ejpam-6091	155	8	36	36	NUM
ejpam-6091	155	9	)	)	PUNCT
ejpam-6091	155	10	,	,	PUNCT
ejpam-6091	155	11	equation	equation	NOUN
ejpam-6091	155	12	(	(	PUNCT
ejpam-6091	155	13	66	66	NUM
ejpam-6091	155	14	)	)	PUNCT
ejpam-6091	155	15	can	can	AUX
ejpam-6091	155	16	be	be	AUX
ejpam-6091	155	17	finally	finally	ADV
ejpam-6091	155	18	written	write	VERB
ejpam-6091	155	19	as	as	SCONJ
ejpam-6091	155	20	follows	follow	VERB
ejpam-6091	155	21	:	:	PUNCT
ejpam-6091	156	1	ẋ	ẋ	PROPN
ejpam-6091	156	2	=	=	PUNCT
ejpam-6091	157	1	θ̇	θ̇	ADJ
ejpam-6091	157	2	cosφ	cosφ	NOUN
ejpam-6091	157	3	.	.	PUNCT
ejpam-6091	158	1	(	(	PUNCT
ejpam-6091	158	2	67	67	NUM
ejpam-6091	158	3	)	)	PUNCT
ejpam-6091	158	4	substituting	substitute	VERB
ejpam-6091	158	5	equations	equation	NOUN
ejpam-6091	158	6	(	(	PUNCT
ejpam-6091	158	7	52–54	52–54	NUM
ejpam-6091	158	8	)	)	PUNCT
ejpam-6091	158	9	into	into	ADP
ejpam-6091	158	10	equation	equation	NOUN
ejpam-6091	158	11	(	(	PUNCT
ejpam-6091	158	12	64	64	NUM
ejpam-6091	158	13	)	)	PUNCT
ejpam-6091	158	14	,	,	PUNCT
ejpam-6091	158	15	we	we	PRON
ejpam-6091	158	16	get	get	VERB
ejpam-6091	158	17	:	:	PUNCT
ejpam-6091	158	18	ẏ	ẏ	PROPN
ejpam-6091	158	19	=	=	SYM
ejpam-6091	158	20	α2(−α4	α2(−α4	NUM
ejpam-6091	158	21	sinφ	sinφ	NOUN
ejpam-6091	158	22	)	)	PUNCT
ejpam-6091	159	1	=	=	SYM
ejpam-6091	159	2	−α2α4	−α2α4	PROPN
ejpam-6091	159	3	sinφ	sinφ	NOUN
ejpam-6091	159	4	,	,	PUNCT
ejpam-6091	159	5	or	or	CCONJ
ejpam-6091	159	6	,	,	PUNCT
ejpam-6091	159	7	using	use	VERB
ejpam-6091	159	8	α4	α4	NOUN
ejpam-6091	159	9	=	=	SYM
ejpam-6091	159	10	−α1	−α1	PROPN
ejpam-6091	159	11	/	/	SYM
ejpam-6091	159	12	α2	α2	PROPN
ejpam-6091	159	13	(	(	PUNCT
ejpam-6091	159	14	from	from	ADP
ejpam-6091	159	15	the	the	DET
ejpam-6091	159	16	context	context	NOUN
ejpam-6091	159	17	of	of	ADP
ejpam-6091	159	18	eq	eq	PROPN
ejpam-6091	159	19	.	.	PROPN
ejpam-6091	159	20	41	41	NUM
ejpam-6091	159	21	):	):	PUNCT
ejpam-6091	159	22	ẏ	ẏ	PROPN
ejpam-6091	159	23	=	=	SYM
ejpam-6091	159	24	α1	α1	PROPN
ejpam-6091	159	25	sinφ	sinφ	NOUN
ejpam-6091	159	26	.	.	PUNCT
ejpam-6091	160	1	(	(	PUNCT
ejpam-6091	160	2	68	68	NUM
ejpam-6091	160	3	)	)	PUNCT
ejpam-6091	160	4	according	accord	VERB
ejpam-6091	160	5	to	to	ADP
ejpam-6091	160	6	equation	equation	NOUN
ejpam-6091	160	7	(	(	PUNCT
ejpam-6091	160	8	36	36	NUM
ejpam-6091	160	9	)	)	PUNCT
ejpam-6091	160	10	,	,	PUNCT
ejpam-6091	160	11	equation	equation	NOUN
ejpam-6091	160	12	(	(	PUNCT
ejpam-6091	160	13	68	68	NUM
ejpam-6091	160	14	)	)	PUNCT
ejpam-6091	160	15	can	can	AUX
ejpam-6091	160	16	be	be	AUX
ejpam-6091	160	17	finally	finally	ADV
ejpam-6091	160	18	written	write	VERB
ejpam-6091	160	19	as	as	SCONJ
ejpam-6091	160	20	follows	follow	VERB
ejpam-6091	160	21	:	:	PUNCT
ejpam-6091	161	1	ẏ	ẏ	PROPN
ejpam-6091	161	2	=	=	PUNCT
ejpam-6091	162	1	θ̇	θ̇	DET
ejpam-6091	162	2	sinφ	sinφ	NOUN
ejpam-6091	162	3	.	.	PUNCT
ejpam-6091	163	1	(	(	PUNCT
ejpam-6091	163	2	69	69	NUM
ejpam-6091	163	3	)	)	PUNCT
ejpam-6091	163	4	using	use	VERB
ejpam-6091	163	5	equation	equation	NOUN
ejpam-6091	163	6	(	(	PUNCT
ejpam-6091	163	7	15	15	NUM
ejpam-6091	163	8	)	)	PUNCT
ejpam-6091	163	9	,	,	PUNCT
ejpam-6091	163	10	this	this	DET
ejpam-6091	163	11	yields	yield	NOUN
ejpam-6091	163	12	ṗθ	ṗθ	PROPN
ejpam-6091	163	13	=	=	SYM
ejpam-6091	163	14	−∂h	−∂h	PROPN
ejpam-6091	163	15	∂θ	∂θ	PROPN
ejpam-6091	164	1	+	+	CCONJ
ejpam-6091	164	2	λ1	λ1	ADJ
ejpam-6091	164	3	∂f1	∂f1	NOUN
ejpam-6091	164	4	∂θ̇	∂θ̇	VERB
ejpam-6091	164	5	+	+	CCONJ
ejpam-6091	164	6	λ2	λ2	NOUN
ejpam-6091	164	7	∂f2	∂f2	VERB
ejpam-6091	164	8	∂θ̇	∂θ̇	VERB
ejpam-6091	164	9	,	,	PUNCT
ejpam-6091	164	10	(	(	PUNCT
ejpam-6091	164	11	70	70	NUM
ejpam-6091	164	12	)	)	PUNCT
ejpam-6091	164	13	k.	k.	PROPN
ejpam-6091	164	14	i.	i.	PROPN
ejpam-6091	164	15	nawafleh	nawafleh	PROPN
ejpam-6091	164	16	/	/	SYM
ejpam-6091	164	17	eur	eur	PROPN
ejpam-6091	164	18	.	.	PUNCT
ejpam-6091	165	1	j.	j.	PROPN
ejpam-6091	165	2	pure	pure	PROPN
ejpam-6091	165	3	appl	appl	PROPN
ejpam-6091	165	4	.	.	PROPN
ejpam-6091	165	5	math	math	PROPN
ejpam-6091	165	6	,	,	PUNCT
ejpam-6091	165	7	18	18	NUM
ejpam-6091	165	8	(	(	PUNCT
ejpam-6091	165	9	3	3	NUM
ejpam-6091	165	10	)	)	PUNCT
ejpam-6091	165	11	(	(	PUNCT
ejpam-6091	165	12	2025	2025	NUM
ejpam-6091	165	13	)	)	PUNCT
ejpam-6091	165	14	,	,	PUNCT
ejpam-6091	165	15	6091	6091	NUM
ejpam-6091	165	16	9	9	NUM
ejpam-6091	165	17	of	of	ADP
ejpam-6091	165	18	15	15	NUM
ejpam-6091	165	19	ṗφ	ṗφ	PROPN
ejpam-6091	165	20	=	=	PUNCT
ejpam-6091	165	21	−∂h	−∂h	PROPN
ejpam-6091	165	22	∂φ	∂φ	PROPN
ejpam-6091	166	1	+	+	CCONJ
ejpam-6091	166	2	λ1	λ1	ADJ
ejpam-6091	166	3	∂f1	∂f1	NOUN
ejpam-6091	166	4	∂φ̇	∂φ̇	ADP
ejpam-6091	166	5	+	+	NUM
ejpam-6091	166	6	λ2	λ2	NOUN
ejpam-6091	166	7	∂f2	∂f2	VERB
ejpam-6091	166	8	∂φ̇	∂φ̇	NOUN
ejpam-6091	166	9	,	,	PUNCT
ejpam-6091	166	10	(	(	PUNCT
ejpam-6091	166	11	71	71	NUM
ejpam-6091	166	12	)	)	PUNCT
ejpam-6091	166	13	ṗx	ṗx	NOUN
ejpam-6091	166	14	=	=	SYM
ejpam-6091	166	15	−∂h	−∂h	PROPN
ejpam-6091	166	16	∂x	∂x	PROPN
ejpam-6091	167	1	+	+	CCONJ
ejpam-6091	168	1	λ1	λ1	ADJ
ejpam-6091	168	2	∂f1	∂f1	PROPN
ejpam-6091	168	3	∂ẋ	∂ẋ	PROPN
ejpam-6091	168	4	,	,	PUNCT
ejpam-6091	168	5	(	(	PUNCT
ejpam-6091	168	6	72	72	NUM
ejpam-6091	168	7	)	)	PUNCT
ejpam-6091	168	8	ṗy	ṗy	NOUN
ejpam-6091	168	9	=	=	SYM
ejpam-6091	169	1	−∂h	−∂h	PROPN
ejpam-6091	169	2	∂y	∂y	SYM
ejpam-6091	170	1	+	+	NUM
ejpam-6091	170	2	λ2	λ2	NOUN
ejpam-6091	170	3	∂f2	∂f2	VERB
ejpam-6091	170	4	∂ẏ	∂ẏ	ADJ
ejpam-6091	170	5	.	.	PUNCT
ejpam-6091	171	1	(	(	PUNCT
ejpam-6091	171	2	73	73	NUM
ejpam-6091	171	3	)	)	PUNCT
ejpam-6091	171	4	these	these	PRON
ejpam-6091	171	5	give	give	VERB
ejpam-6091	171	6	ṗθ	ṗθ	NOUN
ejpam-6091	171	7	=	=	PUNCT
ejpam-6091	171	8	−λ1	−λ1	PROPN
ejpam-6091	171	9	cosφ−	cosφ−	NOUN
ejpam-6091	171	10	λ2	λ2	NOUN
ejpam-6091	171	11	sinφ	sinφ	NOUN
ejpam-6091	171	12	,	,	PUNCT
ejpam-6091	171	13	(	(	PUNCT
ejpam-6091	171	14	74	74	X
ejpam-6091	171	15	)	)	PUNCT
ejpam-6091	171	16	ṗφ	ṗφ	PROPN
ejpam-6091	172	1	=	=	PUNCT
ejpam-6091	172	2	0	0	PROPN
ejpam-6091	172	3	,	,	PUNCT
ejpam-6091	172	4	(	(	PUNCT
ejpam-6091	172	5	75	75	NUM
ejpam-6091	172	6	)	)	PUNCT
ejpam-6091	172	7	ṗx	ṗx	PROPN
ejpam-6091	172	8	=	=	SYM
ejpam-6091	172	9	λ1	λ1	PROPN
ejpam-6091	172	10	,	,	PUNCT
ejpam-6091	172	11	(	(	PUNCT
ejpam-6091	172	12	76	76	NUM
ejpam-6091	172	13	)	)	PUNCT
ejpam-6091	172	14	ṗy	ṗy	NOUN
ejpam-6091	172	15	=	=	SYM
ejpam-6091	172	16	λ2	λ2	NOUN
ejpam-6091	172	17	.	.	PUNCT
ejpam-6091	173	1	(	(	PUNCT
ejpam-6091	173	2	77	77	X
ejpam-6091	173	3	)	)	PUNCT
ejpam-6091	173	4	these	these	DET
ejpam-6091	173	5	equations	equation	NOUN
ejpam-6091	173	6	are	be	AUX
ejpam-6091	173	7	similar	similar	ADJ
ejpam-6091	173	8	to	to	ADP
ejpam-6091	173	9	equations	equation	NOUN
ejpam-6091	173	10	(	(	PUNCT
ejpam-6091	173	11	27	27	NUM
ejpam-6091	173	12	)	)	PUNCT
ejpam-6091	173	13	,	,	PUNCT
ejpam-6091	173	14	(	(	PUNCT
ejpam-6091	173	15	28	28	NUM
ejpam-6091	173	16	)	)	PUNCT
ejpam-6091	173	17	,	,	PUNCT
ejpam-6091	173	18	(	(	PUNCT
ejpam-6091	173	19	25	25	NUM
ejpam-6091	173	20	)	)	PUNCT
ejpam-6091	173	21	and	and	CCONJ
ejpam-6091	173	22	(	(	PUNCT
ejpam-6091	173	23	26	26	NUM
ejpam-6091	173	24	)	)	PUNCT
ejpam-6091	173	25	respectively	respectively	ADV
ejpam-6091	173	26	,	,	PUNCT
ejpam-6091	173	27	so	so	SCONJ
ejpam-6091	173	28	that	that	SCONJ
ejpam-6091	173	29	:	:	PUNCT
ejpam-6091	173	30	ṗθ	ṗθ	NOUN
ejpam-6091	173	31	=	=	SYM
ejpam-6091	173	32	θ̈	θ̈	CCONJ
ejpam-6091	173	33	,	,	PUNCT
ejpam-6091	173	34	(	(	PUNCT
ejpam-6091	173	35	78	78	X
ejpam-6091	173	36	)	)	PUNCT
ejpam-6091	173	37	ṗφ	ṗφ	PROPN
ejpam-6091	174	1	=	=	PUNCT
ejpam-6091	174	2	φ̈	φ̈	X
ejpam-6091	174	3	,	,	PUNCT
ejpam-6091	174	4	(	(	PUNCT
ejpam-6091	174	5	79	79	X
ejpam-6091	174	6	)	)	PUNCT
ejpam-6091	174	7	ṗx	ṗx	PROPN
ejpam-6091	174	8	=	=	SYM
ejpam-6091	174	9	ẍ	ẍ	PROPN
ejpam-6091	174	10	,	,	PUNCT
ejpam-6091	174	11	(	(	PUNCT
ejpam-6091	174	12	80	80	NUM
ejpam-6091	174	13	)	)	PUNCT
ejpam-6091	174	14	ṗy	ṗy	NOUN
ejpam-6091	174	15	=	=	SYM
ejpam-6091	174	16	ÿ	ÿ	PROPN
ejpam-6091	174	17	.	.	PUNCT
ejpam-6091	175	1	(	(	PUNCT
ejpam-6091	175	2	81	81	NUM
ejpam-6091	175	3	)	)	PUNCT
ejpam-6091	175	4	we	we	PRON
ejpam-6091	175	5	see	see	VERB
ejpam-6091	175	6	that	that	SCONJ
ejpam-6091	175	7	the	the	DET
ejpam-6091	175	8	equations	equation	NOUN
ejpam-6091	175	9	of	of	ADP
ejpam-6091	175	10	motion	motion	NOUN
ejpam-6091	175	11	that	that	PRON
ejpam-6091	175	12	obtained	obtain	VERB
ejpam-6091	175	13	by	by	ADP
ejpam-6091	175	14	the	the	DET
ejpam-6091	175	15	hamilton	hamilton	PROPN
ejpam-6091	175	16	-	-	PUNCT
ejpam-6091	175	17	jacobi	jacobi	PROPN
ejpam-6091	175	18	methods	method	NOUN
ejpam-6091	175	19	are	be	AUX
ejpam-6091	175	20	equivalent	equivalent	ADJ
ejpam-6091	175	21	to	to	ADP
ejpam-6091	175	22	those	those	PRON
ejpam-6091	175	23	which	which	PRON
ejpam-6091	175	24	obtained	obtain	VERB
ejpam-6091	175	25	by	by	ADP
ejpam-6091	175	26	the	the	DET
ejpam-6091	175	27	lagrange	lagrange	NOUN
ejpam-6091	175	28	-	-	PUNCT
ejpam-6091	175	29	d’alembert	d’alembert	NOUN
ejpam-6091	175	30	principle	principle	NOUN
ejpam-6091	175	31	.	.	PUNCT
ejpam-6091	176	1	example	example	NOUN
ejpam-6091	176	2	2	2	NUM
ejpam-6091	176	3	as	as	ADP
ejpam-6091	176	4	a	a	DET
ejpam-6091	176	5	second	second	ADJ
ejpam-6091	176	6	example	example	NOUN
ejpam-6091	176	7	for	for	ADP
ejpam-6091	176	8	nonholonomic	nonholonomic	ADJ
ejpam-6091	176	9	constraints	constraint	NOUN
ejpam-6091	176	10	consider	consider	VERB
ejpam-6091	176	11	the	the	DET
ejpam-6091	176	12	knife	knife	NOUN
ejpam-6091	176	13	edge	edge	NOUN
ejpam-6091	176	14	on	on	ADP
ejpam-6091	176	15	an	an	DET
ejpam-6091	176	16	inclined	inclined	ADJ
ejpam-6091	176	17	plane	plane	NOUN
ejpam-6091	176	18	.	.	PUNCT
ejpam-6091	177	1	the	the	DET
ejpam-6091	177	2	plane	plane	NOUN
ejpam-6091	177	3	corresponds	correspond	VERB
ejpam-6091	177	4	physically	physically	ADV
ejpam-6091	177	5	to	to	ADP
ejpam-6091	177	6	a	a	DET
ejpam-6091	177	7	blade	blade	NOUN
ejpam-6091	177	8	moving	move	VERB
ejpam-6091	177	9	in	in	ADP
ejpam-6091	177	10	the	the	DET
ejpam-6091	177	11	xy	xy	NOUN
ejpam-6091	177	12	-	-	PUNCT
ejpam-6091	177	13	plane	plane	NOUN
ejpam-6091	177	14	at	at	ADP
ejpam-6091	177	15	an	an	DET
ejpam-6091	177	16	angle	angle	NOUN
ejpam-6091	177	17	φ	φ	NOUN
ejpam-6091	177	18	to	to	ADP
ejpam-6091	177	19	the	the	DET
ejpam-6091	177	20	x	x	NOUN
ejpam-6091	177	21	-	-	NOUN
ejpam-6091	177	22	axis	axis	NOUN
ejpam-6091	177	23	.	.	PUNCT
ejpam-6091	178	1	the	the	DET
ejpam-6091	178	2	lagrangian	lagrangian	NOUN
ejpam-6091	178	3	of	of	ADP
ejpam-6091	178	4	the	the	DET
ejpam-6091	178	5	system	system	NOUN
ejpam-6091	178	6	is	be	AUX
ejpam-6091	178	7	:	:	PUNCT
ejpam-6091	178	8	l	l	NOUN
ejpam-6091	178	9	=	=	SYM
ejpam-6091	178	10	1	1	NUM
ejpam-6091	178	11	2	2	NUM
ejpam-6091	178	12	m(ẋ2	m(ẋ2	NOUN
ejpam-6091	178	13	+	+	CCONJ
ejpam-6091	178	14	ẏ2	ẏ2	NOUN
ejpam-6091	178	15	)	)	PUNCT
ejpam-6091	178	16	+	+	CCONJ
ejpam-6091	178	17	1	1	NUM
ejpam-6091	178	18	2	2	NUM
ejpam-6091	178	19	jφ̇2	jφ̇2	NOUN
ejpam-6091	178	20	,	,	PUNCT
ejpam-6091	178	21	(	(	PUNCT
ejpam-6091	178	22	82	82	NUM
ejpam-6091	178	23	)	)	PUNCT
ejpam-6091	178	24	where	where	SCONJ
ejpam-6091	178	25	j	j	PROPN
ejpam-6091	178	26	is	be	AUX
ejpam-6091	178	27	the	the	DET
ejpam-6091	178	28	moment	moment	NOUN
ejpam-6091	178	29	of	of	ADP
ejpam-6091	178	30	inertia	inertia	NOUN
ejpam-6091	178	31	of	of	ADP
ejpam-6091	178	32	the	the	DET
ejpam-6091	178	33	blade	blade	NOUN
ejpam-6091	178	34	about	about	ADP
ejpam-6091	178	35	a	a	DET
ejpam-6091	178	36	vertical	vertical	ADJ
ejpam-6091	178	37	axis	axis	NOUN
ejpam-6091	178	38	through	through	ADP
ejpam-6091	178	39	the	the	DET
ejpam-6091	178	40	point	point	NOUN
ejpam-6091	178	41	of	of	ADP
ejpam-6091	178	42	contact	contact	NOUN
ejpam-6091	178	43	.	.	PUNCT
ejpam-6091	179	1	we	we	PRON
ejpam-6091	179	2	assume	assume	VERB
ejpam-6091	179	3	that	that	SCONJ
ejpam-6091	179	4	the	the	DET
ejpam-6091	179	5	mass	mass	NOUN
ejpam-6091	179	6	and	and	CCONJ
ejpam-6091	179	7	the	the	DET
ejpam-6091	179	8	moments	moment	NOUN
ejpam-6091	179	9	of	of	ADP
ejpam-6091	179	10	inertia	inertia	PROPN
ejpam-6091	179	11	j	j	PROPN
ejpam-6091	179	12	are	be	AUX
ejpam-6091	179	13	equal	equal	ADJ
ejpam-6091	179	14	to	to	ADP
ejpam-6091	179	15	unity	unity	NOUN
ejpam-6091	179	16	.	.	PUNCT
ejpam-6091	180	1	thus	thus	ADV
ejpam-6091	180	2	the	the	DET
ejpam-6091	180	3	lagrangian	lagrangian	NOUN
ejpam-6091	180	4	of	of	ADP
ejpam-6091	180	5	the	the	DET
ejpam-6091	180	6	system	system	NOUN
ejpam-6091	180	7	is	be	AUX
ejpam-6091	180	8	given	give	VERB
ejpam-6091	180	9	by	by	ADP
ejpam-6091	180	10	:	:	PUNCT
ejpam-6091	180	11	l	l	NOUN
ejpam-6091	180	12	=	=	SYM
ejpam-6091	180	13	1	1	NUM
ejpam-6091	180	14	2	2	NUM
ejpam-6091	180	15	(	(	PUNCT
ejpam-6091	180	16	ẋ2	ẋ2	PROPN
ejpam-6091	180	17	+	+	PUNCT
ejpam-6091	180	18	ẏ2	ẏ2	PROPN
ejpam-6091	180	19	+	+	CCONJ
ejpam-6091	180	20	φ̇2	φ̇2	PROPN
ejpam-6091	180	21	)	)	PUNCT
ejpam-6091	180	22	.	.	PUNCT
ejpam-6091	181	1	(	(	PUNCT
ejpam-6091	181	2	83	83	NUM
ejpam-6091	181	3	)	)	PUNCT
ejpam-6091	181	4	the	the	DET
ejpam-6091	181	5	system	system	NOUN
ejpam-6091	181	6	has	have	VERB
ejpam-6091	181	7	the	the	DET
ejpam-6091	181	8	following	follow	VERB
ejpam-6091	181	9	nonholonomic	nonholonomic	ADJ
ejpam-6091	181	10	constraint	constraint	NOUN
ejpam-6091	181	11	:	:	PUNCT
ejpam-6091	181	12	f	f	X
ejpam-6091	181	13	=	=	SYM
ejpam-6091	181	14	ẋ	ẋ	PROPN
ejpam-6091	181	15	sinφ−	sinφ−	NOUN
ejpam-6091	181	16	ẏ	ẏ	PROPN
ejpam-6091	181	17	cosφ	cosφ	NOUN
ejpam-6091	181	18	=	=	SYM
ejpam-6091	181	19	0	0	NUM
ejpam-6091	181	20	,	,	PUNCT
ejpam-6091	181	21	(	(	PUNCT
ejpam-6091	181	22	84	84	NUM
ejpam-6091	181	23	)	)	PUNCT
ejpam-6091	181	24	this	this	DET
ejpam-6091	181	25	constraint	constraint	NOUN
ejpam-6091	181	26	can	can	AUX
ejpam-6091	181	27	be	be	AUX
ejpam-6091	181	28	rewritten	rewrite	VERB
ejpam-6091	181	29	as	as	ADP
ejpam-6091	181	30	ẏ	ẏ	PROPN
ejpam-6091	181	31	=	=	SYM
ejpam-6091	181	32	ẋ	ẋ	PROPN
ejpam-6091	181	33	tanφ	tanφ	PROPN
ejpam-6091	181	34	.	.	PUNCT
ejpam-6091	182	1	(	(	PUNCT
ejpam-6091	182	2	85	85	NUM
ejpam-6091	182	3	)	)	PUNCT
ejpam-6091	182	4	k.	k.	PROPN
ejpam-6091	182	5	i.	i.	PROPN
ejpam-6091	182	6	nawafleh	nawafleh	PROPN
ejpam-6091	182	7	/	/	SYM
ejpam-6091	182	8	eur	eur	PROPN
ejpam-6091	182	9	.	.	PUNCT
ejpam-6091	183	1	j.	j.	PROPN
ejpam-6091	183	2	pure	pure	PROPN
ejpam-6091	183	3	appl	appl	PROPN
ejpam-6091	183	4	.	.	PROPN
ejpam-6091	183	5	math	math	PROPN
ejpam-6091	183	6	,	,	PUNCT
ejpam-6091	183	7	18	18	NUM
ejpam-6091	183	8	(	(	PUNCT
ejpam-6091	183	9	3	3	NUM
ejpam-6091	183	10	)	)	PUNCT
ejpam-6091	183	11	(	(	PUNCT
ejpam-6091	183	12	2025	2025	NUM
ejpam-6091	183	13	)	)	PUNCT
ejpam-6091	183	14	,	,	PUNCT
ejpam-6091	183	15	6091	6091	NUM
ejpam-6091	183	16	10	10	NUM
ejpam-6091	183	17	of	of	ADP
ejpam-6091	183	18	15	15	NUM
ejpam-6091	183	19	following	follow	VERB
ejpam-6091	183	20	equation	equation	NOUN
ejpam-6091	183	21	(	(	PUNCT
ejpam-6091	183	22	2.19	2.19	NUM
ejpam-6091	183	23	)	)	PUNCT
ejpam-6091	183	24	(	(	PUNCT
ejpam-6091	183	25	note	note	VERB
ejpam-6091	183	26	:	:	PUNCT
ejpam-6091	183	27	this	this	PRON
ejpam-6091	183	28	refers	refer	VERB
ejpam-6091	183	29	to	to	ADP
ejpam-6091	183	30	an	an	DET
ejpam-6091	183	31	internal	internal	ADJ
ejpam-6091	183	32	numbering	numbering	NOUN
ejpam-6091	183	33	,	,	PUNCT
ejpam-6091	183	34	likely	likely	ADJ
ejpam-6091	183	35	eq	eq	NOUN
ejpam-6091	183	36	.	.	PROPN
ejpam-6091	183	37	15	15	NUM
ejpam-6091	183	38	in	in	ADP
ejpam-6091	183	39	this	this	DET
ejpam-6091	183	40	paper	paper	NOUN
ejpam-6091	183	41	,	,	PUNCT
ejpam-6091	183	42	or	or	CCONJ
ejpam-6091	183	43	a	a	DET
ejpam-6091	183	44	general	general	ADJ
ejpam-6091	183	45	formalism	formalism	NOUN
ejpam-6091	183	46	section	section	NOUN
ejpam-6091	183	47	)	)	PUNCT
ejpam-6091	183	48	,	,	PUNCT
ejpam-6091	183	49	the	the	DET
ejpam-6091	183	50	equations	equation	NOUN
ejpam-6091	183	51	of	of	ADP
ejpam-6091	183	52	motion	motion	NOUN
ejpam-6091	183	53	can	can	AUX
ejpam-6091	183	54	be	be	AUX
ejpam-6091	183	55	obtained	obtain	VERB
ejpam-6091	183	56	as	as	ADP
ejpam-6091	183	57	d	d	X
ejpam-6091	183	58	dt	dt	X
ejpam-6091	183	59	(	(	PUNCT
ejpam-6091	183	60	∂l	∂l	PROPN
ejpam-6091	183	61	∂ẋ	∂ẋ	ADJ
ejpam-6091	183	62	)	)	PUNCT
ejpam-6091	183	63	−	−	PROPN
ejpam-6091	184	1	∂l	∂l	NOUN
ejpam-6091	184	2	∂x	∂x	NOUN
ejpam-6091	184	3	=	=	SYM
ejpam-6091	184	4	λ	λ	PROPN
ejpam-6091	184	5	∂f	∂f	PROPN
ejpam-6091	184	6	∂ẋ	∂ẋ	ADJ
ejpam-6091	184	7	,	,	PUNCT
ejpam-6091	184	8	(	(	PUNCT
ejpam-6091	184	9	86	86	NUM
ejpam-6091	184	10	)	)	PUNCT
ejpam-6091	185	1	d	d	NOUN
ejpam-6091	185	2	dt	dt	X
ejpam-6091	186	1	(	(	PUNCT
ejpam-6091	186	2	∂l	∂l	X
ejpam-6091	186	3	∂ẏ	∂ẏ	X
ejpam-6091	186	4	)	)	PUNCT
ejpam-6091	187	1	−	−	PUNCT
ejpam-6091	188	1	∂l	∂l	NOUN
ejpam-6091	188	2	∂y	∂y	SYM
ejpam-6091	188	3	=	=	SYM
ejpam-6091	188	4	λ	λ	X
ejpam-6091	188	5	∂f	∂f	PROPN
ejpam-6091	188	6	∂ẏ	∂ẏ	ADJ
ejpam-6091	188	7	,	,	PUNCT
ejpam-6091	188	8	(	(	PUNCT
ejpam-6091	188	9	87	87	NUM
ejpam-6091	189	1	)	)	PUNCT
ejpam-6091	189	2	d	d	NOUN
ejpam-6091	189	3	dt	dt	X
ejpam-6091	189	4	(	(	PUNCT
ejpam-6091	189	5	∂l	∂l	INTJ
ejpam-6091	189	6	∂φ̇	∂φ̇	ADV
ejpam-6091	189	7	)	)	PUNCT
ejpam-6091	189	8	−	−	PROPN
ejpam-6091	190	1	∂l	∂l	NOUN
ejpam-6091	190	2	∂φ	∂φ	PUNCT
ejpam-6091	191	1	=	=	PUNCT
ejpam-6091	191	2	λ	λ	X
ejpam-6091	191	3	∂f	∂f	PROPN
ejpam-6091	191	4	∂φ̇	∂φ̇	ADV
ejpam-6091	191	5	.	.	PUNCT
ejpam-6091	192	1	(	(	PUNCT
ejpam-6091	192	2	88	88	NUM
ejpam-6091	192	3	)	)	PUNCT
ejpam-6091	192	4	these	these	PRON
ejpam-6091	192	5	give	give	VERB
ejpam-6091	192	6	:	:	PUNCT
ejpam-6091	192	7	ẍ	ẍ	X
ejpam-6091	193	1	=	=	SYM
ejpam-6091	194	1	λ	λ	NOUN
ejpam-6091	194	2	sinφ	sinφ	NOUN
ejpam-6091	194	3	,	,	PUNCT
ejpam-6091	194	4	(	(	PUNCT
ejpam-6091	194	5	89	89	NUM
ejpam-6091	194	6	)	)	PUNCT
ejpam-6091	194	7	ÿ	ÿ	NOUN
ejpam-6091	194	8	=	=	NOUN
ejpam-6091	194	9	−λ	−λ	VERB
ejpam-6091	194	10	cosφ	cosφ	NOUN
ejpam-6091	194	11	,	,	PUNCT
ejpam-6091	194	12	(	(	PUNCT
ejpam-6091	194	13	90	90	NUM
ejpam-6091	194	14	)	)	PUNCT
ejpam-6091	194	15	φ̈	φ̈	X
ejpam-6091	194	16	=	=	NOUN
ejpam-6091	194	17	0	0	X
ejpam-6091	194	18	.	.	PUNCT
ejpam-6091	194	19	(	(	PUNCT
ejpam-6091	194	20	91	91	NUM
ejpam-6091	194	21	)	)	PUNCT
ejpam-6091	194	22	from	from	ADP
ejpam-6091	194	23	equations	equation	NOUN
ejpam-6091	194	24	(	(	PUNCT
ejpam-6091	194	25	89	89	NUM
ejpam-6091	194	26	)	)	PUNCT
ejpam-6091	194	27	and	and	CCONJ
ejpam-6091	194	28	(	(	PUNCT
ejpam-6091	194	29	90	90	NUM
ejpam-6091	194	30	)	)	PUNCT
ejpam-6091	194	31	,	,	PUNCT
ejpam-6091	194	32	we	we	PRON
ejpam-6091	194	33	obtain	obtain	VERB
ejpam-6091	194	34	ÿ	ÿ	NOUN
ejpam-6091	194	35	=	=	SYM
ejpam-6091	194	36	−	−	PROPN
ejpam-6091	194	37	ẍ	ẍ	X
ejpam-6091	194	38	tanφ	tanφ	PROPN
ejpam-6091	194	39	,	,	PUNCT
ejpam-6091	194	40	(	(	PUNCT
ejpam-6091	194	41	92	92	NUM
ejpam-6091	194	42	)	)	PUNCT
ejpam-6091	194	43	differentiating	differentiate	VERB
ejpam-6091	194	44	constraint	constraint	NOUN
ejpam-6091	194	45	equation	equation	NOUN
ejpam-6091	194	46	(	(	PUNCT
ejpam-6091	194	47	85	85	NUM
ejpam-6091	194	48	)	)	PUNCT
ejpam-6091	194	49	with	with	ADP
ejpam-6091	194	50	respect	respect	NOUN
ejpam-6091	194	51	to	to	ADP
ejpam-6091	194	52	time	time	NOUN
ejpam-6091	194	53	to	to	PART
ejpam-6091	194	54	eliminate	eliminate	VERB
ejpam-6091	194	55	λ	λ	PROPN
ejpam-6091	194	56	,	,	PUNCT
ejpam-6091	194	57	we	we	PRON
ejpam-6091	194	58	find	find	VERB
ejpam-6091	194	59	ÿ	ÿ	NOUN
ejpam-6091	194	60	=	=	SYM
ejpam-6091	194	61	ẍ	ẍ	PROPN
ejpam-6091	194	62	tanφ+	tanφ+	X
ejpam-6091	194	63	φ̇ẋ	φ̇ẋ	PROPN
ejpam-6091	194	64	sec2	sec2	PROPN
ejpam-6091	194	65	φ	φ	PROPN
ejpam-6091	194	66	,	,	PUNCT
ejpam-6091	194	67	(	(	PUNCT
ejpam-6091	194	68	93	93	NUM
ejpam-6091	194	69	)	)	PUNCT
ejpam-6091	194	70	inserting	insert	VERB
ejpam-6091	194	71	equation	equation	NOUN
ejpam-6091	194	72	(	(	PUNCT
ejpam-6091	194	73	92	92	NUM
ejpam-6091	194	74	)	)	PUNCT
ejpam-6091	194	75	in	in	ADP
ejpam-6091	194	76	(	(	PUNCT
ejpam-6091	194	77	93	93	NUM
ejpam-6091	194	78	)	)	PUNCT
ejpam-6091	194	79	and	and	CCONJ
ejpam-6091	194	80	multiplying	multiply	VERB
ejpam-6091	194	81	the	the	DET
ejpam-6091	194	82	result	result	NOUN
ejpam-6091	194	83	by	by	ADP
ejpam-6091	194	84	(	(	PUNCT
ejpam-6091	194	85	−	−	PROPN
ejpam-6091	194	86	tanφ	tanφ	PROPN
ejpam-6091	194	87	)	)	PUNCT
ejpam-6091	194	88	leads	lead	VERB
ejpam-6091	194	89	to	to	ADP
ejpam-6091	194	90	:	:	PUNCT
ejpam-6091	194	91	ẍ	ẍ	X
ejpam-6091	194	92	=	=	PUNCT
ejpam-6091	195	1	−ẍ	−ẍ	ADJ
ejpam-6091	195	2	tan2	tan2	PROPN
ejpam-6091	195	3	φ−	φ−	PROPN
ejpam-6091	195	4	φ̇ẋ	φ̇ẋ	PROPN
ejpam-6091	195	5	sec2	sec2	PROPN
ejpam-6091	195	6	φ	φ	PROPN
ejpam-6091	195	7	tanφ	tanφ	PROPN
ejpam-6091	195	8	,	,	PUNCT
ejpam-6091	195	9	(	(	PUNCT
ejpam-6091	195	10	94	94	NUM
ejpam-6091	195	11	)	)	PUNCT
ejpam-6091	195	12	by	by	ADP
ejpam-6091	195	13	using	use	VERB
ejpam-6091	195	14	the	the	DET
ejpam-6091	195	15	identity	identity	NOUN
ejpam-6091	195	16	1	1	NUM
ejpam-6091	195	17	+	+	NUM
ejpam-6091	195	18	tan2	tan2	PROPN
ejpam-6091	195	19	φ	φ	PROPN
ejpam-6091	195	20	=	=	PROPN
ejpam-6091	195	21	sec2	sec2	PROPN
ejpam-6091	195	22	φ	φ	PROPN
ejpam-6091	195	23	,	,	PUNCT
ejpam-6091	195	24	equation	equation	NOUN
ejpam-6091	195	25	(	(	PUNCT
ejpam-6091	195	26	94	94	NUM
ejpam-6091	195	27	)	)	PUNCT
ejpam-6091	195	28	reduces	reduce	VERB
ejpam-6091	195	29	to	to	ADP
ejpam-6091	195	30	:	:	PUNCT
ejpam-6091	195	31	ẍ	ẍ	X
ejpam-6091	196	1	=	=	SYM
ejpam-6091	196	2	−φ̇ẋ	−φ̇ẋ	PROPN
ejpam-6091	196	3	tanφ	tanφ	PROPN
ejpam-6091	196	4	.	.	PUNCT
ejpam-6091	197	1	(	(	PUNCT
ejpam-6091	197	2	95	95	NUM
ejpam-6091	197	3	)	)	PUNCT
ejpam-6091	197	4	from	from	ADP
ejpam-6091	197	5	which	which	PRON
ejpam-6091	197	6	we	we	PRON
ejpam-6091	197	7	obtain	obtain	VERB
ejpam-6091	197	8	the	the	DET
ejpam-6091	197	9	constrained	constrain	VERB
ejpam-6091	197	10	equations	equation	NOUN
ejpam-6091	197	11	:	:	PUNCT
ejpam-6091	197	12	φ̈	φ̈	X
ejpam-6091	197	13	=	=	SYM
ejpam-6091	197	14	0	0	NUM
ejpam-6091	197	15	,	,	PUNCT
ejpam-6091	197	16	ẍ	ẍ	X
ejpam-6091	197	17	=	=	PROPN
ejpam-6091	198	1	−φ̇ẋ	−φ̇ẋ	PROPN
ejpam-6091	198	2	tanφ	tanφ	PROPN
ejpam-6091	198	3	,	,	PUNCT
ejpam-6091	198	4	ẏ	ẏ	PROPN
ejpam-6091	198	5	=	=	SYM
ejpam-6091	198	6	ẋ	ẋ	PROPN
ejpam-6091	198	7	tanφ	tanφ	PROPN
ejpam-6091	198	8	.	.	PUNCT
ejpam-6091	199	1	(	(	PUNCT
ejpam-6091	199	2	96	96	NUM
ejpam-6091	199	3	)	)	PUNCT
ejpam-6091	199	4	now	now	ADV
ejpam-6091	199	5	we	we	PRON
ejpam-6091	199	6	can	can	AUX
ejpam-6091	199	7	solve	solve	VERB
ejpam-6091	199	8	φ(t	φ(t	PROPN
ejpam-6091	199	9	)	)	PUNCT
ejpam-6091	199	10	,	,	PUNCT
ejpam-6091	199	11	x(t	x(t	PROPN
ejpam-6091	199	12	)	)	PUNCT
ejpam-6091	199	13	,	,	PUNCT
ejpam-6091	199	14	y(t	y(t	NUM
ejpam-6091	199	15	)	)	PUNCT
ejpam-6091	199	16	as	as	SCONJ
ejpam-6091	199	17	follows	follow	VERB
ejpam-6091	199	18	:	:	PUNCT
ejpam-6091	199	19	the	the	DET
ejpam-6091	199	20	first	first	ADJ
ejpam-6091	199	21	equation	equation	NOUN
ejpam-6091	199	22	can	can	AUX
ejpam-6091	199	23	be	be	AUX
ejpam-6091	199	24	easily	easily	ADV
ejpam-6091	199	25	integrated	integrate	VERB
ejpam-6091	199	26	to	to	PART
ejpam-6091	199	27	give	give	VERB
ejpam-6091	199	28	:	:	PUNCT
ejpam-6091	199	29	φ(t	φ(t	NUM
ejpam-6091	199	30	)	)	PUNCT
ejpam-6091	200	1	=	=	PUNCT
ejpam-6091	200	2	α1t+	α1t+	NOUN
ejpam-6091	200	3	β1	β1	PROPN
ejpam-6091	200	4	.	.	PUNCT
ejpam-6091	201	1	(	(	PUNCT
ejpam-6091	201	2	97	97	NUM
ejpam-6091	201	3	)	)	PUNCT
ejpam-6091	201	4	differentiating	differentiate	VERB
ejpam-6091	201	5	equation	equation	NOUN
ejpam-6091	201	6	(	(	PUNCT
ejpam-6091	201	7	97	97	NUM
ejpam-6091	201	8	)	)	PUNCT
ejpam-6091	201	9	with	with	ADP
ejpam-6091	201	10	respect	respect	NOUN
ejpam-6091	201	11	to	to	ADP
ejpam-6091	201	12	time	time	NOUN
ejpam-6091	201	13	,	,	PUNCT
ejpam-6091	201	14	we	we	PRON
ejpam-6091	201	15	obtain	obtain	VERB
ejpam-6091	201	16	φ̇	φ̇	ADJ
ejpam-6091	201	17	=	=	SYM
ejpam-6091	201	18	α1	α1	PROPN
ejpam-6091	201	19	.	.	PUNCT
ejpam-6091	202	1	(	(	PUNCT
ejpam-6091	202	2	98	98	NUM
ejpam-6091	202	3	)	)	PUNCT
ejpam-6091	202	4	k.	k.	PROPN
ejpam-6091	202	5	i.	i.	PROPN
ejpam-6091	202	6	nawafleh	nawafleh	PROPN
ejpam-6091	202	7	/	/	SYM
ejpam-6091	202	8	eur	eur	PROPN
ejpam-6091	202	9	.	.	PUNCT
ejpam-6091	203	1	j.	j.	PROPN
ejpam-6091	203	2	pure	pure	PROPN
ejpam-6091	203	3	appl	appl	PROPN
ejpam-6091	203	4	.	.	PROPN
ejpam-6091	203	5	math	math	PROPN
ejpam-6091	203	6	,	,	PUNCT
ejpam-6091	203	7	18	18	NUM
ejpam-6091	203	8	(	(	PUNCT
ejpam-6091	203	9	3	3	NUM
ejpam-6091	203	10	)	)	PUNCT
ejpam-6091	203	11	(	(	PUNCT
ejpam-6091	203	12	2025	2025	NUM
ejpam-6091	203	13	)	)	PUNCT
ejpam-6091	203	14	,	,	PUNCT
ejpam-6091	203	15	6091	6091	NUM
ejpam-6091	203	16	11	11	NUM
ejpam-6091	203	17	of	of	ADP
ejpam-6091	203	18	15	15	NUM
ejpam-6091	203	19	now	now	ADV
ejpam-6091	203	20	integrate	integrate	VERB
ejpam-6091	203	21	equation	equation	NOUN
ejpam-6091	203	22	(	(	PUNCT
ejpam-6091	203	23	95	95	NUM
ejpam-6091	203	24	)	)	PUNCT
ejpam-6091	203	25	,	,	PUNCT
ejpam-6091	203	26	we	we	PRON
ejpam-6091	203	27	get∫	get∫	VERB
ejpam-6091	203	28	ẍ	ẍ	X
ejpam-6091	203	29	ẋ	ẋ	PROPN
ejpam-6091	203	30	dt	dt	PUNCT
ejpam-6091	204	1	=	=	SYM
ejpam-6091	204	2	∫	∫	PROPN
ejpam-6091	204	3	(	(	PUNCT
ejpam-6091	204	4	−	−	PROPN
ejpam-6091	204	5	tanφ)dφ	tanφ)dφ	PROPN
ejpam-6091	204	6	,	,	PUNCT
ejpam-6091	204	7	φ̇	φ̇	ADV
ejpam-6091	204	8	=	=	PUNCT
ejpam-6091	204	9	dφ	dφ	PART
ejpam-6091	204	10	dt	dt	X
ejpam-6091	204	11	.	.	PUNCT
ejpam-6091	205	1	(	(	PUNCT
ejpam-6091	205	2	99	99	NUM
ejpam-6091	205	3	)	)	PUNCT
ejpam-6091	205	4	this	this	PRON
ejpam-6091	205	5	gives	give	VERB
ejpam-6091	205	6	:	:	PUNCT
ejpam-6091	205	7	ln	ln	PROPN
ejpam-6091	205	8	ẋ	ẋ	PROPN
ejpam-6091	206	1	=	=	PUNCT
ejpam-6091	206	2	ln	ln	ADJ
ejpam-6091	206	3	cosφ	cosφ	NOUN
ejpam-6091	206	4	,	,	PUNCT
ejpam-6091	206	5	or	or	CCONJ
ejpam-6091	206	6	,	,	PUNCT
ejpam-6091	206	7	ẋ	ẋ	PROPN
ejpam-6091	206	8	=	=	PUNCT
ejpam-6091	206	9	cosφ	cosφ	NOUN
ejpam-6091	206	10	.	.	PUNCT
ejpam-6091	207	1	(	(	PUNCT
ejpam-6091	207	2	100	100	NUM
ejpam-6091	207	3	)	)	PUNCT
ejpam-6091	207	4	substituting	substitute	VERB
ejpam-6091	207	5	equation	equation	NOUN
ejpam-6091	207	6	(	(	PUNCT
ejpam-6091	207	7	97	97	NUM
ejpam-6091	207	8	)	)	PUNCT
ejpam-6091	207	9	into	into	ADP
ejpam-6091	207	10	equation	equation	NOUN
ejpam-6091	207	11	(	(	PUNCT
ejpam-6091	207	12	100	100	NUM
ejpam-6091	207	13	)	)	PUNCT
ejpam-6091	207	14	and	and	CCONJ
ejpam-6091	207	15	integrating	integrate	VERB
ejpam-6091	207	16	the	the	DET
ejpam-6091	207	17	result	result	NOUN
ejpam-6091	207	18	equation:∫	equation:∫	PROPN
ejpam-6091	207	19	ẋdt	ẋdt	PUNCT
ejpam-6091	208	1	=	=	SYM
ejpam-6091	208	2	∫	∫	PROPN
ejpam-6091	208	3	cos(α1t+	cos(α1t+	PROPN
ejpam-6091	208	4	β1)dt	β1)dt	PROPN
ejpam-6091	208	5	,	,	PUNCT
ejpam-6091	208	6	(	(	PUNCT
ejpam-6091	208	7	101	101	NUM
ejpam-6091	208	8	)	)	PUNCT
ejpam-6091	208	9	leads	lead	VERB
ejpam-6091	208	10	to	to	ADP
ejpam-6091	208	11	x(t	x(t	NOUN
ejpam-6091	208	12	)	)	PUNCT
ejpam-6091	209	1	=	=	PUNCT
ejpam-6091	209	2	α2	α2	PROPN
ejpam-6091	209	3	sinφ+	sinφ+	PROPN
ejpam-6091	209	4	β2	β2	PROPN
ejpam-6091	209	5	,	,	PUNCT
ejpam-6091	209	6	(	(	PUNCT
ejpam-6091	209	7	102	102	NUM
ejpam-6091	209	8	)	)	PUNCT
ejpam-6091	209	9	where	where	SCONJ
ejpam-6091	209	10	α2	α2	ADJ
ejpam-6091	209	11	=	=	SYM
ejpam-6091	209	12	1	1	NUM
ejpam-6091	209	13	α1	α1	PROPN
ejpam-6091	209	14	.	.	PUNCT
ejpam-6091	210	1	now	now	ADV
ejpam-6091	210	2	substituting	substitute	VERB
ejpam-6091	210	3	equation	equation	NOUN
ejpam-6091	210	4	(	(	PUNCT
ejpam-6091	210	5	100	100	NUM
ejpam-6091	210	6	)	)	PUNCT
ejpam-6091	210	7	in	in	ADP
ejpam-6091	210	8	constraint	constraint	NOUN
ejpam-6091	210	9	equation	equation	NOUN
ejpam-6091	210	10	(	(	PUNCT
ejpam-6091	210	11	85	85	NUM
ejpam-6091	210	12	)	)	PUNCT
ejpam-6091	210	13	we	we	PRON
ejpam-6091	210	14	get	get	VERB
ejpam-6091	210	15	:	:	PUNCT
ejpam-6091	210	16	ẏ	ẏ	PROPN
ejpam-6091	210	17	=	=	SYM
ejpam-6091	210	18	sinφ	sinφ	NOUN
ejpam-6091	210	19	,	,	PUNCT
ejpam-6091	210	20	(	(	PUNCT
ejpam-6091	210	21	103	103	X
ejpam-6091	210	22	)	)	PUNCT
ejpam-6091	210	23	inserting	insert	VERB
ejpam-6091	210	24	equation	equation	NOUN
ejpam-6091	210	25	(	(	PUNCT
ejpam-6091	210	26	97	97	NUM
ejpam-6091	210	27	)	)	PUNCT
ejpam-6091	210	28	into	into	ADP
ejpam-6091	210	29	equation	equation	NOUN
ejpam-6091	210	30	(	(	PUNCT
ejpam-6091	210	31	103	103	NUM
ejpam-6091	210	32	)	)	PUNCT
ejpam-6091	210	33	and	and	CCONJ
ejpam-6091	210	34	integrating	integrate	VERB
ejpam-6091	210	35	the	the	DET
ejpam-6091	210	36	result	result	NOUN
ejpam-6091	210	37	equation∫	equation∫	NOUN
ejpam-6091	210	38	ẏdt	ẏdt	PUNCT
ejpam-6091	211	1	=	=	SYM
ejpam-6091	211	2	∫	∫	PROPN
ejpam-6091	211	3	sin(α1t+	sin(α1t+	PROPN
ejpam-6091	211	4	β1)dt	β1)dt	PROPN
ejpam-6091	211	5	,	,	PUNCT
ejpam-6091	211	6	(	(	PUNCT
ejpam-6091	211	7	104	104	X
ejpam-6091	211	8	)	)	PUNCT
ejpam-6091	211	9	we	we	PRON
ejpam-6091	211	10	find	find	VERB
ejpam-6091	211	11	y(t	y(t	NUM
ejpam-6091	211	12	)	)	PUNCT
ejpam-6091	212	1	=	=	SYM
ejpam-6091	212	2	α3	α3	NOUN
ejpam-6091	212	3	cosφ+	cosφ+	NOUN
ejpam-6091	212	4	β3	β3	ADJ
ejpam-6091	212	5	,	,	PUNCT
ejpam-6091	212	6	(	(	PUNCT
ejpam-6091	212	7	105	105	NUM
ejpam-6091	212	8	)	)	PUNCT
ejpam-6091	212	9	where	where	SCONJ
ejpam-6091	212	10	α3	α3	NOUN
ejpam-6091	212	11	=	=	SYM
ejpam-6091	212	12	−	−	PROPN
ejpam-6091	212	13	1	1	NUM
ejpam-6091	212	14	α1	α1	PROPN
ejpam-6091	212	15	.	.	PUNCT
ejpam-6091	213	1	again	again	ADV
ejpam-6091	213	2	β1	β1	PROPN
ejpam-6091	213	3	,	,	PUNCT
ejpam-6091	213	4	β2	β2	NOUN
ejpam-6091	213	5	and	and	CCONJ
ejpam-6091	213	6	β3	β3	NOUN
ejpam-6091	213	7	are	be	AUX
ejpam-6091	213	8	constant	constant	ADJ
ejpam-6091	213	9	of	of	ADP
ejpam-6091	213	10	integration	integration	NOUN
ejpam-6091	213	11	related	relate	VERB
ejpam-6091	213	12	to	to	ADP
ejpam-6091	213	13	the	the	DET
ejpam-6091	213	14	initial	initial	ADJ
ejpam-6091	213	15	values	value	NOUN
ejpam-6091	213	16	of	of	ADP
ejpam-6091	213	17	φ	φ	PROPN
ejpam-6091	213	18	,	,	PUNCT
ejpam-6091	213	19	x	x	PRON
ejpam-6091	213	20	,	,	PUNCT
ejpam-6091	213	21	y	y	PROPN
ejpam-6091	213	22	while	while	SCONJ
ejpam-6091	213	23	α1	α1	PROPN
ejpam-6091	213	24	,	,	PUNCT
ejpam-6091	213	25	α2	α2	ADJ
ejpam-6091	213	26	and	and	CCONJ
ejpam-6091	213	27	α3	α3	PROPN
ejpam-6091	213	28	are	be	AUX
ejpam-6091	213	29	the	the	DET
ejpam-6091	213	30	initial	initial	ADJ
ejpam-6091	213	31	values	value	NOUN
ejpam-6091	213	32	of	of	ADP
ejpam-6091	213	33	velocities	velocity	NOUN
ejpam-6091	213	34	.	.	PUNCT
ejpam-6091	214	1	following	follow	VERB
ejpam-6091	214	2	the	the	DET
ejpam-6091	214	3	same	same	ADJ
ejpam-6091	214	4	steps	step	NOUN
ejpam-6091	214	5	as	as	ADP
ejpam-6091	214	6	in	in	ADP
ejpam-6091	214	7	the	the	DET
ejpam-6091	214	8	preceding	precede	VERB
ejpam-6091	214	9	example	example	NOUN
ejpam-6091	214	10	we	we	PRON
ejpam-6091	214	11	may	may	AUX
ejpam-6091	214	12	rewrite	rewrite	VERB
ejpam-6091	214	13	equations	equation	NOUN
ejpam-6091	214	14	(	(	PUNCT
ejpam-6091	214	15	97	97	NUM
ejpam-6091	214	16	)	)	PUNCT
ejpam-6091	214	17	,	,	PUNCT
ejpam-6091	214	18	(	(	PUNCT
ejpam-6091	214	19	102	102	NUM
ejpam-6091	214	20	)	)	PUNCT
ejpam-6091	214	21	and	and	CCONJ
ejpam-6091	214	22	(	(	PUNCT
ejpam-6091	214	23	105	105	NUM
ejpam-6091	214	24	)	)	PUNCT
ejpam-6091	214	25	respectively	respectively	ADV
ejpam-6091	214	26	as	as	ADP
ejpam-6091	214	27	:	:	PUNCT
ejpam-6091	214	28	β1	β1	PROPN
ejpam-6091	214	29	=	=	SYM
ejpam-6091	214	30	φ−	φ−	PROPN
ejpam-6091	214	31	α1	α1	PROPN
ejpam-6091	214	32	t	t	NOUN
ejpam-6091	214	33	=	=	SYM
ejpam-6091	214	34	∂s1	∂s1	PROPN
ejpam-6091	214	35	∂α1	∂α1	PROPN
ejpam-6091	214	36	,	,	PUNCT
ejpam-6091	214	37	(	(	PUNCT
ejpam-6091	214	38	106	106	NUM
ejpam-6091	214	39	)	)	PUNCT
ejpam-6091	214	40	β2	β2	NOUN
ejpam-6091	214	41	=	=	SYM
ejpam-6091	214	42	x−	x−	PROPN
ejpam-6091	214	43	α2	α2	PROPN
ejpam-6091	214	44	sinφ	sinφ	NOUN
ejpam-6091	215	1	=	=	PUNCT
ejpam-6091	215	2	∂s2	∂s2	NOUN
ejpam-6091	215	3	∂α2	∂α2	NOUN
ejpam-6091	215	4	,	,	PUNCT
ejpam-6091	215	5	(	(	PUNCT
ejpam-6091	215	6	107	107	NUM
ejpam-6091	215	7	)	)	PUNCT
ejpam-6091	215	8	β3	β3	NOUN
ejpam-6091	215	9	=	=	SYM
ejpam-6091	215	10	y	y	PROPN
ejpam-6091	215	11	−	−	NOUN
ejpam-6091	215	12	α3	α3	NOUN
ejpam-6091	215	13	cosφ	cosφ	NOUN
ejpam-6091	216	1	=	=	SYM
ejpam-6091	217	1	∂s3	∂s3	PROPN
ejpam-6091	218	1	∂α3	∂α3	PROPN
ejpam-6091	218	2	.	.	PUNCT
ejpam-6091	219	1	(	(	PUNCT
ejpam-6091	219	2	108	108	NUM
ejpam-6091	219	3	)	)	PUNCT
ejpam-6091	219	4	k.	k.	PROPN
ejpam-6091	219	5	i.	i.	PROPN
ejpam-6091	219	6	nawafleh	nawafleh	PROPN
ejpam-6091	219	7	/	/	SYM
ejpam-6091	219	8	eur	eur	PROPN
ejpam-6091	219	9	.	.	PUNCT
ejpam-6091	220	1	j.	j.	PROPN
ejpam-6091	220	2	pure	pure	PROPN
ejpam-6091	220	3	appl	appl	PROPN
ejpam-6091	220	4	.	.	PROPN
ejpam-6091	220	5	math	math	PROPN
ejpam-6091	220	6	,	,	PUNCT
ejpam-6091	220	7	18	18	NUM
ejpam-6091	220	8	(	(	PUNCT
ejpam-6091	220	9	3	3	NUM
ejpam-6091	220	10	)	)	PUNCT
ejpam-6091	220	11	(	(	PUNCT
ejpam-6091	220	12	2025	2025	NUM
ejpam-6091	220	13	)	)	PUNCT
ejpam-6091	220	14	,	,	PUNCT
ejpam-6091	220	15	6091	6091	NUM
ejpam-6091	220	16	12	12	NUM
ejpam-6091	220	17	of	of	ADP
ejpam-6091	220	18	15	15	NUM
ejpam-6091	220	19	solving	solving	NOUN
ejpam-6091	220	20	equations	equation	NOUN
ejpam-6091	220	21	(	(	PUNCT
ejpam-6091	220	22	106–108	106–108	NUM
ejpam-6091	220	23	)	)	PUNCT
ejpam-6091	220	24	simultaneously	simultaneously	ADV
ejpam-6091	220	25	,	,	PUNCT
ejpam-6091	220	26	we	we	PRON
ejpam-6091	220	27	obtain	obtain	VERB
ejpam-6091	220	28	:	:	PUNCT
ejpam-6091	220	29	s1(φ	s1(φ	PROPN
ejpam-6091	220	30	,	,	PUNCT
ejpam-6091	220	31	α1	α1	PROPN
ejpam-6091	220	32	)	)	PUNCT
ejpam-6091	220	33	=	=	PUNCT
ejpam-6091	221	1	φα1	φα1	NOUN
ejpam-6091	221	2	−	−	NOUN
ejpam-6091	221	3	1	1	NUM
ejpam-6091	221	4	2	2	NUM
ejpam-6091	221	5	α2	α2	NOUN
ejpam-6091	221	6	1	1	NUM
ejpam-6091	221	7	t	t	NOUN
ejpam-6091	221	8	,	,	PUNCT
ejpam-6091	221	9	(	(	PUNCT
ejpam-6091	221	10	109	109	NUM
ejpam-6091	221	11	)	)	PUNCT
ejpam-6091	221	12	s2(x	s2(x	PROPN
ejpam-6091	221	13	,	,	PUNCT
ejpam-6091	221	14	α2	α2	ADJ
ejpam-6091	221	15	)	)	PUNCT
ejpam-6091	221	16	=	=	PUNCT
ejpam-6091	222	1	xα2	xα2	NOUN
ejpam-6091	223	1	−	−	NOUN
ejpam-6091	223	2	1	1	NUM
ejpam-6091	223	3	2	2	NUM
ejpam-6091	223	4	α2	α2	ADJ
ejpam-6091	223	5	2	2	NUM
ejpam-6091	223	6	sinφ	sinφ	NOUN
ejpam-6091	223	7	,	,	PUNCT
ejpam-6091	223	8	(	(	PUNCT
ejpam-6091	223	9	110	110	NUM
ejpam-6091	223	10	)	)	PUNCT
ejpam-6091	223	11	s3(y	s3(y	PROPN
ejpam-6091	223	12	,	,	PUNCT
ejpam-6091	223	13	α3	α3	NOUN
ejpam-6091	223	14	)	)	PUNCT
ejpam-6091	223	15	=	=	SYM
ejpam-6091	224	1	yα3	yα3	NOUN
ejpam-6091	224	2	−	−	NOUN
ejpam-6091	224	3	1	1	NUM
ejpam-6091	224	4	2	2	NUM
ejpam-6091	224	5	α2	α2	ADJ
ejpam-6091	224	6	3	3	NUM
ejpam-6091	224	7	cosφ	cosφ	NOUN
ejpam-6091	224	8	.	.	PUNCT
ejpam-6091	225	1	(	(	PUNCT
ejpam-6091	225	2	111	111	NUM
ejpam-6091	225	3	)	)	PUNCT
ejpam-6091	225	4	following	follow	VERB
ejpam-6091	225	5	equation	equation	NOUN
ejpam-6091	225	6	(	(	PUNCT
ejpam-6091	225	7	11	11	NUM
ejpam-6091	225	8	)	)	PUNCT
ejpam-6091	225	9	,	,	PUNCT
ejpam-6091	225	10	we	we	PRON
ejpam-6091	225	11	finally	finally	ADV
ejpam-6091	225	12	collect	collect	VERB
ejpam-6091	225	13	expressions	expression	NOUN
ejpam-6091	225	14	from	from	ADP
ejpam-6091	225	15	equations	equation	NOUN
ejpam-6091	225	16	(	(	PUNCT
ejpam-6091	225	17	109–111	109–111	NUM
ejpam-6091	225	18	)	)	PUNCT
ejpam-6091	225	19	,	,	PUNCT
ejpam-6091	225	20	which	which	PRON
ejpam-6091	225	21	give	give	VERB
ejpam-6091	225	22	the	the	DET
ejpam-6091	225	23	hamilton	hamilton	PROPN
ejpam-6091	225	24	-	-	PUNCT
ejpam-6091	225	25	jacobi	jacobi	PROPN
ejpam-6091	225	26	function	function	PROPN
ejpam-6091	225	27	s(φ	s(φ	PROPN
ejpam-6091	225	28	,	,	PUNCT
ejpam-6091	225	29	x	x	X
ejpam-6091	225	30	,	,	PUNCT
ejpam-6091	225	31	y	y	PROPN
ejpam-6091	225	32	,	,	PUNCT
ejpam-6091	225	33	α1	α1	PROPN
ejpam-6091	225	34	,	,	PUNCT
ejpam-6091	225	35	α2	α2	ADJ
ejpam-6091	225	36	,	,	PUNCT
ejpam-6091	225	37	α3	α3	PROPN
ejpam-6091	225	38	,	,	PUNCT
ejpam-6091	225	39	t	t	PROPN
ejpam-6091	225	40	):	):	PUNCT
ejpam-6091	225	41	s	s	NOUN
ejpam-6091	225	42	=	=	PUNCT
ejpam-6091	225	43	φα1	φα1	NOUN
ejpam-6091	225	44	+	+	CCONJ
ejpam-6091	225	45	xα2	xα2	X
ejpam-6091	226	1	+	+	CCONJ
ejpam-6091	226	2	yα3	yα3	NOUN
ejpam-6091	226	3	−	−	NOUN
ejpam-6091	226	4	1	1	NUM
ejpam-6091	226	5	2	2	NUM
ejpam-6091	226	6	α2	α2	NOUN
ejpam-6091	226	7	1t−	1t−	NUM
ejpam-6091	226	8	1	1	NUM
ejpam-6091	226	9	2	2	NUM
ejpam-6091	226	10	α2	α2	NOUN
ejpam-6091	226	11	2	2	NUM
ejpam-6091	226	12	sinφ−	sinφ−	NOUN
ejpam-6091	226	13	1	1	NUM
ejpam-6091	226	14	2	2	NUM
ejpam-6091	226	15	α2	α2	ADJ
ejpam-6091	226	16	3	3	NUM
ejpam-6091	226	17	cosφ	cosφ	NOUN
ejpam-6091	226	18	.	.	PUNCT
ejpam-6091	227	1	(	(	PUNCT
ejpam-6091	227	2	112	112	NUM
ejpam-6091	227	3	)	)	PUNCT
ejpam-6091	227	4	the	the	DET
ejpam-6091	227	5	generalized	generalized	ADJ
ejpam-6091	227	6	momenta	momenta	NOUN
ejpam-6091	227	7	can	can	AUX
ejpam-6091	227	8	be	be	AUX
ejpam-6091	227	9	derived	derive	VERB
ejpam-6091	227	10	as	as	ADP
ejpam-6091	227	11	pφ	pφ	ADP
ejpam-6091	227	12	=	=	PUNCT
ejpam-6091	227	13	∂s	∂s	PROPN
ejpam-6091	227	14	∂φ	∂φ	PROPN
ejpam-6091	228	1	=	=	SYM
ejpam-6091	228	2	α1	α1	PROPN
ejpam-6091	228	3	−	−	NUM
ejpam-6091	228	4	1	1	NUM
ejpam-6091	228	5	2	2	NUM
ejpam-6091	228	6	α2	α2	ADJ
ejpam-6091	228	7	2	2	NUM
ejpam-6091	228	8	cosφ+	cosφ+	SYM
ejpam-6091	228	9	1	1	NUM
ejpam-6091	228	10	2	2	NUM
ejpam-6091	228	11	α2	α2	ADJ
ejpam-6091	228	12	3	3	NUM
ejpam-6091	228	13	sinφ	sinφ	NOUN
ejpam-6091	228	14	,	,	PUNCT
ejpam-6091	228	15	(	(	PUNCT
ejpam-6091	228	16	113	113	NUM
ejpam-6091	228	17	)	)	PUNCT
ejpam-6091	228	18	px	px	NOUN
ejpam-6091	229	1	=	=	PUNCT
ejpam-6091	229	2	∂s	∂s	PROPN
ejpam-6091	229	3	∂x	∂x	PROPN
ejpam-6091	229	4	=	=	SYM
ejpam-6091	229	5	α2	α2	PROPN
ejpam-6091	229	6	,	,	PUNCT
ejpam-6091	229	7	(	(	PUNCT
ejpam-6091	229	8	114	114	NUM
ejpam-6091	229	9	)	)	PUNCT
ejpam-6091	230	1	py	py	NOUN
ejpam-6091	231	1	=	=	PUNCT
ejpam-6091	231	2	∂s	∂s	PROPN
ejpam-6091	231	3	∂y	∂y	SYM
ejpam-6091	231	4	=	=	SYM
ejpam-6091	231	5	α3	α3	PROPN
ejpam-6091	231	6	.	.	PUNCT
ejpam-6091	232	1	(	(	PUNCT
ejpam-6091	232	2	115	115	NUM
ejpam-6091	232	3	)	)	PUNCT
ejpam-6091	232	4	from	from	ADP
ejpam-6091	232	5	the	the	DET
ejpam-6091	232	6	above	above	ADJ
ejpam-6091	232	7	equations	equation	NOUN
ejpam-6091	232	8	we	we	PRON
ejpam-6091	232	9	can	can	AUX
ejpam-6091	232	10	obtain	obtain	VERB
ejpam-6091	232	11	α1	α1	NOUN
ejpam-6091	232	12	,	,	PUNCT
ejpam-6091	232	13	α2	α2	ADJ
ejpam-6091	232	14	,	,	PUNCT
ejpam-6091	232	15	α3	α3	NOUN
ejpam-6091	232	16	as	as	ADP
ejpam-6091	232	17	functions	function	NOUN
ejpam-6091	232	18	of	of	ADP
ejpam-6091	232	19	pi	pi	NOUN
ejpam-6091	232	20	and	and	CCONJ
ejpam-6091	232	21	qi	qi	PROPN
ejpam-6091	232	22	.	.	PUNCT
ejpam-6091	232	23	α1	α1	PROPN
ejpam-6091	233	1	=	=	SYM
ejpam-6091	233	2	pφ	pφ	ADP
ejpam-6091	233	3	+	+	NOUN
ejpam-6091	233	4	1	1	NUM
ejpam-6091	233	5	2	2	NUM
ejpam-6091	233	6	α2	α2	NOUN
ejpam-6091	233	7	2	2	NUM
ejpam-6091	233	8	cosφ−	cosφ−	NOUN
ejpam-6091	233	9	1	1	NUM
ejpam-6091	233	10	2	2	NUM
ejpam-6091	233	11	α2	α2	NOUN
ejpam-6091	233	12	3	3	NUM
ejpam-6091	233	13	sinφ	sinφ	NOUN
ejpam-6091	233	14	,	,	PUNCT
ejpam-6091	233	15	(	(	PUNCT
ejpam-6091	233	16	116	116	X
ejpam-6091	233	17	)	)	PUNCT
ejpam-6091	233	18	α2	α2	NOUN
ejpam-6091	233	19	=	=	SYM
ejpam-6091	233	20	px	px	PROPN
ejpam-6091	233	21	,	,	PUNCT
ejpam-6091	233	22	(	(	PUNCT
ejpam-6091	233	23	117	117	NUM
ejpam-6091	233	24	)	)	PUNCT
ejpam-6091	233	25	α3	α3	NOUN
ejpam-6091	233	26	=	=	SYM
ejpam-6091	233	27	py	py	PROPN
ejpam-6091	233	28	.	.	PUNCT
ejpam-6091	234	1	(	(	PUNCT
ejpam-6091	234	2	118	118	NUM
ejpam-6091	234	3	)	)	PUNCT
ejpam-6091	234	4	making	make	VERB
ejpam-6091	234	5	use	use	VERB
ejpam-6091	234	6	the	the	DET
ejpam-6091	234	7	definition	definition	NOUN
ejpam-6091	234	8	of	of	ADP
ejpam-6091	234	9	equation	equation	NOUN
ejpam-6091	234	10	(	(	PUNCT
ejpam-6091	234	11	14	14	NUM
ejpam-6091	234	12	)	)	PUNCT
ejpam-6091	234	13	,	,	PUNCT
ejpam-6091	234	14	the	the	DET
ejpam-6091	234	15	hamiltonian	hamiltonian	NOUN
ejpam-6091	234	16	is	be	AUX
ejpam-6091	234	17	defined	define	VERB
ejpam-6091	234	18	as	as	ADP
ejpam-6091	234	19	:	:	PUNCT
ejpam-6091	234	20	h	h	NOUN
ejpam-6091	234	21	=	=	PUNCT
ejpam-6091	234	22	−∂s	−∂s	NUM
ejpam-6091	234	23	∂t	∂t	PROPN
ejpam-6091	234	24	=	=	SYM
ejpam-6091	234	25	1	1	NUM
ejpam-6091	234	26	2	2	NUM
ejpam-6091	234	27	α2	α2	NOUN
ejpam-6091	234	28	1	1	NUM
ejpam-6091	234	29	,	,	PUNCT
ejpam-6091	234	30	(	(	PUNCT
ejpam-6091	234	31	119	119	NUM
ejpam-6091	234	32	)	)	PUNCT
ejpam-6091	234	33	inserting	insert	VERB
ejpam-6091	234	34	equation	equation	NOUN
ejpam-6091	234	35	(	(	PUNCT
ejpam-6091	234	36	116	116	NUM
ejpam-6091	234	37	)	)	PUNCT
ejpam-6091	234	38	into	into	ADP
ejpam-6091	234	39	equation	equation	NOUN
ejpam-6091	234	40	(	(	PUNCT
ejpam-6091	234	41	119	119	NUM
ejpam-6091	234	42	)	)	PUNCT
ejpam-6091	234	43	we	we	PRON
ejpam-6091	234	44	get	get	VERB
ejpam-6091	234	45	the	the	DET
ejpam-6091	234	46	following	follow	VERB
ejpam-6091	234	47	expression	expression	NOUN
ejpam-6091	234	48	for	for	ADP
ejpam-6091	234	49	the	the	DET
ejpam-6091	234	50	hamiltonian	hamiltonian	NOUN
ejpam-6091	234	51	:	:	PUNCT
ejpam-6091	234	52	h	h	NOUN
ejpam-6091	234	53	=	=	NOUN
ejpam-6091	234	54	1	1	NUM
ejpam-6091	234	55	2	2	NUM
ejpam-6091	234	56	[	[	PUNCT
ejpam-6091	234	57	pφ	pφ	ADP
ejpam-6091	234	58	+	+	NOUN
ejpam-6091	234	59	1	1	NUM
ejpam-6091	234	60	2	2	NUM
ejpam-6091	234	61	(	(	PUNCT
ejpam-6091	234	62	p	p	NOUN
ejpam-6091	234	63	2	2	NUM
ejpam-6091	234	64	x	x	SYM
ejpam-6091	234	65	cosφ−	cosφ−	NOUN
ejpam-6091	234	66	p2y	p2y	NOUN
ejpam-6091	234	67	sinφ	sinφ	PROPN
ejpam-6091	234	68	)	)	PUNCT
ejpam-6091	235	1	]	]	PUNCT
ejpam-6091	235	2	2	2	X
ejpam-6091	235	3	.	.	PUNCT
ejpam-6091	236	1	(	(	PUNCT
ejpam-6091	236	2	120	120	NUM
ejpam-6091	236	3	)	)	PUNCT
ejpam-6091	236	4	the	the	DET
ejpam-6091	236	5	corresponding	corresponding	PROPN
ejpam-6091	236	6	hamilton	hamilton	PROPN
ejpam-6091	236	7	’s	’s	PART
ejpam-6091	236	8	equations	equation	NOUN
ejpam-6091	236	9	of	of	ADP
ejpam-6091	236	10	motion	motion	NOUN
ejpam-6091	236	11	can	can	AUX
ejpam-6091	236	12	be	be	AUX
ejpam-6091	236	13	found	find	VERB
ejpam-6091	236	14	from	from	ADP
ejpam-6091	236	15	equation	equation	NOUN
ejpam-6091	236	16	(	(	PUNCT
ejpam-6091	236	17	15	15	NUM
ejpam-6091	236	18	)	)	PUNCT
ejpam-6091	236	19	.	.	PUNCT
ejpam-6091	237	1	so	so	ADV
ejpam-6091	237	2	the	the	DET
ejpam-6091	237	3	generalized	generalized	ADJ
ejpam-6091	237	4	velocities	velocity	NOUN
ejpam-6091	237	5	corresponding	correspond	VERB
ejpam-6091	237	6	to	to	ADP
ejpam-6091	237	7	this	this	DET
ejpam-6091	237	8	hamiltonian	hamiltonian	NOUN
ejpam-6091	237	9	are	be	AUX
ejpam-6091	237	10	:	:	PUNCT
ejpam-6091	237	11	φ̇	φ̇	ADV
ejpam-6091	237	12	=	=	PUNCT
ejpam-6091	238	1	∂h	∂h	VERB
ejpam-6091	238	2	∂pφ	∂pφ	PROPN
ejpam-6091	238	3	=	=	PUNCT
ejpam-6091	239	1	[	[	PUNCT
ejpam-6091	239	2	pφ	pφ	ADP
ejpam-6091	239	3	+	+	NOUN
ejpam-6091	239	4	1	1	NUM
ejpam-6091	239	5	2	2	NUM
ejpam-6091	239	6	(	(	PUNCT
ejpam-6091	239	7	p	p	NOUN
ejpam-6091	239	8	2	2	NUM
ejpam-6091	239	9	x	x	SYM
ejpam-6091	239	10	cosφ−	cosφ−	NOUN
ejpam-6091	239	11	p2y	p2y	NOUN
ejpam-6091	239	12	sinφ	sinφ	PROPN
ejpam-6091	239	13	)	)	PUNCT
ejpam-6091	239	14	]	]	PUNCT
ejpam-6091	239	15	,	,	PUNCT
ejpam-6091	239	16	(	(	PUNCT
ejpam-6091	239	17	121	121	NUM
ejpam-6091	239	18	)	)	PUNCT
ejpam-6091	239	19	ẋ	ẋ	PUNCT
ejpam-6091	240	1	=	=	SYM
ejpam-6091	240	2	∂h	∂h	PROPN
ejpam-6091	240	3	∂px	∂px	NOUN
ejpam-6091	240	4	=	=	PUNCT
ejpam-6091	240	5	[	[	PUNCT
ejpam-6091	240	6	pφ	pφ	ADP
ejpam-6091	240	7	+	+	NOUN
ejpam-6091	240	8	1	1	NUM
ejpam-6091	240	9	2	2	NUM
ejpam-6091	240	10	(	(	PUNCT
ejpam-6091	240	11	p	p	NOUN
ejpam-6091	240	12	2	2	NUM
ejpam-6091	240	13	x	x	SYM
ejpam-6091	240	14	cosφ−	cosφ−	NOUN
ejpam-6091	240	15	p2y	p2y	NOUN
ejpam-6091	240	16	sinφ	sinφ	PROPN
ejpam-6091	240	17	)	)	PUNCT
ejpam-6091	240	18	]	]	PUNCT
ejpam-6091	241	1	(	(	PUNCT
ejpam-6091	241	2	px	px	NOUN
ejpam-6091	241	3	cosφ	cosφ	NOUN
ejpam-6091	241	4	)	)	PUNCT
ejpam-6091	241	5	,	,	PUNCT
ejpam-6091	241	6	(	(	PUNCT
ejpam-6091	241	7	122	122	NUM
ejpam-6091	241	8	)	)	PUNCT
ejpam-6091	241	9	k.	k.	PROPN
ejpam-6091	241	10	i.	i.	PROPN
ejpam-6091	241	11	nawafleh	nawafleh	PROPN
ejpam-6091	241	12	/	/	SYM
ejpam-6091	241	13	eur	eur	PROPN
ejpam-6091	241	14	.	.	PUNCT
ejpam-6091	242	1	j.	j.	PROPN
ejpam-6091	242	2	pure	pure	PROPN
ejpam-6091	242	3	appl	appl	PROPN
ejpam-6091	242	4	.	.	PROPN
ejpam-6091	242	5	math	math	PROPN
ejpam-6091	242	6	,	,	PUNCT
ejpam-6091	242	7	18	18	NUM
ejpam-6091	242	8	(	(	PUNCT
ejpam-6091	242	9	3	3	NUM
ejpam-6091	242	10	)	)	PUNCT
ejpam-6091	242	11	(	(	PUNCT
ejpam-6091	242	12	2025	2025	NUM
ejpam-6091	242	13	)	)	PUNCT
ejpam-6091	242	14	,	,	PUNCT
ejpam-6091	242	15	6091	6091	NUM
ejpam-6091	242	16	13	13	NUM
ejpam-6091	242	17	of	of	ADP
ejpam-6091	242	18	15	15	NUM
ejpam-6091	242	19	ẏ	ẏ	NOUN
ejpam-6091	242	20	=	=	SYM
ejpam-6091	243	1	∂h	∂h	PROPN
ejpam-6091	243	2	∂py	∂py	PROPN
ejpam-6091	244	1	=	=	PUNCT
ejpam-6091	244	2	[	[	PUNCT
ejpam-6091	244	3	pφ	pφ	ADP
ejpam-6091	244	4	+	+	NOUN
ejpam-6091	244	5	1	1	NUM
ejpam-6091	244	6	2	2	NUM
ejpam-6091	244	7	(	(	PUNCT
ejpam-6091	244	8	p	p	NOUN
ejpam-6091	244	9	2	2	NUM
ejpam-6091	244	10	x	x	SYM
ejpam-6091	244	11	cosφ−	cosφ−	NOUN
ejpam-6091	244	12	p2y	p2y	NOUN
ejpam-6091	244	13	sinφ	sinφ	PROPN
ejpam-6091	244	14	)	)	PUNCT
ejpam-6091	244	15	]	]	PUNCT
ejpam-6091	244	16	(	(	PUNCT
ejpam-6091	244	17	−py	−py	NOUN
ejpam-6091	244	18	sinφ	sinφ	NOUN
ejpam-6091	244	19	)	)	PUNCT
ejpam-6091	244	20	.	.	PUNCT
ejpam-6091	245	1	(	(	PUNCT
ejpam-6091	245	2	123	123	NUM
ejpam-6091	245	3	)	)	PUNCT
ejpam-6091	245	4	substituting	substitute	VERB
ejpam-6091	245	5	equations	equation	NOUN
ejpam-6091	245	6	(	(	PUNCT
ejpam-6091	245	7	113–115	113–115	NUM
ejpam-6091	245	8	)	)	PUNCT
ejpam-6091	245	9	into	into	ADP
ejpam-6091	245	10	equation	equation	NOUN
ejpam-6091	245	11	(	(	PUNCT
ejpam-6091	245	12	121	121	NUM
ejpam-6091	245	13	)	)	PUNCT
ejpam-6091	245	14	,	,	PUNCT
ejpam-6091	245	15	we	we	PRON
ejpam-6091	245	16	find	find	VERB
ejpam-6091	245	17	φ̇	φ̇	ADV
ejpam-6091	245	18	=	=	PUNCT
ejpam-6091	245	19	[	[	PUNCT
ejpam-6091	245	20	α1	α1	PROPN
ejpam-6091	245	21	−	−	PROPN
ejpam-6091	245	22	1	1	NUM
ejpam-6091	245	23	2	2	NUM
ejpam-6091	245	24	α2	α2	ADJ
ejpam-6091	245	25	2	2	NUM
ejpam-6091	245	26	cosφ+	cosφ+	SYM
ejpam-6091	245	27	1	1	NUM
ejpam-6091	245	28	2	2	NUM
ejpam-6091	245	29	α2	α2	ADJ
ejpam-6091	245	30	3	3	NUM
ejpam-6091	245	31	sinφ+	sinφ+	NOUN
ejpam-6091	245	32	1	1	NUM
ejpam-6091	245	33	2	2	NUM
ejpam-6091	245	34	α2	α2	NOUN
ejpam-6091	245	35	2	2	NUM
ejpam-6091	245	36	cosφ−	cosφ−	NOUN
ejpam-6091	245	37	1	1	NUM
ejpam-6091	245	38	2	2	NUM
ejpam-6091	245	39	α2	α2	NOUN
ejpam-6091	245	40	3	3	NUM
ejpam-6091	245	41	sinφ	sinφ	NOUN
ejpam-6091	245	42	]	]	PUNCT
ejpam-6091	245	43	,	,	PUNCT
ejpam-6091	245	44	or	or	CCONJ
ejpam-6091	245	45	,	,	PUNCT
ejpam-6091	245	46	φ̇	φ̇	ADJ
ejpam-6091	245	47	=	=	SYM
ejpam-6091	245	48	α1	α1	PROPN
ejpam-6091	245	49	.	.	PUNCT
ejpam-6091	246	1	(	(	PUNCT
ejpam-6091	246	2	124	124	NUM
ejpam-6091	246	3	)	)	PUNCT
ejpam-6091	246	4	inserting	insert	VERB
ejpam-6091	246	5	equations	equation	NOUN
ejpam-6091	246	6	(	(	PUNCT
ejpam-6091	246	7	113–115	113–115	NUM
ejpam-6091	246	8	)	)	PUNCT
ejpam-6091	246	9	into	into	ADP
ejpam-6091	246	10	equation	equation	NOUN
ejpam-6091	246	11	(	(	PUNCT
ejpam-6091	246	12	122	122	NUM
ejpam-6091	246	13	)	)	PUNCT
ejpam-6091	246	14	,	,	PUNCT
ejpam-6091	246	15	and	and	CCONJ
ejpam-6091	246	16	using	use	VERB
ejpam-6091	246	17	px	px	X
ejpam-6091	246	18	=	=	SYM
ejpam-6091	246	19	px	px	PROPN
ejpam-6091	246	20	=	=	PROPN
ejpam-6091	246	21	α2	α2	PROPN
ejpam-6091	246	22	:	:	PUNCT
ejpam-6091	246	23	ẋ	ẋ	PROPN
ejpam-6091	247	1	=	=	PUNCT
ejpam-6091	247	2	α1α2	α1α2	PUNCT
ejpam-6091	247	3	cosφ	cosφ	NOUN
ejpam-6091	247	4	or	or	CCONJ
ejpam-6091	247	5	,	,	PUNCT
ejpam-6091	247	6	using	use	VERB
ejpam-6091	247	7	α2	α2	PROPN
ejpam-6091	247	8	=	=	SYM
ejpam-6091	247	9	1	1	NUM
ejpam-6091	247	10	/	/	SYM
ejpam-6091	247	11	α1	α1	PROPN
ejpam-6091	247	12	(	(	PUNCT
ejpam-6091	247	13	from	from	ADP
ejpam-6091	247	14	context	context	NOUN
ejpam-6091	247	15	of	of	ADP
ejpam-6091	247	16	eq	eq	PROPN
ejpam-6091	247	17	.	.	PROPN
ejpam-6091	247	18	102	102	NUM
ejpam-6091	247	19	):	):	PUNCT
ejpam-6091	247	20	ẋ	ẋ	PROPN
ejpam-6091	247	21	=	=	PUNCT
ejpam-6091	247	22	cosφ	cosφ	NOUN
ejpam-6091	247	23	.	.	PUNCT
ejpam-6091	248	1	(	(	PUNCT
ejpam-6091	248	2	125	125	NUM
ejpam-6091	248	3	)	)	PUNCT
ejpam-6091	248	4	substituting	substitute	VERB
ejpam-6091	248	5	equations	equation	NOUN
ejpam-6091	248	6	(	(	PUNCT
ejpam-6091	248	7	113–115	113–115	NUM
ejpam-6091	248	8	)	)	PUNCT
ejpam-6091	248	9	into	into	ADP
ejpam-6091	248	10	equation	equation	NOUN
ejpam-6091	248	11	(	(	PUNCT
ejpam-6091	248	12	123	123	NUM
ejpam-6091	248	13	)	)	PUNCT
ejpam-6091	248	14	,	,	PUNCT
ejpam-6091	248	15	and	and	CCONJ
ejpam-6091	248	16	using	use	VERB
ejpam-6091	248	17	py	py	PROPN
ejpam-6091	248	18	=	=	SYM
ejpam-6091	248	19	α3	α3	NOUN
ejpam-6091	248	20	:	:	PUNCT
ejpam-6091	248	21	ẏ	ẏ	PROPN
ejpam-6091	248	22	=	=	SYM
ejpam-6091	248	23	α1(−α3	α1(−α3	NUM
ejpam-6091	248	24	sinφ	sinφ	NOUN
ejpam-6091	248	25	)	)	PUNCT
ejpam-6091	249	1	=	=	SYM
ejpam-6091	249	2	−α1α3	−α1α3	ADJ
ejpam-6091	249	3	sinφ	sinφ	NOUN
ejpam-6091	249	4	,	,	PUNCT
ejpam-6091	249	5	or	or	CCONJ
ejpam-6091	249	6	,	,	PUNCT
ejpam-6091	249	7	using	use	VERB
ejpam-6091	249	8	α3	α3	NOUN
ejpam-6091	249	9	=	=	SYM
ejpam-6091	249	10	−1	−1	NOUN
ejpam-6091	249	11	/	/	SYM
ejpam-6091	249	12	α1	α1	PROPN
ejpam-6091	249	13	(	(	PUNCT
ejpam-6091	249	14	from	from	ADP
ejpam-6091	249	15	context	context	NOUN
ejpam-6091	249	16	of	of	ADP
ejpam-6091	249	17	eq	eq	PROPN
ejpam-6091	249	18	.	.	PROPN
ejpam-6091	249	19	105	105	NUM
ejpam-6091	249	20	):	):	PUNCT
ejpam-6091	249	21	ẏ	ẏ	PROPN
ejpam-6091	249	22	=	=	SYM
ejpam-6091	249	23	sinφ	sinφ	NOUN
ejpam-6091	249	24	.	.	PUNCT
ejpam-6091	250	1	(	(	PUNCT
ejpam-6091	250	2	126	126	X
ejpam-6091	250	3	)	)	PUNCT
ejpam-6091	250	4	using	use	VERB
ejpam-6091	250	5	equation	equation	NOUN
ejpam-6091	250	6	(	(	PUNCT
ejpam-6091	250	7	15	15	NUM
ejpam-6091	250	8	)	)	PUNCT
ejpam-6091	250	9	,	,	PUNCT
ejpam-6091	250	10	this	this	DET
ejpam-6091	250	11	yields	yield	VERB
ejpam-6091	250	12	:	:	PUNCT
ejpam-6091	250	13	ṗφ	ṗφ	PROPN
ejpam-6091	250	14	=	=	PUNCT
ejpam-6091	250	15	−∂h	−∂h	PROPN
ejpam-6091	250	16	∂φ	∂φ	PROPN
ejpam-6091	251	1	+	+	CCONJ
ejpam-6091	251	2	λ	λ	X
ejpam-6091	251	3	∂f	∂f	PROPN
ejpam-6091	251	4	∂φ̇	∂φ̇	NOUN
ejpam-6091	251	5	,	,	PUNCT
ejpam-6091	251	6	(	(	PUNCT
ejpam-6091	251	7	127	127	NUM
ejpam-6091	251	8	)	)	PUNCT
ejpam-6091	251	9	ṗx	ṗx	PROPN
ejpam-6091	251	10	=	=	SYM
ejpam-6091	251	11	−∂h	−∂h	PROPN
ejpam-6091	251	12	∂x	∂x	PROPN
ejpam-6091	251	13	+	+	CCONJ
ejpam-6091	251	14	λ	λ	PROPN
ejpam-6091	251	15	∂f	∂f	PROPN
ejpam-6091	251	16	∂ẋ	∂ẋ	ADJ
ejpam-6091	251	17	,	,	PUNCT
ejpam-6091	251	18	(	(	PUNCT
ejpam-6091	251	19	128	128	NUM
ejpam-6091	251	20	)	)	PUNCT
ejpam-6091	251	21	ṗy	ṗy	NOUN
ejpam-6091	251	22	=	=	SYM
ejpam-6091	252	1	−∂h	−∂h	PROPN
ejpam-6091	252	2	∂y	∂y	SYM
ejpam-6091	253	1	+	+	PUNCT
ejpam-6091	253	2	λ	λ	X
ejpam-6091	253	3	∂f	∂f	PROPN
ejpam-6091	253	4	∂ẏ	∂ẏ	ADJ
ejpam-6091	253	5	.	.	PUNCT
ejpam-6091	254	1	(	(	PUNCT
ejpam-6091	254	2	129	129	NUM
ejpam-6091	254	3	)	)	PUNCT
ejpam-6091	254	4	these	these	PRON
ejpam-6091	254	5	give	give	VERB
ejpam-6091	254	6	ṗφ	ṗφ	PROPN
ejpam-6091	254	7	=	=	PUNCT
ejpam-6091	254	8	0	0	PROPN
ejpam-6091	254	9	,	,	PUNCT
ejpam-6091	254	10	(	(	PUNCT
ejpam-6091	254	11	130	130	NUM
ejpam-6091	254	12	)	)	PUNCT
ejpam-6091	254	13	ṗx	ṗx	NOUN
ejpam-6091	254	14	=	=	SYM
ejpam-6091	254	15	λ	λ	NOUN
ejpam-6091	254	16	sinφ	sinφ	NOUN
ejpam-6091	254	17	,	,	PUNCT
ejpam-6091	254	18	(	(	PUNCT
ejpam-6091	254	19	131	131	X
ejpam-6091	254	20	)	)	PUNCT
ejpam-6091	255	1	ṗy	ṗy	NOUN
ejpam-6091	255	2	=	=	PUNCT
ejpam-6091	255	3	−λ	−λ	VERB
ejpam-6091	255	4	cosφ	cosφ	NOUN
ejpam-6091	255	5	.	.	PUNCT
ejpam-6091	256	1	(	(	PUNCT
ejpam-6091	256	2	132	132	X
ejpam-6091	256	3	)	)	PUNCT
ejpam-6091	256	4	these	these	DET
ejpam-6091	256	5	equations	equation	NOUN
ejpam-6091	256	6	similar	similar	ADJ
ejpam-6091	256	7	to	to	ADP
ejpam-6091	256	8	equations	equation	NOUN
ejpam-6091	256	9	(	(	PUNCT
ejpam-6091	256	10	91	91	NUM
ejpam-6091	256	11	)	)	PUNCT
ejpam-6091	256	12	,	,	PUNCT
ejpam-6091	256	13	(	(	PUNCT
ejpam-6091	256	14	89	89	NUM
ejpam-6091	256	15	)	)	PUNCT
ejpam-6091	256	16	and	and	CCONJ
ejpam-6091	256	17	(	(	PUNCT
ejpam-6091	256	18	90	90	NUM
ejpam-6091	256	19	)	)	PUNCT
ejpam-6091	256	20	respectively	respectively	ADV
ejpam-6091	256	21	so	so	ADV
ejpam-6091	256	22	:	:	PUNCT
ejpam-6091	256	23	ṗφ	ṗφ	PROPN
ejpam-6091	256	24	=	=	PUNCT
ejpam-6091	256	25	φ̈	φ̈	X
ejpam-6091	256	26	,	,	PUNCT
ejpam-6091	256	27	(	(	PUNCT
ejpam-6091	256	28	133	133	NUM
ejpam-6091	256	29	)	)	PUNCT
ejpam-6091	256	30	ṗx	ṗx	PROPN
ejpam-6091	256	31	=	=	SYM
ejpam-6091	256	32	ẍ	ẍ	PROPN
ejpam-6091	256	33	,	,	PUNCT
ejpam-6091	256	34	(	(	PUNCT
ejpam-6091	256	35	134	134	NUM
ejpam-6091	256	36	)	)	PUNCT
ejpam-6091	256	37	ṗy	ṗy	NOUN
ejpam-6091	256	38	=	=	SYM
ejpam-6091	256	39	ÿ	ÿ	PROPN
ejpam-6091	256	40	.	.	PUNCT
ejpam-6091	257	1	(	(	PUNCT
ejpam-6091	257	2	135	135	NUM
ejpam-6091	257	3	)	)	PUNCT
ejpam-6091	257	4	according	accord	VERB
ejpam-6091	257	5	to	to	ADP
ejpam-6091	257	6	the	the	DET
ejpam-6091	257	7	previous	previous	ADJ
ejpam-6091	257	8	discussion	discussion	NOUN
ejpam-6091	257	9	we	we	PRON
ejpam-6091	257	10	see	see	VERB
ejpam-6091	257	11	that	that	SCONJ
ejpam-6091	257	12	the	the	DET
ejpam-6091	257	13	equations	equation	NOUN
ejpam-6091	257	14	of	of	ADP
ejpam-6091	257	15	motion	motion	NOUN
ejpam-6091	257	16	that	that	PRON
ejpam-6091	257	17	obtained	obtain	VERB
ejpam-6091	257	18	by	by	ADP
ejpam-6091	257	19	the	the	DET
ejpam-6091	257	20	hamilton	hamilton	PROPN
ejpam-6091	257	21	-	-	PUNCT
ejpam-6091	257	22	jacobi	jacobi	PROPN
ejpam-6091	257	23	methods	method	NOUN
ejpam-6091	257	24	are	be	AUX
ejpam-6091	257	25	equivalent	equivalent	ADJ
ejpam-6091	257	26	to	to	ADP
ejpam-6091	257	27	those	those	PRON
ejpam-6091	257	28	obtained	obtain	VERB
ejpam-6091	257	29	by	by	ADP
ejpam-6091	257	30	the	the	DET
ejpam-6091	257	31	lagrange	lagrange	NOUN
ejpam-6091	257	32	-	-	PUNCT
ejpam-6091	257	33	d’alembert	d’alembert	NOUN
ejpam-6091	257	34	principle	principle	NOUN
ejpam-6091	257	35	.	.	PUNCT
ejpam-6091	258	1	k.	k.	PROPN
ejpam-6091	258	2	i.	i.	PROPN
ejpam-6091	258	3	nawafleh	nawafleh	PROPN
ejpam-6091	258	4	/	/	SYM
ejpam-6091	258	5	eur	eur	PROPN
ejpam-6091	258	6	.	.	PUNCT
ejpam-6091	259	1	j.	j.	PROPN
ejpam-6091	259	2	pure	pure	PROPN
ejpam-6091	259	3	appl	appl	PROPN
ejpam-6091	259	4	.	.	PROPN
ejpam-6091	259	5	math	math	PROPN
ejpam-6091	259	6	,	,	PUNCT
ejpam-6091	259	7	18	18	NUM
ejpam-6091	259	8	(	(	PUNCT
ejpam-6091	259	9	3	3	NUM
ejpam-6091	259	10	)	)	PUNCT
ejpam-6091	259	11	(	(	PUNCT
ejpam-6091	259	12	2025	2025	NUM
ejpam-6091	259	13	)	)	PUNCT
ejpam-6091	259	14	,	,	PUNCT
ejpam-6091	259	15	6091	6091	NUM
ejpam-6091	259	16	14	14	NUM
ejpam-6091	259	17	of	of	ADP
ejpam-6091	259	18	15	15	NUM
ejpam-6091	259	19	4	4	NUM
ejpam-6091	259	20	.	.	PUNCT
ejpam-6091	260	1	conclusion	conclusion	NOUN
ejpam-6091	260	2	this	this	DET
ejpam-6091	260	3	work	work	NOUN
ejpam-6091	260	4	shedding	shed	VERB
ejpam-6091	260	5	further	further	ADJ
ejpam-6091	260	6	light	light	NOUN
ejpam-6091	260	7	on	on	ADP
ejpam-6091	260	8	constrained	constrained	ADJ
ejpam-6091	260	9	systems	system	NOUN
ejpam-6091	260	10	of	of	ADP
ejpam-6091	260	11	type	type	NOUN
ejpam-6091	260	12	nonholonomic	nonholonomic	ADJ
ejpam-6091	260	13	constraints	constraint	NOUN
ejpam-6091	260	14	,	,	PUNCT
ejpam-6091	260	15	especially	especially	ADV
ejpam-6091	260	16	on	on	ADP
ejpam-6091	260	17	determining	determine	VERB
ejpam-6091	260	18	the	the	DET
ejpam-6091	260	19	hamilton	hamilton	PROPN
ejpam-6091	260	20	-	-	PUNCT
ejpam-6091	260	21	jacobi	jacobi	PROPN
ejpam-6091	260	22	function	function	PROPN
ejpam-6091	260	23	s.	s.	PROPN
ejpam-6091	260	24	finding	find	VERB
ejpam-6091	260	25	s	s	PRON
ejpam-6091	260	26	enables	enable	VERB
ejpam-6091	260	27	us	we	PRON
ejpam-6091	260	28	to	to	PART
ejpam-6091	260	29	get	get	VERB
ejpam-6091	260	30	the	the	DET
ejpam-6091	260	31	solutions	solution	NOUN
ejpam-6091	260	32	of	of	ADP
ejpam-6091	260	33	the	the	DET
ejpam-6091	260	34	equations	equation	NOUN
ejpam-6091	260	35	of	of	ADP
ejpam-6091	260	36	motion	motion	NOUN
ejpam-6091	260	37	.	.	PUNCT
ejpam-6091	261	1	these	these	DET
ejpam-6091	261	2	solutions	solution	NOUN
ejpam-6091	261	3	are	be	AUX
ejpam-6091	261	4	obtained	obtain	VERB
ejpam-6091	261	5	in	in	ADP
ejpam-6091	261	6	terms	term	NOUN
ejpam-6091	261	7	of	of	ADP
ejpam-6091	261	8	the	the	DET
ejpam-6091	261	9	time	time	NOUN
ejpam-6091	261	10	and	and	CCONJ
ejpam-6091	261	11	the	the	DET
ejpam-6091	261	12	coordinates	coordinate	NOUN
ejpam-6091	261	13	that	that	PRON
ejpam-6091	261	14	correspond	correspond	VERB
ejpam-6091	261	15	to	to	ADP
ejpam-6091	261	16	dependent	dependent	ADJ
ejpam-6091	261	17	momenta	momenta	NOUN
ejpam-6091	261	18	;	;	PUNCT
ejpam-6091	261	19	these	these	PRON
ejpam-6091	261	20	are	be	AUX
ejpam-6091	261	21	treated	treat	VERB
ejpam-6091	261	22	as	as	ADP
ejpam-6091	261	23	independent	independent	ADJ
ejpam-6091	261	24	variables	variable	NOUN
ejpam-6091	261	25	,	,	PUNCT
ejpam-6091	261	26	just	just	ADV
ejpam-6091	261	27	like	like	ADP
ejpam-6091	261	28	the	the	DET
ejpam-6091	261	29	time	time	NOUN
ejpam-6091	261	30	t.	t.	PROPN
ejpam-6091	261	31	this	this	PRON
ejpam-6091	261	32	is	be	AUX
ejpam-6091	261	33	followed	follow	VERB
ejpam-6091	261	34	by	by	ADP
ejpam-6091	261	35	determining	determine	VERB
ejpam-6091	261	36	a	a	DET
ejpam-6091	261	37	new	new	ADJ
ejpam-6091	261	38	method	method	NOUN
ejpam-6091	261	39	to	to	PART
ejpam-6091	261	40	integrate	integrate	VERB
ejpam-6091	261	41	the	the	DET
ejpam-6091	261	42	dynamical	dynamical	ADJ
ejpam-6091	261	43	equations	equation	NOUN
ejpam-6091	261	44	in	in	ADP
ejpam-6091	261	45	particular	particular	ADJ
ejpam-6091	261	46	,	,	PUNCT
ejpam-6091	261	47	nonholonomic	nonholonomic	ADJ
ejpam-6091	261	48	systems	system	NOUN
ejpam-6091	261	49	.	.	PUNCT
ejpam-6091	262	1	we	we	PRON
ejpam-6091	262	2	obtain	obtain	VERB
ejpam-6091	262	3	the	the	DET
ejpam-6091	262	4	equations	equation	NOUN
ejpam-6091	262	5	of	of	ADP
ejpam-6091	262	6	motion	motion	NOUN
ejpam-6091	262	7	for	for	ADP
ejpam-6091	262	8	a	a	DET
ejpam-6091	262	9	lagrangian	lagrangian	ADJ
ejpam-6091	262	10	system	system	NOUN
ejpam-6091	262	11	with	with	ADP
ejpam-6091	262	12	nonholonomic	nonholonomic	ADJ
ejpam-6091	262	13	constraints	constraint	NOUN
ejpam-6091	262	14	making	make	VERB
ejpam-6091	262	15	use	use	NOUN
ejpam-6091	262	16	of	of	ADP
ejpam-6091	262	17	the	the	DET
ejpam-6091	262	18	d’alembert	d’alembert	NOUN
ejpam-6091	262	19	principle	principle	NOUN
ejpam-6091	262	20	.	.	PUNCT
ejpam-6091	263	1	it	it	PRON
ejpam-6091	263	2	is	be	AUX
ejpam-6091	263	3	shown	show	VERB
ejpam-6091	263	4	that	that	SCONJ
ejpam-6091	263	5	the	the	DET
ejpam-6091	263	6	results	result	NOUN
ejpam-6091	263	7	obtained	obtain	VERB
ejpam-6091	263	8	using	use	VERB
ejpam-6091	263	9	the	the	DET
ejpam-6091	263	10	hamiltonjacobi	hamiltonjacobi	NOUN
ejpam-6091	263	11	method	method	NOUN
ejpam-6091	263	12	are	be	AUX
ejpam-6091	263	13	equivalent	equivalent	ADJ
ejpam-6091	263	14	to	to	ADP
ejpam-6091	263	15	those	those	PRON
ejpam-6091	263	16	obtained	obtain	VERB
ejpam-6091	263	17	by	by	ADP
ejpam-6091	263	18	the	the	DET
ejpam-6091	263	19	lagrange	lagrange	NOUN
ejpam-6091	263	20	-	-	PUNCT
ejpam-6091	263	21	d’alembert	d’alembert	NOUN
ejpam-6091	263	22	principle	principle	NOUN
ejpam-6091	263	23	.	.	PUNCT
ejpam-6091	264	1	the	the	DET
ejpam-6091	264	2	method	method	NOUN
ejpam-6091	264	3	is	be	AUX
ejpam-6091	264	4	applied	apply	VERB
ejpam-6091	264	5	for	for	ADP
ejpam-6091	264	6	two	two	NUM
ejpam-6091	264	7	examples	example	NOUN
ejpam-6091	264	8	:	:	PUNCT
ejpam-6091	264	9	the	the	DET
ejpam-6091	264	10	first	first	ADJ
ejpam-6091	264	11	one	one	NOUN
ejpam-6091	264	12	is	be	AUX
ejpam-6091	264	13	the	the	DET
ejpam-6091	264	14	motion	motion	NOUN
ejpam-6091	264	15	of	of	ADP
ejpam-6091	264	16	a	a	DET
ejpam-6091	264	17	flat	flat	ADJ
ejpam-6091	264	18	uniform	uniform	NOUN
ejpam-6091	264	19	disk	disk	NOUN
ejpam-6091	264	20	rolls	roll	NOUN
ejpam-6091	264	21	upright	upright	ADJ
ejpam-6091	264	22	without	without	ADP
ejpam-6091	264	23	slipping	slip	VERB
ejpam-6091	264	24	on	on	ADP
ejpam-6091	264	25	horizontal	horizontal	ADJ
ejpam-6091	264	26	plane	plane	NOUN
ejpam-6091	264	27	,	,	PUNCT
ejpam-6091	264	28	and	and	CCONJ
ejpam-6091	264	29	the	the	DET
ejpam-6091	264	30	second	second	ADJ
ejpam-6091	264	31	one	one	NOUN
ejpam-6091	264	32	is	be	AUX
ejpam-6091	264	33	the	the	DET
ejpam-6091	264	34	motion	motion	NOUN
ejpam-6091	264	35	of	of	ADP
ejpam-6091	264	36	a	a	DET
ejpam-6091	264	37	knife	knife	NOUN
ejpam-6091	264	38	edge	edge	NOUN
ejpam-6091	264	39	on	on	ADP
ejpam-6091	264	40	an	an	DET
ejpam-6091	264	41	inclined	inclined	ADJ
ejpam-6091	264	42	plane	plane	NOUN
ejpam-6091	264	43	.	.	PUNCT
ejpam-6091	265	1	references	reference	NOUN
ejpam-6091	265	2	[	[	X
ejpam-6091	265	3	1	1	NUM
ejpam-6091	265	4	]	]	PUNCT
ejpam-6091	265	5	l.	l.	PROPN
ejpam-6091	265	6	bates	bates	PROPN
ejpam-6091	265	7	and	and	CCONJ
ejpam-6091	265	8	j.	j.	PROPN
ejpam-6091	265	9	sniatycki	sniatycki	PROPN
ejpam-6091	265	10	.	.	PUNCT
ejpam-6091	266	1	nonholonomic	nonholonomic	ADJ
ejpam-6091	266	2	reduction	reduction	NOUN
ejpam-6091	266	3	.	.	PUNCT
ejpam-6091	267	1	reports	report	NOUN
ejpam-6091	267	2	on	on	ADP
ejpam-6091	267	3	mathematical	mathematical	ADJ
ejpam-6091	267	4	physics	physics	NOUN
ejpam-6091	267	5	,	,	PUNCT
ejpam-6091	267	6	32:99	32:99	NUM
ejpam-6091	267	7	,	,	PUNCT
ejpam-6091	267	8	1993	1993	NUM
ejpam-6091	267	9	.	.	PUNCT
ejpam-6091	268	1	[	[	X
ejpam-6091	268	2	2	2	NUM
ejpam-6091	268	3	]	]	PUNCT
ejpam-6091	268	4	a.	a.	NOUN
ejpam-6091	268	5	m.	m.	PROPN
ejpam-6091	268	6	bloch	bloch	PROPN
ejpam-6091	268	7	.	.	PUNCT
ejpam-6091	269	1	nonholonomic	nonholonomic	ADJ
ejpam-6091	269	2	mechanics	mechanic	NOUN
ejpam-6091	269	3	and	and	CCONJ
ejpam-6091	269	4	control	control	NOUN
ejpam-6091	269	5	.	.	PUNCT
ejpam-6091	270	1	springer	springer	PROPN
ejpam-6091	270	2	verlag	verlag	PROPN
ejpam-6091	270	3	,	,	PUNCT
ejpam-6091	270	4	2003	2003	NUM
ejpam-6091	270	5	.	.	PUNCT
ejpam-6091	271	1	[	[	X
ejpam-6091	271	2	3	3	NUM
ejpam-6091	271	3	]	]	PUNCT
ejpam-6091	271	4	a.	a.	NOUN
ejpam-6091	271	5	j.	j.	PROPN
ejpam-6091	271	6	van	van	PROPN
ejpam-6091	271	7	der	der	PROPN
ejpam-6091	271	8	schaft	schaft	NOUN
ejpam-6091	271	9	and	and	CCONJ
ejpam-6091	271	10	b.	b.	PROPN
ejpam-6091	271	11	m.	m.	PROPN
ejpam-6091	271	12	maschke	maschke	PROPN
ejpam-6091	271	13	.	.	PUNCT
ejpam-6091	272	1	on	on	ADP
ejpam-6091	272	2	the	the	DET
ejpam-6091	272	3	hamiltonian	hamiltonian	ADJ
ejpam-6091	272	4	formulation	formulation	NOUN
ejpam-6091	272	5	of	of	ADP
ejpam-6091	272	6	nonholonomic	nonholonomic	ADJ
ejpam-6091	272	7	mechanical	mechanical	ADJ
ejpam-6091	272	8	systems	system	NOUN
ejpam-6091	272	9	.	.	PUNCT
ejpam-6091	273	1	reports	report	NOUN
ejpam-6091	273	2	on	on	ADP
ejpam-6091	273	3	mathematical	mathematical	ADJ
ejpam-6091	273	4	physics	physics	NOUN
ejpam-6091	273	5	,	,	PUNCT
ejpam-6091	273	6	34:225	34:225	PROPN
ejpam-6091	273	7	,	,	PUNCT
ejpam-6091	273	8	1994	1994	NUM
ejpam-6091	273	9	.	.	PUNCT
ejpam-6091	274	1	[	[	X
ejpam-6091	274	2	4	4	X
ejpam-6091	274	3	]	]	PUNCT
ejpam-6091	274	4	l.	l.	PROPN
ejpam-6091	274	5	lur’e	lur’e	PROPN
ejpam-6091	274	6	.	.	PUNCT
ejpam-6091	275	1	mecanique	mecanique	PROPN
ejpam-6091	275	2	analytique	analytique	PROPN
ejpam-6091	275	3	.	.	PUNCT
ejpam-6091	276	1	librairie	librairie	PROPN
ejpam-6091	276	2	universitaire	universitaire	PROPN
ejpam-6091	276	3	,	,	PUNCT
ejpam-6091	276	4	louvain	louvain	NOUN
ejpam-6091	276	5	,	,	PUNCT
ejpam-6091	276	6	1968	1968	NUM
ejpam-6091	276	7	.	.	PUNCT
ejpam-6091	277	1	[	[	X
ejpam-6091	277	2	5	5	NUM
ejpam-6091	277	3	]	]	PUNCT
ejpam-6091	277	4	a.	a.	NOUN
ejpam-6091	277	5	m.	m.	PROPN
ejpam-6091	277	6	bloch	bloch	PROPN
ejpam-6091	277	7	,	,	PUNCT
ejpam-6091	277	8	o.	o.	PROPN
ejpam-6091	277	9	e.	e.	PROPN
ejpam-6091	277	10	fernandez	fernandez	PROPN
ejpam-6091	277	11	,	,	PUNCT
ejpam-6091	277	12	and	and	CCONJ
ejpam-6091	277	13	t.	t.	PROPN
ejpam-6091	277	14	mestdag	mestdag	PROPN
ejpam-6091	277	15	.	.	PUNCT
ejpam-6091	278	1	hamiltonization	hamiltonization	NOUN
ejpam-6091	278	2	of	of	ADP
ejpam-6091	278	3	nonholonomic	nonholonomic	ADJ
ejpam-6091	278	4	systems	system	NOUN
ejpam-6091	278	5	and	and	CCONJ
ejpam-6091	278	6	the	the	DET
ejpam-6091	278	7	inverse	inverse	NOUN
ejpam-6091	278	8	problem	problem	NOUN
ejpam-6091	278	9	of	of	ADP
ejpam-6091	278	10	the	the	DET
ejpam-6091	278	11	calculus	calculus	NOUN
ejpam-6091	278	12	of	of	ADP
ejpam-6091	278	13	variations	variation	NOUN
ejpam-6091	278	14	.	.	PUNCT
ejpam-6091	279	1	reports	report	NOUN
ejpam-6091	279	2	on	on	ADP
ejpam-6091	279	3	mathematical	mathematical	ADJ
ejpam-6091	279	4	physics	physics	NOUN
ejpam-6091	279	5	,	,	PUNCT
ejpam-6091	279	6	63:225	63:225	PROPN
ejpam-6091	279	7	,	,	PUNCT
ejpam-6091	279	8	2009	2009	NUM
ejpam-6091	279	9	.	.	PUNCT
ejpam-6091	280	1	[	[	X
ejpam-6091	280	2	6	6	NUM
ejpam-6091	280	3	]	]	PUNCT
ejpam-6091	280	4	j.	j.	PROPN
ejpam-6091	280	5	i.	i.	PROPN
ejpam-6091	280	6	neimark	neimark	PROPN
ejpam-6091	280	7	and	and	CCONJ
ejpam-6091	280	8	n.	n.	PROPN
ejpam-6091	280	9	a.	a.	NOUN
ejpam-6091	280	10	fufaev	fufaev	PROPN
ejpam-6091	280	11	.	.	PUNCT
ejpam-6091	281	1	dynamics	dynamic	NOUN
ejpam-6091	281	2	of	of	ADP
ejpam-6091	281	3	nonholonomic	nonholonomic	ADJ
ejpam-6091	281	4	systems	system	NOUN
ejpam-6091	281	5	,	,	PUNCT
ejpam-6091	281	6	volume	volume	NOUN
ejpam-6091	281	7	33	33	NUM
ejpam-6091	281	8	of	of	ADP
ejpam-6091	281	9	translations	translation	NOUN
ejpam-6091	281	10	of	of	ADP
ejpam-6091	281	11	mathematical	mathematical	ADJ
ejpam-6091	281	12	monographs	monograph	NOUN
ejpam-6091	281	13	.	.	PUNCT
ejpam-6091	282	1	american	american	PROPN
ejpam-6091	282	2	mathematical	mathematical	PROPN
ejpam-6091	282	3	society	society	NOUN
ejpam-6091	282	4	,	,	PUNCT
ejpam-6091	282	5	providence	providence	NOUN
ejpam-6091	282	6	,	,	PUNCT
ejpam-6091	282	7	ri	ri	PROPN
ejpam-6091	282	8	,	,	PUNCT
ejpam-6091	282	9	1967	1967	NUM
ejpam-6091	282	10	.	.	PUNCT
ejpam-6091	283	1	[	[	X
ejpam-6091	283	2	7	7	X
ejpam-6091	283	3	]	]	X
ejpam-6091	283	4	t.	t.	NOUN
ejpam-6091	283	5	ohsawa	ohsawa	PROPN
ejpam-6091	283	6	,	,	PUNCT
ejpam-6091	283	7	a.	a.	NOUN
ejpam-6091	283	8	m.	m.	PROPN
ejpam-6091	283	9	bloch	bloch	PROPN
ejpam-6091	283	10	,	,	PUNCT
ejpam-6091	283	11	and	and	CCONJ
ejpam-6091	283	12	m.	m.	NOUN
ejpam-6091	283	13	leok	leok	PROPN
ejpam-6091	283	14	.	.	PUNCT
ejpam-6091	284	1	nonholonomic	nonholonomic	PROPN
ejpam-6091	284	2	hamilton	hamilton	PROPN
ejpam-6091	284	3	-	-	PUNCT
ejpam-6091	284	4	jacobi	jacobi	PROPN
ejpam-6091	284	5	theory	theory	NOUN
ejpam-6091	284	6	,	,	PUNCT
ejpam-6091	284	7	2009	2009	NUM
ejpam-6091	284	8	.	.	PUNCT
ejpam-6091	285	1	arxiv	arxiv	PROPN
ejpam-6091	285	2	preprint	preprint	VERB
ejpam-6091	285	3	arxiv:0911.2258	arxiv:0911.2258	PROPN
ejpam-6091	285	4	.	.	PUNCT
ejpam-6091	286	1	[	[	X
ejpam-6091	286	2	8	8	NUM
ejpam-6091	286	3	]	]	X
ejpam-6091	286	4	l.	l.	PROPN
ejpam-6091	286	5	a.	a.	PROPN
ejpam-6091	286	6	pars	pars	PROPN
ejpam-6091	286	7	.	.	PUNCT
ejpam-6091	287	1	a	a	DET
ejpam-6091	287	2	treatise	treatise	NOUN
ejpam-6091	287	3	on	on	ADP
ejpam-6091	287	4	analytical	analytical	ADJ
ejpam-6091	287	5	dynamics	dynamic	NOUN
ejpam-6091	287	6	.	.	PUNCT
ejpam-6091	288	1	heinemann	heinemann	PROPN
ejpam-6091	288	2	,	,	PUNCT
ejpam-6091	288	3	london	london	PROPN
ejpam-6091	288	4	,	,	PUNCT
ejpam-6091	288	5	1965	1965	NUM
ejpam-6091	288	6	.	.	PUNCT
ejpam-6091	289	1	[	[	X
ejpam-6091	289	2	9	9	NUM
ejpam-6091	289	3	]	]	PUNCT
ejpam-6091	289	4	rene	rene	NOUN
ejpam-6091	289	5	van	van	PROPN
ejpam-6091	289	6	dooren	dooren	PROPN
ejpam-6091	289	7	.	.	PUNCT
ejpam-6091	290	1	second	second	ADJ
ejpam-6091	290	2	form	form	NOUN
ejpam-6091	290	3	of	of	ADP
ejpam-6091	290	4	the	the	DET
ejpam-6091	290	5	generalized	generalize	VERB
ejpam-6091	290	6	hamilton	hamilton	PROPN
ejpam-6091	290	7	-	-	PUNCT
ejpam-6091	290	8	jacobi	jacobi	PROPN
ejpam-6091	290	9	method	method	NOUN
ejpam-6091	290	10	for	for	ADP
ejpam-6091	290	11	nonholonomic	nonholonomic	ADJ
ejpam-6091	290	12	dynamical	dynamical	ADJ
ejpam-6091	290	13	systems	system	NOUN
ejpam-6091	290	14	.	.	PUNCT
ejpam-6091	291	1	journal	journal	NOUN
ejpam-6091	291	2	of	of	ADP
ejpam-6091	291	3	applied	apply	VERB
ejpam-6091	291	4	mathematics	mathematic	NOUN
ejpam-6091	291	5	and	and	CCONJ
ejpam-6091	291	6	physics	physics	NOUN
ejpam-6091	291	7	(	(	PUNCT
ejpam-6091	291	8	zamp	zamp	PROPN
ejpam-6091	291	9	)	)	PUNCT
ejpam-6091	291	10	,	,	PUNCT
ejpam-6091	291	11	1978	1978	NUM
ejpam-6091	291	12	.	.	PUNCT
ejpam-6091	292	1	[	[	X
ejpam-6091	292	2	10	10	NUM
ejpam-6091	292	3	]	]	X
ejpam-6091	292	4	e.	e.	PROPN
ejpam-6091	292	5	j.	j.	PROPN
ejpam-6091	292	6	saletan	saletan	PROPN
ejpam-6091	292	7	and	and	CCONJ
ejpam-6091	292	8	a.	a.	PROPN
ejpam-6091	292	9	h.	h.	PROPN
ejpam-6091	292	10	cromer	cromer	PROPN
ejpam-6091	292	11	.	.	PUNCT
ejpam-6091	293	1	a	a	DET
ejpam-6091	293	2	variational	variational	ADJ
ejpam-6091	293	3	principle	principle	NOUN
ejpam-6091	293	4	for	for	ADP
ejpam-6091	293	5	nonholonomic	nonholonomic	ADJ
ejpam-6091	293	6	systems	system	NOUN
ejpam-6091	293	7	.	.	PUNCT
ejpam-6091	294	1	american	american	PROPN
ejpam-6091	294	2	journal	journal	PROPN
ejpam-6091	294	3	of	of	ADP
ejpam-6091	294	4	physics	physics	PROPN
ejpam-6091	294	5	,	,	PUNCT
ejpam-6091	294	6	38(7):892	38(7):892	PROPN
ejpam-6091	294	7	,	,	PUNCT
ejpam-6091	294	8	1970	1970	NUM
ejpam-6091	294	9	.	.	PUNCT
ejpam-6091	295	1	[	[	X
ejpam-6091	295	2	11	11	NUM
ejpam-6091	295	3	]	]	PUNCT
ejpam-6091	295	4	q.	q.	PROPN
ejpam-6091	295	5	k.	k.	PROPN
ejpam-6091	295	6	ghori	ghori	PROPN
ejpam-6091	295	7	.	.	PUNCT
ejpam-6091	296	1	a	a	DET
ejpam-6091	296	2	hamiltonian	hamiltonian	ADJ
ejpam-6091	296	3	approach	approach	NOUN
ejpam-6091	296	4	to	to	ADP
ejpam-6091	296	5	nonholonomic	nonholonomic	ADJ
ejpam-6091	296	6	systems	system	NOUN
ejpam-6091	296	7	.	.	PUNCT
ejpam-6091	297	1	journal	journal	PROPN
ejpam-6091	297	2	of	of	ADP
ejpam-6091	297	3	applied	apply	VERB
ejpam-6091	297	4	mathematics	mathematic	NOUN
ejpam-6091	297	5	and	and	CCONJ
ejpam-6091	297	6	physics	physics	NOUN
ejpam-6091	297	7	(	(	PUNCT
ejpam-6091	297	8	zamp	zamp	NOUN
ejpam-6091	297	9	)	)	PUNCT
ejpam-6091	297	10	,	,	PUNCT
ejpam-6091	297	11	50:563	50:563	NUM
ejpam-6091	297	12	,	,	PUNCT
ejpam-6091	297	13	1970	1970	NUM
ejpam-6091	297	14	.	.	PUNCT
ejpam-6091	298	1	[	[	X
ejpam-6091	298	2	12	12	NUM
ejpam-6091	298	3	]	]	PUNCT
ejpam-6091	298	4	e.	e.	PROPN
ejpam-6091	298	5	k.	k.	PROPN
ejpam-6091	298	6	nzaziev	nzaziev	PROPN
ejpam-6091	298	7	.	.	PUNCT
ejpam-6091	299	1	on	on	ADP
ejpam-6091	299	2	motion	motion	NOUN
ejpam-6091	299	3	of	of	ADP
ejpam-6091	299	4	nonholonomic	nonholonomic	ADJ
ejpam-6091	299	5	systems	system	NOUN
ejpam-6091	299	6	.	.	PUNCT
ejpam-6091	300	1	prikl	prikl	VERB
ejpam-6091	300	2	.	.	PUNCT
ejpam-6091	301	1	mat	mat	PROPN
ejpam-6091	301	2	.	.	PUNCT
ejpam-6091	301	3	mek	mek	PROPN
ejpam-6091	301	4	.	.	PROPN
ejpam-6091	301	5	,	,	PUNCT
ejpam-6091	301	6	36:1108	36:1108	NUM
ejpam-6091	301	7	,	,	PUNCT
ejpam-6091	301	8	1972	1972	NUM
ejpam-6091	301	9	.	.	PUNCT
ejpam-6091	302	1	[	[	X
ejpam-6091	302	2	13	13	NUM
ejpam-6091	302	3	]	]	PUNCT
ejpam-6091	302	4	m.	m.	NOUN
ejpam-6091	302	5	abud	abud	PROPN
ejpam-6091	302	6	,	,	PUNCT
ejpam-6091	302	7	l.	l.	PROPN
ejpam-6091	302	8	c.	c.	PROPN
ejpam-6091	302	9	gomes	gomes	PROPN
ejpam-6091	302	10	,	,	PUNCT
ejpam-6091	302	11	and	and	CCONJ
ejpam-6091	302	12	f.	f.	PROPN
ejpam-6091	302	13	r.	r.	PROPN
ejpam-6091	302	14	a.	a.	PROPN
ejpam-6091	302	15	simao	simao	PROPN
ejpam-6091	302	16	.	.	PUNCT
ejpam-6091	303	1	the	the	DET
ejpam-6091	303	2	quantization	quantization	NOUN
ejpam-6091	303	3	of	of	ADP
ejpam-6091	303	4	classical	classical	ADJ
ejpam-6091	303	5	nonholonomic	nonholonomic	ADJ
ejpam-6091	303	6	systems	system	NOUN
ejpam-6091	303	7	.	.	PUNCT
ejpam-6091	304	1	revista	revista	PROPN
ejpam-6091	304	2	brasileira	brasileira	PROPN
ejpam-6091	304	3	de	de	PROPN
ejpam-6091	304	4	fisica	fisica	PROPN
ejpam-6091	304	5	,	,	PUNCT
ejpam-6091	304	6	13(2	13(2	PROPN
ejpam-6091	304	7	)	)	PUNCT
ejpam-6091	304	8	,	,	PUNCT
ejpam-6091	304	9	1983	1983	NUM
ejpam-6091	304	10	.	.	PUNCT
ejpam-6091	305	1	k.	k.	PROPN
ejpam-6091	305	2	i.	i.	PROPN
ejpam-6091	305	3	nawafleh	nawafleh	PROPN
ejpam-6091	305	4	/	/	SYM
ejpam-6091	305	5	eur	eur	PROPN
ejpam-6091	305	6	.	.	PUNCT
ejpam-6091	306	1	j.	j.	PROPN
ejpam-6091	306	2	pure	pure	PROPN
ejpam-6091	306	3	appl	appl	PROPN
ejpam-6091	306	4	.	.	PROPN
ejpam-6091	306	5	math	math	PROPN
ejpam-6091	306	6	,	,	PUNCT
ejpam-6091	306	7	18	18	NUM
ejpam-6091	306	8	(	(	PUNCT
ejpam-6091	306	9	3	3	NUM
ejpam-6091	306	10	)	)	PUNCT
ejpam-6091	306	11	(	(	PUNCT
ejpam-6091	306	12	2025	2025	NUM
ejpam-6091	306	13	)	)	PUNCT
ejpam-6091	306	14	,	,	PUNCT
ejpam-6091	306	15	6091	6091	NUM
ejpam-6091	306	16	15	15	NUM
ejpam-6091	306	17	of	of	ADP
ejpam-6091	306	18	15	15	NUM
ejpam-6091	306	19	[	[	SYM
ejpam-6091	306	20	14	14	NUM
ejpam-6091	306	21	]	]	PUNCT
ejpam-6091	306	22	rene	rene	PROPN
ejpam-6091	306	23	van	van	PROPN
ejpam-6091	306	24	dooren	dooren	PROPN
ejpam-6091	306	25	.	.	PUNCT
ejpam-6091	307	1	motion	motion	NOUN
ejpam-6091	307	2	of	of	ADP
ejpam-6091	307	3	a	a	DET
ejpam-6091	307	4	rolling	rolling	ADJ
ejpam-6091	307	5	disk	disk	NOUN
ejpam-6091	307	6	by	by	ADP
ejpam-6091	307	7	a	a	DET
ejpam-6091	307	8	new	new	ADJ
ejpam-6091	307	9	generalized	generalized	ADJ
ejpam-6091	307	10	hamilton	hamilton	PROPN
ejpam-6091	307	11	-	-	PUNCT
ejpam-6091	307	12	jacobi	jacobi	PROPN
ejpam-6091	307	13	method	method	PROPN
ejpam-6091	307	14	.	.	PUNCT
ejpam-6091	308	1	journal	journal	PROPN
ejpam-6091	308	2	of	of	ADP
ejpam-6091	308	3	applied	apply	VERB
ejpam-6091	308	4	mathematics	mathematic	NOUN
ejpam-6091	308	5	and	and	CCONJ
ejpam-6091	308	6	physics	physics	NOUN
ejpam-6091	308	7	(	(	PUNCT
ejpam-6091	308	8	zamp	zamp	PROPN
ejpam-6091	308	9	)	)	PUNCT
ejpam-6091	308	10	,	,	PUNCT
ejpam-6091	308	11	1976	1976	NUM
ejpam-6091	308	12	.	.	PUNCT
ejpam-6091	309	1	[	[	X
ejpam-6091	309	2	15	15	NUM
ejpam-6091	309	3	]	]	X
ejpam-6091	309	4	j.	j.	PROPN
ejpam-6091	309	5	i.	i.	PROPN
ejpam-6091	309	6	neimark	neimark	PROPN
ejpam-6091	309	7	and	and	CCONJ
ejpam-6091	309	8	n.	n.	PROPN
ejpam-6091	309	9	a.	a.	NOUN
ejpam-6091	309	10	fufaev	fufaev	PROPN
ejpam-6091	309	11	.	.	PUNCT
ejpam-6091	310	1	dynamics	dynamic	NOUN
ejpam-6091	310	2	of	of	ADP
ejpam-6091	310	3	nonholonomic	nonholonomic	ADJ
ejpam-6091	310	4	systems	system	NOUN
ejpam-6091	310	5	,	,	PUNCT
ejpam-6091	310	6	volume	volume	NOUN
ejpam-6091	310	7	33	33	NUM
ejpam-6091	310	8	of	of	ADP
ejpam-6091	310	9	translations	translation	NOUN
ejpam-6091	310	10	of	of	ADP
ejpam-6091	310	11	mathematical	mathematical	ADJ
ejpam-6091	310	12	monographs	monograph	NOUN
ejpam-6091	310	13	.	.	PUNCT
ejpam-6091	311	1	american	american	PROPN
ejpam-6091	311	2	mathematical	mathematical	PROPN
ejpam-6091	311	3	society	society	NOUN
ejpam-6091	311	4	,	,	PUNCT
ejpam-6091	311	5	providence	providence	NOUN
ejpam-6091	311	6	,	,	PUNCT
ejpam-6091	311	7	ri	ri	PROPN
ejpam-6091	311	8	,	,	PUNCT
ejpam-6091	311	9	1972	1972	NUM
ejpam-6091	311	10	.	.	PUNCT
ejpam-6091	312	1	[	[	X
ejpam-6091	312	2	16	16	X
ejpam-6091	312	3	]	]	PUNCT
ejpam-6091	312	4	v.	v.	PROPN
ejpam-6091	312	5	e.	e.	PROPN
ejpam-6091	312	6	tarasov	tarasov	PROPN
ejpam-6091	312	7	and	and	CCONJ
ejpam-6091	312	8	g.	g.	PROPN
ejpam-6091	312	9	m.	m.	PROPN
ejpam-6091	312	10	zaslavsky	zaslavsky	PROPN
ejpam-6091	312	11	.	.	PUNCT
ejpam-6091	313	1	dynamics	dynamic	NOUN
ejpam-6091	313	2	with	with	ADP
ejpam-6091	313	3	low	low	ADJ
ejpam-6091	313	4	-	-	PUNCT
ejpam-6091	313	5	level	level	NOUN
ejpam-6091	313	6	fractionality	fractionality	NOUN
ejpam-6091	313	7	.	.	PUNCT
ejpam-6091	314	1	journal	journal	PROPN
ejpam-6091	314	2	of	of	ADP
ejpam-6091	314	3	physics	physics	PROPN
ejpam-6091	314	4	a	a	PRON
ejpam-6091	314	5	:	:	PUNCT
ejpam-6091	314	6	mathematical	mathematical	ADJ
ejpam-6091	314	7	and	and	CCONJ
ejpam-6091	314	8	general	general	ADJ
ejpam-6091	314	9	,	,	PUNCT
ejpam-6091	314	10	39(31):9629	39(31):9629	NUM
ejpam-6091	314	11	,	,	PUNCT
ejpam-6091	314	12	2006	2006	NUM
ejpam-6091	314	13	.	.	PUNCT
ejpam-6091	315	1	[	[	X
ejpam-6091	315	2	17	17	NUM
ejpam-6091	315	3	]	]	X
ejpam-6091	315	4	e.	e.	PROPN
ejpam-6091	315	5	m.	m.	PROPN
ejpam-6091	315	6	rabei	rabei	PROPN
ejpam-6091	315	7	,	,	PUNCT
ejpam-6091	315	8	k.	k.	PROPN
ejpam-6091	315	9	i.	i.	PROPN
ejpam-6091	315	10	nawafleh	nawafleh	PROPN
ejpam-6091	315	11	,	,	PUNCT
ejpam-6091	315	12	and	and	CCONJ
ejpam-6091	315	13	h.	h.	PROPN
ejpam-6091	315	14	b.	b.	PROPN
ejpam-6091	315	15	ghassib	ghassib	PROPN
ejpam-6091	315	16	.	.	PUNCT
ejpam-6091	316	1	quantization	quantization	NOUN
ejpam-6091	316	2	of	of	ADP
ejpam-6091	316	3	constrained	constrained	ADJ
ejpam-6091	316	4	systems	system	NOUN
ejpam-6091	316	5	using	use	VERB
ejpam-6091	316	6	the	the	DET
ejpam-6091	316	7	wkb	wkb	NOUN
ejpam-6091	316	8	approximation	approximation	NOUN
ejpam-6091	316	9	.	.	PUNCT
ejpam-6091	317	1	physical	physical	ADJ
ejpam-6091	317	2	review	review	PROPN
ejpam-6091	317	3	a	a	PRON
ejpam-6091	317	4	,	,	PUNCT
ejpam-6091	317	5	66:024101	66:024101	NUM
ejpam-6091	317	6	,	,	PUNCT
ejpam-6091	317	7	2002	2002	NUM
ejpam-6091	317	8	.	.	PUNCT
ejpam-6091	318	1	[	[	X
ejpam-6091	318	2	18	18	NUM
ejpam-6091	318	3	]	]	X
ejpam-6091	318	4	khaled	khaled	PROPN
ejpam-6091	318	5	i.	i.	PROPN
ejpam-6091	318	6	nawafleh	nawafleh	PROPN
ejpam-6091	318	7	,	,	PUNCT
ejpam-6091	318	8	eqab	eqab	NOUN
ejpam-6091	318	9	m.	m.	NOUN
ejpam-6091	318	10	rabei	rabei	NOUN
ejpam-6091	318	11	,	,	PUNCT
ejpam-6091	318	12	and	and	CCONJ
ejpam-6091	318	13	humam	humam	PROPN
ejpam-6091	318	14	b.	b.	PROPN
ejpam-6091	318	15	ghassib	ghassib	PROPN
ejpam-6091	318	16	.	.	PUNCT
ejpam-6091	319	1	quantization	quantization	NOUN
ejpam-6091	319	2	of	of	ADP
ejpam-6091	319	3	singular	singular	ADJ
ejpam-6091	319	4	systems	system	NOUN
ejpam-6091	319	5	using	use	VERB
ejpam-6091	319	6	canonical	canonical	ADJ
ejpam-6091	319	7	transformations	transformation	NOUN
ejpam-6091	319	8	.	.	PUNCT
ejpam-6091	320	1	international	international	ADJ
ejpam-6091	320	2	journal	journal	NOUN
ejpam-6091	320	3	of	of	ADP
ejpam-6091	320	4	modern	modern	ADJ
ejpam-6091	320	5	physics	physics	PROPN
ejpam-6091	320	6	a	a	PRON
ejpam-6091	320	7	,	,	PUNCT
ejpam-6091	320	8	19:347–354	19:347–354	PROPN
ejpam-6091	320	9	,	,	PUNCT
ejpam-6091	320	10	2004	2004	NUM
ejpam-6091	320	11	.	.	PUNCT
ejpam-6091	321	1	[	[	X
ejpam-6091	321	2	19	19	NUM
ejpam-6091	321	3	]	]	PUNCT
ejpam-6091	321	4	eqab	eqab	NOUN
ejpam-6091	321	5	m.	m.	NOUN
ejpam-6091	321	6	rabei	rabei	PROPN
ejpam-6091	321	7	,	,	PUNCT
ejpam-6091	321	8	khaled	khaled	PROPN
ejpam-6091	321	9	i.	i.	PROPN
ejpam-6091	321	10	nawafleh	nawafleh	PROPN
ejpam-6091	321	11	,	,	PUNCT
ejpam-6091	321	12	and	and	CCONJ
ejpam-6091	321	13	humam	humam	PROPN
ejpam-6091	321	14	b.	b.	PROPN
ejpam-6091	321	15	ghassib	ghassib	PROPN
ejpam-6091	321	16	.	.	PUNCT
ejpam-6091	322	1	hamilton	hamilton	PROPN
ejpam-6091	322	2	-	-	PUNCT
ejpam-6091	322	3	jacobi	jacobi	PROPN
ejpam-6091	322	4	treatment	treatment	NOUN
ejpam-6091	322	5	of	of	ADP
ejpam-6091	322	6	constrained	constrained	ADJ
ejpam-6091	322	7	systems	system	NOUN
ejpam-6091	322	8	.	.	PUNCT
ejpam-6091	323	1	journal	journal	NOUN
ejpam-6091	323	2	of	of	ADP
ejpam-6091	323	3	dynamical	dynamical	ADJ
ejpam-6091	323	4	systems	system	NOUN
ejpam-6091	323	5	and	and	CCONJ
ejpam-6091	323	6	geometric	geometric	ADJ
ejpam-6091	323	7	theories	theory	NOUN
ejpam-6091	323	8	,	,	PUNCT
ejpam-6091	323	9	2:1–6	2:1–6	NUM
ejpam-6091	323	10	,	,	PUNCT
ejpam-6091	323	11	2004	2004	NUM
ejpam-6091	323	12	.	.	PUNCT
ejpam-6091	324	1	[	[	X
ejpam-6091	324	2	20	20	NUM
ejpam-6091	324	3	]	]	PUNCT
ejpam-6091	324	4	khaled	khaled	PROPN
ejpam-6091	324	5	i.	i.	PROPN
ejpam-6091	324	6	nawafleh	nawafleh	PROPN
ejpam-6091	324	7	,	,	PUNCT
ejpam-6091	324	8	eqab	eqab	NOUN
ejpam-6091	324	9	m.	m.	NOUN
ejpam-6091	324	10	rabei	rabei	NOUN
ejpam-6091	324	11	,	,	PUNCT
ejpam-6091	324	12	and	and	CCONJ
ejpam-6091	324	13	humam	humam	PROPN
ejpam-6091	324	14	b.	b.	PROPN
ejpam-6091	324	15	ghassib	ghassib	PROPN
ejpam-6091	324	16	.	.	PUNCT
ejpam-6091	325	1	hamilton	hamilton	PROPN
ejpam-6091	325	2	-	-	PUNCT
ejpam-6091	325	3	jacobi	jacobi	PROPN
ejpam-6091	325	4	quantization	quantization	NOUN
ejpam-6091	325	5	of	of	ADP
ejpam-6091	325	6	nonholonomic	nonholonomic	ADJ
ejpam-6091	325	7	constrained	constrain	VERB
ejpam-6091	325	8	systems	system	NOUN
ejpam-6091	325	9	.	.	PUNCT
ejpam-6091	326	1	turkish	turkish	ADJ
ejpam-6091	326	2	journal	journal	PROPN
ejpam-6091	326	3	of	of	ADP
ejpam-6091	326	4	physics	physics	PROPN
ejpam-6091	326	5	,	,	PUNCT
ejpam-6091	326	6	29:151–162	29:151–162	NUM
ejpam-6091	326	7	,	,	PUNCT
ejpam-6091	326	8	2005	2005	NUM
ejpam-6091	326	9	.	.	PUNCT
ejpam-6091	327	1	[	[	X
ejpam-6091	327	2	21	21	NUM
ejpam-6091	327	3	]	]	X
ejpam-6091	327	4	ola	ola	PROPN
ejpam-6091	327	5	a.	a.	PROPN
ejpam-6091	327	6	jarab’ah	jarab’ah	PROPN
ejpam-6091	327	7	,	,	PUNCT
ejpam-6091	327	8	khaled	khaled	PROPN
ejpam-6091	327	9	i.	i.	PROPN
ejpam-6091	327	10	nawafleh	nawafleh	PROPN
ejpam-6091	327	11	,	,	PUNCT
ejpam-6091	327	12	and	and	CCONJ
ejpam-6091	327	13	humam	humam	PROPN
ejpam-6091	327	14	b.	b.	PROPN
ejpam-6091	327	15	ghassib	ghassib	PROPN
ejpam-6091	327	16	.	.	PUNCT
ejpam-6091	328	1	canonical	canonical	ADJ
ejpam-6091	328	2	quantization	quantization	NOUN
ejpam-6091	328	3	of	of	ADP
ejpam-6091	328	4	dissipative	dissipative	ADJ
ejpam-6091	328	5	systems	system	NOUN
ejpam-6091	328	6	.	.	PUNCT
ejpam-6091	329	1	european	european	ADJ
ejpam-6091	329	2	scientific	scientific	ADJ
ejpam-6091	329	3	journal	journal	NOUN
ejpam-6091	329	4	,	,	PUNCT
ejpam-6091	329	5	9(36):132–154	9(36):132–154	NUM
ejpam-6091	329	6	,	,	PUNCT
ejpam-6091	329	7	2013	2013	NUM
ejpam-6091	329	8	.	.	PUNCT
ejpam-6091	330	1	[	[	X
ejpam-6091	330	2	22	22	NUM
ejpam-6091	330	3	]	]	X
ejpam-6091	330	4	ola	ola	PROPN
ejpam-6091	330	5	a.	a.	PROPN
ejpam-6091	330	6	jarab’ah	jarab’ah	PROPN
ejpam-6091	330	7	,	,	PUNCT
ejpam-6091	330	8	eyad	eyad	PROPN
ejpam-6091	330	9	h.	h.	PROPN
ejpam-6091	330	10	hasan	hasan	PROPN
ejpam-6091	330	11	,	,	PUNCT
ejpam-6091	330	12	and	and	CCONJ
ejpam-6091	330	13	khaled	khaled	PROPN
ejpam-6091	330	14	i.	i.	PROPN
ejpam-6091	330	15	nawafleh	nawafleh	PROPN
ejpam-6091	330	16	.	.	PUNCT
ejpam-6091	331	1	quantization	quantization	NOUN
ejpam-6091	331	2	of	of	ADP
ejpam-6091	331	3	dissipative	dissipative	ADJ
ejpam-6091	331	4	systems	system	NOUN
ejpam-6091	331	5	with	with	ADP
ejpam-6091	331	6	second	second	ADJ
ejpam-6091	331	7	order	order	NOUN
ejpam-6091	331	8	lagrangian	lagrangian	ADJ
ejpam-6091	331	9	.	.	PUNCT
ejpam-6091	332	1	european	european	ADJ
ejpam-6091	332	2	scientific	scientific	ADJ
ejpam-6091	332	3	journal	journal	NOUN
ejpam-6091	332	4	,	,	PUNCT
ejpam-6091	332	5	10(9):135–142	10(9):135–142	PROPN
ejpam-6091	332	6	,	,	PUNCT
ejpam-6091	332	7	2014	2014	NUM
ejpam-6091	332	8	.	.	PUNCT
ejpam-6091	333	1	[	[	X
ejpam-6091	333	2	23	23	NUM
ejpam-6091	333	3	]	]	X
ejpam-6091	333	4	ola	ola	PROPN
ejpam-6091	333	5	a.	a.	PROPN
ejpam-6091	333	6	jarab’ah	jarab’ah	PROPN
ejpam-6091	333	7	and	and	CCONJ
ejpam-6091	333	8	khaled	khaled	PROPN
ejpam-6091	333	9	i.	i.	PROPN
ejpam-6091	333	10	nawafleh	nawafleh	PROPN
ejpam-6091	333	11	.	.	PUNCT
ejpam-6091	334	1	new	new	ADJ
ejpam-6091	334	2	approach	approach	NOUN
ejpam-6091	334	3	to	to	ADP
ejpam-6091	334	4	the	the	DET
ejpam-6091	334	5	quantization	quantization	NOUN
ejpam-6091	334	6	of	of	ADP
ejpam-6091	334	7	constrained	constrained	ADJ
ejpam-6091	334	8	dissipative	dissipative	ADJ
ejpam-6091	334	9	systems	system	NOUN
ejpam-6091	334	10	.	.	PUNCT
ejpam-6091	335	1	journal	journal	NOUN
ejpam-6091	335	2	of	of	ADP
ejpam-6091	335	3	applied	apply	VERB
ejpam-6091	335	4	mathematics	mathematic	NOUN
ejpam-6091	335	5	and	and	CCONJ
ejpam-6091	335	6	physics	physics	NOUN
ejpam-6091	335	7	,	,	PUNCT
ejpam-6091	335	8	6:1637	6:1637	NUM
ejpam-6091	335	9	–	–	PUNCT
ejpam-6091	335	10	1641	1641	NUM
ejpam-6091	335	11	,	,	PUNCT
ejpam-6091	335	12	2018	2018	NUM
ejpam-6091	335	13	.	.	PUNCT
ejpam-6091	336	1	[	[	X
ejpam-6091	336	2	24	24	NUM
ejpam-6091	336	3	]	]	PUNCT
ejpam-6091	336	4	anoud	anoud	NOUN
ejpam-6091	336	5	k.	k.	PROPN
ejpam-6091	336	6	fuqara	fuqara	PROPN
ejpam-6091	336	7	,	,	PUNCT
ejpam-6091	336	8	amer	amer	PROPN
ejpam-6091	336	9	d.	d.	PROPN
ejpam-6091	336	10	al	al	PROPN
ejpam-6091	336	11	-	-	PUNCT
ejpam-6091	336	12	oqali	oqali	PROPN
ejpam-6091	336	13	,	,	PUNCT
ejpam-6091	336	14	and	and	CCONJ
ejpam-6091	336	15	khaled	khaled	PROPN
ejpam-6091	336	16	i.	i.	PROPN
ejpam-6091	336	17	nawafleh	nawafleh	PROPN
ejpam-6091	336	18	.	.	PUNCT
ejpam-6091	337	1	hamilton	hamilton	PROPN
ejpam-6091	337	2	-	-	PUNCT
ejpam-6091	337	3	jacobi	jacobi	PROPN
ejpam-6091	337	4	equation	equation	NOUN
ejpam-6091	337	5	of	of	ADP
ejpam-6091	337	6	time	time	NOUN
ejpam-6091	337	7	dependent	dependent	ADJ
ejpam-6091	337	8	hamiltonians	hamiltonian	NOUN
ejpam-6091	337	9	.	.	PUNCT
ejpam-6091	338	1	oriental	oriental	ADJ
ejpam-6091	338	2	journal	journal	PROPN
ejpam-6091	338	3	of	of	ADP
ejpam-6091	338	4	physical	physical	ADJ
ejpam-6091	338	5	sciences	science	NOUN
ejpam-6091	338	6	,	,	PUNCT
ejpam-6091	338	7	5(1	5(1	NUM
ejpam-6091	338	8	-	-	SYM
ejpam-6091	338	9	2):9	2):9	NUM
ejpam-6091	338	10	–	–	PUNCT
ejpam-6091	338	11	15	15	NUM
ejpam-6091	338	12	,	,	PUNCT
ejpam-6091	338	13	2020	2020	NUM
ejpam-6091	338	14	.	.	PUNCT