id	sid	tid	token	lemma	pos
ap-4605	1	1	acta	acta	PROPN
ap-4605	1	2	polytechnica	polytechnica	PROPN
ap-4605	1	3	doi:10.14311	doi:10.14311	PROPN
ap-4605	1	4	/	/	SYM
ap-4605	1	5	ap.2017.57.0373	ap.2017.57.0373	PROPN
ap-4605	1	6	acta	acta	PROPN
ap-4605	1	7	polytechnica	polytechnica	PROPN
ap-4605	1	8	57(6):373–378	57(6):373–378	PROPN
ap-4605	1	9	,	,	PUNCT
ap-4605	1	10	2017	2017	NUM
ap-4605	1	11	©	©	PROPN
ap-4605	1	12	czech	czech	PROPN
ap-4605	1	13	technical	technical	PROPN
ap-4605	1	14	university	university	PROPN
ap-4605	1	15	in	in	ADP
ap-4605	1	16	prague	prague	PROPN
ap-4605	1	17	,	,	PUNCT
ap-4605	1	18	2017	2017	NUM
ap-4605	1	19	available	available	ADJ
ap-4605	1	20	online	online	ADV
ap-4605	1	21	at	at	ADP
ap-4605	1	22	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-4605	1	23	functional	functional	ADJ
ap-4605	1	24	realizations	realization	NOUN
ap-4605	1	25	of	of	ADP
ap-4605	1	26	lie	lie	NOUN
ap-4605	1	27	algebras	algebra	NOUN
ap-4605	1	28	as	as	SCONJ
ap-4605	1	29	noether	noether	ADJ
ap-4605	1	30	point	point	NOUN
ap-4605	1	31	symmetries	symmetry	NOUN
ap-4605	1	32	of	of	ADP
ap-4605	1	33	systems	system	NOUN
ap-4605	1	34	rutwig	rutwig	PROPN
ap-4605	1	35	campoamor	campoamor	NOUN
ap-4605	1	36	-	-	PUNCT
ap-4605	1	37	stursberg	stursberg	PROPN
ap-4605	1	38	instituto	instituto	PROPN
ap-4605	1	39	de	de	PROPN
ap-4605	1	40	matemática	matemática	PROPN
ap-4605	1	41	interdisciplinar	interdisciplinar	PROPN
ap-4605	1	42	-	-	PUNCT
ap-4605	1	43	ucm	ucm	PROPN
ap-4605	1	44	,	,	PUNCT
ap-4605	1	45	plaza	plaza	PROPN
ap-4605	1	46	de	de	X
ap-4605	1	47	ciencias	ciencias	PROPN
ap-4605	1	48	3	3	NUM
ap-4605	1	49	,	,	PUNCT
ap-4605	1	50	e-28040	e-28040	PROPN
ap-4605	1	51	madrid	madrid	PROPN
ap-4605	1	52	,	,	PUNCT
ap-4605	1	53	spain	spain	PROPN
ap-4605	1	54	correspondence	correspondence	NOUN
ap-4605	1	55	:	:	PUNCT
ap-4605	2	1	rutwig@ucm.es	rutwig@ucm.es	PROPN
ap-4605	2	2	abstract	abstract	ADJ
ap-4605	2	3	.	.	PUNCT
ap-4605	3	1	functional	functional	ADJ
ap-4605	3	2	realizations	realization	NOUN
ap-4605	3	3	of	of	ADP
ap-4605	3	4	lie	lie	NOUN
ap-4605	3	5	algebras	algebra	NOUN
ap-4605	3	6	are	be	AUX
ap-4605	3	7	applied	apply	VERB
ap-4605	3	8	to	to	ADP
ap-4605	3	9	the	the	DET
ap-4605	3	10	problem	problem	NOUN
ap-4605	3	11	of	of	ADP
ap-4605	3	12	determining	determine	VERB
ap-4605	3	13	lie	lie	NOUN
ap-4605	3	14	and	and	CCONJ
ap-4605	3	15	noether	noether	ADJ
ap-4605	3	16	point	point	NOUN
ap-4605	3	17	symmetries	symmetry	NOUN
ap-4605	3	18	of	of	ADP
ap-4605	3	19	lagrangian	lagrangian	ADJ
ap-4605	3	20	systems	system	NOUN
ap-4605	3	21	in	in	ADP
ap-4605	3	22	n	n	DET
ap-4605	3	23	dimensions	dimension	NOUN
ap-4605	3	24	,	,	PUNCT
ap-4605	3	25	particularly	particularly	ADV
ap-4605	3	26	in	in	ADP
ap-4605	3	27	the	the	DET
ap-4605	3	28	plane	plane	NOUN
ap-4605	3	29	.	.	PUNCT
ap-4605	4	1	this	this	PRON
ap-4605	4	2	encompasses	encompass	VERB
ap-4605	4	3	both	both	DET
ap-4605	4	4	the	the	DET
ap-4605	4	5	case	case	NOUN
ap-4605	4	6	of	of	ADP
ap-4605	4	7	symmetry	symmetry	NOUN
ap-4605	4	8	-	-	PUNCT
ap-4605	4	9	preserving	preserve	VERB
ap-4605	4	10	perturbations	perturbation	NOUN
ap-4605	4	11	of	of	ADP
ap-4605	4	12	a	a	DET
ap-4605	4	13	given	give	VERB
ap-4605	4	14	system	system	NOUN
ap-4605	4	15	,	,	PUNCT
ap-4605	4	16	as	as	ADV
ap-4605	4	17	well	well	ADV
ap-4605	4	18	as	as	ADP
ap-4605	4	19	the	the	DET
ap-4605	4	20	generic	generic	ADJ
ap-4605	4	21	analysis	analysis	NOUN
ap-4605	4	22	on	on	ADP
ap-4605	4	23	the	the	DET
ap-4605	4	24	structure	structure	NOUN
ap-4605	4	25	of	of	ADP
ap-4605	4	26	(	(	PUNCT
ap-4605	4	27	regular	regular	ADJ
ap-4605	4	28	)	)	PUNCT
ap-4605	4	29	lagrangians	lagrangian	NOUN
ap-4605	4	30	in	in	ADP
ap-4605	4	31	order	order	NOUN
ap-4605	4	32	to	to	PART
ap-4605	4	33	admit	admit	VERB
ap-4605	4	34	a	a	DET
ap-4605	4	35	symmetry	symmetry	NOUN
ap-4605	4	36	algebra	algebra	NOUN
ap-4605	4	37	belonging	belong	VERB
ap-4605	4	38	to	to	ADP
ap-4605	4	39	a	a	DET
ap-4605	4	40	specific	specific	ADJ
ap-4605	4	41	isomorphy	isomorphy	NOUN
ap-4605	4	42	class	class	NOUN
ap-4605	4	43	.	.	PUNCT
ap-4605	5	1	keywords	keyword	NOUN
ap-4605	5	2	:	:	PUNCT
ap-4605	5	3	lagrangian	lagrangian	ADJ
ap-4605	5	4	;	;	PUNCT
ap-4605	5	5	lie	lie	NOUN
ap-4605	5	6	point	point	NOUN
ap-4605	5	7	symmetry	symmetry	NOUN
ap-4605	5	8	;	;	PUNCT
ap-4605	5	9	noether	noether	ADJ
ap-4605	5	10	symmetry	symmetry	NOUN
ap-4605	5	11	;	;	PUNCT
ap-4605	5	12	perturbation	perturbation	NOUN
ap-4605	5	13	.	.	PUNCT
ap-4605	6	1	1	1	X
ap-4605	6	2	.	.	X
ap-4605	6	3	introduction	introduction	NOUN
ap-4605	6	4	the	the	DET
ap-4605	6	5	study	study	NOUN
ap-4605	6	6	of	of	ADP
ap-4605	6	7	the	the	DET
ap-4605	6	8	precise	precise	ADJ
ap-4605	6	9	relation	relation	NOUN
ap-4605	6	10	between	between	ADP
ap-4605	6	11	constants	constant	NOUN
ap-4605	6	12	of	of	ADP
ap-4605	6	13	the	the	DET
ap-4605	6	14	motion	motion	NOUN
ap-4605	6	15	of	of	ADP
ap-4605	6	16	a	a	DET
ap-4605	6	17	dynamical	dynamical	ADJ
ap-4605	6	18	system	system	NOUN
ap-4605	6	19	and	and	CCONJ
ap-4605	6	20	the	the	DET
ap-4605	6	21	symmetry	symmetry	NOUN
ap-4605	6	22	properties	property	NOUN
ap-4605	6	23	of	of	ADP
ap-4605	6	24	the	the	DET
ap-4605	6	25	corresponding	corresponding	ADJ
ap-4605	6	26	equations	equation	NOUN
ap-4605	6	27	of	of	ADP
ap-4605	6	28	the	the	DET
ap-4605	6	29	motion	motion	NOUN
ap-4605	6	30	(	(	PUNCT
ap-4605	6	31	alternatively	alternatively	ADV
ap-4605	6	32	,	,	PUNCT
ap-4605	6	33	an	an	DET
ap-4605	6	34	associated	associated	ADJ
ap-4605	6	35	lagrangian	lagrangian	NOUN
ap-4605	6	36	)	)	PUNCT
ap-4605	6	37	goes	go	VERB
ap-4605	6	38	back	back	ADV
ap-4605	6	39	to	to	ADP
ap-4605	6	40	the	the	DET
ap-4605	6	41	seminal	seminal	ADJ
ap-4605	6	42	paper	paper	NOUN
ap-4605	6	43	of	of	ADP
ap-4605	6	44	e.	e.	PROPN
ap-4605	6	45	noether	noether	PROPN
ap-4605	7	1	[	[	X
ap-4605	7	2	1	1	NUM
ap-4605	7	3	]	]	PUNCT
ap-4605	7	4	,	,	PUNCT
ap-4605	7	5	a	a	DET
ap-4605	7	6	key	key	ADJ
ap-4605	7	7	result	result	NOUN
ap-4605	7	8	that	that	SCONJ
ap-4605	7	9	,	,	PUNCT
ap-4605	7	10	combined	combine	VERB
ap-4605	7	11	with	with	ADP
ap-4605	7	12	the	the	DET
ap-4605	7	13	lie	lie	NOUN
ap-4605	7	14	group	group	NOUN
ap-4605	7	15	theoretical	theoretical	ADJ
ap-4605	7	16	approach	approach	NOUN
ap-4605	7	17	to	to	ADP
ap-4605	7	18	differential	differential	ADJ
ap-4605	7	19	equations	equation	NOUN
ap-4605	7	20	,	,	PUNCT
ap-4605	7	21	has	have	AUX
ap-4605	7	22	become	become	VERB
ap-4605	7	23	an	an	DET
ap-4605	7	24	essential	essential	ADJ
ap-4605	7	25	tool	tool	NOUN
ap-4605	7	26	in	in	ADP
ap-4605	7	27	many	many	ADJ
ap-4605	7	28	branches	branch	NOUN
ap-4605	7	29	of	of	ADP
ap-4605	7	30	applied	apply	VERB
ap-4605	7	31	mathematics	mathematic	NOUN
ap-4605	7	32	and	and	CCONJ
ap-4605	7	33	mechanics	mechanic	NOUN
ap-4605	7	34	(	(	PUNCT
ap-4605	7	35	see	see	VERB
ap-4605	7	36	,	,	PUNCT
ap-4605	7	37	e.g.	e.g.	ADV
ap-4605	7	38	,	,	PUNCT
ap-4605	7	39	[	[	X
ap-4605	7	40	2	2	NUM
ap-4605	7	41	,	,	PUNCT
ap-4605	7	42	3	3	NUM
ap-4605	7	43	]	]	PUNCT
ap-4605	7	44	and	and	CCONJ
ap-4605	7	45	references	reference	NOUN
ap-4605	7	46	therein	therein	ADV
ap-4605	7	47	)	)	PUNCT
ap-4605	7	48	.	.	PUNCT
ap-4605	8	1	usually	usually	ADV
ap-4605	8	2	,	,	PUNCT
ap-4605	8	3	the	the	DET
ap-4605	8	4	noether	noether	ADJ
ap-4605	8	5	symmetry	symmetry	NOUN
ap-4605	8	6	analysis	analysis	NOUN
ap-4605	8	7	is	be	AUX
ap-4605	8	8	carried	carry	VERB
ap-4605	8	9	out	out	ADP
ap-4605	8	10	mainly	mainly	ADV
ap-4605	8	11	for	for	ADP
ap-4605	8	12	conservative	conservative	ADJ
ap-4605	8	13	systems	system	NOUN
ap-4605	8	14	,	,	PUNCT
ap-4605	8	15	due	due	ADP
ap-4605	8	16	to	to	ADP
ap-4605	8	17	requirements	requirement	NOUN
ap-4605	8	18	of	of	ADP
ap-4605	8	19	the	the	DET
ap-4605	8	20	hamiltonian	hamiltonian	ADJ
ap-4605	8	21	formalism	formalism	NOUN
ap-4605	8	22	and	and	CCONJ
ap-4605	8	23	the	the	DET
ap-4605	8	24	corresponding	corresponding	ADJ
ap-4605	8	25	quantization	quantization	NOUN
ap-4605	8	26	of	of	ADP
ap-4605	8	27	the	the	DET
ap-4605	8	28	systems	system	NOUN
ap-4605	8	29	[	[	X
ap-4605	8	30	4	4	NUM
ap-4605	8	31	]	]	PUNCT
ap-4605	8	32	.	.	PUNCT
ap-4605	9	1	however	however	ADV
ap-4605	9	2	,	,	PUNCT
ap-4605	9	3	there	there	PRON
ap-4605	9	4	is	be	VERB
ap-4605	9	5	no	no	DET
ap-4605	9	6	restriction	restriction	NOUN
ap-4605	9	7	,	,	PUNCT
ap-4605	9	8	at	at	ADP
ap-4605	9	9	least	least	ADJ
ap-4605	9	10	from	from	ADP
ap-4605	9	11	the	the	DET
ap-4605	9	12	lie	lie	NOUN
ap-4605	9	13	algebraic	algebraic	ADJ
ap-4605	9	14	point	point	NOUN
ap-4605	9	15	of	of	ADP
ap-4605	9	16	view	view	NOUN
ap-4605	9	17	,	,	PUNCT
ap-4605	9	18	to	to	PART
ap-4605	9	19	treat	treat	VERB
ap-4605	9	20	both	both	CCONJ
ap-4605	9	21	conservative	conservative	ADJ
ap-4605	9	22	and	and	CCONJ
ap-4605	9	23	dissipative	dissipative	ADJ
ap-4605	9	24	systems	system	NOUN
ap-4605	9	25	simultaneously	simultaneously	ADV
ap-4605	9	26	.	.	PUNCT
ap-4605	10	1	this	this	PRON
ap-4605	10	2	can	can	AUX
ap-4605	10	3	be	be	AUX
ap-4605	10	4	done	do	VERB
ap-4605	10	5	introducing	introduce	VERB
ap-4605	10	6	appropriate	appropriate	ADJ
ap-4605	10	7	functional	functional	ADJ
ap-4605	10	8	realizations	realization	NOUN
ap-4605	10	9	of	of	ADP
ap-4605	10	10	lie	lie	NOUN
ap-4605	10	11	algebras	algebra	NOUN
ap-4605	10	12	,	,	PUNCT
ap-4605	10	13	the	the	DET
ap-4605	10	14	symmetry	symmetry	NOUN
ap-4605	10	15	generators	generator	NOUN
ap-4605	10	16	of	of	ADP
ap-4605	10	17	which	which	PRON
ap-4605	10	18	depend	depend	VERB
ap-4605	10	19	on	on	ADP
ap-4605	10	20	the	the	DET
ap-4605	10	21	coordinates	coordinate	NOUN
ap-4605	10	22	of	of	ADP
ap-4605	10	23	the	the	DET
ap-4605	10	24	extended	extended	ADJ
ap-4605	10	25	configuration	configuration	NOUN
ap-4605	10	26	space	space	NOUN
ap-4605	10	27	,	,	PUNCT
ap-4605	10	28	and	and	CCONJ
ap-4605	10	29	considering	consider	VERB
ap-4605	10	30	the	the	DET
ap-4605	10	31	constraints	constraint	NOUN
ap-4605	10	32	imposed	impose	VERB
ap-4605	10	33	by	by	ADP
ap-4605	10	34	this	this	DET
ap-4605	10	35	timedependence	timedependence	NOUN
ap-4605	10	36	.	.	PUNCT
ap-4605	11	1	this	this	DET
ap-4605	11	2	extended	extended	ADJ
ap-4605	11	3	approach	approach	NOUN
ap-4605	11	4	allows	allow	VERB
ap-4605	11	5	to	to	PART
ap-4605	11	6	cover	cover	VERB
ap-4605	11	7	physically	physically	ADV
ap-4605	11	8	relevant	relevant	ADJ
ap-4605	11	9	systems	system	NOUN
ap-4605	11	10	,	,	PUNCT
ap-4605	11	11	such	such	ADJ
ap-4605	11	12	as	as	ADP
ap-4605	11	13	time	time	NOUN
ap-4605	11	14	-	-	PUNCT
ap-4605	11	15	modulated	modulate	VERB
ap-4605	11	16	oscillators	oscillator	NOUN
ap-4605	11	17	,	,	PUNCT
ap-4605	11	18	and	and	CCONJ
ap-4605	11	19	has	have	VERB
ap-4605	11	20	further	further	ADJ
ap-4605	11	21	applications	application	NOUN
ap-4605	11	22	in	in	ADP
ap-4605	11	23	the	the	DET
ap-4605	11	24	context	context	NOUN
ap-4605	11	25	of	of	ADP
ap-4605	11	26	perturbation	perturbation	NOUN
ap-4605	11	27	theory	theory	NOUN
ap-4605	11	28	,	,	PUNCT
ap-4605	11	29	such	such	ADJ
ap-4605	11	30	as	as	ADP
ap-4605	11	31	the	the	DET
ap-4605	11	32	study	study	NOUN
ap-4605	11	33	of	of	ADP
ap-4605	11	34	some	some	DET
ap-4605	11	35	geometric	geometric	ADJ
ap-4605	11	36	properties	property	NOUN
ap-4605	11	37	of	of	ADP
ap-4605	11	38	the	the	DET
ap-4605	11	39	orbits	orbit	NOUN
ap-4605	11	40	of	of	ADP
ap-4605	11	41	a	a	DET
ap-4605	11	42	given	give	VERB
ap-4605	11	43	system	system	NOUN
ap-4605	11	44	[	[	X
ap-4605	11	45	5	5	NUM
ap-4605	11	46	]	]	PUNCT
ap-4605	11	47	.	.	PUNCT
ap-4605	12	1	within	within	ADP
ap-4605	12	2	the	the	DET
ap-4605	12	3	context	context	NOUN
ap-4605	12	4	of	of	ADP
ap-4605	12	5	inverse	inverse	NOUN
ap-4605	12	6	of	of	ADP
ap-4605	12	7	problems	problem	NOUN
ap-4605	12	8	in	in	ADP
ap-4605	12	9	dynamics	dynamic	NOUN
ap-4605	12	10	[	[	X
ap-4605	12	11	5	5	NUM
ap-4605	12	12	,	,	PUNCT
ap-4605	12	13	6	6	NUM
ap-4605	12	14	]	]	PUNCT
ap-4605	12	15	,	,	PUNCT
ap-4605	12	16	in	in	ADP
ap-4605	12	17	this	this	DET
ap-4605	12	18	work	work	NOUN
ap-4605	12	19	we	we	PRON
ap-4605	12	20	consider	consider	VERB
ap-4605	12	21	an	an	DET
ap-4605	12	22	inverse	inverse	NOUN
ap-4605	12	23	approach	approach	NOUN
ap-4605	12	24	to	to	ADP
ap-4605	12	25	dynamics	dynamic	NOUN
ap-4605	12	26	based	base	VERB
ap-4605	12	27	on	on	ADP
ap-4605	12	28	functional	functional	ADJ
ap-4605	12	29	realizations	realization	NOUN
ap-4605	12	30	of	of	ADP
ap-4605	12	31	lie	lie	NOUN
ap-4605	12	32	algebras	algebra	NOUN
ap-4605	12	33	that	that	PRON
ap-4605	12	34	are	be	AUX
ap-4605	12	35	required	require	VERB
ap-4605	12	36	to	to	PART
ap-4605	12	37	satisfy	satisfy	VERB
ap-4605	12	38	the	the	DET
ap-4605	12	39	noether	noether	ADJ
ap-4605	12	40	symmetry	symmetry	NOUN
ap-4605	12	41	condition	condition	NOUN
ap-4605	12	42	for	for	ADP
ap-4605	12	43	a	a	DET
ap-4605	12	44	(	(	PUNCT
ap-4605	12	45	regular	regular	ADJ
ap-4605	12	46	)	)	PUNCT
ap-4605	12	47	lagrangian	lagrangian	ADJ
ap-4605	12	48	system	system	NOUN
ap-4605	12	49	.	.	PUNCT
ap-4605	13	1	this	this	PRON
ap-4605	13	2	allows	allow	VERB
ap-4605	13	3	two	two	NUM
ap-4605	13	4	approaches	approach	NOUN
ap-4605	13	5	,	,	PUNCT
ap-4605	13	6	either	either	CCONJ
ap-4605	13	7	starting	start	VERB
ap-4605	13	8	from	from	ADP
ap-4605	13	9	a	a	DET
ap-4605	13	10	given	give	VERB
ap-4605	13	11	system	system	NOUN
ap-4605	13	12	and	and	CCONJ
ap-4605	13	13	analyzing	analyze	VERB
ap-4605	13	14	perturbations	perturbation	NOUN
ap-4605	13	15	that	that	PRON
ap-4605	13	16	preserve	preserve	VERB
ap-4605	13	17	certain	certain	ADJ
ap-4605	13	18	of	of	ADP
ap-4605	13	19	the	the	DET
ap-4605	13	20	symmetries	symmetry	NOUN
ap-4605	13	21	,	,	PUNCT
ap-4605	13	22	or	or	CCONJ
ap-4605	13	23	determining	determine	VERB
ap-4605	13	24	families	family	NOUN
ap-4605	13	25	of	of	ADP
ap-4605	13	26	systems	system	NOUN
ap-4605	13	27	invariant	invariant	ADJ
ap-4605	13	28	with	with	ADP
ap-4605	13	29	respect	respect	NOUN
ap-4605	13	30	to	to	ADP
ap-4605	13	31	these	these	DET
ap-4605	13	32	realizations	realization	NOUN
ap-4605	13	33	.	.	PUNCT
ap-4605	14	1	for	for	ADP
ap-4605	14	2	the	the	DET
ap-4605	14	3	purpose	purpose	NOUN
ap-4605	14	4	of	of	ADP
ap-4605	14	5	illustration	illustration	NOUN
ap-4605	14	6	,	,	PUNCT
ap-4605	14	7	the	the	DET
ap-4605	14	8	plane	plane	NOUN
ap-4605	14	9	case	case	NOUN
ap-4605	14	10	is	be	AUX
ap-4605	14	11	considered	consider	VERB
ap-4605	14	12	,	,	PUNCT
ap-4605	14	13	although	although	SCONJ
ap-4605	14	14	the	the	DET
ap-4605	14	15	ansatz	ansatz	NOUN
ap-4605	14	16	can	can	AUX
ap-4605	14	17	also	also	ADV
ap-4605	14	18	be	be	AUX
ap-4605	14	19	formulated	formulate	VERB
ap-4605	14	20	in	in	ADP
ap-4605	14	21	arbitrary	arbitrary	ADJ
ap-4605	14	22	dimensions	dimension	NOUN
ap-4605	14	23	.	.	PUNCT
ap-4605	15	1	2	2	X
ap-4605	15	2	.	.	X
ap-4605	15	3	lie	lie	NOUN
ap-4605	15	4	and	and	CCONJ
ap-4605	15	5	noether	noether	ADJ
ap-4605	15	6	point	point	NOUN
ap-4605	15	7	symmetries	symmetry	NOUN
ap-4605	15	8	of	of	ADP
ap-4605	15	9	systems	system	NOUN
ap-4605	15	10	let	let	VERB
ap-4605	15	11	l	l	PROPN
ap-4605	15	12	(	(	PUNCT
ap-4605	15	13	t	t	PROPN
ap-4605	15	14	,	,	PUNCT
ap-4605	15	15	q	q	NOUN
ap-4605	15	16	,	,	PUNCT
ap-4605	15	17	q̇	q̇	ADV
ap-4605	15	18	)	)	PUNCT
ap-4605	15	19	be	be	AUX
ap-4605	15	20	a	a	DET
ap-4605	15	21	regular	regular	ADJ
ap-4605	15	22	lagrangian	lagrangian	NOUN
ap-4605	15	23	in	in	ADP
ap-4605	15	24	n	n	NOUN
ap-4605	15	25	-	-	PUNCT
ap-4605	15	26	dimensions	dimension	NOUN
ap-4605	15	27	and	and	CCONJ
ap-4605	15	28	let	let	VERB
ap-4605	15	29	d	d	INTJ
ap-4605	15	30	dt	dt	X
ap-4605	15	31	(	(	PUNCT
ap-4605	15	32	∂l	∂l	PROPN
ap-4605	15	33	∂q̇i	∂q̇i	VERB
ap-4605	15	34	)	)	PUNCT
ap-4605	16	1	−	−	PROPN
ap-4605	16	2	∂l	∂l	NOUN
ap-4605	16	3	∂qi	∂qi	NOUN
ap-4605	16	4	=	=	SYM
ap-4605	16	5	0	0	NUM
ap-4605	16	6	,	,	PUNCT
ap-4605	16	7	1	1	NUM
ap-4605	16	8	≤	≤	NUM
ap-4605	16	9	i	i	PRON
ap-4605	16	10	≤	≤	ADJ
ap-4605	16	11	n	n	CCONJ
ap-4605	16	12	(	(	PUNCT
ap-4605	16	13	1	1	X
ap-4605	16	14	)	)	PUNCT
ap-4605	16	15	be	be	AUX
ap-4605	16	16	the	the	DET
ap-4605	16	17	corresponding	corresponding	ADJ
ap-4605	16	18	equations	equation	NOUN
ap-4605	16	19	of	of	ADP
ap-4605	16	20	the	the	DET
ap-4605	16	21	motion	motion	NOUN
ap-4605	16	22	.	.	PUNCT
ap-4605	17	1	by	by	ADP
ap-4605	17	2	regularity	regularity	NOUN
ap-4605	17	3	,	,	PUNCT
ap-4605	17	4	we	we	PRON
ap-4605	17	5	can	can	AUX
ap-4605	17	6	always	always	ADV
ap-4605	17	7	rewrite	rewrite	VERB
ap-4605	17	8	the	the	DET
ap-4605	17	9	equations	equation	NOUN
ap-4605	17	10	of	of	ADP
ap-4605	17	11	motion	motion	NOUN
ap-4605	17	12	in	in	ADP
ap-4605	17	13	normal	normal	ADJ
ap-4605	17	14	form	form	NOUN
ap-4605	17	15	,	,	PUNCT
ap-4605	17	16	i.e.	i.e.	X
ap-4605	17	17	,	,	PUNCT
ap-4605	17	18	q̈i	q̈i	ADV
ap-4605	17	19	=	=	PUNCT
ap-4605	17	20	ωi(t	ωi(t	NOUN
ap-4605	17	21	,	,	PUNCT
ap-4605	17	22	q̇j	q̇j	PROPN
ap-4605	17	23	,	,	PUNCT
ap-4605	17	24	qj	qj	PROPN
ap-4605	17	25	)	)	PUNCT
ap-4605	18	1	=	=	SYM
ap-4605	18	2	gij	gij	NOUN
ap-4605	18	3	(	(	PUNCT
ap-4605	18	4	∂l	∂l	PROPN
ap-4605	18	5	∂qj	∂qj	PROPN
ap-4605	18	6	−	−	PROPN
ap-4605	18	7	∂2l	∂2l	PROPN
ap-4605	18	8	∂t∂q̇j	∂t∂q̇j	PROPN
ap-4605	19	1	−	−	PROPN
ap-4605	20	1	∂2l	∂2l	PROPN
ap-4605	20	2	∂q̇j∂qk	∂q̇j∂qk	NOUN
ap-4605	20	3	q̇k	q̇k	PROPN
ap-4605	20	4	)	)	PUNCT
ap-4605	20	5	,	,	PUNCT
ap-4605	20	6	(	(	PUNCT
ap-4605	20	7	2	2	X
ap-4605	20	8	)	)	PUNCT
ap-4605	20	9	for	for	ADP
ap-4605	20	10	1	1	NUM
ap-4605	20	11	≤	≤	NUM
ap-4605	20	12	i	i	PRON
ap-4605	20	13	≤	≤	NOUN
ap-4605	20	14	n	n	CCONJ
ap-4605	20	15	,	,	PUNCT
ap-4605	20	16	with	with	ADP
ap-4605	20	17	gij	gij	ADJ
ap-4605	20	18	denoting	denote	VERB
ap-4605	20	19	the	the	DET
ap-4605	20	20	inverse	inverse	ADJ
ap-4605	20	21	hessian	hessian	NOUN
ap-4605	20	22	matrix	matrix	NOUN
ap-4605	20	23	of	of	ADP
ap-4605	20	24	l.	l.	PROPN
ap-4605	20	25	as	as	SCONJ
ap-4605	20	26	is	be	AUX
ap-4605	20	27	well	well	ADV
ap-4605	20	28	known	know	VERB
ap-4605	20	29	,	,	PUNCT
ap-4605	20	30	the	the	DET
ap-4605	20	31	system	system	NOUN
ap-4605	20	32	(	(	PUNCT
ap-4605	20	33	2	2	X
ap-4605	20	34	)	)	PUNCT
ap-4605	20	35	can	can	AUX
ap-4605	20	36	be	be	AUX
ap-4605	20	37	reformulated	reformulate	VERB
ap-4605	20	38	in	in	ADP
ap-4605	20	39	equivalent	equivalent	ADJ
ap-4605	20	40	form	form	NOUN
ap-4605	20	41	as	as	ADP
ap-4605	20	42	the	the	DET
ap-4605	20	43	first	first	ADJ
ap-4605	20	44	order	order	NOUN
ap-4605	20	45	partial	partial	ADJ
ap-4605	20	46	differential	differential	NOUN
ap-4605	20	47	equation	equation	NOUN
ap-4605	20	48	af	af	PROPN
ap-4605	20	49	=	=	PUNCT
ap-4605	20	50	(	(	PUNCT
ap-4605	20	51	∂	∂	NUM
ap-4605	20	52	∂t	∂t	PROPN
ap-4605	20	53	+	+	NUM
ap-4605	20	54	q̇i	q̇i	PROPN
ap-4605	20	55	∂	∂	NUM
ap-4605	20	56	∂qi	∂qi	PROPN
ap-4605	20	57	+	+	SYM
ap-4605	20	58	ωi	ωi	PROPN
ap-4605	20	59	∂	∂	NOUN
ap-4605	20	60	∂q̇i	∂q̇i	VERB
ap-4605	20	61	)	)	PUNCT
ap-4605	21	1	f	f	X
ap-4605	21	2	=	=	PUNCT
ap-4605	21	3	0	0	PROPN
ap-4605	21	4	.	.	PUNCT
ap-4605	22	1	(	(	PUNCT
ap-4605	22	2	3	3	X
ap-4605	22	3	)	)	PUNCT
ap-4605	22	4	we	we	PRON
ap-4605	22	5	call	call	VERB
ap-4605	22	6	a	a	DET
ap-4605	22	7	vector	vector	NOUN
ap-4605	22	8	field	field	NOUN
ap-4605	22	9	x	x	PUNCT
ap-4605	22	10	=	=	SYM
ap-4605	22	11	ξ(t	ξ(t	NOUN
ap-4605	22	12	,	,	PUNCT
ap-4605	22	13	q	q	NOUN
ap-4605	22	14	)	)	PUNCT
ap-4605	22	15	∂∂t	∂∂t	PROPN
ap-4605	22	16	+	+	CCONJ
ap-4605	22	17	ηj(t	ηj(t	PROPN
ap-4605	22	18	,	,	PUNCT
ap-4605	22	19	q	q	NOUN
ap-4605	22	20	)	)	PUNCT
ap-4605	22	21	∂	∂	NUM
ap-4605	22	22	∂qj	∂qj	PROPN
ap-4605	22	23	∈	∈	PROPN
ap-4605	22	24	x(rn+1	x(rn+1	PROPN
ap-4605	22	25	)	)	PUNCT
ap-4605	22	26	a	a	DET
ap-4605	22	27	lie	lie	NOUN
ap-4605	22	28	point	point	NOUN
ap-4605	22	29	symmetry	symmetry	NOUN
ap-4605	22	30	of	of	ADP
ap-4605	22	31	the	the	DET
ap-4605	22	32	equations	equation	NOUN
ap-4605	22	33	(	(	PUNCT
ap-4605	22	34	2	2	X
ap-4605	22	35	)	)	PUNCT
ap-4605	22	36	if	if	SCONJ
ap-4605	22	37	its	its	PRON
ap-4605	22	38	first	first	ADJ
ap-4605	22	39	prolongation	prolongation	NOUN
ap-4605	22	40	ẋ	ẋ	PUNCT
ap-4605	23	1	=	=	PUNCT
ap-4605	23	2	x	x	PUNCT
ap-4605	24	1	+	+	NUM
ap-4605	24	2	η̇j	η̇j	NOUN
ap-4605	24	3	(	(	PUNCT
ap-4605	24	4	t	t	PROPN
ap-4605	24	5	,	,	PUNCT
ap-4605	24	6	q	q	NOUN
ap-4605	24	7	,	,	PUNCT
ap-4605	24	8	q̇	q̇	ADJ
ap-4605	24	9	)	)	PUNCT
ap-4605	24	10	∂	∂	NOUN
ap-4605	24	11	∂q̇j	∂q̇j	NOUN
ap-4605	24	12	with	with	ADP
ap-4605	24	13	η̇j	η̇j	NOUN
ap-4605	24	14	=	=	SYM
ap-4605	24	15	−dξdt	−dξdt	PART
ap-4605	24	16	q̇j	q̇j	PROPN
ap-4605	24	17	+	+	CCONJ
ap-4605	24	18	dηj	dηj	NOUN
ap-4605	24	19	dt	dt	NOUN
ap-4605	24	20	satisfies	satisfy	VERB
ap-4605	24	21	the	the	DET
ap-4605	24	22	commutator	commutator	NOUN
ap-4605	24	23	[	[	PUNCT
ap-4605	24	24	ẋ,a	ẋ,a	NOUN
ap-4605	24	25	]	]	X
ap-4605	25	1	=	=	PUNCT
ap-4605	25	2	−dξ	−dξ	X
ap-4605	25	3	dt	dt	X
ap-4605	25	4	a.	a.	NOUN
ap-4605	25	5	(	(	PUNCT
ap-4605	25	6	4	4	X
ap-4605	25	7	)	)	PUNCT
ap-4605	25	8	lie	lie	NOUN
ap-4605	25	9	point	point	NOUN
ap-4605	25	10	symmetries	symmetry	NOUN
ap-4605	25	11	span	span	VERB
ap-4605	25	12	a	a	DET
ap-4605	25	13	finite	finite	ADJ
ap-4605	25	14	-	-	ADJ
ap-4605	25	15	dimensional	dimensional	ADJ
ap-4605	25	16	lie	lie	NOUN
ap-4605	25	17	algebra	algebra	NOUN
ap-4605	25	18	lps	lps	PROPN
ap-4605	25	19	,	,	PUNCT
ap-4605	25	20	called	call	VERB
ap-4605	25	21	the	the	DET
ap-4605	25	22	lie	lie	NOUN
ap-4605	25	23	(	(	PUNCT
ap-4605	25	24	point	point	NOUN
ap-4605	25	25	)	)	PUNCT
ap-4605	25	26	symmetry	symmetry	NOUN
ap-4605	25	27	algebra	algebra	NOUN
ap-4605	25	28	of	of	ADP
ap-4605	25	29	the	the	DET
ap-4605	25	30	system	system	NOUN
ap-4605	25	31	,	,	PUNCT
ap-4605	25	32	that	that	PRON
ap-4605	25	33	be	be	AUX
ap-4605	25	34	seen	see	VERB
ap-4605	25	35	to	to	PART
ap-4605	25	36	be	be	AUX
ap-4605	25	37	always	always	ADV
ap-4605	25	38	a	a	DET
ap-4605	25	39	subalgebra	subalgebra	NOUN
ap-4605	25	40	of	of	ADP
ap-4605	25	41	the	the	DET
ap-4605	25	42	simple	simple	ADJ
ap-4605	25	43	algebra	algebra	NOUN
ap-4605	25	44	sl(n	sl(n	PUNCT
ap-4605	25	45	+	+	CCONJ
ap-4605	25	46	2,r	2,r	NUM
ap-4605	25	47	)	)	PUNCT
ap-4605	25	48	,	,	PUNCT
ap-4605	25	49	corresponding	correspond	VERB
ap-4605	25	50	to	to	ADP
ap-4605	25	51	the	the	DET
ap-4605	25	52	free	free	ADJ
ap-4605	25	53	system	system	NOUN
ap-4605	25	54	q̈	q̈	PUNCT
ap-4605	25	55	=	=	SYM
ap-4605	25	56	0	0	PUNCT
ap-4605	26	1	[	[	X
ap-4605	26	2	7	7	NUM
ap-4605	26	3	,	,	PUNCT
ap-4605	26	4	8	8	NUM
ap-4605	26	5	]	]	PUNCT
ap-4605	26	6	.	.	PUNCT
ap-4605	27	1	whenever	whenever	SCONJ
ap-4605	27	2	the	the	DET
ap-4605	27	3	system	system	NOUN
ap-4605	27	4	arises	arise	VERB
ap-4605	27	5	from	from	ADP
ap-4605	27	6	a	a	DET
ap-4605	27	7	lagrangian	lagrangian	ADJ
ap-4605	27	8	,	,	PUNCT
ap-4605	27	9	a	a	DET
ap-4605	27	10	constant	constant	NOUN
ap-4605	27	11	of	of	ADP
ap-4605	27	12	the	the	DET
ap-4605	27	13	motion	motion	NOUN
ap-4605	27	14	of	of	ADP
ap-4605	27	15	(	(	PUNCT
ap-4605	27	16	2	2	NUM
ap-4605	27	17	)	)	PUNCT
ap-4605	27	18	is	be	AUX
ap-4605	27	19	defined	define	VERB
ap-4605	27	20	as	as	ADP
ap-4605	27	21	a	a	DET
ap-4605	27	22	function	function	NOUN
ap-4605	27	23	f	f	X
ap-4605	27	24	(	(	PUNCT
ap-4605	27	25	t	t	PROPN
ap-4605	27	26	,	,	PUNCT
ap-4605	27	27	q	q	NOUN
ap-4605	27	28	,	,	PUNCT
ap-4605	27	29	q̇	q̇	ADV
ap-4605	27	30	)	)	PUNCT
ap-4605	27	31	satisfying	satisfy	VERB
ap-4605	27	32	the	the	DET
ap-4605	27	33	condition	condition	NOUN
ap-4605	27	34	df	df	NOUN
ap-4605	27	35	dt	dt	NOUN
ap-4605	28	1	=	=	SYM
ap-4605	28	2	∂f	∂f	PROPN
ap-4605	28	3	∂t	∂t	PROPN
ap-4605	28	4	+	+	CCONJ
ap-4605	28	5	q̇i	q̇i	NOUN
ap-4605	28	6	∂f	∂f	PROPN
ap-4605	28	7	∂qi	∂qi	PROPN
ap-4605	28	8	+	+	CCONJ
ap-4605	28	9	q̈i	q̈i	ADV
ap-4605	29	1	∂f	∂f	PROPN
ap-4605	29	2	∂q̇i	∂q̇i	VERB
ap-4605	29	3	=	=	PUNCT
ap-4605	29	4	a(f	a(f	PROPN
ap-4605	29	5	)	)	PUNCT
ap-4605	30	1	=	=	PUNCT
ap-4605	30	2	0	0	X
ap-4605	30	3	.	.	PUNCT
ap-4605	31	1	(	(	PUNCT
ap-4605	31	2	5	5	X
ap-4605	31	3	)	)	PUNCT
ap-4605	31	4	373	373	NUM
ap-4605	31	5	http://dx.doi.org/10.14311/ap.2017.57.0373	http://dx.doi.org/10.14311/ap.2017.57.0373	X
ap-4605	31	6	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	AUX
ap-4605	31	7	rutwig	rutwig	NOUN
ap-4605	31	8	campoamor	campoamor	NOUN
ap-4605	31	9	-	-	PUNCT
ap-4605	31	10	stursberg	stursberg	PROPN
ap-4605	31	11	acta	acta	PROPN
ap-4605	31	12	polytechnica	polytechnica	PROPN
ap-4605	31	13	in	in	ADP
ap-4605	31	14	the	the	DET
ap-4605	31	15	following	following	NOUN
ap-4605	31	16	,	,	PUNCT
ap-4605	31	17	we	we	PRON
ap-4605	31	18	will	will	AUX
ap-4605	31	19	mainly	mainly	ADV
ap-4605	31	20	consider	consider	VERB
ap-4605	31	21	lie	lie	NOUN
ap-4605	31	22	point	point	NOUN
ap-4605	31	23	and	and	CCONJ
ap-4605	31	24	noether	noether	ADJ
ap-4605	31	25	point	point	NOUN
ap-4605	31	26	symmetries	symmetry	NOUN
ap-4605	31	27	and	and	CCONJ
ap-4605	31	28	the	the	DET
ap-4605	31	29	conservation	conservation	NOUN
ap-4605	31	30	laws	law	NOUN
ap-4605	31	31	associated	associate	VERB
ap-4605	31	32	to	to	ADP
ap-4605	31	33	them	they	PRON
ap-4605	31	34	.	.	PUNCT
ap-4605	32	1	in	in	ADP
ap-4605	32	2	this	this	DET
ap-4605	32	3	context	context	NOUN
ap-4605	32	4	,	,	PUNCT
ap-4605	32	5	a	a	DET
ap-4605	32	6	vector	vector	NOUN
ap-4605	32	7	field	field	NOUN
ap-4605	32	8	x	x	X
ap-4605	32	9	=	=	SYM
ap-4605	32	10	ξ	ξ	PROPN
ap-4605	32	11	(	(	PUNCT
ap-4605	32	12	t	t	PROPN
ap-4605	32	13	,	,	PUNCT
ap-4605	32	14	q	q	NOUN
ap-4605	32	15	)	)	PUNCT
ap-4605	32	16	∂	∂	NOUN
ap-4605	33	1	∂t	∂t	PROPN
ap-4605	34	1	+	+	CCONJ
ap-4605	34	2	ηj	ηj	PROPN
ap-4605	34	3	(	(	PUNCT
ap-4605	34	4	t	t	PROPN
ap-4605	34	5	,	,	PUNCT
ap-4605	34	6	q	q	NOUN
ap-4605	34	7	)	)	PUNCT
ap-4605	34	8	∂	∂	NOUN
ap-4605	34	9	∂qj	∂qj	PROPN
ap-4605	34	10	(	(	PUNCT
ap-4605	34	11	6	6	NUM
ap-4605	34	12	)	)	PUNCT
ap-4605	34	13	is	be	AUX
ap-4605	34	14	called	call	VERB
ap-4605	34	15	a	a	DET
ap-4605	34	16	noether	noether	ADJ
ap-4605	34	17	point	point	NOUN
ap-4605	34	18	symmetry	symmetry	NOUN
ap-4605	34	19	of	of	ADP
ap-4605	34	20	(	(	PUNCT
ap-4605	34	21	2	2	X
ap-4605	34	22	)	)	PUNCT
ap-4605	34	23	if	if	SCONJ
ap-4605	34	24	it	it	PRON
ap-4605	34	25	satisfies	satisfy	VERB
ap-4605	34	26	the	the	DET
ap-4605	34	27	constraint	constraint	NOUN
ap-4605	34	28	ẋ	ẋ	PROPN
ap-4605	35	1	(	(	PUNCT
ap-4605	35	2	l	l	NOUN
ap-4605	35	3	)	)	PUNCT
ap-4605	35	4	+	+	CCONJ
ap-4605	35	5	a	a	DET
ap-4605	35	6	(	(	PUNCT
ap-4605	35	7	ξ)l−a	ξ)l−a	NUM
ap-4605	35	8	(	(	PUNCT
ap-4605	35	9	v	v	NOUN
ap-4605	35	10	)	)	PUNCT
ap-4605	35	11	=	=	SYM
ap-4605	35	12	0	0	NUM
ap-4605	35	13	,	,	PUNCT
ap-4605	35	14	(	(	PUNCT
ap-4605	35	15	7	7	X
ap-4605	35	16	)	)	PUNCT
ap-4605	35	17	for	for	ADP
ap-4605	35	18	some	some	DET
ap-4605	35	19	function	function	NOUN
ap-4605	35	20	v	v	NOUN
ap-4605	35	21	(	(	PUNCT
ap-4605	35	22	t	t	PROPN
ap-4605	35	23	,	,	PUNCT
ap-4605	35	24	q	q	NOUN
ap-4605	35	25	)	)	PUNCT
ap-4605	35	26	that	that	PRON
ap-4605	35	27	does	do	AUX
ap-4605	35	28	not	not	PART
ap-4605	35	29	depend	depend	VERB
ap-4605	35	30	on	on	ADP
ap-4605	35	31	the	the	DET
ap-4605	35	32	velocities	velocity	NOUN
ap-4605	35	33	,	,	PUNCT
ap-4605	35	34	and	and	CCONJ
ap-4605	35	35	that	that	SCONJ
ap-4605	35	36	we	we	PRON
ap-4605	35	37	usually	usually	ADV
ap-4605	35	38	refer	refer	VERB
ap-4605	35	39	to	to	ADP
ap-4605	35	40	as	as	ADP
ap-4605	35	41	the	the	DET
ap-4605	35	42	gauge	gauge	ADJ
ap-4605	35	43	term	term	NOUN
ap-4605	35	44	of	of	ADP
ap-4605	35	45	the	the	DET
ap-4605	35	46	symmetry	symmetry	NOUN
ap-4605	35	47	generator	generator	PROPN
ap-4605	35	48	.	.	PUNCT
ap-4605	36	1	expanding	expand	VERB
ap-4605	36	2	the	the	DET
ap-4605	36	3	symmetry	symmetry	NOUN
ap-4605	36	4	condition	condition	NOUN
ap-4605	36	5	(	(	PUNCT
ap-4605	36	6	7	7	X
ap-4605	36	7	)	)	PUNCT
ap-4605	36	8	provides	provide	VERB
ap-4605	36	9	the	the	DET
ap-4605	36	10	following	follow	VERB
ap-4605	36	11	partial	partial	ADJ
ap-4605	36	12	differential	differential	NOUN
ap-4605	36	13	equation	equation	NOUN
ap-4605	36	14	ξ	ξ	PROPN
ap-4605	36	15	(	(	PUNCT
ap-4605	36	16	t	t	PROPN
ap-4605	36	17	,	,	PUNCT
ap-4605	36	18	q	q	NOUN
ap-4605	36	19	)	)	PUNCT
ap-4605	36	20	∂l	∂l	PROPN
ap-4605	37	1	∂t	∂t	PROPN
ap-4605	38	1	+	+	CCONJ
ap-4605	38	2	ηj	ηj	PROPN
ap-4605	38	3	(	(	PUNCT
ap-4605	38	4	t	t	PROPN
ap-4605	38	5	,	,	PUNCT
ap-4605	38	6	q	q	NOUN
ap-4605	38	7	)	)	PUNCT
ap-4605	38	8	∂l	∂l	PROPN
ap-4605	38	9	∂qj	∂qj	PROPN
ap-4605	38	10	+	+	NUM
ap-4605	38	11	η̇j	η̇j	PROPN
ap-4605	38	12	(	(	PUNCT
ap-4605	38	13	t	t	PROPN
ap-4605	38	14	,	,	PUNCT
ap-4605	38	15	q	q	NOUN
ap-4605	38	16	,	,	PUNCT
ap-4605	38	17	q̇	q̇	ADJ
ap-4605	38	18	)	)	PUNCT
ap-4605	38	19	∂l	∂l	NOUN
ap-4605	38	20	∂q̇j	∂q̇j	NOUN
ap-4605	38	21	+	+	CCONJ
ap-4605	38	22	dξ	dξ	PROPN
ap-4605	38	23	dt	dt	PROPN
ap-4605	38	24	l	l	PROPN
ap-4605	38	25	(	(	PUNCT
ap-4605	38	26	t	t	PROPN
ap-4605	38	27	,	,	PUNCT
ap-4605	38	28	q	q	NOUN
ap-4605	38	29	,	,	PUNCT
ap-4605	38	30	q̇)−	q̇)−	PROPN
ap-4605	38	31	∂v	∂v	PROPN
ap-4605	39	1	∂t	∂t	PROPN
ap-4605	40	1	−	−	PROPN
ap-4605	40	2	q̇j	q̇j	PROPN
ap-4605	40	3	∂v	∂v	PROPN
ap-4605	40	4	∂qj	∂qj	PROPN
ap-4605	40	5	=	=	PUNCT
ap-4605	40	6	0	0	X
ap-4605	40	7	.	.	PUNCT
ap-4605	41	1	the	the	DET
ap-4605	41	2	first	first	ADJ
ap-4605	41	3	noether	noether	ADJ
ap-4605	41	4	theorem	theorem	NOUN
ap-4605	41	5	(	(	PUNCT
ap-4605	41	6	see	see	VERB
ap-4605	41	7	e.g.	e.g.	ADV
ap-4605	41	8	[	[	X
ap-4605	41	9	1	1	NUM
ap-4605	41	10	]	]	PUNCT
ap-4605	41	11	)	)	PUNCT
ap-4605	41	12	states	state	VERB
ap-4605	41	13	that	that	SCONJ
ap-4605	41	14	to	to	ADP
ap-4605	41	15	any	any	DET
ap-4605	41	16	symmetry	symmetry	NOUN
ap-4605	41	17	(	(	PUNCT
ap-4605	41	18	6	6	NUM
ap-4605	41	19	)	)	PUNCT
ap-4605	41	20	there	there	PRON
ap-4605	41	21	corresponds	correspond	VERB
ap-4605	41	22	a	a	DET
ap-4605	41	23	constant	constant	NOUN
ap-4605	41	24	of	of	ADP
ap-4605	41	25	the	the	DET
ap-4605	41	26	motion	motion	NOUN
ap-4605	41	27	determined	determine	VERB
ap-4605	41	28	by	by	ADP
ap-4605	41	29	the	the	DET
ap-4605	41	30	rule	rule	NOUN
ap-4605	42	1	j	j	PROPN
ap-4605	42	2	=	=	SYM
ap-4605	42	3	ξ	ξ	PROPN
ap-4605	42	4	(	(	PUNCT
ap-4605	42	5	q̇k	q̇k	NOUN
ap-4605	42	6	∂l	∂l	PROPN
ap-4605	42	7	∂q̇k	∂q̇k	NOUN
ap-4605	42	8	−	−	PROPN
ap-4605	42	9	l	l	NOUN
ap-4605	42	10	)	)	PUNCT
ap-4605	43	1	−	−	ADP
ap-4605	43	2	ηk	ηk	VERB
ap-4605	43	3	∂l	∂l	PROPN
ap-4605	43	4	∂q̇k	∂q̇k	NOUN
ap-4605	43	5	+	+	CCONJ
ap-4605	43	6	v	v	NOUN
ap-4605	43	7	(	(	PUNCT
ap-4605	43	8	t	t	PROPN
ap-4605	43	9	,	,	PUNCT
ap-4605	43	10	q	q	NOUN
ap-4605	43	11	)	)	PUNCT
ap-4605	43	12	.	.	PUNCT
ap-4605	44	1	(	(	PUNCT
ap-4605	44	2	8)	8)	NUM
ap-4605	44	3	it	it	PRON
ap-4605	44	4	follows	follow	VERB
ap-4605	44	5	in	in	ADP
ap-4605	44	6	particular	particular	ADJ
ap-4605	44	7	that	that	SCONJ
ap-4605	44	8	a	a	DET
ap-4605	44	9	constant	constant	NOUN
ap-4605	44	10	of	of	ADP
ap-4605	44	11	the	the	DET
ap-4605	44	12	motion	motion	NOUN
ap-4605	44	13	j	j	PROPN
ap-4605	44	14	is	be	AUX
ap-4605	44	15	an	an	DET
ap-4605	44	16	invariant	invariant	NOUN
ap-4605	44	17	of	of	ADP
ap-4605	44	18	ẋ	ẋ	PROPN
ap-4605	44	19	,	,	PUNCT
ap-4605	44	20	i.e.	i.e.	X
ap-4605	44	21	,	,	PUNCT
ap-4605	44	22	the	the	DET
ap-4605	44	23	condition	condition	NOUN
ap-4605	44	24	ẋ(j	ẋ(j	PUNCT
ap-4605	44	25	)	)	PUNCT
ap-4605	45	1	=	=	SYM
ap-4605	45	2	0	0	NUM
ap-4605	45	3	is	be	AUX
ap-4605	45	4	satisfied	satisfied	ADJ
ap-4605	45	5	.	.	PUNCT
ap-4605	46	1	2.1	2.1	NUM
ap-4605	46	2	.	.	PUNCT
ap-4605	46	3	perturbations	perturbation	NOUN
ap-4605	46	4	that	that	PRON
ap-4605	46	5	preserve	preserve	VERB
ap-4605	46	6	symmetry	symmetry	NOUN
ap-4605	46	7	subalgebras	subalgebras	PROPN
ap-4605	46	8	given	give	VERB
ap-4605	46	9	a	a	DET
ap-4605	46	10	system	system	NOUN
ap-4605	46	11	described	describe	VERB
ap-4605	46	12	by	by	ADP
ap-4605	46	13	a	a	DET
ap-4605	46	14	lagrangian	lagrangian	ADJ
ap-4605	46	15	l	l	NOUN
ap-4605	46	16	(	(	PUNCT
ap-4605	46	17	t	t	PROPN
ap-4605	46	18	,	,	PUNCT
ap-4605	46	19	q	q	NOUN
ap-4605	46	20	,	,	PUNCT
ap-4605	46	21	q̇	q̇	ADV
ap-4605	46	22	)	)	PUNCT
ap-4605	46	23	and	and	CCONJ
ap-4605	46	24	having	have	VERB
ap-4605	46	25	an	an	DET
ap-4605	46	26	r	r	NOUN
ap-4605	46	27	-	-	PUNCT
ap-4605	46	28	dimensional	dimensional	ADJ
ap-4605	46	29	lie	lie	NOUN
ap-4605	46	30	algebra	algebra	VERB
ap-4605	46	31	lns	lns	PROPN
ap-4605	46	32	of	of	ADP
ap-4605	46	33	noether	noether	PROPN
ap-4605	46	34	point	point	NOUN
ap-4605	46	35	symmetries	symmetry	NOUN
ap-4605	46	36	,	,	PUNCT
ap-4605	46	37	fixing	fix	VERB
ap-4605	46	38	a	a	DET
ap-4605	46	39	certain	certain	ADJ
ap-4605	46	40	subalgebra	subalgebra	NOUN
ap-4605	46	41	l0	l0	PROPN
ap-4605	46	42	<	<	X
ap-4605	46	43	lns	lns	PROPN
ap-4605	46	44	of	of	ADP
ap-4605	46	45	dimension	dimension	NOUN
ap-4605	46	46	r0	r0	NOUN
ap-4605	46	47	<	<	X
ap-4605	46	48	r	r	NOUN
ap-4605	46	49	we	we	PRON
ap-4605	46	50	can	can	AUX
ap-4605	46	51	ask	ask	VERB
ap-4605	46	52	whether	whether	SCONJ
ap-4605	46	53	a	a	DET
ap-4605	46	54	perturbed	perturb	VERB
ap-4605	46	55	lagrangian	lagrangian	ADJ
ap-4605	46	56	l̂	l̂	PUNCT
ap-4605	46	57	=	=	PUNCT
ap-4605	46	58	l+	l+	X
ap-4605	46	59	εs	εs	ADP
ap-4605	46	60	(	(	PUNCT
ap-4605	46	61	t	t	PROPN
ap-4605	46	62	,	,	PUNCT
ap-4605	46	63	q	q	NOUN
ap-4605	46	64	,	,	PUNCT
ap-4605	46	65	q̇	q̇	ADV
ap-4605	46	66	)	)	PUNCT
ap-4605	46	67	exists	exist	VERB
ap-4605	46	68	such	such	ADJ
ap-4605	46	69	that	that	SCONJ
ap-4605	46	70	the	the	DET
ap-4605	46	71	symmetry	symmetry	NOUN
ap-4605	46	72	generators	generator	VERB
ap-4605	46	73	xj	xj	PROPN
ap-4605	46	74	(	(	PUNCT
ap-4605	46	75	1	1	NUM
ap-4605	46	76	≤	≤	NUM
ap-4605	46	77	j	j	PROPN
ap-4605	46	78	≤	≤	PROPN
ap-4605	46	79	r0	r0	NOUN
ap-4605	46	80	)	)	PUNCT
ap-4605	46	81	of	of	ADP
ap-4605	46	82	l0	l0	PROPN
ap-4605	46	83	are	be	AUX
ap-4605	46	84	still	still	ADV
ap-4605	46	85	noether	noether	ADJ
ap-4605	46	86	point	point	NOUN
ap-4605	46	87	symmetries	symmetry	NOUN
ap-4605	46	88	of	of	ADP
ap-4605	46	89	l̂.	l̂.	NOUN
ap-4605	46	90	clearly	clearly	ADV
ap-4605	46	91	,	,	PUNCT
ap-4605	46	92	the	the	DET
ap-4605	46	93	equations	equation	NOUN
ap-4605	46	94	of	of	ADP
ap-4605	46	95	the	the	DET
ap-4605	46	96	motion	motion	NOUN
ap-4605	46	97	(	(	PUNCT
ap-4605	46	98	1	1	NUM
ap-4605	46	99	)	)	PUNCT
ap-4605	46	100	of	of	ADP
ap-4605	46	101	l̂	l̂	PROPN
ap-4605	46	102	are	be	AUX
ap-4605	46	103	given	give	VERB
ap-4605	46	104	by	by	ADP
ap-4605	46	105	d	d	X
ap-4605	46	106	dt	dt	X
ap-4605	46	107	(	(	PUNCT
ap-4605	46	108	∂l	∂l	PROPN
ap-4605	46	109	∂q̇i	∂q̇i	VERB
ap-4605	46	110	)	)	PUNCT
ap-4605	47	1	−	−	PROPN
ap-4605	47	2	∂l	∂l	NOUN
ap-4605	48	1	∂qi	∂qi	NOUN
ap-4605	49	1	+	+	CCONJ
ap-4605	49	2	d	d	X
ap-4605	49	3	dt	dt	X
ap-4605	50	1	(	(	PUNCT
ap-4605	50	2	∂s	∂s	PROPN
ap-4605	50	3	∂q̇i	∂q̇i	VERB
ap-4605	50	4	)	)	PUNCT
ap-4605	51	1	−	−	PROPN
ap-4605	52	1	∂s	∂s	PROPN
ap-4605	52	2	∂qi	∂qi	PROPN
ap-4605	52	3	=	=	SYM
ap-4605	52	4	0	0	NUM
ap-4605	52	5	,	,	PUNCT
ap-4605	52	6	(	(	PUNCT
ap-4605	52	7	9	9	NUM
ap-4605	52	8	)	)	PUNCT
ap-4605	52	9	so	so	SCONJ
ap-4605	52	10	that	that	SCONJ
ap-4605	52	11	the	the	DET
ap-4605	52	12	symmetry	symmetry	NOUN
ap-4605	52	13	condition	condition	NOUN
ap-4605	52	14	for	for	ADP
ap-4605	52	15	the	the	DET
ap-4605	52	16	subalgebra	subalgebra	PROPN
ap-4605	52	17	l0	l0	NOUN
ap-4605	52	18	leads	lead	NOUN
ap-4605	52	19	,	,	PUNCT
ap-4605	52	20	for	for	ADP
ap-4605	52	21	each	each	DET
ap-4605	52	22	generator	generator	NOUN
ap-4605	52	23	xk	xk	PROPN
ap-4605	52	24	(	(	PUNCT
ap-4605	52	25	1	1	NUM
ap-4605	52	26	≤	≤	NUM
ap-4605	52	27	k	k	PROPN
ap-4605	52	28	≤	≤	PROPN
ap-4605	52	29	r0	r0	NOUN
ap-4605	52	30	)	)	PUNCT
ap-4605	52	31	,	,	PUNCT
ap-4605	52	32	to	to	ADP
ap-4605	52	33	the	the	DET
ap-4605	52	34	differential	differential	ADJ
ap-4605	52	35	equation	equation	NOUN
ap-4605	52	36	ẋk	ẋk	PROPN
ap-4605	52	37	(	(	PUNCT
ap-4605	52	38	l̂	l̂	X
ap-4605	52	39	)	)	PUNCT
ap-4605	53	1	+	+	CCONJ
ap-4605	53	2	a	a	DET
ap-4605	53	3	(	(	PUNCT
ap-4605	53	4	ξk	ξk	NOUN
ap-4605	53	5	)	)	PUNCT
ap-4605	53	6	l̂−a	l̂−a	VERB
ap-4605	53	7	(	(	PUNCT
ap-4605	53	8	vk	vk	NOUN
ap-4605	53	9	)	)	PUNCT
ap-4605	53	10	=	=	PUNCT
ap-4605	53	11	ẋk	ẋk	PROPN
ap-4605	53	12	(	(	PUNCT
ap-4605	53	13	l	l	NOUN
ap-4605	53	14	)	)	PUNCT
ap-4605	53	15	+	+	CCONJ
ap-4605	53	16	a	a	DET
ap-4605	53	17	(	(	PUNCT
ap-4605	53	18	ξk)l−a	ξk)l−a	PROPN
ap-4605	53	19	(	(	PUNCT
ap-4605	53	20	vk	vk	PROPN
ap-4605	53	21	)	)	PUNCT
ap-4605	53	22	+	+	CCONJ
ap-4605	53	23	ẋk	ẋk	PROPN
ap-4605	53	24	(	(	PUNCT
ap-4605	53	25	s	s	X
ap-4605	53	26	)	)	PUNCT
ap-4605	53	27	+	+	X
ap-4605	53	28	dξk	dξk	NOUN
ap-4605	53	29	dt	dt	X
ap-4605	53	30	s	s	NOUN
ap-4605	53	31	=	=	NOUN
ap-4605	53	32	0	0	PROPN
ap-4605	53	33	.	.	PUNCT
ap-4605	54	1	(	(	PUNCT
ap-4605	54	2	10	10	NUM
ap-4605	54	3	)	)	PUNCT
ap-4605	54	4	now	now	ADV
ap-4605	54	5	the	the	DET
ap-4605	54	6	vector	vector	NOUN
ap-4605	54	7	fields	field	NOUN
ap-4605	54	8	xk	xk	PROPN
ap-4605	54	9	are	be	AUX
ap-4605	54	10	noether	noether	ADJ
ap-4605	54	11	symmetries	symmetry	NOUN
ap-4605	54	12	of	of	ADP
ap-4605	54	13	the	the	DET
ap-4605	54	14	lagrangian	lagrangian	ADJ
ap-4605	54	15	l	l	NOUN
ap-4605	54	16	,	,	PUNCT
ap-4605	54	17	and	and	CCONJ
ap-4605	54	18	fixing	fix	VERB
ap-4605	54	19	the	the	DET
ap-4605	54	20	gauge	gauge	ADJ
ap-4605	54	21	terms	term	NOUN
ap-4605	54	22	vk(t	vk(t	VERB
ap-4605	54	23	,	,	PUNCT
ap-4605	54	24	q	q	NOUN
ap-4605	54	25	)	)	PUNCT
ap-4605	54	26	,	,	PUNCT
ap-4605	54	27	the	the	DET
ap-4605	54	28	equation	equation	NOUN
ap-4605	54	29	(	(	PUNCT
ap-4605	54	30	10	10	NUM
ap-4605	54	31	)	)	PUNCT
ap-4605	54	32	simplifies	simplifie	NOUN
ap-4605	54	33	to	to	ADP
ap-4605	54	34	a	a	DET
ap-4605	54	35	pde	pde	NOUN
ap-4605	54	36	involving	involve	VERB
ap-4605	54	37	merely	merely	ADV
ap-4605	54	38	the	the	DET
ap-4605	54	39	perturbation	perturbation	NOUN
ap-4605	54	40	term	term	NOUN
ap-4605	54	41	s	s	PART
ap-4605	54	42	(	(	PUNCT
ap-4605	54	43	t	t	PROPN
ap-4605	54	44	,	,	PUNCT
ap-4605	54	45	q	q	NOUN
ap-4605	54	46	,	,	PUNCT
ap-4605	54	47	q̇	q̇	ADV
ap-4605	54	48	):	):	PUNCT
ap-4605	54	49	ẋk	ẋk	PROPN
ap-4605	54	50	(	(	PUNCT
ap-4605	54	51	s)+	s)+	PROPN
ap-4605	54	52	dξk	dξk	NOUN
ap-4605	54	53	dt	dt	X
ap-4605	54	54	s	s	X
ap-4605	54	55	(	(	PUNCT
ap-4605	54	56	t	t	PROPN
ap-4605	54	57	,	,	PUNCT
ap-4605	54	58	q	q	NOUN
ap-4605	54	59	,	,	PUNCT
ap-4605	54	60	q̇	q̇	NOUN
ap-4605	54	61	)	)	PUNCT
ap-4605	55	1	=	=	SYM
ap-4605	55	2	ξk	ξk	ADP
ap-4605	55	3	(	(	PUNCT
ap-4605	55	4	t	t	PROPN
ap-4605	55	5	,	,	PUNCT
ap-4605	55	6	q	q	NOUN
ap-4605	55	7	)	)	PUNCT
ap-4605	55	8	∂s	∂s	PROPN
ap-4605	56	1	∂t	∂t	PROPN
ap-4605	57	1	+	+	NUM
ap-4605	57	2	ηjk	ηjk	NOUN
ap-4605	57	3	(	(	PUNCT
ap-4605	57	4	t	t	PROPN
ap-4605	57	5	,	,	PUNCT
ap-4605	57	6	q	q	NOUN
ap-4605	57	7	)	)	PUNCT
ap-4605	57	8	∂s	∂s	PROPN
ap-4605	58	1	∂qj	∂qj	PROPN
ap-4605	58	2	+	+	CCONJ
ap-4605	58	3	η̇jk	η̇jk	PROPN
ap-4605	58	4	(	(	PUNCT
ap-4605	58	5	t	t	PROPN
ap-4605	58	6	,	,	PUNCT
ap-4605	58	7	q	q	NOUN
ap-4605	58	8	,	,	PUNCT
ap-4605	58	9	q̇	q̇	ADJ
ap-4605	58	10	)	)	PUNCT
ap-4605	58	11	∂s	∂s	NOUN
ap-4605	58	12	∂q̇j	∂q̇j	NOUN
ap-4605	58	13	+	+	CCONJ
ap-4605	58	14	dξk	dξk	NOUN
ap-4605	58	15	dt	dt	X
ap-4605	58	16	s	s	X
ap-4605	58	17	(	(	PUNCT
ap-4605	58	18	t	t	PROPN
ap-4605	58	19	,	,	PUNCT
ap-4605	58	20	q	q	NOUN
ap-4605	58	21	,	,	PUNCT
ap-4605	58	22	q̇	q̇	NOUN
ap-4605	58	23	)	)	PUNCT
ap-4605	58	24	=	=	SYM
ap-4605	58	25	0	0	NUM
ap-4605	58	26	,	,	PUNCT
ap-4605	58	27	(	(	PUNCT
ap-4605	58	28	11	11	NUM
ap-4605	58	29	)	)	PUNCT
ap-4605	58	30	where	where	SCONJ
ap-4605	58	31	1	1	NUM
ap-4605	58	32	≤	≤	NUM
ap-4605	58	33	k	k	PROPN
ap-4605	58	34	≤	≤	PROPN
ap-4605	58	35	r0	r0	NOUN
ap-4605	58	36	.	.	PUNCT
ap-4605	59	1	in	in	ADP
ap-4605	59	2	the	the	DET
ap-4605	59	3	case	case	NOUN
ap-4605	59	4	of	of	ADP
ap-4605	59	5	velocity	velocity	NOUN
ap-4605	59	6	-	-	PUNCT
ap-4605	59	7	independent	independent	ADJ
ap-4605	59	8	perturbation	perturbation	NOUN
ap-4605	59	9	terms	term	NOUN
ap-4605	59	10	,	,	PUNCT
ap-4605	59	11	a	a	DET
ap-4605	59	12	straightforward	straightforward	ADJ
ap-4605	59	13	verification	verification	NOUN
ap-4605	59	14	shows	show	VERB
ap-4605	59	15	that	that	SCONJ
ap-4605	59	16	a	a	DET
ap-4605	59	17	noether	noether	ADJ
ap-4605	59	18	symmetry	symmetry	NOUN
ap-4605	59	19	is	be	AUX
ap-4605	59	20	preserved	preserve	VERB
ap-4605	59	21	only	only	ADV
ap-4605	59	22	if	if	SCONJ
ap-4605	59	23	∂ξk	∂ξk	PROPN
ap-4605	59	24	∂qj	∂qj	PROPN
ap-4605	59	25	=	=	SYM
ap-4605	59	26	0	0	NUM
ap-4605	59	27	holds	hold	VERB
ap-4605	59	28	for	for	SCONJ
ap-4605	59	29	all	all	DET
ap-4605	59	30	1	1	NUM
ap-4605	59	31	≤	≤	NUM
ap-4605	59	32	k	k	NOUN
ap-4605	59	33	≤	≤	NOUN
ap-4605	59	34	r0	r0	NOUN
ap-4605	59	35	and	and	CCONJ
ap-4605	59	36	1	1	NUM
ap-4605	59	37	≤	≤	NUM
ap-4605	59	38	j	j	PROPN
ap-4605	59	39	≤	≤	PROPN
ap-4605	59	40	n.	n.	NOUN
ap-4605	59	41	this	this	PRON
ap-4605	59	42	allows	allow	VERB
ap-4605	59	43	to	to	PART
ap-4605	59	44	restrict	restrict	VERB
ap-4605	59	45	the	the	DET
ap-4605	59	46	perturbation	perturbation	NOUN
ap-4605	59	47	analysis	analysis	NOUN
ap-4605	59	48	to	to	ADP
ap-4605	59	49	subalgebras	subalgebras	PROPN
ap-4605	59	50	l0	l0	PROPN
ap-4605	59	51	,	,	PUNCT
ap-4605	59	52	the	the	DET
ap-4605	59	53	generators	generator	NOUN
ap-4605	59	54	of	of	ADP
ap-4605	59	55	which	which	PRON
ap-4605	59	56	have	have	VERB
ap-4605	59	57	components	component	NOUN
ap-4605	59	58	of	of	ADP
ap-4605	59	59	the	the	DET
ap-4605	59	60	type	type	NOUN
ap-4605	59	61	ξk	ξk	ADP
ap-4605	59	62	=	=	NOUN
ap-4605	59	63	ϕk(t	ϕk(t	X
ap-4605	59	64	)	)	PUNCT
ap-4605	59	65	.	.	PUNCT
ap-4605	60	1	this	this	PRON
ap-4605	60	2	agrees	agree	VERB
ap-4605	60	3	with	with	ADP
ap-4605	60	4	the	the	DET
ap-4605	60	5	usually	usually	ADV
ap-4605	60	6	observed	observe	VERB
ap-4605	60	7	pattern	pattern	NOUN
ap-4605	60	8	of	of	ADP
ap-4605	60	9	lie	lie	NOUN
ap-4605	60	10	point	point	NOUN
ap-4605	60	11	symmetries	symmetry	NOUN
ap-4605	60	12	of	of	ADP
ap-4605	60	13	nonlinear	nonlinear	ADJ
ap-4605	60	14	second	second	ADJ
ap-4605	60	15	-	-	PUNCT
ap-4605	60	16	order	order	NOUN
ap-4605	60	17	systems	system	NOUN
ap-4605	60	18	of	of	ADP
ap-4605	60	19	differential	differential	ADJ
ap-4605	60	20	equations	equation	NOUN
ap-4605	60	21	of	of	ADP
ap-4605	60	22	the	the	DET
ap-4605	60	23	type	type	NOUN
ap-4605	60	24	q̈	q̈	PROPN
ap-4605	60	25	=	=	SYM
ap-4605	60	26	ω	ω	PROPN
ap-4605	60	27	(	(	PUNCT
ap-4605	60	28	t	t	PROPN
ap-4605	60	29	,	,	PUNCT
ap-4605	60	30	q	q	NOUN
ap-4605	60	31	)	)	PUNCT
ap-4605	61	1	[	[	X
ap-4605	61	2	7	7	NUM
ap-4605	61	3	,	,	PUNCT
ap-4605	61	4	8	8	NUM
ap-4605	61	5	]	]	PUNCT
ap-4605	61	6	.	.	PUNCT
ap-4605	62	1	3	3	X
ap-4605	62	2	.	.	X
ap-4605	62	3	functional	functional	ADJ
ap-4605	62	4	realizations	realization	NOUN
ap-4605	62	5	of	of	ADP
ap-4605	62	6	sl(2,r	sl(2,r	NOUN
ap-4605	62	7	)	)	PUNCT
ap-4605	62	8	as	as	ADP
ap-4605	62	9	noether	noether	ADJ
ap-4605	62	10	symmetry	symmetry	NOUN
ap-4605	62	11	algebra	algebra	PROPN
ap-4605	62	12	as	as	SCONJ
ap-4605	62	13	has	have	AUX
ap-4605	62	14	been	be	AUX
ap-4605	62	15	already	already	ADV
ap-4605	62	16	pointed	point	VERB
ap-4605	62	17	out	out	ADP
ap-4605	62	18	in	in	ADP
ap-4605	62	19	many	many	ADJ
ap-4605	62	20	contexts	context	NOUN
ap-4605	62	21	,	,	PUNCT
ap-4605	62	22	the	the	DET
ap-4605	62	23	non	non	ADJ
ap-4605	62	24	-	-	ADJ
ap-4605	62	25	compact	compact	ADJ
ap-4605	62	26	lie	lie	NOUN
ap-4605	62	27	algebra	algebra	NOUN
ap-4605	62	28	sl(2,r	sl(2,r	NOUN
ap-4605	62	29	)	)	PUNCT
ap-4605	62	30	plays	play	VERB
ap-4605	62	31	a	a	DET
ap-4605	62	32	relevant	relevant	ADJ
ap-4605	62	33	role	role	NOUN
ap-4605	62	34	within	within	ADP
ap-4605	62	35	the	the	DET
ap-4605	62	36	group	group	NOUN
ap-4605	62	37	-	-	PUNCT
ap-4605	62	38	theoretic	theoretic	NOUN
ap-4605	62	39	analysis	analysis	NOUN
ap-4605	62	40	of	of	ADP
ap-4605	62	41	differential	differential	ADJ
ap-4605	62	42	equations	equation	NOUN
ap-4605	62	43	,	,	PUNCT
ap-4605	62	44	in	in	ADP
ap-4605	62	45	particular	particular	ADJ
ap-4605	62	46	,	,	PUNCT
ap-4605	62	47	concerning	concern	VERB
ap-4605	62	48	the	the	DET
ap-4605	62	49	(	(	PUNCT
ap-4605	62	50	super)integrability	super)integrability	NOUN
ap-4605	62	51	of	of	ADP
ap-4605	62	52	plane	plane	NOUN
ap-4605	62	53	systems	system	NOUN
ap-4605	62	54	and	and	CCONJ
ap-4605	62	55	the	the	DET
ap-4605	62	56	linearization	linearization	NOUN
ap-4605	62	57	analysis	analysis	NOUN
ap-4605	62	58	[	[	X
ap-4605	62	59	9–11	9–11	X
ap-4605	62	60	]	]	PUNCT
ap-4605	62	61	.	.	PUNCT
ap-4605	63	1	this	this	DET
ap-4605	63	2	fact	fact	NOUN
ap-4605	63	3	suggests	suggest	VERB
ap-4605	63	4	to	to	PART
ap-4605	63	5	consider	consider	VERB
ap-4605	63	6	this	this	DET
ap-4605	63	7	lie	lie	NOUN
ap-4605	63	8	algebra	algebra	VERB
ap-4605	63	9	more	more	ADV
ap-4605	63	10	closely	closely	ADV
ap-4605	63	11	in	in	ADP
ap-4605	63	12	the	the	DET
ap-4605	63	13	context	context	NOUN
ap-4605	63	14	of	of	ADP
ap-4605	63	15	inverse	inverse	NOUN
ap-4605	63	16	problems	problem	NOUN
ap-4605	63	17	,	,	PUNCT
ap-4605	63	18	as	as	SCONJ
ap-4605	63	19	done	do	VERB
ap-4605	63	20	in	in	ADP
ap-4605	63	21	[	[	X
ap-4605	63	22	12	12	NUM
ap-4605	63	23	]	]	PUNCT
ap-4605	63	24	.	.	PUNCT
ap-4605	64	1	for	for	ADP
ap-4605	64	2	these	these	DET
ap-4605	64	3	reasons	reason	NOUN
ap-4605	64	4	,	,	PUNCT
ap-4605	64	5	in	in	ADP
ap-4605	64	6	the	the	DET
ap-4605	64	7	following	following	NOUN
ap-4605	64	8	we	we	PRON
ap-4605	64	9	restrict	restrict	VERB
ap-4605	64	10	our	our	PRON
ap-4605	64	11	analysis	analysis	NOUN
ap-4605	64	12	to	to	ADP
ap-4605	64	13	sl(2,r	sl(2,r	NOUN
ap-4605	64	14	)	)	PUNCT
ap-4605	64	15	.	.	PUNCT
ap-4605	65	1	prior	prior	ADV
ap-4605	65	2	to	to	ADP
ap-4605	65	3	analyzing	analyze	VERB
ap-4605	65	4	a	a	DET
ap-4605	65	5	functional	functional	ADJ
ap-4605	65	6	realization	realization	NOUN
ap-4605	65	7	of	of	ADP
ap-4605	65	8	sl(2,r	sl(2,r	NOUN
ap-4605	65	9	)	)	PUNCT
ap-4605	65	10	,	,	PUNCT
ap-4605	65	11	we	we	PRON
ap-4605	65	12	make	make	VERB
ap-4605	65	13	some	some	DET
ap-4605	65	14	observations	observation	NOUN
ap-4605	65	15	on	on	ADP
ap-4605	65	16	the	the	DET
ap-4605	65	17	generic	generic	ADJ
ap-4605	65	18	structure	structure	NOUN
ap-4605	65	19	of	of	ADP
ap-4605	65	20	noether	noether	ADJ
ap-4605	65	21	point	point	NOUN
ap-4605	65	22	symmetries	symmetry	NOUN
ap-4605	65	23	.	.	PUNCT
ap-4605	66	1	consider	consider	VERB
ap-4605	66	2	to	to	ADP
ap-4605	66	3	this	this	DET
ap-4605	66	4	extent	extent	NOUN
ap-4605	66	5	a	a	DET
ap-4605	66	6	lagrangian	lagrangian	ADJ
ap-4605	66	7	adopting	adopt	VERB
ap-4605	66	8	the	the	DET
ap-4605	66	9	kinetic	kinetic	ADJ
ap-4605	66	10	form	form	NOUN
ap-4605	66	11	t	t	NOUN
ap-4605	66	12	=	=	SYM
ap-4605	66	13	1	1	NUM
ap-4605	66	14	2aij(q)q̇iq̇j	2aij(q)q̇iq̇j	NOUN
ap-4605	66	15	,	,	PUNCT
ap-4605	66	16	(	(	PUNCT
ap-4605	66	17	12	12	NUM
ap-4605	66	18	)	)	PUNCT
ap-4605	66	19	such	such	ADJ
ap-4605	66	20	that	that	DET
ap-4605	66	21	a11(q)a22(q)−a12(q)2	a11(q)a22(q)−a12(q)2	PROPN
ap-4605	66	22	6=	6=	ADP
ap-4605	66	23	0	0	NUM
ap-4605	66	24	holds	hold	NOUN
ap-4605	66	25	.	.	PUNCT
ap-4605	67	1	lemma	lemma	PROPN
ap-4605	67	2	1	1	X
ap-4605	67	3	.	.	PUNCT
ap-4605	68	1	let	let	VERB
ap-4605	68	2	x	x	SYM
ap-4605	68	3	=	=	SYM
ap-4605	68	4	ξ(t	ξ(t	NOUN
ap-4605	68	5	,	,	PUNCT
ap-4605	68	6	q	q	NOUN
ap-4605	68	7	)	)	PUNCT
ap-4605	68	8	∂∂t	∂∂t	PROPN
ap-4605	68	9	+	+	CCONJ
ap-4605	68	10	ηj(t	ηj(t	PROPN
ap-4605	68	11	,	,	PUNCT
ap-4605	68	12	q	q	NOUN
ap-4605	68	13	)	)	PUNCT
ap-4605	68	14	∂	∂	NOUN
ap-4605	68	15	∂qj	∂qj	PROPN
ap-4605	68	16	be	be	VERB
ap-4605	68	17	a	a	DET
ap-4605	68	18	noether	noether	ADJ
ap-4605	68	19	point	point	NOUN
ap-4605	68	20	symmetry	symmetry	NOUN
ap-4605	68	21	of	of	ADP
ap-4605	68	22	a	a	DET
ap-4605	68	23	lagrangian	lagrangian	ADJ
ap-4605	68	24	(	(	PUNCT
ap-4605	68	25	12	12	NUM
ap-4605	68	26	)	)	PUNCT
ap-4605	68	27	.	.	PUNCT
ap-4605	69	1	then	then	ADV
ap-4605	69	2	the	the	DET
ap-4605	69	3	components	component	NOUN
ap-4605	69	4	have	have	VERB
ap-4605	69	5	the	the	DET
ap-4605	69	6	generic	generic	ADJ
ap-4605	69	7	structure	structure	NOUN
ap-4605	69	8	ξ(t	ξ(t	NOUN
ap-4605	69	9	,	,	PUNCT
ap-4605	69	10	q	q	NOUN
ap-4605	69	11	)	)	PUNCT
ap-4605	69	12	=	=	SYM
ap-4605	69	13	c1	c1	PROPN
ap-4605	69	14	t	t	PROPN
ap-4605	69	15	2	2	NUM
ap-4605	69	16	+	+	CCONJ
ap-4605	69	17	c2t+	c2t+	NOUN
ap-4605	69	18	c3	c3	NOUN
ap-4605	69	19	,	,	PUNCT
ap-4605	69	20	ηj(t	ηj(t	X
ap-4605	69	21	,	,	PUNCT
ap-4605	69	22	q	q	NOUN
ap-4605	69	23	)	)	PUNCT
ap-4605	69	24	=	=	VERB
ap-4605	69	25	ηj1(q)t+	ηj1(q)t+	NOUN
ap-4605	69	26	ηj2(q	ηj2(q	PROPN
ap-4605	69	27	)	)	PUNCT
ap-4605	69	28	.	.	PUNCT
ap-4605	70	1	(	(	PUNCT
ap-4605	70	2	13	13	NUM
ap-4605	70	3	)	)	PUNCT
ap-4605	70	4	moreover	moreover	ADV
ap-4605	70	5	,	,	PUNCT
ap-4605	70	6	the	the	DET
ap-4605	70	7	gauge	gauge	ADJ
ap-4605	70	8	term	term	NOUN
ap-4605	70	9	does	do	AUX
ap-4605	70	10	not	not	PART
ap-4605	70	11	explicitly	explicitly	ADV
ap-4605	70	12	depend	depend	VERB
ap-4605	70	13	of	of	ADP
ap-4605	70	14	time	time	NOUN
ap-4605	70	15	,	,	PUNCT
ap-4605	70	16	i.e.	i.e.	X
ap-4605	70	17	,	,	PUNCT
ap-4605	70	18	v	v	NOUN
ap-4605	70	19	=	=	SYM
ap-4605	70	20	v	v	NOUN
ap-4605	70	21	(	(	PUNCT
ap-4605	70	22	q	q	NOUN
ap-4605	70	23	)	)	PUNCT
ap-4605	70	24	.	.	PUNCT
ap-4605	71	1	proof	proof	NOUN
ap-4605	71	2	.	.	PUNCT
ap-4605	72	1	developing	develop	VERB
ap-4605	72	2	the	the	DET
ap-4605	72	3	symmetry	symmetry	NOUN
ap-4605	72	4	condition	condition	NOUN
ap-4605	72	5	(	(	PUNCT
ap-4605	72	6	7	7	NUM
ap-4605	72	7	)	)	PUNCT
ap-4605	72	8	and	and	CCONJ
ap-4605	72	9	keeping	keep	VERB
ap-4605	72	10	only	only	ADV
ap-4605	72	11	the	the	DET
ap-4605	72	12	independent	independent	ADJ
ap-4605	72	13	term	term	NOUN
ap-4605	72	14	,	,	PUNCT
ap-4605	72	15	as	as	ADV
ap-4605	72	16	well	well	ADV
ap-4605	72	17	as	as	ADP
ap-4605	72	18	the	the	DET
ap-4605	72	19	terms	term	NOUN
ap-4605	72	20	with	with	ADP
ap-4605	72	21	highest	high	ADJ
ap-4605	72	22	power	power	NOUN
ap-4605	72	23	in	in	ADP
ap-4605	72	24	q	q	NOUN
ap-4605	72	25	,	,	PUNCT
ap-4605	72	26	we	we	PRON
ap-4605	72	27	obtain	obtain	VERB
ap-4605	72	28	that	that	SCONJ
ap-4605	72	29	∂v	∂v	PROPN
ap-4605	72	30	∂t	∂t	PROPN
ap-4605	72	31	=	=	SYM
ap-4605	72	32	0	0	PROPN
ap-4605	72	33	and	and	CCONJ
ap-4605	72	34	the	the	DET
ap-4605	72	35	conditions	condition	NOUN
ap-4605	72	36	∂ξ	∂ξ	NOUN
ap-4605	72	37	∂q1	∂q1	NOUN
ap-4605	72	38	a11(q	a11(q	ADV
ap-4605	72	39	)	)	PUNCT
ap-4605	72	40	=	=	SYM
ap-4605	73	1	0	0	NUM
ap-4605	73	2	,	,	PUNCT
ap-4605	73	3	∂ξ	∂ξ	ADJ
ap-4605	73	4	∂q2	∂q2	ADJ
ap-4605	73	5	a22(q	a22(q	NOUN
ap-4605	73	6	)	)	PUNCT
ap-4605	73	7	=	=	SYM
ap-4605	74	1	0	0	NUM
ap-4605	74	2	,	,	PUNCT
ap-4605	74	3	∂ξ	∂ξ	NOUN
ap-4605	74	4	∂q2	∂q2	ADJ
ap-4605	74	5	a12(q	a12(q	NOUN
ap-4605	74	6	)	)	PUNCT
ap-4605	75	1	+	+	CCONJ
ap-4605	75	2	1	1	NUM
ap-4605	75	3	2	2	NUM
ap-4605	75	4	∂ξ	∂ξ	NOUN
ap-4605	75	5	∂q1	∂q1	NOUN
ap-4605	75	6	a22(q	a22(q	NOUN
ap-4605	75	7	)	)	PUNCT
ap-4605	75	8	=	=	SYM
ap-4605	75	9	0	0	NUM
ap-4605	75	10	,	,	PUNCT
ap-4605	75	11	∂ξ	∂ξ	NOUN
ap-4605	75	12	∂q1	∂q1	NOUN
ap-4605	75	13	a12(q	a12(q	ADV
ap-4605	75	14	)	)	PUNCT
ap-4605	76	1	+	+	CCONJ
ap-4605	76	2	1	1	NUM
ap-4605	76	3	2	2	NUM
ap-4605	76	4	∂ξ	∂ξ	NUM
ap-4605	76	5	∂q2	∂q2	NOUN
ap-4605	76	6	a22.(q	a22.(q	PROPN
ap-4605	76	7	)	)	PUNCT
ap-4605	76	8	=	=	NOUN
ap-4605	77	1	0	0	X
ap-4605	77	2	.	.	NOUN
ap-4605	77	3	374	374	NUM
ap-4605	77	4	vol	vol	NOUN
ap-4605	77	5	.	.	PUNCT
ap-4605	78	1	57	57	NUM
ap-4605	78	2	no	no	NOUN
ap-4605	78	3	.	.	PUNCT
ap-4605	79	1	6/2017	6/2017	AUX
ap-4605	79	2	noether	noether	ADJ
ap-4605	79	3	point	point	NOUN
ap-4605	79	4	symmetries	symmetry	NOUN
ap-4605	79	5	of	of	ADP
ap-4605	79	6	systems	system	NOUN
ap-4605	79	7	as	as	ADP
ap-4605	79	8	a11(q)a22(q)−a12(q)2	a11(q)a22(q)−a12(q)2	PROPN
ap-4605	79	9	6=	6=	PROPN
ap-4605	79	10	0	0	NUM
ap-4605	79	11	,	,	PUNCT
ap-4605	79	12	a	a	DET
ap-4605	79	13	short	short	ADJ
ap-4605	79	14	computation	computation	NOUN
ap-4605	79	15	shows	show	VERB
ap-4605	79	16	that	that	SCONJ
ap-4605	79	17	the	the	DET
ap-4605	79	18	condition	condition	NOUN
ap-4605	79	19	∂ξ	∂ξ	NOUN
ap-4605	79	20	∂q1	∂q1	PROPN
ap-4605	79	21	=	=	SYM
ap-4605	79	22	∂ξ	∂ξ	NOUN
ap-4605	80	1	∂q2	∂q2	NOUN
ap-4605	81	1	=	=	SYM
ap-4605	81	2	0	0	PUNCT
ap-4605	81	3	must	must	AUX
ap-4605	81	4	be	be	AUX
ap-4605	81	5	necessarily	necessarily	ADV
ap-4605	81	6	satisfied	satisfied	ADJ
ap-4605	81	7	.	.	PUNCT
ap-4605	82	1	introducing	introduce	VERB
ap-4605	82	2	this	this	PRON
ap-4605	82	3	into	into	ADP
ap-4605	82	4	the	the	DET
ap-4605	82	5	symmetry	symmetry	NOUN
ap-4605	82	6	condition	condition	NOUN
ap-4605	82	7	,	,	PUNCT
ap-4605	82	8	the	the	DET
ap-4605	82	9	following	follow	VERB
ap-4605	82	10	relations	relation	NOUN
ap-4605	82	11	are	be	AUX
ap-4605	82	12	obtained	obtain	VERB
ap-4605	82	13	for	for	ADP
ap-4605	82	14	the	the	DET
ap-4605	82	15	terms	term	NOUN
ap-4605	82	16	linear	linear	VERB
ap-4605	82	17	in	in	ADP
ap-4605	82	18	q	q	NOUN
ap-4605	82	19	:	:	PUNCT
ap-4605	82	20	∂η2	∂η2	PROPN
ap-4605	82	21	∂t	∂t	PROPN
ap-4605	82	22	a12(q	a12(q	NOUN
ap-4605	82	23	)	)	PUNCT
ap-4605	83	1	+	+	CCONJ
ap-4605	83	2	∂η1	∂η1	PROPN
ap-4605	83	3	∂t	∂t	PROPN
ap-4605	83	4	a11(q)−	a11(q)−	PROPN
ap-4605	83	5	∂v	∂v	PROPN
ap-4605	83	6	∂q1	∂q1	VERB
ap-4605	83	7	=	=	SYM
ap-4605	83	8	0	0	NUM
ap-4605	83	9	,	,	PUNCT
ap-4605	83	10	∂η1	∂η1	PROPN
ap-4605	83	11	∂t	∂t	PROPN
ap-4605	83	12	a12(q	a12(q	NOUN
ap-4605	83	13	)	)	PUNCT
ap-4605	84	1	+	+	CCONJ
ap-4605	84	2	∂η2	∂η2	VERB
ap-4605	84	3	∂t	∂t	PROPN
ap-4605	84	4	a22(q)−	a22(q)−	ADP
ap-4605	84	5	∂v	∂v	PROPN
ap-4605	84	6	∂q2	∂q2	PROPN
ap-4605	84	7	=	=	PUNCT
ap-4605	84	8	0	0	X
ap-4605	84	9	.	.	PUNCT
ap-4605	85	1	(	(	PUNCT
ap-4605	85	2	14	14	NUM
ap-4605	85	3	)	)	PUNCT
ap-4605	85	4	multiplying	multiply	VERB
ap-4605	85	5	the	the	DET
ap-4605	85	6	first	first	ADJ
ap-4605	85	7	equation	equation	NOUN
ap-4605	85	8	by	by	ADP
ap-4605	85	9	a12	a12	NOUN
ap-4605	85	10	,	,	PUNCT
ap-4605	85	11	the	the	DET
ap-4605	85	12	second	second	ADJ
ap-4605	85	13	by	by	ADP
ap-4605	85	14	−a11	−a11	PRON
ap-4605	85	15	and	and	CCONJ
ap-4605	85	16	adding	add	VERB
ap-4605	85	17	them	they	PRON
ap-4605	85	18	leads	lead	VERB
ap-4605	85	19	to	to	ADP
ap-4605	85	20	the	the	DET
ap-4605	85	21	expression	expression	NOUN
ap-4605	85	22	∂η2	∂η2	VERB
ap-4605	85	23	∂t	∂t	PROPN
ap-4605	85	24	(	(	PUNCT
ap-4605	85	25	a2	a2	PROPN
ap-4605	85	26	12	12	NUM
ap-4605	85	27	−a11a22	−a11a22	NOUN
ap-4605	85	28	)	)	PUNCT
ap-4605	86	1	+	+	ADP
ap-4605	86	2	a12	a12	PROPN
ap-4605	86	3	∂v	∂v	NOUN
ap-4605	86	4	∂q1	∂q1	VERB
ap-4605	86	5	+	+	NUM
ap-4605	86	6	a11	a11	NOUN
ap-4605	86	7	∂v	∂v	PROPN
ap-4605	86	8	∂q2	∂q2	PROPN
ap-4605	86	9	=	=	PUNCT
ap-4605	86	10	0	0	NUM
ap-4605	86	11	,	,	PUNCT
ap-4605	86	12	(	(	PUNCT
ap-4605	86	13	15	15	NUM
ap-4605	86	14	)	)	PUNCT
ap-4605	86	15	from	from	ADP
ap-4605	86	16	which	which	PRON
ap-4605	86	17	we	we	PRON
ap-4605	86	18	conclude	conclude	VERB
ap-4605	86	19	that	that	SCONJ
ap-4605	86	20	η2	η2	PROPN
ap-4605	86	21	is	be	AUX
ap-4605	86	22	at	at	ADP
ap-4605	86	23	most	most	ADJ
ap-4605	86	24	linear	linear	ADJ
ap-4605	86	25	in	in	ADP
ap-4605	86	26	t	t	PROPN
ap-4605	86	27	,	,	PUNCT
ap-4605	86	28	hence	hence	ADV
ap-4605	86	29	it	it	PRON
ap-4605	86	30	admits	admit	VERB
ap-4605	86	31	a	a	DET
ap-4605	86	32	decomposition	decomposition	NOUN
ap-4605	86	33	η2(t	η2(t	PROPN
ap-4605	86	34	,	,	PUNCT
ap-4605	86	35	q	q	NOUN
ap-4605	86	36	)	)	PUNCT
ap-4605	86	37	=	=	SYM
ap-4605	86	38	η21(q	η21(q	NOUN
ap-4605	86	39	)	)	PUNCT
ap-4605	86	40	t+	t+	X
ap-4605	86	41	η22(q	η22(q	ADJ
ap-4605	86	42	)	)	PUNCT
ap-4605	86	43	.	.	PUNCT
ap-4605	87	1	for	for	ADP
ap-4605	87	2	η1(t	η1(t	PROPN
ap-4605	87	3	,	,	PUNCT
ap-4605	87	4	q	q	NOUN
ap-4605	87	5	)	)	PUNCT
ap-4605	87	6	the	the	DET
ap-4605	87	7	assertion	assertion	NOUN
ap-4605	87	8	is	be	AUX
ap-4605	87	9	obtained	obtain	VERB
ap-4605	87	10	similarly	similarly	ADV
ap-4605	87	11	.	.	PUNCT
ap-4605	88	1	finally	finally	ADV
ap-4605	88	2	,	,	PUNCT
ap-4605	88	3	for	for	ADP
ap-4605	88	4	the	the	DET
ap-4605	88	5	terms	term	NOUN
ap-4605	88	6	quadratic	quadratic	ADJ
ap-4605	88	7	in	in	ADP
ap-4605	88	8	q	q	NOUN
ap-4605	88	9	in	in	ADP
ap-4605	88	10	the	the	DET
ap-4605	88	11	symmetry	symmetry	NOUN
ap-4605	88	12	condition	condition	NOUN
ap-4605	88	13	(	(	PUNCT
ap-4605	88	14	7	7	NUM
ap-4605	88	15	)	)	PUNCT
ap-4605	88	16	,	,	PUNCT
ap-4605	88	17	we	we	PRON
ap-4605	88	18	have	have	VERB
ap-4605	88	19	expression	expression	NOUN
ap-4605	88	20	of	of	ADP
ap-4605	88	21	the	the	DET
ap-4605	88	22	type	type	NOUN
ap-4605	88	23	−	−	PROPN
ap-4605	88	24	1	1	NUM
ap-4605	88	25	2aij(q)dξ	2aij(q)dξ	NUM
ap-4605	88	26	dt	dt	NOUN
ap-4605	88	27	+	+	CCONJ
ap-4605	88	28	tψ1(q	tψ1(q	NUM
ap-4605	88	29	)	)	PUNCT
ap-4605	89	1	+	+	PUNCT
ap-4605	89	2	ψ2(q	ψ2(q	X
ap-4605	89	3	)	)	PUNCT
ap-4605	89	4	=	=	SYM
ap-4605	89	5	0	0	NUM
ap-4605	89	6	,	,	PUNCT
ap-4605	89	7	(	(	PUNCT
ap-4605	89	8	16	16	NUM
ap-4605	89	9	)	)	PUNCT
ap-4605	89	10	showing	show	VERB
ap-4605	89	11	that	that	PRON
ap-4605	89	12	ξ(t	ξ(t	NOUN
ap-4605	89	13	)	)	PUNCT
ap-4605	89	14	is	be	AUX
ap-4605	89	15	at	at	ADP
ap-4605	89	16	most	most	ADJ
ap-4605	89	17	quadratic	quadratic	ADJ
ap-4605	89	18	in	in	ADP
ap-4605	89	19	t	t	PROPN
ap-4605	89	20	,	,	PUNCT
ap-4605	89	21	from	from	ADP
ap-4605	89	22	which	which	PRON
ap-4605	89	23	the	the	DET
ap-4605	89	24	assertion	assertion	NOUN
ap-4605	89	25	follows	follow	VERB
ap-4605	89	26	.	.	PUNCT
ap-4605	90	1	we	we	PRON
ap-4605	90	2	observe	observe	VERB
ap-4605	90	3	that	that	SCONJ
ap-4605	90	4	the	the	DET
ap-4605	90	5	generalization	generalization	NOUN
ap-4605	90	6	of	of	ADP
ap-4605	90	7	the	the	DET
ap-4605	90	8	latter	latter	ADJ
ap-4605	90	9	result	result	NOUN
ap-4605	90	10	to	to	ADP
ap-4605	90	11	n	n	NOUN
ap-4605	90	12	-	-	PUNCT
ap-4605	90	13	dimensions	dimension	NOUN
ap-4605	90	14	is	be	AUX
ap-4605	90	15	straightforward	straightforward	ADJ
ap-4605	90	16	.	.	PUNCT
ap-4605	91	1	now	now	ADV
ap-4605	91	2	let	let	VERB
ap-4605	91	3	f(q	f(q	NOUN
ap-4605	91	4	)	)	PUNCT
ap-4605	91	5	and	and	CCONJ
ap-4605	91	6	g(q	g(q	NOUN
ap-4605	91	7	)	)	PUNCT
ap-4605	91	8	be	be	AUX
ap-4605	91	9	arbitrary	arbitrary	ADJ
ap-4605	91	10	non	non	ADJ
ap-4605	91	11	-	-	ADJ
ap-4605	91	12	vanishing	vanishing	ADJ
ap-4605	91	13	functions	function	NOUN
ap-4605	91	14	and	and	CCONJ
ap-4605	91	15	consider	consider	VERB
ap-4605	91	16	the	the	DET
ap-4605	91	17	lie	lie	NOUN
ap-4605	91	18	algebra	algebra	NOUN
ap-4605	91	19	generated	generate	VERB
ap-4605	91	20	by	by	ADP
ap-4605	91	21	the	the	DET
ap-4605	91	22	following	follow	VERB
ap-4605	91	23	vector	vector	NOUN
ap-4605	91	24	fields	field	NOUN
ap-4605	91	25	:	:	PUNCT
ap-4605	91	26	x1	x1	PROPN
ap-4605	91	27	=	=	SYM
ap-4605	91	28	t2	t2	PROPN
ap-4605	91	29	∂	∂	NOUN
ap-4605	91	30	∂t	∂t	PROPN
ap-4605	91	31	+	+	CCONJ
ap-4605	91	32	tf(q	tf(q	NUM
ap-4605	91	33	)	)	PUNCT
ap-4605	91	34	∂	∂	NUM
ap-4605	91	35	∂q1	∂q1	NOUN
ap-4605	91	36	+	+	CCONJ
ap-4605	91	37	tg(q	tg(q	NUM
ap-4605	91	38	)	)	PUNCT
ap-4605	91	39	∂	∂	NOUN
ap-4605	92	1	∂q2	∂q2	NOUN
ap-4605	92	2	,	,	PUNCT
ap-4605	92	3	x2	x2	PROPN
ap-4605	92	4	=	=	NOUN
ap-4605	92	5	1	1	NUM
ap-4605	92	6	2	2	NUM
ap-4605	92	7	d	d	NOUN
ap-4605	92	8	dt	dt	NOUN
ap-4605	93	1	x1	x1	PROPN
ap-4605	93	2	=	=	SYM
ap-4605	93	3	t	t	PROPN
ap-4605	93	4	∂	∂	NOUN
ap-4605	93	5	∂t	∂t	PROPN
ap-4605	94	1	+	+	CCONJ
ap-4605	94	2	1	1	NUM
ap-4605	94	3	2f(q	2f(q	NUM
ap-4605	94	4	)	)	PUNCT
ap-4605	94	5	∂	∂	NUM
ap-4605	94	6	∂q1	∂q1	NOUN
ap-4605	94	7	+	+	CCONJ
ap-4605	94	8	1	1	NUM
ap-4605	94	9	2g(q	2g(q	NUM
ap-4605	94	10	)	)	PUNCT
ap-4605	94	11	∂	∂	NOUN
ap-4605	94	12	∂q2	∂q2	NOUN
ap-4605	94	13	,	,	PUNCT
ap-4605	94	14	(	(	PUNCT
ap-4605	94	15	17	17	NUM
ap-4605	94	16	)	)	PUNCT
ap-4605	94	17	x3	x3	NOUN
ap-4605	94	18	=	=	SYM
ap-4605	95	1	1	1	NUM
ap-4605	95	2	2	2	NUM
ap-4605	95	3	d2	d2	PROPN
ap-4605	95	4	dt2	dt2	PROPN
ap-4605	95	5	x1	x1	PROPN
ap-4605	95	6	=	=	SYM
ap-4605	95	7	∂	∂	NUM
ap-4605	95	8	∂t	∂t	PROPN
ap-4605	95	9	.	.	PUNCT
ap-4605	96	1	it	it	PRON
ap-4605	96	2	follows	follow	VERB
ap-4605	96	3	at	at	ADP
ap-4605	96	4	once	once	ADV
ap-4605	96	5	that	that	PRON
ap-4605	96	6	[	[	X
ap-4605	96	7	x1	x1	X
ap-4605	96	8	,	,	PUNCT
ap-4605	96	9	x2	x2	PROPN
ap-4605	96	10	]	]	X
ap-4605	96	11	=	=	SYM
ap-4605	96	12	−x1	−x1	PROPN
ap-4605	96	13	,	,	PUNCT
ap-4605	96	14	[	[	X
ap-4605	96	15	x1	x1	ADJ
ap-4605	96	16	,	,	PUNCT
ap-4605	96	17	x3	x3	ADJ
ap-4605	96	18	]	]	PUNCT
ap-4605	96	19	=	=	SYM
ap-4605	96	20	−2x2	−2x2	X
ap-4605	96	21	and	and	CCONJ
ap-4605	96	22	[	[	X
ap-4605	96	23	x2	x2	X
ap-4605	96	24	,	,	PUNCT
ap-4605	96	25	x3	x3	ADJ
ap-4605	96	26	]	]	X
ap-4605	96	27	=	=	SYM
ap-4605	96	28	−x3	−x3	PROPN
ap-4605	96	29	,	,	PUNCT
ap-4605	96	30	showing	show	VERB
ap-4605	96	31	that	that	SCONJ
ap-4605	96	32	the	the	DET
ap-4605	96	33	lie	lie	NOUN
ap-4605	96	34	algebra	algebra	NOUN
ap-4605	96	35	is	be	AUX
ap-4605	96	36	isomorphic	isomorphic	ADJ
ap-4605	96	37	to	to	ADP
ap-4605	96	38	sl(2,r	sl(2,r	VERB
ap-4605	96	39	)	)	PUNCT
ap-4605	96	40	for	for	ADP
ap-4605	96	41	any	any	DET
ap-4605	96	42	choices	choice	NOUN
ap-4605	96	43	of	of	ADP
ap-4605	96	44	f	f	PROPN
ap-4605	96	45	and	and	CCONJ
ap-4605	96	46	g.	g.	PROPN
ap-4605	96	47	we	we	PRON
ap-4605	96	48	observe	observe	VERB
ap-4605	96	49	that	that	SCONJ
ap-4605	96	50	the	the	DET
ap-4605	96	51	structure	structure	NOUN
ap-4605	96	52	of	of	ADP
ap-4605	96	53	the	the	DET
ap-4605	96	54	sl(2,r	sl(2,r	NOUN
ap-4605	96	55	)	)	PUNCT
ap-4605	96	56	lie	lie	NOUN
ap-4605	96	57	algebra	algebra	NOUN
ap-4605	96	58	generalizes	generalize	VERB
ap-4605	96	59	naturally	naturally	ADV
ap-4605	96	60	that	that	PRON
ap-4605	96	61	studied	study	VERB
ap-4605	96	62	in	in	ADP
ap-4605	96	63	[	[	X
ap-4605	96	64	8	8	NUM
ap-4605	96	65	,	,	PUNCT
ap-4605	96	66	12	12	NUM
ap-4605	96	67	]	]	PUNCT
ap-4605	96	68	.	.	PUNCT
ap-4605	97	1	in	in	ADP
ap-4605	97	2	these	these	DET
ap-4605	97	3	conditions	condition	NOUN
ap-4605	97	4	,	,	PUNCT
ap-4605	97	5	it	it	PRON
ap-4605	97	6	can	can	AUX
ap-4605	97	7	be	be	AUX
ap-4605	97	8	asked	ask	VERB
ap-4605	97	9	which	which	PRON
ap-4605	97	10	is	be	AUX
ap-4605	97	11	the	the	DET
ap-4605	97	12	most	most	ADV
ap-4605	97	13	general	general	ADJ
ap-4605	97	14	(	(	PUNCT
ap-4605	97	15	kinetic	kinetic	NOUN
ap-4605	97	16	)	)	PUNCT
ap-4605	97	17	lagrangian	lagrangian	NOUN
ap-4605	97	18	such	such	ADJ
ap-4605	97	19	that	that	SCONJ
ap-4605	97	20	it	it	PRON
ap-4605	97	21	admits	admit	VERB
ap-4605	97	22	this	this	DET
ap-4605	97	23	lie	lie	NOUN
ap-4605	97	24	algebra	algebra	NOUN
ap-4605	97	25	as	as	ADP
ap-4605	97	26	an	an	DET
ap-4605	97	27	algebra	algebra	NOUN
ap-4605	97	28	of	of	ADP
ap-4605	97	29	noether	noether	ADJ
ap-4605	97	30	point	point	NOUN
ap-4605	97	31	symmetries	symmetry	NOUN
ap-4605	97	32	.	.	PUNCT
ap-4605	98	1	it	it	PRON
ap-4605	98	2	suffices	suffice	VERB
ap-4605	98	3	to	to	PART
ap-4605	98	4	impose	impose	VERB
ap-4605	98	5	the	the	DET
ap-4605	98	6	invariance	invariance	NOUN
ap-4605	98	7	with	with	ADP
ap-4605	98	8	respect	respect	NOUN
ap-4605	98	9	to	to	ADP
ap-4605	98	10	x1	x1	PROPN
ap-4605	98	11	and	and	CCONJ
ap-4605	98	12	x3	x3	VERB
ap-4605	98	13	in	in	ADP
ap-4605	98	14	order	order	NOUN
ap-4605	98	15	to	to	PART
ap-4605	98	16	ensure	ensure	VERB
ap-4605	98	17	that	that	SCONJ
ap-4605	98	18	the	the	DET
ap-4605	98	19	system	system	NOUN
ap-4605	98	20	is	be	AUX
ap-4605	98	21	sl(2,r)invariant	sl(2,r)invariant	NOUN
ap-4605	98	22	.	.	PUNCT
ap-4605	99	1	the	the	DET
ap-4605	99	2	symmetry	symmetry	NOUN
ap-4605	99	3	condition	condition	NOUN
ap-4605	99	4	(	(	PUNCT
ap-4605	99	5	7	7	X
ap-4605	99	6	)	)	PUNCT
ap-4605	99	7	applied	apply	VERB
ap-4605	99	8	to	to	ADP
ap-4605	99	9	x3	x3	PROPN
ap-4605	99	10	is	be	AUX
ap-4605	99	11	trivially	trivially	ADV
ap-4605	99	12	satisfied	satisfied	ADJ
ap-4605	99	13	for	for	ADP
ap-4605	99	14	the	the	DET
ap-4605	99	15	gauge	gauge	ADJ
ap-4605	99	16	term	term	NOUN
ap-4605	99	17	v	v	NOUN
ap-4605	99	18	(	(	PUNCT
ap-4605	99	19	t	t	PROPN
ap-4605	99	20	,	,	PUNCT
ap-4605	99	21	q	q	NOUN
ap-4605	99	22	)	)	PUNCT
ap-4605	100	1	=	=	SYM
ap-4605	100	2	0	0	X
ap-4605	100	3	.	.	X
ap-4605	100	4	analyzing	analyze	VERB
ap-4605	100	5	now	now	ADV
ap-4605	100	6	the	the	DET
ap-4605	100	7	invariance	invariance	NOUN
ap-4605	100	8	with	with	ADP
ap-4605	100	9	respect	respect	NOUN
ap-4605	100	10	to	to	ADP
ap-4605	100	11	x1	x1	NUM
ap-4605	100	12	,	,	PUNCT
ap-4605	100	13	and	and	CCONJ
ap-4605	100	14	inspecting	inspect	VERB
ap-4605	100	15	first	first	ADV
ap-4605	100	16	the	the	DET
ap-4605	100	17	terms	term	NOUN
ap-4605	100	18	linear	linear	VERB
ap-4605	100	19	in	in	ADP
ap-4605	100	20	q̇	q̇	PROPN
ap-4605	100	21	,	,	PUNCT
ap-4605	100	22	leads	lead	VERB
ap-4605	100	23	to	to	ADP
ap-4605	100	24	the	the	DET
ap-4605	100	25	constraints	constraint	NOUN
ap-4605	100	26	f(q)a11(q	f(q)a11(q	NUM
ap-4605	100	27	)	)	PUNCT
ap-4605	101	1	+	+	CCONJ
ap-4605	101	2	g(q)a12(q)−	g(q)a12(q)−	PROPN
ap-4605	101	3	∂v	∂v	PROPN
ap-4605	101	4	∂q1	∂q1	VERB
ap-4605	101	5	=	=	SYM
ap-4605	101	6	0	0	NUM
ap-4605	101	7	,	,	PUNCT
ap-4605	101	8	g(q)a22(q	g(q)a22(q	PROPN
ap-4605	101	9	)	)	PUNCT
ap-4605	102	1	+	+	CCONJ
ap-4605	102	2	f(q)a12(q)−	f(q)a12(q)−	NUM
ap-4605	102	3	∂v	∂v	PROPN
ap-4605	102	4	∂q2	∂q2	NOUN
ap-4605	102	5	=	=	PUNCT
ap-4605	102	6	0	0	NUM
ap-4605	102	7	,	,	PUNCT
ap-4605	102	8	for	for	ADP
ap-4605	102	9	the	the	DET
ap-4605	102	10	gauge	gauge	ADJ
ap-4605	102	11	term	term	NOUN
ap-4605	102	12	v	v	NOUN
ap-4605	102	13	(	(	PUNCT
ap-4605	102	14	q	q	NOUN
ap-4605	102	15	)	)	PUNCT
ap-4605	102	16	.	.	PUNCT
ap-4605	103	1	as	as	ADP
ap-4605	103	2	f(q)g(q	f(q)g(q	NOUN
ap-4605	103	3	)	)	PUNCT
ap-4605	103	4	6=	6=	ADP
ap-4605	103	5	0	0	NUM
ap-4605	103	6	,	,	PUNCT
ap-4605	103	7	this	this	PRON
ap-4605	103	8	allows	allow	VERB
ap-4605	103	9	us	we	PRON
ap-4605	103	10	to	to	PART
ap-4605	103	11	set	set	VERB
ap-4605	103	12	f2(q)a11(q)−g2(q)a22(q)−f(q	f2(q)a11(q)−g2(q)a22(q)−f(q	NOUN
ap-4605	103	13	)	)	PUNCT
ap-4605	103	14	∂v	∂v	PROPN
ap-4605	103	15	∂q1	∂q1	VERB
ap-4605	103	16	−g(q	−g(q	NOUN
ap-4605	103	17	)	)	PUNCT
ap-4605	103	18	∂v	∂v	NOUN
ap-4605	103	19	∂q2	∂q2	NOUN
ap-4605	104	1	=	=	PUNCT
ap-4605	105	1	0	0	X
ap-4605	105	2	.	.	PUNCT
ap-4605	106	1	in	in	ADP
ap-4605	106	2	order	order	NOUN
ap-4605	106	3	to	to	PART
ap-4605	106	4	completely	completely	ADV
ap-4605	106	5	satisfy	satisfy	VERB
ap-4605	106	6	the	the	DET
ap-4605	106	7	symmetry	symmetry	NOUN
ap-4605	106	8	condition	condition	NOUN
ap-4605	106	9	,	,	PUNCT
ap-4605	106	10	the	the	DET
ap-4605	106	11	functions	function	NOUN
ap-4605	106	12	aij(q	aij(q	PROPN
ap-4605	106	13	)	)	PUNCT
ap-4605	106	14	must	must	AUX
ap-4605	106	15	be	be	AUX
ap-4605	106	16	solutions	solution	NOUN
ap-4605	106	17	to	to	ADP
ap-4605	106	18	the	the	DET
ap-4605	106	19	following	follow	VERB
ap-4605	106	20	system	system	NOUN
ap-4605	106	21	of	of	ADP
ap-4605	106	22	pdes	pde	NOUN
ap-4605	106	23	:	:	PUNCT
ap-4605	106	24	f(q)∂a11	f(q)∂a11	NOUN
ap-4605	106	25	∂q1	∂q1	VERB
ap-4605	106	26	+	+	CCONJ
ap-4605	106	27	g(q)∂a11	g(q)∂a11	X
ap-4605	106	28	∂q2	∂q2	ADJ
ap-4605	106	29	+	+	CCONJ
ap-4605	106	30	2a11(q	2a11(q	NUM
ap-4605	106	31	)	)	PUNCT
ap-4605	106	32	(	(	PUNCT
ap-4605	106	33	∂f	∂f	PROPN
ap-4605	106	34	∂q1	∂q1	VERB
ap-4605	106	35	−	−	PROPN
ap-4605	106	36	1	1	NUM
ap-4605	106	37	)	)	PUNCT
ap-4605	107	1	+	+	CCONJ
ap-4605	107	2	2a12(q	2a12(q	X
ap-4605	107	3	)	)	PUNCT
ap-4605	108	1	∂g	∂g	NOUN
ap-4605	108	2	∂q1	∂q1	NOUN
ap-4605	108	3	=	=	SYM
ap-4605	108	4	0	0	NUM
ap-4605	108	5	,	,	PUNCT
ap-4605	108	6	f(q)∂a22	f(q)∂a22	NOUN
ap-4605	108	7	∂q1	∂q1	VERB
ap-4605	108	8	+	+	CCONJ
ap-4605	108	9	g(q)∂a22	g(q)∂a22	NOUN
ap-4605	108	10	∂q2	∂q2	NOUN
ap-4605	108	11	+	+	CCONJ
ap-4605	108	12	2a22(q	2a22(q	NUM
ap-4605	108	13	)	)	PUNCT
ap-4605	108	14	(	(	PUNCT
ap-4605	108	15	∂g	∂g	PROPN
ap-4605	108	16	∂q2	∂q2	NOUN
ap-4605	108	17	−	−	NOUN
ap-4605	108	18	1	1	NUM
ap-4605	108	19	)	)	PUNCT
ap-4605	109	1	+	+	CCONJ
ap-4605	109	2	2a12(q	2a12(q	X
ap-4605	109	3	)	)	PUNCT
ap-4605	109	4	∂f	∂f	PROPN
ap-4605	109	5	∂q2	∂q2	NOUN
ap-4605	109	6	=	=	SYM
ap-4605	109	7	0	0	NUM
ap-4605	109	8	,	,	PUNCT
ap-4605	109	9	f(q)∂a12	f(q)∂a12	NOUN
ap-4605	109	10	∂q1	∂q1	NOUN
ap-4605	109	11	+	+	CCONJ
ap-4605	109	12	g(q)∂a12	g(q)∂a12	X
ap-4605	109	13	∂q2	∂q2	NOUN
ap-4605	110	1	+	+	NOUN
ap-4605	110	2	a12(q	a12(q	NUM
ap-4605	110	3	)	)	PUNCT
ap-4605	110	4	(	(	PUNCT
ap-4605	110	5	∂f	∂f	PROPN
ap-4605	110	6	∂q1	∂q1	VERB
ap-4605	110	7	+	+	CCONJ
ap-4605	110	8	∂g	∂g	PROPN
ap-4605	110	9	∂q2	∂q2	NOUN
ap-4605	110	10	−	−	NOUN
ap-4605	110	11	2	2	NUM
ap-4605	110	12	)	)	PUNCT
ap-4605	111	1	+	+	ADV
ap-4605	111	2	a11(q	a11(q	ADV
ap-4605	111	3	)	)	PUNCT
ap-4605	112	1	∂f	∂f	PROPN
ap-4605	113	1	∂q2	∂q2	ADJ
ap-4605	113	2	+	+	NOUN
ap-4605	113	3	a22(q	a22(q	NOUN
ap-4605	113	4	)	)	PUNCT
ap-4605	114	1	∂g	∂g	PROPN
ap-4605	114	2	∂q1	∂q1	VERB
ap-4605	114	3	=	=	SYM
ap-4605	114	4	0	0	NUM
ap-4605	114	5	.	.	PUNCT
ap-4605	115	1	(	(	PUNCT
ap-4605	115	2	∗	∗	NOUN
ap-4605	115	3	)	)	PUNCT
ap-4605	115	4	there	there	PRON
ap-4605	115	5	are	be	VERB
ap-4605	115	6	in	in	ADP
ap-4605	115	7	principle	principle	NOUN
ap-4605	115	8	two	two	NUM
ap-4605	115	9	different	different	ADJ
ap-4605	115	10	ways	way	NOUN
ap-4605	115	11	to	to	PART
ap-4605	115	12	analyze	analyze	VERB
ap-4605	115	13	these	these	DET
ap-4605	115	14	systems	system	NOUN
ap-4605	115	15	related	relate	VERB
ap-4605	115	16	to	to	ADP
ap-4605	115	17	a	a	DET
ap-4605	115	18	lagrangian	lagrangian	NOUN
ap-4605	115	19	of	of	ADP
ap-4605	115	20	type	type	NOUN
ap-4605	115	21	(	(	PUNCT
ap-4605	115	22	12	12	NUM
ap-4605	115	23	):	):	PUNCT
ap-4605	115	24	either	either	CCONJ
ap-4605	115	25	we	we	PRON
ap-4605	115	26	fix	fix	VERB
ap-4605	115	27	the	the	DET
ap-4605	115	28	latter	latter	ADJ
ap-4605	115	29	and	and	CCONJ
ap-4605	115	30	search	search	VERB
ap-4605	115	31	for	for	ADP
ap-4605	115	32	functions	function	NOUN
ap-4605	115	33	f(q	f(q	NOUN
ap-4605	115	34	)	)	PUNCT
ap-4605	115	35	and	and	CCONJ
ap-4605	115	36	g(q	g(q	NOUN
ap-4605	115	37	)	)	PUNCT
ap-4605	115	38	such	such	ADJ
ap-4605	115	39	that	that	SCONJ
ap-4605	115	40	(	(	PUNCT
ap-4605	115	41	17	17	NUM
ap-4605	115	42	)	)	PUNCT
ap-4605	115	43	is	be	AUX
ap-4605	115	44	a	a	DET
ap-4605	115	45	lie	lie	NOUN
ap-4605	115	46	algebra	algebra	NOUN
ap-4605	115	47	of	of	ADP
ap-4605	115	48	noether	noether	ADJ
ap-4605	115	49	symmetries	symmetry	NOUN
ap-4605	115	50	,	,	PUNCT
ap-4605	115	51	or	or	CCONJ
ap-4605	115	52	we	we	PRON
ap-4605	115	53	fix	fix	VERB
ap-4605	115	54	the	the	DET
ap-4605	115	55	components	component	NOUN
ap-4605	115	56	of	of	ADP
ap-4605	115	57	the	the	DET
ap-4605	115	58	symmetry	symmetry	NOUN
ap-4605	115	59	generators	generator	NOUN
ap-4605	115	60	and	and	CCONJ
ap-4605	115	61	try	try	VERB
ap-4605	115	62	to	to	PART
ap-4605	115	63	determine	determine	VERB
ap-4605	115	64	the	the	DET
ap-4605	115	65	most	most	ADV
ap-4605	115	66	general	general	ADJ
ap-4605	115	67	kinetic	kinetic	ADJ
ap-4605	115	68	term	term	NOUN
ap-4605	115	69	(	(	PUNCT
ap-4605	115	70	12	12	NUM
ap-4605	115	71	)	)	PUNCT
ap-4605	115	72	invariant	invariant	ADJ
ap-4605	115	73	under	under	ADP
ap-4605	115	74	the	the	DET
ap-4605	115	75	algebra	algebra	NOUN
ap-4605	115	76	.	.	PUNCT
ap-4605	116	1	the	the	DET
ap-4605	116	2	same	same	ADJ
ap-4605	116	3	problem	problem	NOUN
ap-4605	116	4	can	can	AUX
ap-4605	116	5	be	be	AUX
ap-4605	116	6	formulated	formulate	VERB
ap-4605	116	7	allowing	allow	VERB
ap-4605	116	8	a	a	DET
ap-4605	116	9	potential	potential	ADJ
ap-4605	116	10	term	term	NOUN
ap-4605	116	11	.	.	PUNCT
ap-4605	117	1	we	we	PRON
ap-4605	117	2	shall	shall	AUX
ap-4605	117	3	exhibit	exhibit	VERB
ap-4605	117	4	examples	example	NOUN
ap-4605	117	5	of	of	ADP
ap-4605	117	6	the	the	DET
ap-4605	117	7	two	two	NUM
ap-4605	117	8	approaches	approach	NOUN
ap-4605	117	9	leading	lead	VERB
ap-4605	117	10	to	to	ADP
ap-4605	117	11	nontrivial	nontrivial	ADJ
ap-4605	117	12	solutions	solution	NOUN
ap-4605	117	13	of	of	ADP
ap-4605	117	14	the	the	DET
ap-4605	117	15	equations	equation	NOUN
ap-4605	117	16	.	.	PUNCT
ap-4605	118	1	3.1	3.1	NUM
ap-4605	118	2	.	.	PUNCT
ap-4605	119	1	separable	separable	ADJ
ap-4605	119	2	kinetic	kinetic	PROPN
ap-4605	119	3	lagrangians	lagrangian	NOUN
ap-4605	119	4	let	let	VERB
ap-4605	119	5	us	we	PRON
ap-4605	119	6	illustrate	illustrate	VERB
ap-4605	119	7	the	the	DET
ap-4605	119	8	preceding	precede	VERB
ap-4605	119	9	situation	situation	NOUN
ap-4605	119	10	first	first	ADV
ap-4605	119	11	for	for	ADP
ap-4605	119	12	the	the	DET
ap-4605	119	13	case	case	NOUN
ap-4605	119	14	of	of	ADP
ap-4605	119	15	the	the	DET
ap-4605	119	16	separable	separable	PROPN
ap-4605	119	17	lagrangians	lagrangians	PROPN
ap-4605	119	18	t	t	PROPN
ap-4605	119	19	=	=	SYM
ap-4605	119	20	1	1	NUM
ap-4605	119	21	2	2	NUM
ap-4605	119	22	(	(	PUNCT
ap-4605	119	23	qk1	qk1	NOUN
ap-4605	119	24	q̇	q̇	ADV
ap-4605	119	25	2	2	NUM
ap-4605	119	26	1	1	NUM
ap-4605	119	27	+	+	NUM
ap-4605	119	28	ql2q̇	ql2q̇	NOUN
ap-4605	119	29	2	2	NUM
ap-4605	119	30	2	2	NUM
ap-4605	119	31	)	)	PUNCT
ap-4605	119	32	,	,	PUNCT
ap-4605	119	33	where	where	SCONJ
ap-4605	119	34	k	k	NOUN
ap-4605	119	35	,	,	PUNCT
ap-4605	119	36	l	l	PROPN
ap-4605	119	37	6=	6=	ADP
ap-4605	119	38	−2	−2	NOUN
ap-4605	119	39	are	be	AUX
ap-4605	119	40	constants	constant	NOUN
ap-4605	119	41	.	.	PUNCT
ap-4605	120	1	this	this	DET
ap-4605	120	2	case	case	NOUN
ap-4605	120	3	contains	contain	VERB
ap-4605	120	4	in	in	ADP
ap-4605	120	5	particular	particular	ADJ
ap-4605	120	6	that	that	SCONJ
ap-4605	120	7	of	of	ADP
ap-4605	120	8	the	the	DET
ap-4605	120	9	free	free	ADJ
ap-4605	120	10	euclidean	euclidean	ADJ
ap-4605	120	11	lagrangian	lagrangian	NOUN
ap-4605	120	12	,	,	PUNCT
ap-4605	120	13	that	that	PRON
ap-4605	120	14	is	be	AUX
ap-4605	120	15	well	well	ADV
ap-4605	120	16	known	known	ADJ
ap-4605	120	17	to	to	PART
ap-4605	120	18	allow	allow	VERB
ap-4605	120	19	a	a	DET
ap-4605	120	20	sl(2,r)-subalgebra	sl(2,r)-subalgebra	PROPN
ap-4605	120	21	of	of	ADP
ap-4605	120	22	noether	noether	ADJ
ap-4605	120	23	symmetries	symmetry	NOUN
ap-4605	120	24	[	[	X
ap-4605	120	25	4	4	NUM
ap-4605	120	26	]	]	PUNCT
ap-4605	120	27	.	.	PUNCT
ap-4605	121	1	the	the	DET
ap-4605	121	2	symmetry	symmetry	NOUN
ap-4605	121	3	condition	condition	NOUN
ap-4605	121	4	(	(	PUNCT
ap-4605	121	5	∗	∗	NOUN
ap-4605	121	6	)	)	PUNCT
ap-4605	121	7	thus	thus	ADV
ap-4605	121	8	requires	require	VERB
ap-4605	121	9	the	the	DET
ap-4605	121	10	solving	solving	NOUN
ap-4605	121	11	for	for	ADP
ap-4605	121	12	the	the	DET
ap-4605	121	13	unknown	unknown	ADJ
ap-4605	121	14	functions	function	NOUN
ap-4605	121	15	f(q	f(q	NOUN
ap-4605	121	16	)	)	PUNCT
ap-4605	121	17	and	and	CCONJ
ap-4605	121	18	g(q	g(q	NOUN
ap-4605	121	19	)	)	PUNCT
ap-4605	121	20	,	,	PUNCT
ap-4605	121	21	as	as	ADV
ap-4605	121	22	well	well	ADV
ap-4605	121	23	as	as	ADP
ap-4605	121	24	the	the	DET
ap-4605	121	25	gauge	gauge	ADJ
ap-4605	121	26	term	term	NOUN
ap-4605	121	27	v	v	NOUN
ap-4605	121	28	(	(	PUNCT
ap-4605	121	29	q	q	NOUN
ap-4605	121	30	)	)	PUNCT
ap-4605	121	31	for	for	ADP
ap-4605	121	32	the	the	DET
ap-4605	121	33	symmetry	symmetry	NOUN
ap-4605	121	34	generator	generator	PROPN
ap-4605	121	35	x1	x1	PROPN
ap-4605	121	36	.	.	PUNCT
ap-4605	122	1	the	the	DET
ap-4605	122	2	resulting	result	VERB
ap-4605	122	3	equations	equation	NOUN
ap-4605	122	4	are	be	AUX
ap-4605	122	5	lg(q	lg(q	NOUN
ap-4605	122	6	)	)	PUNCT
ap-4605	123	1	+	+	NUM
ap-4605	124	1	2q2	2q2	NUM
ap-4605	124	2	(	(	PUNCT
ap-4605	124	3	∂g	∂g	PROPN
ap-4605	124	4	∂q2	∂q2	NOUN
ap-4605	124	5	−	−	NOUN
ap-4605	124	6	1	1	NUM
ap-4605	124	7	)	)	PUNCT
ap-4605	124	8	=	=	SYM
ap-4605	124	9	0	0	NUM
ap-4605	124	10	,	,	PUNCT
ap-4605	124	11	ql2g(q)−	ql2g(q)−	NOUN
ap-4605	124	12	∂v	∂v	PROPN
ap-4605	124	13	∂q2	∂q2	X
ap-4605	124	14	=	=	SYM
ap-4605	124	15	0	0	NUM
ap-4605	124	16	,	,	PUNCT
ap-4605	124	17	kf(q	kf(q	NOUN
ap-4605	124	18	)	)	PUNCT
ap-4605	125	1	+	+	CCONJ
ap-4605	126	1	2q1	2q1	NUM
ap-4605	126	2	(	(	PUNCT
ap-4605	126	3	∂f	∂f	PROPN
ap-4605	126	4	∂q1	∂q1	VERB
ap-4605	126	5	−	−	PROPN
ap-4605	126	6	1	1	NUM
ap-4605	126	7	)	)	PUNCT
ap-4605	126	8	=	=	SYM
ap-4605	126	9	0	0	NUM
ap-4605	126	10	,	,	PUNCT
ap-4605	126	11	ql1f(q)−	ql1f(q)−	ADP
ap-4605	126	12	∂v	∂v	NOUN
ap-4605	126	13	∂q1	∂q1	VERB
ap-4605	126	14	=	=	NOUN
ap-4605	126	15	0	0	NUM
ap-4605	126	16	.	.	PUNCT
ap-4605	127	1	as	as	SCONJ
ap-4605	127	2	they	they	PRON
ap-4605	127	3	are	be	AUX
ap-4605	127	4	first	first	ADJ
ap-4605	127	5	-	-	PUNCT
ap-4605	127	6	order	order	NOUN
ap-4605	127	7	pdes	pde	NOUN
ap-4605	127	8	,	,	PUNCT
ap-4605	127	9	they	they	PRON
ap-4605	127	10	can	can	AUX
ap-4605	127	11	be	be	AUX
ap-4605	127	12	solved	solve	VERB
ap-4605	127	13	with	with	ADP
ap-4605	127	14	standard	standard	ADJ
ap-4605	127	15	methods	method	NOUN
ap-4605	127	16	(	(	PUNCT
ap-4605	127	17	see	see	VERB
ap-4605	128	1	e.g.	e.g.	ADV
ap-4605	128	2	[	[	X
ap-4605	128	3	13	13	NUM
ap-4605	128	4	]	]	NUM
ap-4605	128	5	)	)	PUNCT
ap-4605	128	6	,	,	PUNCT
ap-4605	128	7	and	and	CCONJ
ap-4605	128	8	the	the	DET
ap-4605	128	9	solution	solution	NOUN
ap-4605	128	10	can	can	AUX
ap-4605	128	11	be	be	AUX
ap-4605	128	12	expressed	express	VERB
ap-4605	128	13	as	as	ADP
ap-4605	128	14	f(q	f(q	NOUN
ap-4605	128	15	)	)	PUNCT
ap-4605	129	1	=	=	SYM
ap-4605	130	1	2q1	2q1	NUM
ap-4605	131	1	k	k	NOUN
ap-4605	131	2	+	+	CCONJ
ap-4605	131	3	2	2	X
ap-4605	131	4	+	+	CCONJ
ap-4605	131	5	a1q	a1q	PROPN
ap-4605	131	6	−k/2	−k/2	NUM
ap-4605	131	7	1	1	NUM
ap-4605	131	8	,	,	PUNCT
ap-4605	131	9	g(q	g(q	X
ap-4605	131	10	)	)	PUNCT
ap-4605	131	11	=	=	SYM
ap-4605	131	12	2q2	2q2	NUM
ap-4605	131	13	l	l	NOUN
ap-4605	132	1	+	+	CCONJ
ap-4605	132	2	2	2	NUM
ap-4605	132	3	+	+	CCONJ
ap-4605	132	4	a2q	a2q	NOUN
ap-4605	132	5	−l/2	−l/2	PROPN
ap-4605	132	6	2	2	NUM
ap-4605	132	7	,	,	PUNCT
ap-4605	132	8	v	v	NOUN
ap-4605	132	9	(	(	PUNCT
ap-4605	132	10	q	q	NOUN
ap-4605	132	11	)	)	PUNCT
ap-4605	132	12	2	2	NUM
ap-4605	132	13	=	=	SYM
ap-4605	132	14	qk+2	qk+2	NOUN
ap-4605	132	15	1	1	NUM
ap-4605	132	16	(	(	PUNCT
ap-4605	132	17	k	k	NOUN
ap-4605	132	18	+	+	CCONJ
ap-4605	132	19	2)2	2)2	NUM
ap-4605	132	20	+	+	CCONJ
ap-4605	132	21	ql+2	ql+2	NOUN
ap-4605	132	22	2	2	NUM
ap-4605	132	23	(	(	PUNCT
ap-4605	132	24	l	l	NOUN
ap-4605	132	25	+	+	CCONJ
ap-4605	132	26	2)2	2)2	NUM
ap-4605	132	27	+	+	CCONJ
ap-4605	132	28	a1q	a1q	PROPN
ap-4605	132	29	(	(	PUNCT
ap-4605	132	30	k+2)/2	k+2)/2	NOUN
ap-4605	132	31	1	1	NUM
ap-4605	133	1	k	k	NOUN
ap-4605	133	2	+	+	CCONJ
ap-4605	133	3	2	2	NUM
ap-4605	133	4	+	+	CCONJ
ap-4605	133	5	a2q	a2q	X
ap-4605	133	6	(	(	PUNCT
ap-4605	133	7	l+2)/2	l+2)/2	NOUN
ap-4605	133	8	2	2	NUM
ap-4605	133	9	l	l	NOUN
ap-4605	133	10	+	+	NOUN
ap-4605	133	11	2	2	NUM
ap-4605	133	12	375	375	NUM
ap-4605	133	13	rutwig	rutwig	NOUN
ap-4605	133	14	campoamor	campoamor	NOUN
ap-4605	133	15	-	-	PUNCT
ap-4605	133	16	stursberg	stursberg	PROPN
ap-4605	133	17	acta	acta	PROPN
ap-4605	133	18	polytechnica	polytechnica	PROPN
ap-4605	133	19	for	for	ADP
ap-4605	133	20	the	the	DET
ap-4605	133	21	component	component	NOUN
ap-4605	133	22	functions	function	NOUN
ap-4605	133	23	and	and	CCONJ
ap-4605	133	24	gauge	gauge	ADJ
ap-4605	133	25	term	term	NOUN
ap-4605	133	26	,	,	PUNCT
ap-4605	133	27	respectively	respectively	ADV
ap-4605	133	28	.	.	PUNCT
ap-4605	134	1	clearly	clearly	ADV
ap-4605	134	2	,	,	PUNCT
ap-4605	134	3	as	as	SCONJ
ap-4605	134	4	the	the	DET
ap-4605	134	5	system	system	NOUN
ap-4605	134	6	related	relate	VERB
ap-4605	134	7	to	to	ADP
ap-4605	134	8	t	t	PROPN
ap-4605	134	9	is	be	AUX
ap-4605	134	10	linearizable	linearizable	ADJ
ap-4605	134	11	,	,	PUNCT
ap-4605	134	12	it	it	PRON
ap-4605	134	13	admits	admit	VERB
ap-4605	134	14	five	five	NUM
ap-4605	134	15	additional	additional	ADJ
ap-4605	134	16	noether	noether	ADJ
ap-4605	134	17	symmetries	symmetry	NOUN
ap-4605	134	18	,	,	PUNCT
ap-4605	134	19	all	all	PRON
ap-4605	134	20	of	of	ADP
ap-4605	134	21	which	which	PRON
ap-4605	134	22	possessing	possess	VERB
ap-4605	134	23	a	a	DET
ap-4605	134	24	zero	zero	NUM
ap-4605	134	25	term	term	NOUN
ap-4605	134	26	in	in	ADP
ap-4605	134	27	∂	∂	NOUN
ap-4605	134	28	∂t	∂t	PROPN
ap-4605	135	1	[	[	X
ap-4605	135	2	11	11	NUM
ap-4605	135	3	]	]	PUNCT
ap-4605	135	4	.	.	PUNCT
ap-4605	136	1	looking	look	VERB
ap-4605	136	2	now	now	ADV
ap-4605	136	3	for	for	ADP
ap-4605	136	4	a	a	DET
ap-4605	136	5	potential	potential	ADJ
ap-4605	136	6	u(t	u(t	NOUN
ap-4605	136	7	,	,	PUNCT
ap-4605	136	8	q	q	NOUN
ap-4605	136	9	)	)	PUNCT
ap-4605	136	10	that	that	PRON
ap-4605	136	11	preserves	preserve	VERB
ap-4605	136	12	the	the	DET
ap-4605	136	13	symmetry	symmetry	NOUN
ap-4605	136	14	,	,	PUNCT
ap-4605	136	15	it	it	PRON
ap-4605	136	16	follows	follow	VERB
ap-4605	136	17	at	at	ADP
ap-4605	136	18	once	once	ADV
ap-4605	136	19	from	from	ADP
ap-4605	136	20	the	the	DET
ap-4605	136	21	x3	x3	ADJ
ap-4605	136	22	-	-	PUNCT
ap-4605	136	23	invariance	invariance	NOUN
ap-4605	136	24	that	that	SCONJ
ap-4605	136	25	∂u	∂u	PROPN
ap-4605	136	26	∂t	∂t	PROPN
ap-4605	136	27	=	=	SYM
ap-4605	136	28	0	0	PROPN
ap-4605	136	29	,	,	PUNCT
ap-4605	136	30	and	and	CCONJ
ap-4605	136	31	thus	thus	ADV
ap-4605	136	32	the	the	DET
ap-4605	136	33	perturbed	perturb	VERB
ap-4605	136	34	system	system	NOUN
ap-4605	136	35	is	be	AUX
ap-4605	136	36	conservative	conservative	ADJ
ap-4605	136	37	.	.	PUNCT
ap-4605	137	1	the	the	DET
ap-4605	137	2	invariance	invariance	NOUN
ap-4605	137	3	by	by	ADP
ap-4605	137	4	x1	x1	PROPN
ap-4605	137	5	implies	imply	VERB
ap-4605	137	6	that	that	SCONJ
ap-4605	137	7	u	u	PRON
ap-4605	137	8	must	must	AUX
ap-4605	137	9	satisfy	satisfy	VERB
ap-4605	137	10	the	the	DET
ap-4605	137	11	first	first	ADJ
ap-4605	137	12	-	-	PUNCT
ap-4605	137	13	order	order	NOUN
ap-4605	137	14	differential	differential	ADJ
ap-4605	137	15	equation	equation	NOUN
ap-4605	137	16	(	(	PUNCT
ap-4605	137	17	see	see	VERB
ap-4605	137	18	(	(	PUNCT
ap-4605	137	19	11	11	NUM
ap-4605	137	20	)	)	PUNCT
ap-4605	137	21	)	)	PUNCT
ap-4605	137	22	f(q	f(q	PROPN
ap-4605	137	23	)	)	PUNCT
ap-4605	137	24	∂u	∂u	PROPN
ap-4605	137	25	∂q1	∂q1	VERB
ap-4605	137	26	+	+	CCONJ
ap-4605	137	27	g(q	g(q	X
ap-4605	137	28	)	)	PUNCT
ap-4605	137	29	∂u	∂u	NOUN
ap-4605	137	30	∂q2	∂q2	NOUN
ap-4605	137	31	+	+	CCONJ
ap-4605	137	32	2u(q	2u(q	NUM
ap-4605	137	33	)	)	PUNCT
ap-4605	137	34	=	=	SYM
ap-4605	137	35	0	0	NUM
ap-4605	137	36	,	,	PUNCT
ap-4605	137	37	(	(	PUNCT
ap-4605	137	38	18	18	NUM
ap-4605	137	39	)	)	PUNCT
ap-4605	137	40	with	with	ADP
ap-4605	137	41	the	the	DET
ap-4605	137	42	functions	function	NOUN
ap-4605	137	43	as	as	SCONJ
ap-4605	137	44	obtained	obtain	VERB
ap-4605	137	45	above	above	ADV
ap-4605	137	46	.	.	PUNCT
ap-4605	138	1	a	a	DET
ap-4605	138	2	routine	routine	ADJ
ap-4605	138	3	but	but	CCONJ
ap-4605	138	4	tedious	tedious	ADJ
ap-4605	138	5	computation	computation	NOUN
ap-4605	138	6	leads	lead	VERB
ap-4605	138	7	to	to	ADP
ap-4605	138	8	the	the	DET
ap-4605	138	9	general	general	ADJ
ap-4605	138	10	solution	solution	NOUN
ap-4605	138	11	u(q	u(q	ADV
ap-4605	138	12	)	)	PUNCT
ap-4605	138	13	=	=	SYM
ap-4605	138	14	ψ(u	ψ(u	PROPN
ap-4605	138	15	)	)	PUNCT
ap-4605	138	16	qk1	qk1	NOUN
ap-4605	138	17	(	(	PUNCT
ap-4605	138	18	2q1	2q1	NUM
ap-4605	139	1	+	+	CCONJ
ap-4605	139	2	a2(k	a2(k	NOUN
ap-4605	139	3	+	+	CCONJ
ap-4605	139	4	2)q−k/2	2)q−k/2	NUM
ap-4605	139	5	1	1	NUM
ap-4605	139	6	)	)	SYM
ap-4605	139	7	2	2	NUM
ap-4605	139	8	,	,	PUNCT
ap-4605	139	9	(	(	PUNCT
ap-4605	139	10	19	19	NUM
ap-4605	139	11	)	)	PUNCT
ap-4605	139	12	where	where	SCONJ
ap-4605	139	13	u	u	NOUN
ap-4605	139	14	=	=	PROPN
ap-4605	139	15	22l2/(2l+4)2	22l2/(2l+4)2	NUM
ap-4605	139	16	q	q	NOUN
ap-4605	139	17	(	(	PUNCT
ap-4605	139	18	1+l)/2	1+l)/2	NOUN
ap-4605	139	19	2	2	NUM
ap-4605	140	1	+	+	CCONJ
ap-4605	140	2	a1(l	a1(l	PROPN
ap-4605	140	3	+	+	ADJ
ap-4605	140	4	2	2	NUM
ap-4605	140	5	)	)	PUNCT
ap-4605	140	6	4q(k+1)/2	4q(k+1)/2	NOUN
ap-4605	140	7	1	1	NUM
ap-4605	141	1	+	+	CCONJ
ap-4605	141	2	2a2(k	2a2(k	NUM
ap-4605	141	3	+	+	CCONJ
ap-4605	141	4	2	2	NUM
ap-4605	141	5	)	)	PUNCT
ap-4605	141	6	.	.	PUNCT
ap-4605	142	1	(	(	PUNCT
ap-4605	142	2	20	20	X
ap-4605	142	3	)	)	PUNCT
ap-4605	142	4	we	we	PRON
ap-4605	142	5	skip	skip	VERB
ap-4605	142	6	the	the	DET
ap-4605	142	7	proof	proof	NOUN
ap-4605	142	8	that	that	SCONJ
ap-4605	142	9	the	the	DET
ap-4605	142	10	perturbed	perturb	VERB
ap-4605	142	11	system	system	NOUN
ap-4605	142	12	t	t	NOUN
ap-4605	142	13	+	+	CCONJ
ap-4605	142	14	εu	εu	ADP
ap-4605	142	15	possesses	possesse	NOUN
ap-4605	142	16	exactly	exactly	ADV
ap-4605	142	17	a	a	DET
ap-4605	142	18	symmetry	symmetry	NOUN
ap-4605	142	19	algebra	algebra	NOUN
ap-4605	142	20	of	of	ADP
ap-4605	142	21	noether	noether	ADJ
ap-4605	142	22	point	point	NOUN
ap-4605	142	23	symmetries	symmetry	NOUN
ap-4605	142	24	isomorphic	isomorphic	ADJ
ap-4605	142	25	to	to	ADP
ap-4605	142	26	sl(2,r	sl(2,r	NOUN
ap-4605	142	27	)	)	PUNCT
ap-4605	142	28	.	.	PUNCT
ap-4605	143	1	we	we	PRON
ap-4605	143	2	observe	observe	VERB
ap-4605	143	3	that	that	SCONJ
ap-4605	143	4	,	,	PUNCT
ap-4605	143	5	considering	consider	VERB
ap-4605	143	6	k	k	PROPN
ap-4605	143	7	and	and	CCONJ
ap-4605	143	8	l	l	NOUN
ap-4605	143	9	as	as	ADP
ap-4605	143	10	parameters	parameter	NOUN
ap-4605	143	11	,	,	PUNCT
ap-4605	143	12	this	this	DET
ap-4605	143	13	approach	approach	NOUN
ap-4605	143	14	also	also	ADV
ap-4605	143	15	allows	allow	VERB
ap-4605	143	16	us	we	PRON
ap-4605	143	17	to	to	PART
ap-4605	143	18	relate	relate	VERB
ap-4605	143	19	different	different	ADJ
ap-4605	143	20	dynamical	dynamical	ADJ
ap-4605	143	21	systems	system	NOUN
ap-4605	143	22	with	with	ADP
ap-4605	143	23	(	(	PUNCT
ap-4605	143	24	k	k	X
ap-4605	143	25	,	,	PUNCT
ap-4605	143	26	l	l	NOUN
ap-4605	143	27	)	)	PUNCT
ap-4605	143	28	6=	6=	ADP
ap-4605	143	29	(	(	PUNCT
ap-4605	143	30	k′	k′	PROPN
ap-4605	143	31	,	,	PUNCT
ap-4605	143	32	l′	l′	NOUN
ap-4605	143	33	)	)	PUNCT
ap-4605	143	34	that	that	PRON
ap-4605	143	35	have	have	VERB
ap-4605	143	36	an	an	DET
ap-4605	143	37	isomorphic	isomorphic	ADJ
ap-4605	143	38	symmetry	symmetry	NOUN
ap-4605	143	39	algebra	algebra	NOUN
ap-4605	143	40	,	,	PUNCT
ap-4605	143	41	the	the	DET
ap-4605	143	42	corresponding	corresponding	ADJ
ap-4605	143	43	symmetry	symmetry	NOUN
ap-4605	143	44	generators	generator	NOUN
ap-4605	143	45	being	be	AUX
ap-4605	143	46	related	relate	VERB
ap-4605	143	47	by	by	ADP
ap-4605	143	48	the	the	DET
ap-4605	143	49	parameterization	parameterization	NOUN
ap-4605	143	50	of	of	ADP
ap-4605	143	51	the	the	DET
ap-4605	143	52	functions	function	NOUN
ap-4605	143	53	f(q	f(q	NOUN
ap-4605	143	54	)	)	PUNCT
ap-4605	143	55	and	and	CCONJ
ap-4605	143	56	g(q	g(q	NOUN
ap-4605	143	57	)	)	PUNCT
ap-4605	143	58	.	.	PUNCT
ap-4605	144	1	3.2	3.2	NUM
ap-4605	144	2	.	.	PUNCT
ap-4605	144	3	systems	system	NOUN
ap-4605	144	4	with	with	ADP
ap-4605	144	5	fixed	fix	VERB
ap-4605	144	6	symmetry	symmetry	NOUN
ap-4605	144	7	let	let	VERB
ap-4605	144	8	us	we	PRON
ap-4605	144	9	now	now	ADV
ap-4605	144	10	consider	consider	VERB
ap-4605	144	11	the	the	DET
ap-4605	144	12	second	second	ADJ
ap-4605	144	13	possibility	possibility	NOUN
ap-4605	144	14	,	,	PUNCT
ap-4605	144	15	namely	namely	ADV
ap-4605	144	16	,	,	PUNCT
ap-4605	144	17	fixing	fix	VERB
ap-4605	144	18	the	the	DET
ap-4605	144	19	functions	function	NOUN
ap-4605	144	20	f(q	f(q	NOUN
ap-4605	144	21	)	)	PUNCT
ap-4605	144	22	and	and	CCONJ
ap-4605	144	23	g(q	g(q	NOUN
ap-4605	144	24	)	)	PUNCT
ap-4605	144	25	in	in	ADP
ap-4605	144	26	(	(	PUNCT
ap-4605	144	27	17	17	NUM
ap-4605	144	28	)	)	PUNCT
ap-4605	144	29	.	.	PUNCT
ap-4605	145	1	to	to	ADP
ap-4605	145	2	this	this	DET
ap-4605	145	3	extent	extent	NOUN
ap-4605	145	4	,	,	PUNCT
ap-4605	145	5	consider	consider	VERB
ap-4605	145	6	f(q	f(q	NOUN
ap-4605	145	7	)	)	PUNCT
ap-4605	146	1	=	=	PUNCT
ap-4605	146	2	qn1	qn1	NOUN
ap-4605	146	3	,	,	PUNCT
ap-4605	146	4	g(q	g(q	X
ap-4605	146	5	)	)	PUNCT
ap-4605	146	6	=	=	PUNCT
ap-4605	146	7	qn2	qn2	NOUN
ap-4605	146	8	for	for	ADP
ap-4605	146	9	simplicity	simplicity	NOUN
ap-4605	146	10	,	,	PUNCT
ap-4605	146	11	where	where	SCONJ
ap-4605	146	12	n	n	X
ap-4605	146	13	6=	6=	PROPN
ap-4605	146	14	0	0	NUM
ap-4605	146	15	.	.	PUNCT
ap-4605	147	1	in	in	ADP
ap-4605	147	2	this	this	DET
ap-4605	147	3	case	case	NOUN
ap-4605	147	4	,	,	PUNCT
ap-4605	147	5	the	the	DET
ap-4605	147	6	symmetry	symmetry	NOUN
ap-4605	147	7	condition	condition	NOUN
ap-4605	147	8	for	for	ADP
ap-4605	147	9	x1	x1	PROPN
ap-4605	147	10	leads	lead	VERB
ap-4605	147	11	to	to	ADP
ap-4605	147	12	the	the	DET
ap-4605	147	13	system	system	NOUN
ap-4605	147	14	(	(	PUNCT
ap-4605	147	15	nqn−1	nqn−1	PROPN
ap-4605	147	16	i	i	PRON
ap-4605	147	17	+	+	PROPN
ap-4605	147	18	nqn−1	nqn−1	PROPN
ap-4605	147	19	j	j	NOUN
ap-4605	147	20	−	−	PROPN
ap-4605	147	21	2	2	NUM
ap-4605	147	22	)	)	PUNCT
ap-4605	147	23	aij(q	aij(q	PROPN
ap-4605	147	24	)	)	PUNCT
ap-4605	148	1	+	+	CCONJ
ap-4605	148	2	qn1	qn1	NOUN
ap-4605	148	3	∂aij	∂aij	ADV
ap-4605	148	4	∂q1	∂q1	NOUN
ap-4605	148	5	+	+	CCONJ
ap-4605	148	6	qn2	qn2	NOUN
ap-4605	148	7	∂aij	∂aij	NUM
ap-4605	148	8	∂q2	∂q2	NOUN
ap-4605	148	9	=	=	SYM
ap-4605	148	10	0	0	NUM
ap-4605	148	11	,	,	PUNCT
ap-4605	148	12	qn1a11	qn1a11	PROPN
ap-4605	148	13	+	+	CCONJ
ap-4605	148	14	qn2a12	qn2a12	PROPN
ap-4605	148	15	−	−	PROPN
ap-4605	148	16	∂v	∂v	PROPN
ap-4605	148	17	∂q1	∂q1	VERB
ap-4605	148	18	=	=	SYM
ap-4605	148	19	0	0	NUM
ap-4605	148	20	,	,	PUNCT
ap-4605	148	21	qn1a12	qn1a12	PROPN
ap-4605	148	22	+	+	CCONJ
ap-4605	148	23	qn2a22	qn2a22	PROPN
ap-4605	148	24	−	−	PROPN
ap-4605	148	25	∂v	∂v	PROPN
ap-4605	148	26	∂q2	∂q2	PROPN
ap-4605	148	27	=	=	NOUN
ap-4605	148	28	0	0	NUM
ap-4605	148	29	for	for	ADP
ap-4605	148	30	(	(	PUNCT
ap-4605	148	31	ij	ij	NOUN
ap-4605	148	32	)	)	PUNCT
ap-4605	148	33	=	=	SYM
ap-4605	148	34	(	(	PUNCT
ap-4605	148	35	11	11	NUM
ap-4605	148	36	)	)	PUNCT
ap-4605	148	37	,	,	PUNCT
ap-4605	148	38	(	(	PUNCT
ap-4605	148	39	12	12	NUM
ap-4605	148	40	)	)	PUNCT
ap-4605	148	41	,	,	PUNCT
ap-4605	148	42	(	(	PUNCT
ap-4605	148	43	22	22	NUM
ap-4605	148	44	)	)	PUNCT
ap-4605	148	45	.	.	PUNCT
ap-4605	149	1	it	it	PRON
ap-4605	149	2	is	be	AUX
ap-4605	149	3	not	not	PART
ap-4605	149	4	too	too	ADV
ap-4605	149	5	difficult	difficult	ADJ
ap-4605	149	6	to	to	PART
ap-4605	149	7	see	see	VERB
ap-4605	149	8	that	that	SCONJ
ap-4605	149	9	if	if	SCONJ
ap-4605	149	10	a11(q	a11(q	ADV
ap-4605	149	11	)	)	PUNCT
ap-4605	149	12	=	=	SYM
ap-4605	149	13	a22(q	a22(q	NOUN
ap-4605	149	14	)	)	PUNCT
ap-4605	149	15	6=	6=	ADP
ap-4605	149	16	0	0	NUM
ap-4605	149	17	holds	hold	NOUN
ap-4605	149	18	,	,	PUNCT
ap-4605	149	19	then	then	ADV
ap-4605	149	20	the	the	DET
ap-4605	149	21	preceding	precede	VERB
ap-4605	149	22	system	system	NOUN
ap-4605	149	23	possesses	possess	VERB
ap-4605	149	24	a	a	DET
ap-4605	149	25	nontrivial	nontrivial	ADJ
ap-4605	149	26	solution	solution	NOUN
ap-4605	149	27	only	only	ADV
ap-4605	149	28	for	for	ADP
ap-4605	149	29	the	the	DET
ap-4605	149	30	values	value	NOUN
ap-4605	149	31	n	n	NOUN
ap-4605	149	32	=	=	SYM
ap-4605	149	33	0	0	NUM
ap-4605	149	34	,	,	PUNCT
ap-4605	149	35	1	1	NUM
ap-4605	149	36	.	.	PUNCT
ap-4605	150	1	in	in	ADP
ap-4605	150	2	order	order	NOUN
ap-4605	150	3	to	to	PART
ap-4605	150	4	find	find	VERB
ap-4605	150	5	manageable	manageable	ADJ
ap-4605	150	6	solutions	solution	NOUN
ap-4605	150	7	for	for	ADP
ap-4605	150	8	arbitrary	arbitrary	ADJ
ap-4605	150	9	n	n	CCONJ
ap-4605	150	10	,	,	PUNCT
ap-4605	150	11	we	we	PRON
ap-4605	150	12	thus	thus	ADV
ap-4605	150	13	assume	assume	VERB
ap-4605	150	14	that	that	SCONJ
ap-4605	150	15	a11(q	a11(q	ADV
ap-4605	150	16	)	)	PUNCT
ap-4605	150	17	=	=	SYM
ap-4605	150	18	a22(q	a22(q	NOUN
ap-4605	150	19	)	)	PUNCT
ap-4605	150	20	=	=	SYM
ap-4605	151	1	0	0	X
ap-4605	151	2	.	.	PUNCT
ap-4605	152	1	then	then	ADV
ap-4605	152	2	the	the	DET
ap-4605	152	3	system	system	NOUN
ap-4605	152	4	can	can	AUX
ap-4605	152	5	be	be	AUX
ap-4605	152	6	reduced	reduce	VERB
ap-4605	152	7	,	,	PUNCT
ap-4605	152	8	and	and	CCONJ
ap-4605	152	9	for	for	ADP
ap-4605	152	10	n	n	PROPN
ap-4605	152	11	6=	6=	NUM
ap-4605	152	12	1	1	NUM
ap-4605	152	13	admits	admit	VERB
ap-4605	152	14	the	the	DET
ap-4605	152	15	solution	solution	NOUN
ap-4605	152	16	a12(q	a12(q	NOUN
ap-4605	152	17	)	)	PUNCT
ap-4605	153	1	=	=	SYM
ap-4605	154	1	(	(	PUNCT
ap-4605	154	2	q1q2)−n	q1q2)−n	PROPN
ap-4605	154	3	exp	exp	PROPN
ap-4605	154	4	(	(	PUNCT
ap-4605	154	5	−(q1−n	−(q1−n	NOUN
ap-4605	154	6	1	1	NUM
ap-4605	154	7	+	+	CCONJ
ap-4605	154	8	q1−n	q1−n	PROPN
ap-4605	154	9	2	2	NUM
ap-4605	154	10	)	)	PUNCT
ap-4605	154	11	n−	n−	NOUN
ap-4605	154	12	1	1	NUM
ap-4605	154	13	)	)	PUNCT
ap-4605	154	14	,	,	PUNCT
ap-4605	154	15	v	v	X
ap-4605	154	16	(	(	PUNCT
ap-4605	154	17	q	q	NOUN
ap-4605	154	18	)	)	PUNCT
ap-4605	154	19	=	=	NOUN
ap-4605	154	20	exp	exp	NOUN
ap-4605	154	21	(	(	PUNCT
ap-4605	154	22	−(q1−n	−(q1−n	NOUN
ap-4605	154	23	1	1	NUM
ap-4605	154	24	+	+	CCONJ
ap-4605	154	25	q1−n	q1−n	PROPN
ap-4605	154	26	2	2	NUM
ap-4605	154	27	)	)	PUNCT
ap-4605	154	28	n−	n−	NOUN
ap-4605	154	29	1	1	NUM
ap-4605	154	30	)	)	PUNCT
ap-4605	154	31	.	.	PUNCT
ap-4605	155	1	for	for	ADP
ap-4605	155	2	n	n	NOUN
ap-4605	155	3	=	=	SYM
ap-4605	155	4	1	1	NUM
ap-4605	155	5	,	,	PUNCT
ap-4605	155	6	we	we	PRON
ap-4605	155	7	merely	merely	ADV
ap-4605	155	8	get	get	VERB
ap-4605	155	9	a12(q	a12(q	NOUN
ap-4605	155	10	)	)	PUNCT
ap-4605	156	1	=	=	SYM
ap-4605	156	2	1	1	NUM
ap-4605	156	3	(	(	PUNCT
ap-4605	156	4	the	the	DET
ap-4605	156	5	free	free	ADJ
ap-4605	156	6	pseudoeuclidean	pseudoeuclidean	NOUN
ap-4605	156	7	lagrangian	lagrangian	NOUN
ap-4605	156	8	)	)	PUNCT
ap-4605	156	9	and	and	CCONJ
ap-4605	156	10	the	the	DET
ap-4605	156	11	gauge	gauge	ADJ
ap-4605	156	12	term	term	NOUN
ap-4605	156	13	v	v	NOUN
ap-4605	156	14	(	(	PUNCT
ap-4605	156	15	q	q	NOUN
ap-4605	156	16	)	)	PUNCT
ap-4605	156	17	=	=	SYM
ap-4605	157	1	q1q2	q1q2	X
ap-4605	157	2	.	.	PUNCT
ap-4605	157	3	further	far	ADV
ap-4605	157	4	,	,	PUNCT
ap-4605	157	5	considering	consider	VERB
ap-4605	157	6	a	a	DET
ap-4605	157	7	potential	potential	ADJ
ap-4605	157	8	u(q	u(q	NOUN
ap-4605	157	9	)	)	PUNCT
ap-4605	157	10	requires	require	VERB
ap-4605	157	11	to	to	PART
ap-4605	157	12	solve	solve	VERB
ap-4605	157	13	the	the	DET
ap-4605	157	14	additional	additional	ADJ
ap-4605	157	15	pde	pde	NOUN
ap-4605	157	16	qn1	qn1	ADP
ap-4605	157	17	∂u	∂u	PROPN
ap-4605	157	18	∂q1	∂q1	VERB
ap-4605	157	19	+	+	CCONJ
ap-4605	157	20	qn1	qn1	NOUN
ap-4605	157	21	∂u	∂u	PROPN
ap-4605	157	22	∂q2	∂q2	NOUN
ap-4605	157	23	+	+	CCONJ
ap-4605	157	24	2u(q	2u(q	NUM
ap-4605	157	25	)	)	PUNCT
ap-4605	157	26	=	=	SYM
ap-4605	158	1	0	0	NUM
ap-4605	158	2	,	,	PUNCT
ap-4605	158	3	(	(	PUNCT
ap-4605	158	4	21	21	NUM
ap-4605	158	5	)	)	PUNCT
ap-4605	158	6	that	that	PRON
ap-4605	158	7	can	can	AUX
ap-4605	158	8	be	be	AUX
ap-4605	158	9	easily	easily	ADV
ap-4605	158	10	seen	see	VERB
ap-4605	158	11	to	to	PART
ap-4605	158	12	provide	provide	VERB
ap-4605	158	13	the	the	DET
ap-4605	158	14	solution	solution	NOUN
ap-4605	158	15	u(q	u(q	ADV
ap-4605	158	16	)	)	PUNCT
ap-4605	159	1	=	=	SYM
ap-4605	159	2	exp	exp	NOUN
ap-4605	159	3	(	(	PUNCT
ap-4605	159	4	2q1−n	2q1−n	NUM
ap-4605	159	5	1	1	NUM
ap-4605	159	6	n−	n−	NOUN
ap-4605	159	7	1	1	NUM
ap-4605	159	8	)	)	PUNCT
ap-4605	159	9	ψ	ψ	X
ap-4605	159	10	(	(	PUNCT
ap-4605	159	11	qn−1	qn−1	ADV
ap-4605	159	12	1	1	NUM
ap-4605	159	13	+	+	CCONJ
ap-4605	159	14	qn−1	qn−1	PROPN
ap-4605	159	15	2	2	NUM
ap-4605	159	16	(	(	PUNCT
ap-4605	159	17	q1q2)n−1	q1q2)n−1	PROPN
ap-4605	159	18	)	)	PUNCT
ap-4605	159	19	.	.	PUNCT
ap-4605	160	1	(	(	PUNCT
ap-4605	160	2	22	22	NUM
ap-4605	160	3	)	)	PUNCT
ap-4605	160	4	if	if	SCONJ
ap-4605	160	5	we	we	PRON
ap-4605	160	6	admit	admit	VERB
ap-4605	160	7	generalized	generalized	ADJ
ap-4605	160	8	potentials	potential	NOUN
ap-4605	160	9	depending	depend	VERB
ap-4605	160	10	on	on	ADP
ap-4605	160	11	q̇	q̇	PROPN
ap-4605	160	12	,	,	PUNCT
ap-4605	160	13	the	the	DET
ap-4605	160	14	integrability	integrability	NOUN
ap-4605	160	15	condition	condition	NOUN
ap-4605	160	16	(	(	PUNCT
ap-4605	160	17	11	11	NUM
ap-4605	160	18	)	)	PUNCT
ap-4605	160	19	can	can	AUX
ap-4605	160	20	be	be	AUX
ap-4605	160	21	separated	separate	VERB
ap-4605	160	22	with	with	ADP
ap-4605	160	23	respect	respect	NOUN
ap-4605	160	24	to	to	ADP
ap-4605	160	25	the	the	DET
ap-4605	160	26	variable	variable	ADJ
ap-4605	160	27	t	t	PROPN
ap-4605	160	28	,	,	PUNCT
ap-4605	160	29	because	because	SCONJ
ap-4605	160	30	of	of	ADP
ap-4605	160	31	the	the	DET
ap-4605	160	32	x3	x3	ADJ
ap-4605	160	33	-	-	PUNCT
ap-4605	160	34	invariance	invariance	NOUN
ap-4605	160	35	.	.	PUNCT
ap-4605	161	1	skipping	skip	VERB
ap-4605	161	2	the	the	DET
ap-4605	161	3	details	detail	NOUN
ap-4605	161	4	,	,	PUNCT
ap-4605	161	5	it	it	PRON
ap-4605	161	6	follows	follow	VERB
ap-4605	161	7	from	from	ADP
ap-4605	161	8	a	a	DET
ap-4605	161	9	routine	routine	ADJ
ap-4605	161	10	computation	computation	NOUN
ap-4605	161	11	that	that	SCONJ
ap-4605	161	12	the	the	DET
ap-4605	161	13	most	most	ADV
ap-4605	161	14	general	general	ADJ
ap-4605	161	15	u	u	NOUN
ap-4605	161	16	preserving	preserve	VERB
ap-4605	161	17	the	the	DET
ap-4605	161	18	subalgebra	subalgebra	NOUN
ap-4605	161	19	sl(2,r	sl(2,r	NOUN
ap-4605	161	20	)	)	PUNCT
ap-4605	161	21	in	in	ADP
ap-4605	161	22	the	the	DET
ap-4605	161	23	preceding	precede	VERB
ap-4605	161	24	realization	realization	NOUN
ap-4605	161	25	is	be	AUX
ap-4605	161	26	given	give	VERB
ap-4605	161	27	by	by	ADP
ap-4605	161	28	u(q	u(q	PROPN
ap-4605	161	29	,	,	PUNCT
ap-4605	161	30	q̇	q̇	ADV
ap-4605	161	31	)	)	PUNCT
ap-4605	161	32	=	=	SYM
ap-4605	161	33	exp	exp	NOUN
ap-4605	161	34	(	(	PUNCT
ap-4605	161	35	2q1−n	2q1−n	NUM
ap-4605	161	36	1	1	NUM
ap-4605	161	37	n−	n−	NOUN
ap-4605	161	38	1	1	NUM
ap-4605	161	39	)	)	PUNCT
ap-4605	161	40	ψ	ψ	X
ap-4605	161	41	(	(	PUNCT
ap-4605	161	42	qn−1	qn−1	ADV
ap-4605	161	43	1	1	NUM
ap-4605	161	44	+	+	CCONJ
ap-4605	161	45	qn−1	qn−1	PROPN
ap-4605	161	46	2	2	NUM
ap-4605	161	47	(	(	PUNCT
ap-4605	161	48	q1q2)n−1	q1q2)n−1	X
ap-4605	161	49	,	,	PUNCT
ap-4605	161	50	u1	u1	PROPN
ap-4605	161	51	,	,	PUNCT
ap-4605	161	52	u2	u2	PROPN
ap-4605	161	53	)	)	PUNCT
ap-4605	161	54	,	,	PUNCT
ap-4605	161	55	where	where	SCONJ
ap-4605	161	56	the	the	DET
ap-4605	161	57	auxiliary	auxiliary	ADJ
ap-4605	161	58	variables	variable	NOUN
ap-4605	161	59	are	be	AUX
ap-4605	161	60	defined	define	VERB
ap-4605	161	61	as	as	ADP
ap-4605	161	62	ui	ui	PROPN
ap-4605	161	63	=	=	PROPN
ap-4605	161	64	q̇iq	q̇iq	NOUN
ap-4605	161	65	1−n	1−n	NUM
ap-4605	161	66	i	i	PRON
ap-4605	161	67	exp	exp	NOUN
ap-4605	161	68	(	(	PUNCT
ap-4605	161	69	−2q1−n	−2q1−n	PROPN
ap-4605	161	70	1	1	NUM
ap-4605	161	71	n−	n−	NOUN
ap-4605	161	72	1	1	NUM
ap-4605	161	73	)	)	PUNCT
ap-4605	161	74	,	,	PUNCT
ap-4605	161	75	i	i	PRON
ap-4605	161	76	=	=	NOUN
ap-4605	161	77	1	1	NUM
ap-4605	161	78	,	,	PUNCT
ap-4605	161	79	2	2	NUM
ap-4605	161	80	.	.	PUNCT
ap-4605	161	81	(	(	PUNCT
ap-4605	161	82	23	23	NUM
ap-4605	161	83	)	)	PUNCT
ap-4605	161	84	for	for	ADP
ap-4605	161	85	generic	generic	ADJ
ap-4605	161	86	choices	choice	NOUN
ap-4605	161	87	of	of	ADP
ap-4605	161	88	the	the	DET
ap-4605	161	89	function	function	NOUN
ap-4605	161	90	ψ	ψ	NOUN
ap-4605	161	91	,	,	PUNCT
ap-4605	161	92	the	the	DET
ap-4605	161	93	system	system	NOUN
ap-4605	161	94	determined	determine	VERB
ap-4605	161	95	by	by	ADP
ap-4605	161	96	t	t	PROPN
ap-4605	161	97	−	−	PROPN
ap-4605	161	98	εu	εu	AUX
ap-4605	161	99	always	always	ADV
ap-4605	161	100	possesses	possess	VERB
ap-4605	161	101	a	a	DET
ap-4605	161	102	noether	noether	ADJ
ap-4605	161	103	point	point	NOUN
ap-4605	161	104	symmetry	symmetry	NOUN
ap-4605	161	105	algebra	algebra	NOUN
ap-4605	161	106	isomorphic	isomorphic	ADJ
ap-4605	161	107	to	to	ADP
ap-4605	161	108	sl(2,r	sl(2,r	NOUN
ap-4605	161	109	)	)	PUNCT
ap-4605	161	110	.	.	PUNCT
ap-4605	162	1	4	4	X
ap-4605	162	2	.	.	NOUN
ap-4605	162	3	time	time	NOUN
ap-4605	162	4	-	-	PUNCT
ap-4605	162	5	dependent	dependent	ADJ
ap-4605	162	6	lagrangians	lagrangian	NOUN
ap-4605	162	7	as	as	SCONJ
ap-4605	162	8	follows	follow	VERB
ap-4605	162	9	from	from	ADP
ap-4605	162	10	lemma	lemma	PROPN
ap-4605	162	11	1	1	NUM
ap-4605	162	12	,	,	PUNCT
ap-4605	162	13	for	for	ADP
ap-4605	162	14	conservative	conservative	ADJ
ap-4605	162	15	systems	system	NOUN
ap-4605	162	16	a	a	DET
ap-4605	162	17	noether	noether	ADJ
ap-4605	162	18	point	point	NOUN
ap-4605	162	19	symmetry	symmetry	NOUN
ap-4605	162	20	depends	depend	VERB
ap-4605	162	21	at	at	ADP
ap-4605	162	22	most	most	ADV
ap-4605	162	23	quadratically	quadratically	ADV
ap-4605	162	24	on	on	ADP
ap-4605	162	25	time	time	NOUN
ap-4605	162	26	.	.	PUNCT
ap-4605	163	1	if	if	SCONJ
ap-4605	163	2	we	we	PRON
ap-4605	163	3	skip	skip	VERB
ap-4605	163	4	the	the	DET
ap-4605	163	5	conservative	conservative	ADJ
ap-4605	163	6	character	character	NOUN
ap-4605	163	7	of	of	ADP
ap-4605	163	8	the	the	DET
ap-4605	163	9	system	system	NOUN
ap-4605	163	10	,	,	PUNCT
ap-4605	163	11	a	a	DET
ap-4605	163	12	more	more	ADV
ap-4605	163	13	wide	wide	ADJ
ap-4605	163	14	class	class	NOUN
ap-4605	163	15	of	of	ADP
ap-4605	163	16	possibilities	possibility	NOUN
ap-4605	163	17	is	be	AUX
ap-4605	163	18	given	give	VERB
ap-4605	163	19	,	,	PUNCT
ap-4605	163	20	and	and	CCONJ
ap-4605	163	21	(	(	PUNCT
ap-4605	163	22	explicitly	explicitly	ADV
ap-4605	163	23	time	time	NOUN
ap-4605	163	24	-	-	PUNCT
ap-4605	163	25	dependent	dependent	ADJ
ap-4605	163	26	)	)	PUNCT
ap-4605	163	27	constants	constant	NOUN
ap-4605	163	28	of	of	ADP
ap-4605	163	29	the	the	DET
ap-4605	163	30	motion	motion	NOUN
ap-4605	163	31	can	can	AUX
ap-4605	163	32	still	still	ADV
ap-4605	163	33	be	be	AUX
ap-4605	163	34	guaranteed	guarantee	VERB
ap-4605	163	35	whenever	whenever	SCONJ
ap-4605	163	36	an	an	DET
ap-4605	163	37	appropriate	appropriate	ADJ
ap-4605	163	38	subalgebra	subalgebra	NOUN
ap-4605	163	39	of	of	ADP
ap-4605	163	40	noether	noether	ADJ
ap-4605	163	41	symmetries	symmetry	NOUN
ap-4605	163	42	is	be	AUX
ap-4605	163	43	chosen	choose	VERB
ap-4605	163	44	[	[	X
ap-4605	163	45	8	8	NUM
ap-4605	163	46	]	]	PUNCT
ap-4605	163	47	.	.	PUNCT
ap-4605	164	1	let	let	AUX
ap-4605	164	2	θ(t	θ(t	NOUN
ap-4605	164	3	)	)	PUNCT
ap-4605	164	4	and	and	CCONJ
ap-4605	164	5	ρ(t	ρ(t	NUM
ap-4605	164	6	)	)	PUNCT
ap-4605	164	7	be	be	VERB
ap-4605	164	8	two	two	NUM
ap-4605	164	9	arbitrary	arbitrary	ADJ
ap-4605	164	10	functions	function	NOUN
ap-4605	164	11	,	,	PUNCT
ap-4605	164	12	and	and	CCONJ
ap-4605	164	13	let	let	VERB
ap-4605	164	14	{	{	PUNCT
ap-4605	164	15	u(t	u(t	NOUN
ap-4605	164	16	)	)	PUNCT
ap-4605	164	17	,	,	PUNCT
ap-4605	164	18	v(t	v(t	NOUN
ap-4605	164	19	)	)	PUNCT
ap-4605	164	20	}	}	PUNCT
ap-4605	164	21	be	be	AUX
ap-4605	164	22	an	an	DET
ap-4605	164	23	independent	independent	ADJ
ap-4605	164	24	set	set	NOUN
ap-4605	164	25	of	of	ADP
ap-4605	164	26	solutions	solution	NOUN
ap-4605	164	27	of	of	ADP
ap-4605	164	28	the	the	DET
ap-4605	164	29	second	second	ADJ
ap-4605	164	30	-	-	PUNCT
ap-4605	164	31	order	order	NOUN
ap-4605	164	32	ode	ode	PROPN
ap-4605	164	33	z̈(t	z̈(t	NUM
ap-4605	164	34	)	)	PUNCT
ap-4605	165	1	+	+	NUM
ap-4605	165	2	ρ(t)ż(t	ρ(t)ż(t	NOUN
ap-4605	165	3	)	)	PUNCT
ap-4605	166	1	+	+	CCONJ
ap-4605	166	2	θ(t)z(t	θ(t)z(t	NOUN
ap-4605	166	3	)	)	PUNCT
ap-4605	166	4	=	=	SYM
ap-4605	166	5	0	0	X
ap-4605	166	6	.	.	PUNCT
ap-4605	167	1	(	(	PUNCT
ap-4605	167	2	24	24	NUM
ap-4605	167	3	)	)	PUNCT
ap-4605	167	4	in	in	ADP
ap-4605	167	5	these	these	DET
ap-4605	167	6	conditions	condition	NOUN
ap-4605	167	7	,	,	PUNCT
ap-4605	167	8	the	the	DET
ap-4605	167	9	function	function	NOUN
ap-4605	167	10	ξ	ξ	PROPN
ap-4605	167	11	(	(	PUNCT
ap-4605	167	12	t	t	NOUN
ap-4605	167	13	)	)	PUNCT
ap-4605	167	14	=	=	SYM
ap-4605	167	15	c1u(t)2	c1u(t)2	NOUN
ap-4605	167	16	+	+	SYM
ap-4605	167	17	c2u(t)v(t	c2u(t)v(t	NOUN
ap-4605	167	18	)	)	PUNCT
ap-4605	168	1	+	+	NUM
ap-4605	168	2	c3v(t)2	c3v(t)2	NUM
ap-4605	168	3	determines	determine	VERB
ap-4605	168	4	the	the	DET
ap-4605	168	5	general	general	ADJ
ap-4605	168	6	solution	solution	NOUN
ap-4605	168	7	of	of	ADP
ap-4605	168	8	the	the	DET
ap-4605	168	9	third	third	ADJ
ap-4605	168	10	-	-	PUNCT
ap-4605	168	11	order	order	NOUN
ap-4605	168	12	ode	ode	NOUN
ap-4605	168	13	...	...	PUNCT
ap-4605	169	1	ξ	ξ	X
ap-4605	170	1	+	+	PUNCT
ap-4605	170	2	3ρ̇ξ̈	3ρ̇ξ̈	ADJ
ap-4605	170	3	+	+	CCONJ
ap-4605	170	4	(	(	PUNCT
ap-4605	170	5	ρ̇+	ρ̇+	PROPN
ap-4605	170	6	2ρ2	2ρ2	NUM
ap-4605	170	7	+	+	NUM
ap-4605	170	8	4θ	4θ	NOUN
ap-4605	170	9	)	)	PUNCT
ap-4605	171	1	ξ̇	ξ̇	NOUN
ap-4605	171	2	+	+	CCONJ
ap-4605	171	3	(	(	PUNCT
ap-4605	171	4	4ρθ	4ρθ	NOUN
ap-4605	171	5	+	+	CCONJ
ap-4605	171	6	2θ̇	2θ̇	NUM
ap-4605	171	7	)	)	PUNCT
ap-4605	172	1	ξ	ξ	X
ap-4605	172	2	=	=	SYM
ap-4605	172	3	0	0	PROPN
ap-4605	172	4	.	.	PUNCT
ap-4605	173	1	(	(	PUNCT
ap-4605	173	2	25	25	NUM
ap-4605	173	3	)	)	PUNCT
ap-4605	173	4	let	let	VERB
ap-4605	173	5	us	we	PRON
ap-4605	173	6	consider	consider	VERB
ap-4605	173	7	vector	vector	NOUN
ap-4605	173	8	fields	field	NOUN
ap-4605	173	9	of	of	ADP
ap-4605	173	10	the	the	DET
ap-4605	173	11	generic	generic	ADJ
ap-4605	173	12	shape	shape	NOUN
ap-4605	173	13	x	x	X
ap-4605	173	14	=	=	SYM
ap-4605	173	15	ξ	ξ	PROPN
ap-4605	173	16	(	(	PUNCT
ap-4605	173	17	t	t	PROPN
ap-4605	173	18	)	)	PUNCT
ap-4605	173	19	∂	∂	NOUN
ap-4605	174	1	∂t	∂t	NOUN
ap-4605	175	1	+	+	CCONJ
ap-4605	175	2	1	1	NUM
ap-4605	175	3	2	2	NUM
ap-4605	175	4	ξ̇	ξ̇	NOUN
ap-4605	175	5	(	(	PUNCT
ap-4605	175	6	t	t	NOUN
ap-4605	175	7	)	)	PUNCT
ap-4605	175	8	qi	qi	PROPN
ap-4605	175	9	∂	∂	NUM
ap-4605	175	10	∂qi	∂qi	PROPN
ap-4605	175	11	,	,	PUNCT
ap-4605	175	12	(	(	PUNCT
ap-4605	175	13	26	26	NUM
ap-4605	175	14	)	)	PUNCT
ap-4605	175	15	and	and	CCONJ
ap-4605	175	16	define	define	VERB
ap-4605	175	17	xi	xi	X
ap-4605	175	18	(	(	PUNCT
ap-4605	175	19	1	1	NUM
ap-4605	175	20	≤	≤	NUM
ap-4605	175	21	i	i	X
ap-4605	175	22	≤	≤	NOUN
ap-4605	175	23	3	3	NUM
ap-4605	175	24	)	)	PUNCT
ap-4605	175	25	as	as	ADP
ap-4605	175	26	the	the	DET
ap-4605	175	27	vector	vector	NOUN
ap-4605	175	28	field	field	NOUN
ap-4605	175	29	associated	associate	VERB
ap-4605	175	30	to	to	ADP
ap-4605	175	31	the	the	DET
ap-4605	175	32	constant	constant	ADJ
ap-4605	175	33	cj	cj	NOUN
ap-4605	175	34	=	=	SYM
ap-4605	175	35	δji	δji	PROPN
ap-4605	175	36	.	.	PUNCT
ap-4605	176	1	computing	compute	VERB
ap-4605	176	2	the	the	DET
ap-4605	176	3	brackets	bracket	NOUN
ap-4605	176	4	,	,	PUNCT
ap-4605	176	5	taking	take	VERB
ap-4605	176	6	into	into	ADP
ap-4605	176	7	account	account	NOUN
ap-4605	176	8	the	the	DET
ap-4605	176	9	constraint	constraint	NOUN
ap-4605	176	10	(	(	PUNCT
ap-4605	176	11	25	25	NUM
ap-4605	176	12	)	)	PUNCT
ap-4605	176	13	,	,	PUNCT
ap-4605	176	14	we	we	PRON
ap-4605	176	15	get	get	VERB
ap-4605	176	16	the	the	DET
ap-4605	176	17	relations	relation	NOUN
ap-4605	177	1	[	[	X
ap-4605	177	2	x1,x2	x1,x2	X
ap-4605	177	3	]	]	X
ap-4605	177	4	=	=	SYM
ap-4605	177	5	w	w	PROPN
ap-4605	177	6	(	(	PUNCT
ap-4605	177	7	u	u	NOUN
ap-4605	177	8	,	,	PUNCT
ap-4605	177	9	v)x1	v)x1	NOUN
ap-4605	177	10	,	,	PUNCT
ap-4605	177	11	[	[	X
ap-4605	177	12	x1,x3	x1,x3	X
ap-4605	177	13	]	]	X
ap-4605	178	1	=	=	X
ap-4605	178	2	2w	2w	NUM
ap-4605	178	3	(	(	PUNCT
ap-4605	178	4	u	u	NOUN
ap-4605	178	5	,	,	PUNCT
ap-4605	178	6	v)x2	v)x2	NOUN
ap-4605	178	7	,	,	PUNCT
ap-4605	178	8	[	[	X
ap-4605	178	9	x2,x3	x2,x3	X
ap-4605	178	10	]	]	X
ap-4605	179	1	=	=	SYM
ap-4605	179	2	w	w	PROPN
ap-4605	179	3	(	(	PUNCT
ap-4605	179	4	u	u	PROPN
ap-4605	179	5	,	,	PUNCT
ap-4605	179	6	v)x3	v)x3	PROPN
ap-4605	179	7	,	,	PUNCT
ap-4605	179	8	(	(	PUNCT
ap-4605	179	9	27	27	NUM
ap-4605	179	10	)	)	PUNCT
ap-4605	179	11	376	376	NUM
ap-4605	179	12	vol	vol	NOUN
ap-4605	179	13	.	.	PUNCT
ap-4605	180	1	57	57	NUM
ap-4605	180	2	no	no	NOUN
ap-4605	180	3	.	.	PUNCT
ap-4605	181	1	6/2017	6/2017	AUX
ap-4605	181	2	noether	noether	ADJ
ap-4605	181	3	point	point	NOUN
ap-4605	181	4	symmetries	symmetry	NOUN
ap-4605	181	5	of	of	ADP
ap-4605	181	6	systems	system	NOUN
ap-4605	181	7	where	where	SCONJ
ap-4605	181	8	w	w	PROPN
ap-4605	181	9	(	(	PUNCT
ap-4605	181	10	u	u	NOUN
ap-4605	181	11	,	,	PUNCT
ap-4605	181	12	v	v	NOUN
ap-4605	181	13	)	)	PUNCT
ap-4605	181	14	=	=	PUNCT
ap-4605	182	1	uv̇	uv̇	ADJ
ap-4605	182	2	−	−	PROPN
ap-4605	182	3	u̇v	u̇v	PROPN
ap-4605	182	4	denotes	denote	VERB
ap-4605	182	5	the	the	DET
ap-4605	182	6	wronskian	wronskian	NOUN
ap-4605	182	7	of	of	ADP
ap-4605	182	8	{	{	PUNCT
ap-4605	182	9	u(t	u(t	PROPN
ap-4605	182	10	)	)	PUNCT
ap-4605	182	11	,	,	PUNCT
ap-4605	182	12	v(t	v(t	NOUN
ap-4605	182	13	)	)	PUNCT
ap-4605	182	14	}	}	PUNCT
ap-4605	182	15	.	.	PUNCT
ap-4605	183	1	now	now	ADV
ap-4605	183	2	,	,	PUNCT
ap-4605	183	3	ifw	ifw	PROPN
ap-4605	183	4	(	(	PUNCT
ap-4605	183	5	u	u	NOUN
ap-4605	183	6	,	,	PUNCT
ap-4605	183	7	v	v	NOUN
ap-4605	183	8	)	)	PUNCT
ap-4605	183	9	reduces	reduce	VERB
ap-4605	183	10	to	to	ADP
ap-4605	183	11	a	a	DET
ap-4605	183	12	constant	constant	ADJ
ap-4605	183	13	λ,1	λ,1	NOUN
ap-4605	183	14	it	it	PRON
ap-4605	183	15	is	be	AUX
ap-4605	183	16	straightforward	straightforward	ADJ
ap-4605	183	17	to	to	PART
ap-4605	183	18	verify	verify	VERB
ap-4605	183	19	that	that	SCONJ
ap-4605	183	20	the	the	DET
ap-4605	183	21	vector	vector	NOUN
ap-4605	183	22	fields	field	VERB
ap-4605	183	23	x1	x1	PROPN
ap-4605	183	24	,	,	PUNCT
ap-4605	184	1	x2	x2	PROPN
ap-4605	184	2	and	and	CCONJ
ap-4605	184	3	x3	x3	PROPN
ap-4605	184	4	span	span	VERB
ap-4605	184	5	a	a	DET
ap-4605	184	6	lie	lie	NOUN
ap-4605	184	7	algebra	algebra	NOUN
ap-4605	184	8	isomorphic	isomorphic	ADJ
ap-4605	184	9	to	to	ADP
ap-4605	184	10	sl(2,r	sl(2,r	NOUN
ap-4605	184	11	)	)	PUNCT
ap-4605	184	12	.	.	PUNCT
ap-4605	185	1	for	for	ADP
ap-4605	185	2	convenience	convenience	NOUN
ap-4605	185	3	,	,	PUNCT
ap-4605	185	4	we	we	PRON
ap-4605	185	5	further	far	ADV
ap-4605	185	6	define	define	VERB
ap-4605	185	7	the	the	DET
ap-4605	185	8	function	function	NOUN
ap-4605	185	9	v	v	NOUN
ap-4605	185	10	(	(	PUNCT
ap-4605	185	11	q	q	NOUN
ap-4605	185	12	)	)	PUNCT
ap-4605	185	13	=	=	SYM
ap-4605	185	14	1	1	NUM
ap-4605	185	15	4	4	NUM
ap-4605	185	16	ξ̈	ξ̈	NUM
ap-4605	185	17	(	(	PUNCT
ap-4605	185	18	t	t	PROPN
ap-4605	185	19	)	)	PUNCT
ap-4605	185	20	(	(	PUNCT
ap-4605	185	21	q2	q2	NOUN
ap-4605	185	22	1	1	NUM
ap-4605	185	23	+	+	NUM
ap-4605	185	24	q2	q2	NOUN
ap-4605	185	25	2	2	NUM
ap-4605	185	26	)	)	PUNCT
ap-4605	185	27	,	,	PUNCT
ap-4605	185	28	which	which	PRON
ap-4605	185	29	shall	shall	AUX
ap-4605	185	30	serve	serve	VERB
ap-4605	185	31	as	as	ADP
ap-4605	185	32	generic	generic	ADJ
ap-4605	185	33	gauge	gauge	NOUN
ap-4605	185	34	term	term	NOUN
ap-4605	185	35	for	for	ADP
ap-4605	185	36	the	the	DET
ap-4605	185	37	symmetry	symmetry	NOUN
ap-4605	185	38	condition	condition	NOUN
ap-4605	185	39	(	(	PUNCT
ap-4605	185	40	11	11	NUM
ap-4605	185	41	)	)	PUNCT
ap-4605	185	42	.	.	PUNCT
ap-4605	186	1	analyzing	analyze	VERB
ap-4605	186	2	the	the	DET
ap-4605	186	3	symmetry	symmetry	NOUN
ap-4605	186	4	condition	condition	NOUN
ap-4605	186	5	(	(	PUNCT
ap-4605	186	6	7	7	NUM
ap-4605	186	7	)	)	PUNCT
ap-4605	186	8	,	,	PUNCT
ap-4605	186	9	the	the	DET
ap-4605	186	10	vector	vector	NOUN
ap-4605	186	11	fields	field	NOUN
ap-4605	186	12	xi	xi	X
ap-4605	186	13	are	be	AUX
ap-4605	186	14	the	the	DET
ap-4605	186	15	symmetry	symmetry	NOUN
ap-4605	186	16	generators	generator	NOUN
ap-4605	186	17	of	of	ADP
ap-4605	186	18	a	a	DET
ap-4605	186	19	noether	noether	ADJ
ap-4605	186	20	point	point	NOUN
ap-4605	186	21	symmetry	symmetry	NOUN
ap-4605	186	22	of	of	ADP
ap-4605	186	23	a	a	DET
ap-4605	186	24	lagrangian	lagrangian	ADJ
ap-4605	186	25	l	l	NOUN
ap-4605	186	26	(	(	PUNCT
ap-4605	186	27	t	t	PROPN
ap-4605	186	28	,	,	PUNCT
ap-4605	186	29	q	q	NOUN
ap-4605	186	30	,	,	PUNCT
ap-4605	186	31	q̇	q̇	ADV
ap-4605	186	32	)	)	PUNCT
ap-4605	186	33	whenever	whenever	SCONJ
ap-4605	186	34	the	the	DET
ap-4605	186	35	first	first	ADJ
ap-4605	186	36	-	-	PUNCT
ap-4605	186	37	order	order	NOUN
ap-4605	186	38	pde	pde	NOUN
ap-4605	186	39	1	1	NUM
ap-4605	186	40	2	2	NUM
ap-4605	186	41	∂l	∂l	NOUN
ap-4605	186	42	∂q̇1	∂q̇1	NOUN
ap-4605	186	43	(	(	PUNCT
ap-4605	186	44	ξ̈q1	ξ̈q1	NOUN
ap-4605	186	45	−	−	PROPN
ap-4605	186	46	ξ̇q̇1	ξ̇q̇1	PROPN
ap-4605	186	47	)	)	PUNCT
ap-4605	187	1	+	+	CCONJ
ap-4605	187	2	1	1	NUM
ap-4605	187	3	2	2	NUM
ap-4605	187	4	∂l	∂l	NOUN
ap-4605	187	5	∂q̇2	∂q̇2	PROPN
ap-4605	187	6	(	(	PUNCT
ap-4605	187	7	ξ̈q2	ξ̈q2	VERB
ap-4605	187	8	−	−	NUM
ap-4605	187	9	ξ̇q̇2	ξ̇q̇2	NOUN
ap-4605	187	10	)	)	PUNCT
ap-4605	187	11	+	+	PUNCT
ap-4605	187	12	ξ	ξ	X
ap-4605	187	13	∂l	∂l	PROPN
ap-4605	188	1	∂t	∂t	PROPN
ap-4605	188	2	+	+	CCONJ
ap-4605	188	3	ξ̇	ξ̇	PROPN
ap-4605	188	4	2	2	NUM
ap-4605	188	5	(	(	PUNCT
ap-4605	188	6	q1	q1	NOUN
ap-4605	188	7	∂l	∂l	NOUN
ap-4605	188	8	∂q1	∂q1	VERB
ap-4605	188	9	+	+	NUM
ap-4605	188	10	q2	q2	NOUN
ap-4605	188	11	∂l	∂l	NOUN
ap-4605	188	12	∂q2	∂q2	PROPN
ap-4605	188	13	)	)	PUNCT
ap-4605	189	1	−	−	PROPN
ap-4605	189	2	...	...	PUNCT
ap-4605	190	1	ξ	ξ	X
ap-4605	190	2	4	4	NUM
ap-4605	190	3	(	(	PUNCT
ap-4605	190	4	q2	q2	NOUN
ap-4605	190	5	1	1	NUM
ap-4605	190	6	+	+	NUM
ap-4605	190	7	q2	q2	NOUN
ap-4605	190	8	2	2	NUM
ap-4605	190	9	)	)	PUNCT
ap-4605	190	10	−	−	NOUN
ap-4605	190	11	1	1	NUM
ap-4605	190	12	2	2	NUM
ap-4605	190	13	ξ̈q̇1q1	ξ̈q̇1q1	NUM
ap-4605	190	14	−	−	NOUN
ap-4605	190	15	1	1	NUM
ap-4605	190	16	2	2	NUM
ap-4605	190	17	ξ̈q̇2q2	ξ̈q̇2q2	NOUN
ap-4605	190	18	+	+	NUM
ap-4605	190	19	ξ̇l	ξ̇l	NOUN
ap-4605	190	20	=	=	SYM
ap-4605	190	21	0	0	NUM
ap-4605	190	22	(	(	PUNCT
ap-4605	190	23	28	28	NUM
ap-4605	190	24	)	)	PUNCT
ap-4605	190	25	is	be	AUX
ap-4605	190	26	satisfied	satisfied	ADJ
ap-4605	190	27	.	.	PUNCT
ap-4605	191	1	the	the	DET
ap-4605	191	2	general	general	ADJ
ap-4605	191	3	solution	solution	NOUN
ap-4605	191	4	to	to	ADP
ap-4605	191	5	the	the	DET
ap-4605	191	6	latter	latter	ADJ
ap-4605	191	7	is	be	AUX
ap-4605	191	8	given	give	VERB
ap-4605	191	9	by	by	ADP
ap-4605	191	10	l	l	PROPN
ap-4605	191	11	(	(	PUNCT
ap-4605	191	12	t	t	PROPN
ap-4605	191	13	,	,	PUNCT
ap-4605	191	14	q	q	NOUN
ap-4605	191	15	,	,	PUNCT
ap-4605	191	16	q̇	q̇	ADJ
ap-4605	191	17	)	)	PUNCT
ap-4605	191	18	=	=	SYM
ap-4605	191	19	(	(	PUNCT
ap-4605	191	20	ξξ̈	ξξ̈	NUM
ap-4605	191	21	−	−	PROPN
ap-4605	191	22	ξ̇2	ξ̇2	PROPN
ap-4605	191	23	)	)	PUNCT
ap-4605	191	24	4ξ2	4ξ2	NUM
ap-4605	192	1	(	(	PUNCT
ap-4605	192	2	q2	q2	NOUN
ap-4605	192	3	1	1	NUM
ap-4605	192	4	+	+	NUM
ap-4605	192	5	q2	q2	NOUN
ap-4605	192	6	2	2	NUM
ap-4605	192	7	)	)	PUNCT
ap-4605	193	1	+	+	CCONJ
ap-4605	193	2	ξ̇	ξ̇	NOUN
ap-4605	193	3	(	(	PUNCT
ap-4605	193	4	q1q̇1	q1q̇1	NOUN
ap-4605	193	5	+	+	CCONJ
ap-4605	193	6	q̇2q2	q̇2q2	NOUN
ap-4605	193	7	)	)	PUNCT
ap-4605	193	8	2ξ	2ξ	NOUN
ap-4605	194	1	+	+	CCONJ
ap-4605	194	2	1	1	NUM
ap-4605	194	3	ξ	ξ	PRON
ap-4605	194	4	ψ	ψ	X
ap-4605	194	5	(	(	PUNCT
ap-4605	194	6	q1√	q1√	PROPN
ap-4605	194	7	ξ	ξ	PROPN
ap-4605	194	8	,	,	PUNCT
ap-4605	194	9	q2√	q2√	PROPN
ap-4605	194	10	ξ	ξ	PROPN
ap-4605	194	11	,	,	PUNCT
ap-4605	194	12	ξ̇q1	ξ̇q1	PROPN
ap-4605	194	13	−	−	PROPN
ap-4605	194	14	2q̇1ξ√	2q̇1ξ√	PROPN
ap-4605	194	15	ξ	ξ	PROPN
ap-4605	194	16	,	,	PUNCT
ap-4605	195	1	ξ̇q2	ξ̇q2	NOUN
ap-4605	195	2	−	−	PROPN
ap-4605	195	3	2q̇2ξ√	2q̇2ξ√	NOUN
ap-4605	195	4	ξ	ξ	PROPN
ap-4605	195	5	)	)	PUNCT
ap-4605	195	6	,	,	PUNCT
ap-4605	195	7	with	with	ADP
ap-4605	195	8	ψ	ψ	PRON
ap-4605	195	9	an	an	DET
ap-4605	195	10	arbitrary	arbitrary	ADJ
ap-4605	195	11	function	function	NOUN
ap-4605	195	12	of	of	ADP
ap-4605	195	13	its	its	PRON
ap-4605	195	14	arguments	argument	NOUN
ap-4605	195	15	.	.	PUNCT
ap-4605	196	1	we	we	PRON
ap-4605	196	2	observe	observe	VERB
ap-4605	196	3	that	that	SCONJ
ap-4605	196	4	the	the	DET
ap-4605	196	5	previous	previous	ADJ
ap-4605	196	6	class	class	NOUN
ap-4605	196	7	of	of	ADP
ap-4605	196	8	lagrangians	lagrangians	PROPN
ap-4605	196	9	contains	contain	VERB
ap-4605	196	10	,	,	PUNCT
ap-4605	196	11	in	in	ADP
ap-4605	196	12	particular	particular	ADJ
ap-4605	196	13	,	,	PUNCT
ap-4605	196	14	a	a	DET
ap-4605	196	15	family	family	NOUN
ap-4605	196	16	giving	give	VERB
ap-4605	196	17	rise	rise	NOUN
ap-4605	196	18	to	to	ADP
ap-4605	196	19	oscillatory	oscillatory	ADJ
ap-4605	196	20	systems	system	NOUN
ap-4605	196	21	with	with	ADP
ap-4605	196	22	a	a	DET
ap-4605	196	23	time	time	NOUN
ap-4605	196	24	-	-	PUNCT
ap-4605	196	25	dependent	dependent	ADJ
ap-4605	196	26	frequency	frequency	NOUN
ap-4605	196	27	:	:	PUNCT
ap-4605	197	1	l	l	NOUN
ap-4605	197	2	=	=	SYM
ap-4605	197	3	1	1	NUM
ap-4605	197	4	2	2	NUM
ap-4605	197	5	(	(	PUNCT
ap-4605	197	6	q̇2	q̇2	NOUN
ap-4605	197	7	1	1	NUM
ap-4605	197	8	+	+	CCONJ
ap-4605	197	9	q̇2	q̇2	NOUN
ap-4605	197	10	2	2	NUM
ap-4605	197	11	)	)	PUNCT
ap-4605	197	12	+	+	CCONJ
ap-4605	197	13	2	2	NUM
ap-4605	197	14	¨ξ(t)ξ(t)−	¨ξ(t)ξ(t)−	PROPN
ap-4605	197	15	1	1	NUM
ap-4605	197	16	ξ(t)2	ξ(t)2	PROPN
ap-4605	197	17	(	(	PUNCT
ap-4605	197	18	q2	q2	NOUN
ap-4605	197	19	1	1	NUM
ap-4605	197	20	+	+	NUM
ap-4605	197	21	q2	q2	NOUN
ap-4605	197	22	2	2	NUM
ap-4605	197	23	)	)	PUNCT
ap-4605	197	24	.	.	PUNCT
ap-4605	198	1	(	(	PUNCT
ap-4605	198	2	29	29	NUM
ap-4605	198	3	)	)	PUNCT
ap-4605	198	4	it	it	PRON
ap-4605	198	5	should	should	AUX
ap-4605	198	6	be	be	AUX
ap-4605	198	7	remarked	remark	VERB
ap-4605	198	8	that	that	SCONJ
ap-4605	198	9	the	the	DET
ap-4605	198	10	realization	realization	NOUN
ap-4605	198	11	of	of	ADP
ap-4605	198	12	type	type	NOUN
ap-4605	198	13	(	(	PUNCT
ap-4605	198	14	26	26	NUM
ap-4605	198	15	)	)	PUNCT
ap-4605	198	16	exhibits	exhibit	VERB
ap-4605	198	17	the	the	DET
ap-4605	198	18	most	most	ADV
ap-4605	198	19	general	general	ADJ
ap-4605	198	20	form	form	NOUN
ap-4605	198	21	that	that	PRON
ap-4605	198	22	the	the	DET
ap-4605	198	23	term	term	NOUN
ap-4605	198	24	in	in	ADP
ap-4605	198	25	∂	∂	NOUN
ap-4605	198	26	∂t	∂t	PROPN
ap-4605	198	27	can	can	AUX
ap-4605	198	28	have	have	VERB
ap-4605	198	29	,	,	PUNCT
ap-4605	198	30	as	as	SCONJ
ap-4605	198	31	follows	follow	VERB
ap-4605	198	32	at	at	ADP
ap-4605	198	33	once	once	ADV
ap-4605	198	34	from	from	ADP
ap-4605	198	35	the	the	DET
ap-4605	198	36	following	follow	VERB
ap-4605	198	37	property	property	NOUN
ap-4605	198	38	:	:	PUNCT
ap-4605	198	39	lemma	lemma	PROPN
ap-4605	198	40	2	2	X
ap-4605	198	41	.	.	PUNCT
ap-4605	199	1	let	let	VERB
ap-4605	199	2	x	x	SYM
ap-4605	199	3	=	=	SYM
ap-4605	199	4	ξ(t	ξ(t	NOUN
ap-4605	199	5	,	,	PUNCT
ap-4605	199	6	q	q	NOUN
ap-4605	199	7	)	)	PUNCT
ap-4605	199	8	∂∂t	∂∂t	PROPN
ap-4605	199	9	+	+	CCONJ
ap-4605	199	10	ηj(t	ηj(t	PROPN
ap-4605	199	11	,	,	PUNCT
ap-4605	199	12	q	q	NOUN
ap-4605	199	13	)	)	PUNCT
ap-4605	199	14	∂	∂	NOUN
ap-4605	199	15	∂qj	∂qj	PROPN
ap-4605	199	16	be	be	VERB
ap-4605	199	17	a	a	DET
ap-4605	199	18	noether	noether	ADJ
ap-4605	199	19	point	point	NOUN
ap-4605	199	20	symmetry	symmetry	NOUN
ap-4605	199	21	of	of	ADP
ap-4605	199	22	a	a	DET
ap-4605	199	23	regular	regular	ADJ
ap-4605	199	24	lagrangian	lagrangian	ADJ
ap-4605	199	25	l	l	NOUN
ap-4605	199	26	=	=	SYM
ap-4605	199	27	aij(t	aij(t	PROPN
ap-4605	199	28	,	,	PUNCT
ap-4605	199	29	q)q̇iq̇j−u(t	q)q̇iq̇j−u(t	NOUN
ap-4605	199	30	,	,	PUNCT
ap-4605	199	31	q	q	NOUN
ap-4605	199	32	)	)	PUNCT
ap-4605	199	33	.	.	PUNCT
ap-4605	200	1	then	then	ADV
ap-4605	200	2	the	the	DET
ap-4605	200	3	condition	condition	NOUN
ap-4605	200	4	∂ξ	∂ξ	NOUN
ap-4605	200	5	∂q	∂q	NOUN
ap-4605	200	6	=	=	SYM
ap-4605	200	7	0	0	NUM
ap-4605	200	8	always	always	ADV
ap-4605	200	9	holds	hold	VERB
ap-4605	200	10	.	.	PUNCT
ap-4605	201	1	the	the	DET
ap-4605	201	2	proof	proof	NOUN
ap-4605	201	3	is	be	AUX
ap-4605	201	4	completely	completely	ADV
ap-4605	201	5	analogous	analogous	ADJ
ap-4605	201	6	to	to	ADP
ap-4605	201	7	that	that	PRON
ap-4605	201	8	of	of	ADP
ap-4605	201	9	lemma	lemma	PROPN
ap-4605	201	10	1	1	NUM
ap-4605	201	11	,	,	PUNCT
ap-4605	201	12	and	and	CCONJ
ap-4605	201	13	follows	follow	VERB
ap-4605	201	14	immediately	immediately	ADV
ap-4605	201	15	from	from	ADP
ap-4605	201	16	the	the	DET
ap-4605	201	17	inspection	inspection	NOUN
ap-4605	201	18	of	of	ADP
ap-4605	201	19	the	the	DET
ap-4605	201	20	terms	term	NOUN
ap-4605	201	21	in	in	ADP
ap-4605	201	22	the	the	DET
ap-4605	201	23	symmetry	symmetry	NOUN
ap-4605	201	24	condition	condition	NOUN
ap-4605	201	25	(	(	PUNCT
ap-4605	201	26	7	7	X
ap-4605	201	27	)	)	PUNCT
ap-4605	201	28	having	have	VERB
ap-4605	201	29	the	the	DET
ap-4605	201	30	highest	high	ADJ
ap-4605	201	31	power	power	NOUN
ap-4605	201	32	in	in	ADP
ap-4605	201	33	the	the	DET
ap-4605	201	34	velocities	velocity	NOUN
ap-4605	201	35	q̇	q̇	ADV
ap-4605	201	36	,	,	PUNCT
ap-4605	201	37	as	as	ADV
ap-4605	201	38	well	well	ADV
ap-4605	201	39	as	as	ADP
ap-4605	201	40	the	the	DET
ap-4605	201	41	regularity	regularity	NOUN
ap-4605	201	42	of	of	ADP
ap-4605	201	43	the	the	DET
ap-4605	201	44	lagrangian	lagrangian	ADJ
ap-4605	201	45	.	.	PUNCT
ap-4605	202	1	5	5	NUM
ap-4605	202	2	.	.	X
ap-4605	202	3	conclusions	conclusion	NOUN
ap-4605	202	4	in	in	ADP
ap-4605	202	5	this	this	DET
ap-4605	202	6	work	work	NOUN
ap-4605	202	7	we	we	PRON
ap-4605	202	8	have	have	AUX
ap-4605	202	9	illustrated	illustrate	VERB
ap-4605	202	10	,	,	PUNCT
ap-4605	202	11	using	use	VERB
ap-4605	202	12	functional	functional	ADJ
ap-4605	202	13	realizations	realization	NOUN
ap-4605	202	14	of	of	ADP
ap-4605	202	15	lie	lie	NOUN
ap-4605	202	16	algebras	algebras	PROPN
ap-4605	202	17	based	base	VERB
ap-4605	202	18	on	on	ADP
ap-4605	202	19	the	the	DET
ap-4605	202	20	simple	simple	ADJ
ap-4605	202	21	lie	lie	NOUN
ap-4605	202	22	algebra	algebra	NOUN
ap-4605	202	23	sl(2,r	sl(2,r	NOUN
ap-4605	202	24	)	)	PUNCT
ap-4605	202	25	,	,	PUNCT
ap-4605	202	26	different	different	ADJ
ap-4605	202	27	possibilities	possibility	NOUN
ap-4605	202	28	to	to	PART
ap-4605	202	29	formulate	formulate	VERB
ap-4605	202	30	a	a	DET
ap-4605	202	31	kind	kind	NOUN
ap-4605	202	32	of	of	ADP
ap-4605	202	33	inverse	inverse	ADJ
ap-4605	202	34	problem	problem	NOUN
ap-4605	202	35	in	in	ADP
ap-4605	202	36	dynamics	dynamic	NOUN
ap-4605	202	37	,	,	PUNCT
ap-4605	202	38	imposing	impose	VERB
ap-4605	202	39	that	that	SCONJ
ap-4605	202	40	1this	1this	NUM
ap-4605	202	41	condition	condition	NOUN
ap-4605	202	42	is	be	AUX
ap-4605	202	43	ensured	ensure	VERB
ap-4605	202	44	whenever	whenever	SCONJ
ap-4605	202	45	we	we	PRON
ap-4605	202	46	set	set	VERB
ap-4605	202	47	ρ(t	ρ(t	NUM
ap-4605	202	48	)	)	PUNCT
ap-4605	203	1	=	=	SYM
ap-4605	203	2	0	0	NUM
ap-4605	204	1	in	in	ADP
ap-4605	204	2	equation	equation	NOUN
ap-4605	204	3	(	(	PUNCT
ap-4605	204	4	24	24	NUM
ap-4605	204	5	)	)	PUNCT
ap-4605	204	6	.	.	PUNCT
ap-4605	205	1	see	see	VERB
ap-4605	205	2	e.g.	e.g.	ADV
ap-4605	205	3	[	[	X
ap-4605	205	4	14	14	NUM
ap-4605	205	5	]	]	PUNCT
ap-4605	205	6	,	,	PUNCT
ap-4605	205	7	p.	p.	NOUN
ap-4605	205	8	512	512	NUM
ap-4605	205	9	.	.	PUNCT
ap-4605	206	1	the	the	DET
ap-4605	206	2	generators	generator	NOUN
ap-4605	206	3	appear	appear	VERB
ap-4605	206	4	as	as	ADP
ap-4605	206	5	noether	noether	ADJ
ap-4605	206	6	point	point	NOUN
ap-4605	206	7	symmetries	symmetry	NOUN
ap-4605	206	8	of	of	ADP
ap-4605	206	9	lagrangian	lagrangian	ADJ
ap-4605	206	10	dynamical	dynamical	ADJ
ap-4605	206	11	systems	system	NOUN
ap-4605	206	12	.	.	PUNCT
ap-4605	207	1	this	this	PRON
ap-4605	207	2	allows	allow	VERB
ap-4605	207	3	either	either	CCONJ
ap-4605	207	4	to	to	PART
ap-4605	207	5	consider	consider	VERB
ap-4605	207	6	symmetry	symmetry	NOUN
ap-4605	207	7	-	-	PUNCT
ap-4605	207	8	preserving	preserve	VERB
ap-4605	207	9	perturbations	perturbation	NOUN
ap-4605	207	10	of	of	ADP
ap-4605	207	11	a	a	DET
ap-4605	207	12	given	give	VERB
ap-4605	207	13	system	system	NOUN
ap-4605	207	14	,	,	PUNCT
ap-4605	207	15	as	as	SCONJ
ap-4605	207	16	developed	develop	VERB
ap-4605	207	17	in	in	ADP
ap-4605	207	18	[	[	X
ap-4605	207	19	12	12	NUM
ap-4605	207	20	]	]	PUNCT
ap-4605	207	21	,	,	PUNCT
ap-4605	207	22	or	or	CCONJ
ap-4605	207	23	to	to	PART
ap-4605	207	24	derive	derive	VERB
ap-4605	207	25	the	the	DET
ap-4605	207	26	most	most	ADV
ap-4605	207	27	general	general	ADJ
ap-4605	207	28	lagrangian	lagrangian	ADJ
ap-4605	207	29	invariant	invariant	NOUN
ap-4605	207	30	by	by	ADP
ap-4605	207	31	the	the	DET
ap-4605	207	32	functional	functional	ADJ
ap-4605	207	33	realization	realization	NOUN
ap-4605	207	34	of	of	ADP
ap-4605	207	35	the	the	DET
ap-4605	207	36	lie	lie	NOUN
ap-4605	207	37	algebra	algebra	NOUN
ap-4605	207	38	.	.	PUNCT
ap-4605	208	1	the	the	DET
ap-4605	208	2	cases	case	NOUN
ap-4605	208	3	of	of	ADP
ap-4605	208	4	conservative	conservative	ADJ
ap-4605	208	5	and	and	CCONJ
ap-4605	208	6	dissipative	dissipative	ADJ
ap-4605	208	7	systems	system	NOUN
ap-4605	208	8	can	can	AUX
ap-4605	208	9	be	be	AUX
ap-4605	208	10	treated	treat	VERB
ap-4605	208	11	simultaneously	simultaneously	ADV
ap-4605	208	12	,	,	PUNCT
ap-4605	208	13	considering	consider	VERB
ap-4605	208	14	realizations	realization	NOUN
ap-4605	208	15	explicitly	explicitly	ADV
ap-4605	208	16	depending	depend	VERB
ap-4605	208	17	on	on	ADP
ap-4605	208	18	timedependent	timedependent	NOUN
ap-4605	208	19	functions	function	NOUN
ap-4605	208	20	.	.	PUNCT
ap-4605	209	1	albeit	albeit	SCONJ
ap-4605	209	2	the	the	DET
ap-4605	209	3	examples	example	NOUN
ap-4605	209	4	have	have	AUX
ap-4605	209	5	been	be	AUX
ap-4605	209	6	restricted	restrict	VERB
ap-4605	209	7	to	to	ADP
ap-4605	209	8	the	the	DET
ap-4605	209	9	plane	plane	NOUN
ap-4605	209	10	by	by	ADP
ap-4605	209	11	simplicity	simplicity	NOUN
ap-4605	209	12	,	,	PUNCT
ap-4605	209	13	there	there	PRON
ap-4605	209	14	is	be	VERB
ap-4605	209	15	no	no	DET
ap-4605	209	16	obstruction	obstruction	NOUN
ap-4605	209	17	to	to	PART
ap-4605	209	18	formulate	formulate	VERB
ap-4605	209	19	the	the	DET
ap-4605	209	20	problem	problem	NOUN
ap-4605	209	21	in	in	ADP
ap-4605	209	22	arbitrary	arbitrary	ADJ
ap-4605	209	23	dimension	dimension	NOUN
ap-4605	209	24	.	.	PUNCT
ap-4605	210	1	however	however	ADV
ap-4605	210	2	,	,	PUNCT
ap-4605	210	3	in	in	ADP
ap-4605	210	4	order	order	NOUN
ap-4605	210	5	to	to	PART
ap-4605	210	6	ensure	ensure	VERB
ap-4605	210	7	that	that	SCONJ
ap-4605	210	8	the	the	DET
ap-4605	210	9	system	system	NOUN
ap-4605	210	10	is	be	AUX
ap-4605	210	11	integrable	integrable	ADJ
ap-4605	210	12	[	[	X
ap-4605	210	13	4	4	NUM
ap-4605	210	14	]	]	PUNCT
ap-4605	210	15	,	,	PUNCT
ap-4605	210	16	it	it	PRON
ap-4605	210	17	is	be	AUX
ap-4605	210	18	convenient	convenient	ADJ
ap-4605	210	19	to	to	PART
ap-4605	210	20	consider	consider	VERB
ap-4605	210	21	a	a	DET
ap-4605	210	22	realization	realization	NOUN
ap-4605	210	23	of	of	ADP
ap-4605	210	24	a	a	DET
ap-4605	210	25	symmetry	symmetry	NOUN
ap-4605	210	26	algebra	algebra	NOUN
ap-4605	210	27	sl(2,r	sl(2,r	NOUN
ap-4605	210	28	)	)	PUNCT
ap-4605	210	29	⊂	⊂	PROPN
ap-4605	210	30	g	g	PROPN
ap-4605	210	31	,	,	PUNCT
ap-4605	210	32	so	so	SCONJ
ap-4605	210	33	that	that	SCONJ
ap-4605	210	34	formula	formula	NOUN
ap-4605	210	35	(	(	PUNCT
ap-4605	210	36	8)	8)	NUM
ap-4605	210	37	provides	provide	VERB
ap-4605	210	38	a	a	DET
ap-4605	210	39	sufficient	sufficient	ADJ
ap-4605	210	40	number	number	NOUN
ap-4605	210	41	of	of	ADP
ap-4605	210	42	independent	independent	ADJ
ap-4605	210	43	constants	constant	NOUN
ap-4605	210	44	of	of	ADP
ap-4605	210	45	the	the	DET
ap-4605	210	46	motion	motion	NOUN
ap-4605	210	47	.	.	PUNCT
ap-4605	211	1	in	in	ADP
ap-4605	211	2	this	this	DET
ap-4605	211	3	situation	situation	NOUN
ap-4605	211	4	,	,	PUNCT
ap-4605	211	5	it	it	PRON
ap-4605	211	6	should	should	AUX
ap-4605	211	7	be	be	AUX
ap-4605	211	8	taken	take	VERB
ap-4605	211	9	into	into	ADP
ap-4605	211	10	account	account	NOUN
ap-4605	211	11	that	that	SCONJ
ap-4605	211	12	this	this	DET
ap-4605	211	13	approach	approach	NOUN
ap-4605	211	14	by	by	ADP
ap-4605	211	15	means	mean	NOUN
ap-4605	211	16	of	of	ADP
ap-4605	211	17	noether	noether	ADJ
ap-4605	211	18	point	point	NOUN
ap-4605	211	19	symmetries	symmetry	NOUN
ap-4605	211	20	in	in	ADP
ap-4605	211	21	the	the	DET
ap-4605	211	22	n	n	ADV
ap-4605	211	23	-dimensional	-dimensional	ADJ
ap-4605	211	24	(	(	PUNCT
ap-4605	211	25	conservative	conservative	ADJ
ap-4605	211	26	)	)	PUNCT
ap-4605	211	27	case	case	NOUN
ap-4605	211	28	is	be	AUX
ap-4605	211	29	somewhat	somewhat	ADV
ap-4605	211	30	restricted	restrict	VERB
ap-4605	211	31	,	,	PUNCT
ap-4605	211	32	as	as	SCONJ
ap-4605	211	33	the	the	DET
ap-4605	211	34	corresponding	corresponding	ADJ
ap-4605	211	35	preserved	preserve	VERB
ap-4605	211	36	symmetry	symmetry	NOUN
ap-4605	211	37	algebras	algebra	NOUN
ap-4605	211	38	are	be	AUX
ap-4605	211	39	subalgebras	subalgebra	NOUN
ap-4605	211	40	of	of	ADP
ap-4605	211	41	the	the	DET
ap-4605	211	42	noether	noether	ADJ
ap-4605	211	43	point	point	NOUN
ap-4605	211	44	symmetry	symmetry	NOUN
ap-4605	211	45	algebra	algebra	NOUN
ap-4605	211	46	of	of	ADP
ap-4605	211	47	the	the	DET
ap-4605	211	48	free	free	ADJ
ap-4605	211	49	system	system	NOUN
ap-4605	211	50	defined	define	VERB
ap-4605	211	51	by	by	ADP
ap-4605	211	52	the	the	DET
ap-4605	211	53	kinetic	kinetic	ADJ
ap-4605	211	54	term	term	NOUN
ap-4605	211	55	t	t	PROPN
ap-4605	211	56	of	of	ADP
ap-4605	211	57	the	the	DET
ap-4605	211	58	lagrangian	lagrangian	NOUN
ap-4605	211	59	.	.	PUNCT
ap-4605	212	1	for	for	ADP
ap-4605	212	2	the	the	DET
ap-4605	212	3	euclidean	euclidean	ADJ
ap-4605	212	4	case	case	NOUN
ap-4605	212	5	,	,	PUNCT
ap-4605	212	6	this	this	PRON
ap-4605	212	7	corresponds	correspond	VERB
ap-4605	212	8	to	to	ADP
ap-4605	212	9	subalgebras	subalgebras	PROPN
ap-4605	212	10	of	of	ADP
ap-4605	212	11	the	the	DET
ap-4605	212	12	schrödinger	schrödinger	ADJ
ap-4605	212	13	algebra	algebra	NOUN
ap-4605	212	14	s(n	s(n	PROPN
ap-4605	212	15	)	)	PUNCT
ap-4605	212	16	,	,	PUNCT
ap-4605	212	17	and	and	CCONJ
ap-4605	212	18	hence	hence	ADV
ap-4605	212	19	any	any	DET
ap-4605	212	20	semisimple	semisimple	NOUN
ap-4605	212	21	lie	lie	NOUN
ap-4605	212	22	algebra	algebra	NOUN
ap-4605	212	23	considered	consider	VERB
ap-4605	212	24	in	in	ADP
ap-4605	212	25	this	this	DET
ap-4605	212	26	frame	frame	NOUN
ap-4605	212	27	must	must	AUX
ap-4605	212	28	be	be	AUX
ap-4605	212	29	taken	take	VERB
ap-4605	212	30	as	as	ADP
ap-4605	212	31	a	a	DET
ap-4605	212	32	subalgebra	subalgebra	NOUN
ap-4605	212	33	of	of	ADP
ap-4605	212	34	sl(2,r)⊕	sl(2,r)⊕	X
ap-4605	212	35	so(n	so(n	NOUN
ap-4605	212	36	)	)	PUNCT
ap-4605	212	37	(	(	PUNCT
ap-4605	212	38	see	see	VERB
ap-4605	212	39	e.g.	e.g.	ADV
ap-4605	212	40	[	[	X
ap-4605	212	41	12	12	NUM
ap-4605	212	42	,	,	PUNCT
ap-4605	212	43	15	15	NUM
ap-4605	212	44	]	]	NUM
ap-4605	212	45	)	)	PUNCT
ap-4605	212	46	.	.	PUNCT
ap-4605	213	1	however	however	ADV
ap-4605	213	2	,	,	PUNCT
ap-4605	213	3	for	for	ADP
ap-4605	213	4	non	non	ADJ
ap-4605	213	5	-	-	ADJ
ap-4605	213	6	euclidean	euclidean	ADJ
ap-4605	213	7	geometries	geometry	NOUN
ap-4605	213	8	,	,	PUNCT
ap-4605	213	9	the	the	DET
ap-4605	213	10	situation	situation	NOUN
ap-4605	213	11	may	may	AUX
ap-4605	213	12	differ	differ	VERB
ap-4605	213	13	.	.	PUNCT
ap-4605	214	1	as	as	ADP
ap-4605	214	2	an	an	DET
ap-4605	214	3	illustrative	illustrative	ADJ
ap-4605	214	4	example	example	NOUN
ap-4605	214	5	consider	consider	VERB
ap-4605	214	6	the	the	DET
ap-4605	214	7	free	free	ADJ
ap-4605	214	8	lagrangian	lagrangian	ADJ
ap-4605	214	9	l0	l0	NOUN
ap-4605	214	10	=	=	SYM
ap-4605	214	11	1	1	NUM
ap-4605	214	12	q2	q2	NOUN
ap-4605	214	13	n	n	CCONJ
ap-4605	214	14	(	(	PUNCT
ap-4605	214	15	q̇2	q̇2	NOUN
ap-4605	214	16	1	1	NUM
ap-4605	214	17	+	+	NUM
ap-4605	214	18	·	·	PUNCT
ap-4605	214	19	·	·	PUNCT
ap-4605	214	20	·	·	PUNCT
ap-4605	215	1	+	+	PUNCT
ap-4605	215	2	q̇2	q̇2	NOUN
ap-4605	215	3	n	n	NOUN
ap-4605	215	4	)	)	PUNCT
ap-4605	215	5	in	in	ADP
ap-4605	215	6	the	the	DET
ap-4605	215	7	upperhalf	upperhalf	ADJ
ap-4605	215	8	space	space	NOUN
ap-4605	215	9	u	u	NOUN
ap-4605	215	10	=	=	PUNCT
ap-4605	215	11	{	{	PUNCT
ap-4605	215	12	q	q	NOUN
ap-4605	215	13	∈	∈	PROPN
ap-4605	215	14	rn|	rn|	PROPN
ap-4605	215	15	qn	qn	NOUN
ap-4605	215	16	>	>	X
ap-4605	215	17	0	0	NUM
ap-4605	215	18	}	}	PUNCT
ap-4605	215	19	endowed	endow	VERB
ap-4605	215	20	with	with	ADP
ap-4605	215	21	the	the	DET
ap-4605	215	22	poincaré	poincaré	PROPN
ap-4605	216	1	metric	metric	ADJ
ap-4605	216	2	ds2	ds2	PROPN
ap-4605	216	3	=	=	SYM
ap-4605	216	4	1	1	NUM
ap-4605	216	5	(	(	PUNCT
ap-4605	216	6	qn)2	qn)2	INTJ
ap-4605	216	7	(	(	PUNCT
ap-4605	216	8	dq1	dq1	PROPN
ap-4605	216	9	⊗	⊗	PROPN
ap-4605	216	10	dx1	dx1	PROPN
ap-4605	216	11	+	+	CCONJ
ap-4605	216	12	·	·	PUNCT
ap-4605	216	13	·	·	PUNCT
ap-4605	216	14	·	·	PUNCT
ap-4605	216	15	+	+	NUM
ap-4605	216	16	dqn	dqn	PROPN
ap-4605	216	17	⊗	⊗	PROPN
ap-4605	216	18	dqn	dqn	NOUN
ap-4605	216	19	)	)	PUNCT
ap-4605	216	20	(	(	PUNCT
ap-4605	216	21	30	30	X
ap-4605	216	22	)	)	PUNCT
ap-4605	216	23	it	it	PRON
ap-4605	216	24	is	be	AUX
ap-4605	216	25	well	well	ADV
ap-4605	216	26	known	know	VERB
ap-4605	216	27	that	that	SCONJ
ap-4605	216	28	it	it	PRON
ap-4605	216	29	admits	admit	VERB
ap-4605	216	30	the	the	DET
ap-4605	216	31	conformal	conformal	ADJ
ap-4605	216	32	group	group	NOUN
ap-4605	217	1	so	so	SCONJ
ap-4605	217	2	(	(	PUNCT
ap-4605	217	3	1	1	NUM
ap-4605	217	4	,	,	PUNCT
ap-4605	217	5	n	n	CCONJ
ap-4605	217	6	)	)	PUNCT
ap-4605	217	7	as	as	ADP
ap-4605	217	8	isometry	isometry	PROPN
ap-4605	217	9	group	group	NOUN
ap-4605	218	1	[	[	X
ap-4605	218	2	16	16	NUM
ap-4605	218	3	]	]	PUNCT
ap-4605	218	4	,	,	PUNCT
ap-4605	218	5	i.e.	i.e.	X
ap-4605	218	6	,	,	PUNCT
ap-4605	218	7	the	the	DET
ap-4605	218	8	corresponding	corresponding	ADJ
ap-4605	218	9	symmetry	symmetry	NOUN
ap-4605	218	10	generators	generator	NOUN
ap-4605	218	11	are	be	AUX
ap-4605	218	12	killing	kill	VERB
ap-4605	218	13	vectors	vector	NOUN
ap-4605	218	14	.	.	PUNCT
ap-4605	219	1	it	it	PRON
ap-4605	219	2	is	be	AUX
ap-4605	219	3	easy	easy	ADJ
ap-4605	219	4	to	to	PART
ap-4605	219	5	show	show	VERB
ap-4605	219	6	that	that	SCONJ
ap-4605	219	7	for	for	ADP
ap-4605	219	8	any	any	DET
ap-4605	219	9	n	n	PRON
ap-4605	219	10	≥	≥	NOUN
ap-4605	219	11	2	2	NUM
ap-4605	219	12	,	,	PUNCT
ap-4605	219	13	the	the	DET
ap-4605	219	14	algebra	algebra	NOUN
ap-4605	219	15	lps	lps	PROPN
ap-4605	219	16	of	of	ADP
ap-4605	219	17	lie	lie	NOUN
ap-4605	219	18	point	point	NOUN
ap-4605	219	19	symmetries	symmetry	NOUN
ap-4605	219	20	of	of	ADP
ap-4605	219	21	the	the	DET
ap-4605	219	22	dynamical	dynamical	ADJ
ap-4605	219	23	system	system	NOUN
ap-4605	219	24	associated	associate	VERB
ap-4605	219	25	to	to	ADP
ap-4605	219	26	l0	l0	PROPN
ap-4605	219	27	is	be	AUX
ap-4605	219	28	isomorphic	isomorphic	ADJ
ap-4605	219	29	to	to	ADP
ap-4605	219	30	the	the	DET
ap-4605	219	31	direct	direct	ADJ
ap-4605	219	32	sum	sum	NOUN
ap-4605	219	33	so	so	CCONJ
ap-4605	219	34	(	(	PUNCT
ap-4605	219	35	1	1	NUM
ap-4605	219	36	,	,	PUNCT
ap-4605	219	37	n	n	CCONJ
ap-4605	219	38	)	)	PUNCT
ap-4605	219	39	⊕	⊕	PROPN
ap-4605	219	40	r2	r2	PROPN
ap-4605	219	41	,	,	PUNCT
ap-4605	219	42	with	with	ADP
ap-4605	219	43	r2	r2	PROPN
ap-4605	219	44	the	the	DET
ap-4605	219	45	2	2	NUM
ap-4605	219	46	-	-	PUNCT
ap-4605	219	47	dimensional	dimensional	ADJ
ap-4605	219	48	affine	affine	NOUN
ap-4605	219	49	lie	lie	NOUN
ap-4605	219	50	algebra	algebra	NOUN
ap-4605	219	51	.	.	PUNCT
ap-4605	220	1	only	only	ADV
ap-4605	220	2	the	the	DET
ap-4605	220	3	lie	lie	NOUN
ap-4605	220	4	point	point	NOUN
ap-4605	220	5	symmetry	symmetry	NOUN
ap-4605	220	6	y	y	PROPN
ap-4605	220	7	=	=	SYM
ap-4605	220	8	t	t	PROPN
ap-4605	220	9	∂∂t	∂∂t	NOUN
ap-4605	220	10	fails	fail	VERB
ap-4605	220	11	to	to	PART
ap-4605	220	12	satisfy	satisfy	VERB
ap-4605	220	13	the	the	DET
ap-4605	220	14	condition	condition	NOUN
ap-4605	220	15	(	(	PUNCT
ap-4605	220	16	7	7	NUM
ap-4605	220	17	)	)	PUNCT
ap-4605	220	18	,	,	PUNCT
ap-4605	220	19	as	as	SCONJ
ap-4605	220	20	it	it	PRON
ap-4605	220	21	leads	lead	VERB
ap-4605	220	22	to	to	ADP
ap-4605	220	23	the	the	DET
ap-4605	220	24	pde	pde	NOUN
ap-4605	221	1	−	−	NOUN
ap-4605	221	2	1	1	NUM
ap-4605	221	3	2q2	2q2	NUM
ap-4605	222	1	n	n	NUM
ap-4605	222	2	n∑	n∑	NOUN
ap-4605	222	3	k=1	k=1	X
ap-4605	223	1	(	(	PUNCT
ap-4605	223	2	q̇2	q̇2	NOUN
ap-4605	223	3	k	k	NOUN
ap-4605	223	4	+	+	CCONJ
ap-4605	223	5	q̇k	q̇k	PROPN
ap-4605	223	6	∂v	∂v	PROPN
ap-4605	223	7	∂qk	∂qk	PROPN
ap-4605	223	8	)	)	PUNCT
ap-4605	224	1	−	−	PROPN
ap-4605	225	1	∂v	∂v	PROPN
ap-4605	225	2	∂t	∂t	PROPN
ap-4605	225	3	,	,	PUNCT
ap-4605	225	4	(	(	PUNCT
ap-4605	225	5	31	31	NUM
ap-4605	225	6	)	)	PUNCT
ap-4605	225	7	which	which	PRON
ap-4605	225	8	has	have	VERB
ap-4605	225	9	no	no	DET
ap-4605	225	10	solution	solution	NOUN
ap-4605	225	11	for	for	ADP
ap-4605	225	12	a	a	DET
ap-4605	225	13	gauge	gauge	ADJ
ap-4605	225	14	term	term	NOUN
ap-4605	225	15	v	v	NOUN
ap-4605	225	16	(	(	PUNCT
ap-4605	225	17	t	t	PROPN
ap-4605	225	18	,	,	PUNCT
ap-4605	225	19	q	q	NOUN
ap-4605	225	20	)	)	PUNCT
ap-4605	225	21	,	,	PUNCT
ap-4605	225	22	thus	thus	ADV
ap-4605	225	23	the	the	DET
ap-4605	225	24	noether	noether	ADJ
ap-4605	225	25	point	point	NOUN
ap-4605	225	26	symmetries	symmetry	NOUN
ap-4605	225	27	are	be	AUX
ap-4605	225	28	given	give	VERB
ap-4605	225	29	by	by	ADP
ap-4605	225	30	the	the	DET
ap-4605	225	31	lie	lie	NOUN
ap-4605	225	32	algebra	algebra	VERB
ap-4605	225	33	lns	lns	PROPN
ap-4605	225	34	'	'	PUNCT
ap-4605	225	35	so	so	CCONJ
ap-4605	225	36	(	(	PUNCT
ap-4605	225	37	1	1	NUM
ap-4605	225	38	,	,	PUNCT
ap-4605	225	39	n)⊕r	n)⊕r	NOUN
ap-4605	225	40	.	.	PROPN
ap-4605	226	1	as	as	ADP
ap-4605	226	2	a	a	DET
ap-4605	226	3	consequence	consequence	NOUN
ap-4605	226	4	,	,	PUNCT
ap-4605	226	5	for	for	ADP
ap-4605	226	6	any	any	DET
ap-4605	226	7	n	n	PRON
ap-4605	226	8	≥	≥	NOUN
ap-4605	226	9	2	2	NUM
ap-4605	226	10	,	,	PUNCT
ap-4605	226	11	the	the	DET
ap-4605	226	12	algebra	algebra	NOUN
ap-4605	226	13	lns	lns	PROPN
ap-4605	226	14	of	of	ADP
ap-4605	226	15	noether	noether	PROPN
ap-4605	226	16	point	point	NOUN
ap-4605	226	17	symmetries	symmetry	NOUN
ap-4605	226	18	of	of	ADP
ap-4605	226	19	a	a	DET
ap-4605	226	20	second	second	ADJ
ap-4605	226	21	-	-	PUNCT
ap-4605	226	22	order	order	NOUN
ap-4605	226	23	system	system	NOUN
ap-4605	226	24	q̈k	q̈k	NOUN
ap-4605	226	25	=	=	SYM
ap-4605	226	26	2q̇kq̇n	2q̇kq̇n	NUM
ap-4605	226	27	qn	qn	NOUN
ap-4605	226	28	−	−	PROPN
ap-4605	226	29	q2	q2	NOUN
ap-4605	226	30	n	n	CCONJ
ap-4605	226	31	2	2	NUM
ap-4605	226	32	∂u	∂u	PROPN
ap-4605	226	33	∂qk	∂qk	PROPN
ap-4605	226	34	,	,	PUNCT
ap-4605	226	35	1	1	NUM
ap-4605	226	36	≤	≤	NUM
ap-4605	226	37	k	k	X
ap-4605	226	38	≤	≤	PROPN
ap-4605	226	39	n−	n−	PROPN
ap-4605	226	40	1	1	NUM
ap-4605	226	41	,	,	PUNCT
ap-4605	226	42	q̈n	q̈n	NOUN
ap-4605	226	43	=	=	SYM
ap-4605	226	44	q̇2	q̇2	PROPN
ap-4605	226	45	n	n	PRON
ap-4605	226	46	−	−	NOUN
ap-4605	226	47	q̇2	q̇2	NOUN
ap-4605	226	48	1	1	NUM
ap-4605	226	49	−	−	NOUN
ap-4605	226	50	·	·	PUNCT
ap-4605	226	51	·	·	PUNCT
ap-4605	226	52	·	·	PUNCT
ap-4605	227	1	−	−	PUNCT
ap-4605	228	1	q̇2	q̇2	NOUN
ap-4605	228	2	n−1	n−1	PROPN
ap-4605	228	3	qn	qn	NOUN
ap-4605	228	4	−	−	PROPN
ap-4605	228	5	q2	q2	NOUN
ap-4605	228	6	n	n	CCONJ
ap-4605	228	7	2	2	NUM
ap-4605	228	8	∂u	∂u	PROPN
ap-4605	228	9	∂qn	∂qn	NOUN
ap-4605	228	10	(	(	PUNCT
ap-4605	228	11	32	32	NUM
ap-4605	228	12	)	)	PUNCT
ap-4605	228	13	with	with	ADP
ap-4605	228	14	lagrangian	lagrangian	ADJ
ap-4605	228	15	l	l	NOUN
ap-4605	228	16	=	=	SYM
ap-4605	228	17	l0	l0	PROPN
ap-4605	228	18	−	−	PROPN
ap-4605	228	19	u	u	NOUN
ap-4605	228	20	(	(	PUNCT
ap-4605	228	21	t	t	PROPN
ap-4605	228	22	,	,	PUNCT
ap-4605	228	23	q	q	NOUN
ap-4605	228	24	)	)	PUNCT
ap-4605	228	25	corresponds	correspond	VERB
ap-4605	228	26	to	to	ADP
ap-4605	228	27	a	a	DET
ap-4605	228	28	subalgebra	subalgebra	NOUN
ap-4605	228	29	of	of	ADP
ap-4605	228	30	so	so	ADV
ap-4605	228	31	(	(	PUNCT
ap-4605	228	32	1	1	NUM
ap-4605	228	33	,	,	PUNCT
ap-4605	228	34	n)⊕	n)⊕	NOUN
ap-4605	228	35	r.	r.	NOUN
ap-4605	228	36	these	these	DET
ap-4605	228	37	two	two	NUM
ap-4605	228	38	cases	case	NOUN
ap-4605	228	39	indicate	indicate	VERB
ap-4605	228	40	377	377	NUM
ap-4605	228	41	rutwig	rutwig	NOUN
ap-4605	228	42	campoamor	campoamor	NOUN
ap-4605	228	43	-	-	PUNCT
ap-4605	228	44	stursberg	stursberg	PROPN
ap-4605	228	45	acta	acta	PROPN
ap-4605	228	46	polytechnica	polytechnica	PROPN
ap-4605	228	47	that	that	SCONJ
ap-4605	228	48	a	a	DET
ap-4605	228	49	detailed	detailed	ADJ
ap-4605	228	50	study	study	NOUN
ap-4605	228	51	of	of	ADP
ap-4605	228	52	the	the	DET
ap-4605	228	53	symmetry	symmetry	NOUN
ap-4605	228	54	algebras	algebra	NOUN
ap-4605	228	55	of	of	ADP
ap-4605	228	56	free	free	PROPN
ap-4605	228	57	lagrangians	lagrangian	NOUN
ap-4605	228	58	corresponding	correspond	VERB
ap-4605	228	59	to	to	ADP
ap-4605	228	60	nonequivalent	nonequivalent	ADJ
ap-4605	228	61	metrics	metric	NOUN
ap-4605	228	62	in	in	ADP
ap-4605	228	63	n	n	NUM
ap-4605	228	64	≥	≥	NUM
ap-4605	228	65	2	2	NUM
ap-4605	228	66	dimensions	dimension	NOUN
ap-4605	228	67	would	would	AUX
ap-4605	228	68	give	give	VERB
ap-4605	228	69	rise	rise	NOUN
ap-4605	228	70	to	to	ADP
ap-4605	228	71	a	a	DET
ap-4605	228	72	hierarchy	hierarchy	NOUN
ap-4605	228	73	of	of	ADP
ap-4605	228	74	lie	lie	NOUN
ap-4605	228	75	algebras	algebra	NOUN
ap-4605	228	76	that	that	PRON
ap-4605	228	77	allows	allow	VERB
ap-4605	228	78	to	to	PART
ap-4605	228	79	systematize	systematize	VERB
ap-4605	228	80	the	the	DET
ap-4605	228	81	symmetry	symmetry	NOUN
ap-4605	228	82	analysis	analysis	NOUN
ap-4605	228	83	of	of	ADP
ap-4605	228	84	perturbed	perturb	VERB
ap-4605	228	85	systems	system	NOUN
ap-4605	228	86	.	.	PUNCT
ap-4605	229	1	for	for	ADP
ap-4605	229	2	some	some	DET
ap-4605	229	3	important	important	ADJ
ap-4605	229	4	types	type	NOUN
ap-4605	229	5	of	of	ADP
ap-4605	229	6	differential	differential	ADJ
ap-4605	229	7	equations	equation	NOUN
ap-4605	229	8	,	,	PUNCT
ap-4605	229	9	this	this	DET
ap-4605	229	10	approach	approach	NOUN
ap-4605	229	11	has	have	AUX
ap-4605	229	12	already	already	ADV
ap-4605	229	13	provided	provide	VERB
ap-4605	229	14	interesting	interesting	ADJ
ap-4605	229	15	results	result	NOUN
ap-4605	229	16	(	(	PUNCT
ap-4605	229	17	see	see	VERB
ap-4605	229	18	[	[	X
ap-4605	229	19	15	15	NUM
ap-4605	229	20	,	,	PUNCT
ap-4605	229	21	17	17	NUM
ap-4605	229	22	]	]	PUNCT
ap-4605	229	23	and	and	CCONJ
ap-4605	229	24	references	reference	NOUN
ap-4605	229	25	therein	therein	ADV
ap-4605	229	26	)	)	PUNCT
ap-4605	229	27	.	.	PUNCT
ap-4605	230	1	further	further	ADJ
ap-4605	230	2	work	work	VERB
ap-4605	230	3	along	along	ADP
ap-4605	230	4	these	these	DET
ap-4605	230	5	lines	line	NOUN
ap-4605	230	6	is	be	AUX
ap-4605	230	7	currently	currently	ADV
ap-4605	230	8	in	in	ADP
ap-4605	230	9	progress	progress	NOUN
ap-4605	230	10	.	.	PUNCT
ap-4605	231	1	finally	finally	ADV
ap-4605	231	2	,	,	PUNCT
ap-4605	231	3	as	as	SCONJ
ap-4605	231	4	follows	follow	VERB
ap-4605	231	5	from	from	ADP
ap-4605	231	6	the	the	DET
ap-4605	231	7	symmetry	symmetry	NOUN
ap-4605	231	8	condition	condition	NOUN
ap-4605	231	9	(	(	PUNCT
ap-4605	231	10	7	7	NUM
ap-4605	231	11	)	)	PUNCT
ap-4605	231	12	,	,	PUNCT
ap-4605	231	13	a	a	DET
ap-4605	231	14	noether	noether	ADJ
ap-4605	231	15	point	point	NOUN
ap-4605	231	16	symmetry	symmetry	NOUN
ap-4605	231	17	of	of	ADP
ap-4605	231	18	a	a	DET
ap-4605	231	19	regular	regular	ADJ
ap-4605	231	20	lagrangian	lagrangian	ADJ
ap-4605	231	21	l	l	NOUN
ap-4605	231	22	necessarily	necessarily	ADV
ap-4605	231	23	possesses	possess	VERB
ap-4605	231	24	the	the	DET
ap-4605	231	25	generic	generic	ADJ
ap-4605	231	26	form	form	NOUN
ap-4605	231	27	x	x	X
ap-4605	231	28	=	=	SYM
ap-4605	231	29	ξ(t	ξ(t	PROPN
ap-4605	231	30	)	)	PUNCT
ap-4605	231	31	∂∂t	∂∂t	NOUN
ap-4605	231	32	+	+	CCONJ
ap-4605	231	33	ηj(t	ηj(t	PROPN
ap-4605	231	34	,	,	PUNCT
ap-4605	231	35	q	q	NOUN
ap-4605	231	36	)	)	PUNCT
ap-4605	231	37	∂	∂	NUM
ap-4605	231	38	∂qj	∂qj	PROPN
ap-4605	231	39	.	.	PUNCT
ap-4605	232	1	this	this	PRON
ap-4605	232	2	suggests	suggest	VERB
ap-4605	232	3	to	to	PART
ap-4605	232	4	study	study	VERB
ap-4605	232	5	specifically	specifically	ADV
ap-4605	232	6	realizations	realization	NOUN
ap-4605	232	7	of	of	ADP
ap-4605	232	8	lie	lie	NOUN
ap-4605	232	9	algebras	algebra	NOUN
ap-4605	232	10	of	of	ADP
ap-4605	232	11	this	this	DET
ap-4605	232	12	type	type	NOUN
ap-4605	232	13	,	,	PUNCT
ap-4605	232	14	in	in	ADP
ap-4605	232	15	order	order	NOUN
ap-4605	232	16	to	to	PART
ap-4605	232	17	characterize	characterize	VERB
ap-4605	232	18	those	those	DET
ap-4605	232	19	isomorphism	isomorphism	NOUN
ap-4605	232	20	classes	class	NOUN
ap-4605	232	21	of	of	ADP
ap-4605	232	22	lie	lie	NOUN
ap-4605	232	23	algebras	algebra	NOUN
ap-4605	232	24	that	that	PRON
ap-4605	232	25	appear	appear	VERB
ap-4605	232	26	as	as	ADP
ap-4605	232	27	noether	noether	ADJ
ap-4605	232	28	symmetries	symmetry	NOUN
ap-4605	232	29	of	of	ADP
ap-4605	232	30	a	a	DET
ap-4605	232	31	system	system	NOUN
ap-4605	232	32	,	,	PUNCT
ap-4605	232	33	but	but	CCONJ
ap-4605	232	34	do	do	AUX
ap-4605	232	35	not	not	PART
ap-4605	232	36	correspond	correspond	VERB
ap-4605	232	37	to	to	ADP
ap-4605	232	38	an	an	DET
ap-4605	232	39	isometry	isometry	NOUN
ap-4605	232	40	generator	generator	NOUN
ap-4605	232	41	of	of	ADP
ap-4605	232	42	the	the	DET
ap-4605	232	43	associated	associated	ADJ
ap-4605	232	44	kinetic	kinetic	ADJ
ap-4605	232	45	lagrangian	lagrangian	NOUN
ap-4605	232	46	.	.	PUNCT
ap-4605	233	1	some	some	DET
ap-4605	233	2	developments	development	NOUN
ap-4605	233	3	in	in	ADP
ap-4605	233	4	this	this	DET
ap-4605	233	5	direction	direction	NOUN
ap-4605	233	6	have	have	AUX
ap-4605	233	7	been	be	AUX
ap-4605	233	8	proposed	propose	VERB
ap-4605	233	9	in	in	ADP
ap-4605	233	10	[	[	X
ap-4605	233	11	18	18	NUM
ap-4605	233	12	]	]	PUNCT
ap-4605	233	13	,	,	PUNCT
ap-4605	233	14	in	in	ADP
ap-4605	233	15	connection	connection	NOUN
ap-4605	233	16	with	with	ADP
ap-4605	233	17	various	various	ADJ
ap-4605	233	18	geometric	geometric	ADJ
ap-4605	233	19	properties	property	NOUN
ap-4605	233	20	.	.	PUNCT
ap-4605	234	1	a	a	DET
ap-4605	234	2	similar	similar	ADJ
ap-4605	234	3	approach	approach	NOUN
ap-4605	234	4	can	can	AUX
ap-4605	234	5	be	be	AUX
ap-4605	234	6	found	find	VERB
ap-4605	234	7	in	in	ADP
ap-4605	234	8	[	[	X
ap-4605	234	9	15	15	NUM
ap-4605	234	10	]	]	PUNCT
ap-4605	234	11	and	and	CCONJ
ap-4605	234	12	some	some	DET
ap-4605	234	13	previous	previous	ADJ
ap-4605	234	14	work	work	NOUN
ap-4605	234	15	,	,	PUNCT
ap-4605	234	16	where	where	SCONJ
ap-4605	234	17	symmetries	symmetry	NOUN
ap-4605	234	18	of	of	ADP
ap-4605	234	19	certain	certain	ADJ
ap-4605	234	20	types	type	NOUN
ap-4605	234	21	of	of	ADP
ap-4605	234	22	non	non	ADJ
ap-4605	234	23	-	-	ADJ
ap-4605	234	24	autonomous	autonomous	ADJ
ap-4605	234	25	systems	system	NOUN
ap-4605	234	26	defined	define	VERB
ap-4605	234	27	in	in	ADP
ap-4605	234	28	riemann	riemann	PROPN
ap-4605	234	29	spaces	space	NOUN
ap-4605	234	30	have	have	AUX
ap-4605	234	31	been	be	AUX
ap-4605	234	32	studied	study	VERB
ap-4605	234	33	,	,	PUNCT
ap-4605	234	34	providing	provide	VERB
ap-4605	234	35	new	new	ADJ
ap-4605	234	36	insights	insight	NOUN
ap-4605	234	37	to	to	ADP
ap-4605	234	38	the	the	DET
ap-4605	234	39	geometrical	geometrical	ADJ
ap-4605	234	40	interpretation	interpretation	NOUN
ap-4605	234	41	of	of	ADP
ap-4605	234	42	dynamical	dynamical	ADJ
ap-4605	234	43	quantities	quantity	NOUN
ap-4605	234	44	.	.	PUNCT
ap-4605	235	1	an	an	DET
ap-4605	235	2	interesting	interesting	ADJ
ap-4605	235	3	problem	problem	NOUN
ap-4605	235	4	worthy	worthy	ADJ
ap-4605	235	5	to	to	PART
ap-4605	235	6	be	be	AUX
ap-4605	235	7	analyzed	analyze	VERB
ap-4605	235	8	in	in	ADP
ap-4605	235	9	the	the	DET
ap-4605	235	10	context	context	NOUN
ap-4605	235	11	of	of	ADP
ap-4605	235	12	the	the	DET
ap-4605	235	13	symmetry	symmetry	NOUN
ap-4605	235	14	analysis	analysis	NOUN
ap-4605	235	15	of	of	ADP
ap-4605	235	16	dynamical	dynamical	ADJ
ap-4605	235	17	systems	system	NOUN
ap-4605	235	18	is	be	AUX
ap-4605	235	19	the	the	DET
ap-4605	235	20	possibility	possibility	NOUN
ap-4605	235	21	of	of	ADP
ap-4605	235	22	combining	combine	VERB
ap-4605	235	23	symmetry	symmetry	NOUN
ap-4605	235	24	groups	group	NOUN
ap-4605	235	25	with	with	ADP
ap-4605	235	26	certain	certain	ADJ
ap-4605	235	27	of	of	ADP
ap-4605	235	28	the	the	DET
ap-4605	235	29	geometric	geometric	ADJ
ap-4605	235	30	properties	property	NOUN
ap-4605	235	31	of	of	ADP
ap-4605	235	32	the	the	DET
ap-4605	235	33	orbits	orbit	NOUN
ap-4605	235	34	determined	determine	VERB
ap-4605	235	35	by	by	ADP
ap-4605	235	36	the	the	DET
ap-4605	235	37	solutions	solution	NOUN
ap-4605	235	38	of	of	ADP
ap-4605	235	39	a	a	DET
ap-4605	235	40	system	system	NOUN
ap-4605	235	41	[	[	X
ap-4605	235	42	5	5	NUM
ap-4605	235	43	]	]	PUNCT
ap-4605	235	44	,	,	PUNCT
ap-4605	235	45	a	a	DET
ap-4605	235	46	question	question	NOUN
ap-4605	235	47	that	that	PRON
ap-4605	235	48	has	have	AUX
ap-4605	235	49	still	still	ADV
ap-4605	235	50	not	not	PART
ap-4605	235	51	exhausted	exhaust	VERB
ap-4605	235	52	the	the	DET
ap-4605	235	53	possibilities	possibility	NOUN
ap-4605	235	54	of	of	ADP
ap-4605	235	55	the	the	DET
ap-4605	235	56	group	group	NOUN
ap-4605	235	57	-	-	PUNCT
ap-4605	235	58	theoretical	theoretical	ADJ
ap-4605	235	59	approach	approach	NOUN
ap-4605	235	60	.	.	PUNCT
ap-4605	236	1	acknowledgements	acknowledgement	NOUN
ap-4605	236	2	the	the	DET
ap-4605	236	3	author	author	NOUN
ap-4605	236	4	expresses	express	VERB
ap-4605	236	5	his	his	PRON
ap-4605	236	6	gratitude	gratitude	NOUN
ap-4605	236	7	to	to	PART
ap-4605	236	8	prof	prof	PROPN
ap-4605	236	9	.	.	PUNCT
ap-4605	237	1	m.	m.	NOUN
ap-4605	237	2	znojil	znojil	PROPN
ap-4605	237	3	for	for	ADP
ap-4605	237	4	the	the	DET
ap-4605	237	5	invitation	invitation	NOUN
ap-4605	237	6	to	to	ADP
ap-4605	237	7	the	the	DET
ap-4605	237	8	aamp	aamp	PROPN
ap-4605	237	9	xiv	xiv	PROPN
ap-4605	237	10	conference	conference	PROPN
ap-4605	237	11	.	.	PUNCT
ap-4605	238	1	during	during	ADP
ap-4605	238	2	the	the	DET
ap-4605	238	3	preparation	preparation	NOUN
ap-4605	238	4	of	of	ADP
ap-4605	238	5	this	this	DET
ap-4605	238	6	work	work	NOUN
ap-4605	238	7	,	,	PUNCT
ap-4605	238	8	the	the	DET
ap-4605	238	9	author	author	NOUN
ap-4605	238	10	was	be	AUX
ap-4605	238	11	financially	financially	ADV
ap-4605	238	12	supported	support	VERB
ap-4605	238	13	by	by	ADP
ap-4605	238	14	the	the	DET
ap-4605	238	15	research	research	NOUN
ap-4605	238	16	project	project	NOUN
ap-4605	238	17	mtm201679422	mtm201679422	ADV
ap-4605	238	18	-	-	PUNCT
ap-4605	238	19	p	p	NOUN
ap-4605	238	20	of	of	ADP
ap-4605	238	21	the	the	DET
ap-4605	238	22	aei	aei	PROPN
ap-4605	238	23	/	/	SYM
ap-4605	238	24	feder	feder	PROPN
ap-4605	238	25	(	(	PUNCT
ap-4605	238	26	eu	eu	PROPN
ap-4605	238	27	)	)	PUNCT
ap-4605	238	28	.	.	PUNCT
ap-4605	239	1	references	reference	NOUN
ap-4605	239	2	[	[	X
ap-4605	239	3	1	1	X
ap-4605	239	4	]	]	PUNCT
ap-4605	239	5	e.	e.	PROPN
ap-4605	239	6	noether	noether	PROPN
ap-4605	239	7	.	.	PUNCT
ap-4605	240	1	invariante	invariante	PROPN
ap-4605	240	2	variationsprobleme	variationsprobleme	PROPN
ap-4605	240	3	.	.	PUNCT
ap-4605	241	1	nachr	nachr	PROPN
ap-4605	241	2	ges	ges	PROPN
ap-4605	241	3	wiss	wiss	PROPN
ap-4605	241	4	göttingen	göttingen	PROPN
ap-4605	241	5	,	,	PUNCT
ap-4605	241	6	math	math	NOUN
ap-4605	241	7	-	-	PUNCT
ap-4605	241	8	phys	phy	NOUN
ap-4605	241	9	kl	kl	NOUN
ap-4605	241	10	1918:235–257	1918:235–257	NOUN
ap-4605	241	11	,	,	PUNCT
ap-4605	241	12	1918	1918	NUM
ap-4605	241	13	.	.	PUNCT
ap-4605	242	1	[	[	X
ap-4605	242	2	2	2	NUM
ap-4605	242	3	]	]	PUNCT
ap-4605	242	4	l.	l.	PROPN
ap-4605	242	5	v.	v.	PROPN
ap-4605	242	6	ovsyannikov	ovsyannikov	PROPN
ap-4605	242	7	.	.	PUNCT
ap-4605	243	1	group	group	NOUN
ap-4605	243	2	analysis	analysis	NOUN
ap-4605	243	3	of	of	ADP
ap-4605	243	4	differential	differential	ADJ
ap-4605	243	5	equations	equation	NOUN
ap-4605	243	6	.	.	PUNCT
ap-4605	244	1	academic	academic	ADJ
ap-4605	244	2	,	,	PUNCT
ap-4605	244	3	new	new	ADJ
ap-4605	244	4	-	-	PUNCT
ap-4605	244	5	york	york	NOUN
ap-4605	244	6	,	,	PUNCT
ap-4605	244	7	1982	1982	NUM
ap-4605	244	8	.	.	PUNCT
ap-4605	245	1	[	[	X
ap-4605	245	2	3	3	X
ap-4605	245	3	]	]	X
ap-4605	245	4	l.	l.	PROPN
ap-4605	245	5	dresner	dresner	NOUN
ap-4605	245	6	.	.	PUNCT
ap-4605	246	1	application	application	NOUN
ap-4605	246	2	of	of	ADP
ap-4605	246	3	lie	lie	PROPN
ap-4605	246	4	’s	’s	PART
ap-4605	246	5	theory	theory	NOUN
ap-4605	246	6	of	of	ADP
ap-4605	246	7	ordinary	ordinary	ADJ
ap-4605	246	8	and	and	CCONJ
ap-4605	246	9	partial	partial	ADJ
ap-4605	246	10	differential	differential	ADJ
ap-4605	246	11	equations	equation	NOUN
ap-4605	246	12	.	.	PUNCT
ap-4605	247	1	iop	iop	PROPN
ap-4605	247	2	publishing	publishing	PROPN
ap-4605	247	3	,	,	PUNCT
ap-4605	247	4	bristol	bristol	PROPN
ap-4605	247	5	,	,	PUNCT
ap-4605	247	6	1999	1999	NUM
ap-4605	247	7	.	.	PUNCT
ap-4605	248	1	[	[	X
ap-4605	248	2	4	4	NUM
ap-4605	248	3	]	]	PUNCT
ap-4605	248	4	a.	a.	NOUN
ap-4605	248	5	m.	m.	NOUN
ap-4605	248	6	perelomov	perelomov	PROPN
ap-4605	248	7	.	.	PUNCT
ap-4605	249	1	integrable	integrable	ADJ
ap-4605	249	2	systems	system	NOUN
ap-4605	249	3	of	of	ADP
ap-4605	249	4	classical	classical	ADJ
ap-4605	249	5	mechanics	mechanic	NOUN
ap-4605	249	6	and	and	CCONJ
ap-4605	249	7	lie	lie	NOUN
ap-4605	249	8	algebras	algebras	PROPN
ap-4605	249	9	.	.	PUNCT
ap-4605	250	1	birkhäuser	birkhäuser	PROPN
ap-4605	250	2	verlag	verlag	PROPN
ap-4605	250	3	,	,	PUNCT
ap-4605	250	4	basel	basel	PROPN
ap-4605	250	5	,	,	PUNCT
ap-4605	250	6	1990	1990	NUM
ap-4605	250	7	.	.	PUNCT
ap-4605	251	1	[	[	X
ap-4605	251	2	5	5	NUM
ap-4605	251	3	]	]	PUNCT
ap-4605	251	4	a.	a.	NOUN
ap-4605	251	5	s.	s.	PROPN
ap-4605	251	6	galiullin	galiullin	PROPN
ap-4605	251	7	.	.	PUNCT
ap-4605	252	1	inverse	inverse	NOUN
ap-4605	252	2	problems	problem	NOUN
ap-4605	252	3	of	of	ADP
ap-4605	252	4	dynamics	dynamic	NOUN
ap-4605	252	5	.	.	PUNCT
ap-4605	253	1	mir	mir	PROPN
ap-4605	253	2	publishers	publisher	NOUN
ap-4605	253	3	,	,	PUNCT
ap-4605	253	4	moscow	moscow	PROPN
ap-4605	253	5	,	,	PUNCT
ap-4605	253	6	1984	1984	NUM
ap-4605	253	7	.	.	PUNCT
ap-4605	254	1	[	[	X
ap-4605	254	2	6	6	NUM
ap-4605	254	3	]	]	PUNCT
ap-4605	254	4	s.	s.	PROPN
ap-4605	254	5	e.	e.	PROPN
ap-4605	254	6	jones	jones	PROPN
ap-4605	254	7	,	,	PUNCT
ap-4605	254	8	b.	b.	PROPN
ap-4605	254	9	g.	g.	PROPN
ap-4605	254	10	vujanovic	vujanovic	PROPN
ap-4605	254	11	.	.	PUNCT
ap-4605	255	1	on	on	ADP
ap-4605	255	2	the	the	DET
ap-4605	255	3	inverse	inverse	ADJ
ap-4605	255	4	lagrangian	lagrangian	ADJ
ap-4605	255	5	problem	problem	NOUN
ap-4605	255	6	.	.	PUNCT
ap-4605	256	1	acta	acta	PROPN
ap-4605	256	2	mech	mech	PROPN
ap-4605	256	3	73:245–251	73:245–251	PROPN
ap-4605	256	4	,	,	PUNCT
ap-4605	256	5	1988	1988	NUM
ap-4605	256	6	.	.	PUNCT
ap-4605	257	1	doi:10.1007	doi:10.1007	PROPN
ap-4605	257	2	/	/	SYM
ap-4605	257	3	bf01177044	bf01177044	PROPN
ap-4605	257	4	.	.	PUNCT
ap-4605	258	1	[	[	X
ap-4605	258	2	7	7	X
ap-4605	258	3	]	]	X
ap-4605	258	4	v.	v.	ADP
ap-4605	258	5	m.	m.	PROPN
ap-4605	258	6	gorringe	gorringe	PROPN
ap-4605	258	7	,	,	PUNCT
ap-4605	258	8	p.	p.	NOUN
ap-4605	258	9	g.	g.	PROPN
ap-4605	258	10	l.	l.	PROPN
ap-4605	258	11	leach	leach	PROPN
ap-4605	258	12	.	.	PUNCT
ap-4605	259	1	lie	lie	NOUN
ap-4605	259	2	point	point	NOUN
ap-4605	259	3	symmetries	symmetry	NOUN
ap-4605	259	4	for	for	ADP
ap-4605	259	5	systems	system	NOUN
ap-4605	259	6	of	of	ADP
ap-4605	259	7	second	second	ADJ
ap-4605	259	8	-	-	PUNCT
ap-4605	259	9	order	order	NOUN
ap-4605	259	10	linear	linear	ADJ
ap-4605	259	11	differential	differential	NOUN
ap-4605	259	12	equations	equation	NOUN
ap-4605	259	13	.	.	PUNCT
ap-4605	260	1	quaest	quaest	PROPN
ap-4605	260	2	math	math	NOUN
ap-4605	260	3	11:95–117	11:95–117	NUM
ap-4605	260	4	,	,	PUNCT
ap-4605	260	5	1988	1988	NUM
ap-4605	260	6	.	.	PUNCT
ap-4605	261	1	doi:10.1080/16073606.1988.9631946	doi:10.1080/16073606.1988.9631946	NOUN
ap-4605	261	2	.	.	PUNCT
ap-4605	262	1	[	[	X
ap-4605	262	2	8	8	NUM
ap-4605	262	3	]	]	X
ap-4605	262	4	r.	r.	PROPN
ap-4605	262	5	campoamor	campoamor	PROPN
ap-4605	262	6	-	-	PUNCT
ap-4605	262	7	stursberg	stursberg	PROPN
ap-4605	262	8	.	.	PUNCT
ap-4605	263	1	on	on	ADP
ap-4605	263	2	certain	certain	ADJ
ap-4605	263	3	types	type	NOUN
ap-4605	263	4	of	of	ADP
ap-4605	263	5	point	point	NOUN
ap-4605	263	6	symmetries	symmetry	NOUN
ap-4605	263	7	of	of	ADP
ap-4605	263	8	systems	system	NOUN
ap-4605	263	9	of	of	ADP
ap-4605	263	10	second	second	ADJ
ap-4605	263	11	-	-	PUNCT
ap-4605	263	12	order	order	NOUN
ap-4605	263	13	ordinary	ordinary	ADJ
ap-4605	263	14	differential	differential	ADJ
ap-4605	263	15	equations	equation	NOUN
ap-4605	263	16	.	.	PUNCT
ap-4605	264	1	comm	comm	NOUN
ap-4605	264	2	nonlinear	nonlinear	PROPN
ap-4605	264	3	sci	sci	PROPN
ap-4605	264	4	num	num	ADJ
ap-4605	264	5	simulat	simulat	PROPN
ap-4605	264	6	19:2602–2614	19:2602–2614	NUM
ap-4605	264	7	,	,	PUNCT
ap-4605	264	8	2014	2014	NUM
ap-4605	264	9	.	.	PUNCT
ap-4605	265	1	doi:10.1016	doi:10.1016	PROPN
ap-4605	265	2	/	/	SYM
ap-4605	265	3	j.cnsns.2014.01.006	j.cnsns.2014.01.006	PROPN
ap-4605	265	4	.	.	PUNCT
ap-4605	266	1	[	[	X
ap-4605	266	2	9	9	NUM
ap-4605	266	3	]	]	PUNCT
ap-4605	266	4	p.	p.	NOUN
ap-4605	266	5	g.	g.	PROPN
ap-4605	266	6	l.	l.	PROPN
ap-4605	266	7	leach	leach	NOUN
ap-4605	266	8	.	.	PUNCT
ap-4605	266	9	equivalence	equivalence	NOUN
ap-4605	266	10	classes	class	NOUN
ap-4605	266	11	of	of	ADP
ap-4605	266	12	second	second	ADJ
ap-4605	266	13	-	-	PUNCT
ap-4605	266	14	order	order	NOUN
ap-4605	266	15	ordinary	ordinary	ADJ
ap-4605	266	16	differential	differential	ADJ
ap-4605	266	17	equations	equation	NOUN
ap-4605	266	18	with	with	ADP
ap-4605	266	19	only	only	ADV
ap-4605	266	20	a	a	DET
ap-4605	266	21	three	three	NUM
ap-4605	266	22	dimensional	dimensional	ADJ
ap-4605	266	23	lie	lie	NOUN
ap-4605	266	24	algebra	algebra	NOUN
ap-4605	266	25	of	of	ADP
ap-4605	266	26	point	point	NOUN
ap-4605	266	27	symmetries	symmetry	NOUN
ap-4605	266	28	and	and	CCONJ
ap-4605	266	29	linearisation	linearisation	NOUN
ap-4605	266	30	.	.	PUNCT
ap-4605	267	1	j	j	PROPN
ap-4605	267	2	math	math	PROPN
ap-4605	267	3	anal	anal	PROPN
ap-4605	267	4	appl	appl	PROPN
ap-4605	267	5	284:31–48	284:31–48	PROPN
ap-4605	267	6	,	,	PUNCT
ap-4605	267	7	2003	2003	NUM
ap-4605	267	8	.	.	PUNCT
ap-4605	268	1	doi:10.1016	doi:10.1016	PROPN
ap-4605	268	2	/	/	SYM
ap-4605	268	3	s0022	s0022	PROPN
ap-4605	268	4	-	-	PUNCT
ap-4605	268	5	247x(03)00147	247x(03)00147	NUM
ap-4605	268	6	-	-	PUNCT
ap-4605	268	7	1	1	NUM
ap-4605	268	8	.	.	PUNCT
ap-4605	269	1	[	[	X
ap-4605	269	2	10	10	NUM
ap-4605	269	3	]	]	X
ap-4605	269	4	a.	a.	NOUN
ap-4605	269	5	ballesteros	ballesteros	PROPN
ap-4605	269	6	,	,	PUNCT
ap-4605	269	7	et	et	PROPN
ap-4605	269	8	al	al	PROPN
ap-4605	269	9	.	.	PUNCT
ap-4605	270	1	n	n	CCONJ
ap-4605	270	2	-dimensional	-dimensional	ADJ
ap-4605	270	3	sl(2)-coalgebra	sl(2)-coalgebra	NOUN
ap-4605	270	4	spaces	space	NOUN
ap-4605	270	5	with	with	ADP
ap-4605	270	6	non	non	ADJ
ap-4605	270	7	-	-	ADJ
ap-4605	270	8	constant	constant	ADJ
ap-4605	270	9	curvature	curvature	NOUN
ap-4605	270	10	.	.	PUNCT
ap-4605	271	1	phys	phy	NOUN
ap-4605	271	2	letters	letter	NOUN
ap-4605	271	3	b	b	NOUN
ap-4605	271	4	652:376–383	652:376–383	NUM
ap-4605	271	5	,	,	PUNCT
ap-4605	271	6	2007	2007	NUM
ap-4605	271	7	.	.	PUNCT
ap-4605	272	1	doi:10.1016	doi:10.1016	PROPN
ap-4605	272	2	/	/	SYM
ap-4605	272	3	j.physletb.2007.07.012	j.physletb.2007.07.012	PROPN
ap-4605	272	4	.	.	PUNCT
ap-4605	273	1	[	[	X
ap-4605	273	2	11	11	NUM
ap-4605	273	3	]	]	X
ap-4605	273	4	g.	g.	PROPN
ap-4605	273	5	gubbioti	gubbioti	PROPN
ap-4605	273	6	,	,	PUNCT
ap-4605	273	7	m.	m.	NOUN
ap-4605	273	8	c.	c.	PROPN
ap-4605	273	9	nucci	nucci	PROPN
ap-4605	273	10	.	.	PUNCT
ap-4605	274	1	are	be	AUX
ap-4605	274	2	all	all	PRON
ap-4605	274	3	classical	classical	ADJ
ap-4605	274	4	superintegrable	superintegrable	ADJ
ap-4605	274	5	systems	system	NOUN
ap-4605	274	6	in	in	ADP
ap-4605	274	7	two	two	NUM
ap-4605	274	8	-	-	PUNCT
ap-4605	274	9	dimensional	dimensional	ADJ
ap-4605	274	10	space	space	NOUN
ap-4605	274	11	linearizable	linearizable	ADJ
ap-4605	274	12	?	?	PUNCT
ap-4605	275	1	j	j	PROPN
ap-4605	275	2	math	math	PROPN
ap-4605	275	3	phys	phy	NOUN
ap-4605	275	4	58:012902	58:012902	NUM
ap-4605	275	5	,	,	PUNCT
ap-4605	275	6	2017	2017	NUM
ap-4605	275	7	.	.	PUNCT
ap-4605	276	1	doi:10.1063/1.4974264	doi:10.1063/1.4974264	NOUN
ap-4605	276	2	.	.	PUNCT
ap-4605	277	1	[	[	X
ap-4605	277	2	12	12	NUM
ap-4605	277	3	]	]	X
ap-4605	277	4	r.	r.	PROPN
ap-4605	277	5	campoamor	campoamor	PROPN
ap-4605	277	6	-	-	PUNCT
ap-4605	277	7	stursberg	stursberg	PROPN
ap-4605	277	8	.	.	PUNCT
ap-4605	278	1	perturbations	perturbation	NOUN
ap-4605	278	2	of	of	ADP
ap-4605	278	3	lagrangian	lagrangian	ADJ
ap-4605	278	4	systems	system	NOUN
ap-4605	278	5	based	base	VERB
ap-4605	278	6	on	on	ADP
ap-4605	278	7	the	the	DET
ap-4605	278	8	preservation	preservation	NOUN
ap-4605	278	9	of	of	ADP
ap-4605	278	10	subalgebras	subalgebras	PROPN
ap-4605	278	11	of	of	ADP
ap-4605	278	12	noether	noether	ADJ
ap-4605	278	13	symmetries	symmetry	NOUN
ap-4605	278	14	.	.	PUNCT
ap-4605	279	1	acta	acta	PROPN
ap-4605	279	2	mech	mech	PROPN
ap-4605	279	3	227:1941–1956	227:1941–1956	NUM
ap-4605	279	4	,	,	PUNCT
ap-4605	279	5	2016	2016	NUM
ap-4605	279	6	.	.	PUNCT
ap-4605	280	1	doi:10.1007	doi:10.1007	VERB
ap-4605	280	2	/	/	SYM
ap-4605	280	3	s0070	s0070	NOUN
ap-4605	280	4	.	.	PUNCT
ap-4605	281	1	[	[	X
ap-4605	281	2	13	13	NUM
ap-4605	281	3	]	]	PUNCT
ap-4605	281	4	e.	e.	PROPN
ap-4605	281	5	kamke	kamke	PROPN
ap-4605	281	6	.	.	PUNCT
ap-4605	282	1	differentialgleichungen	differentialgleichungen	PROPN
ap-4605	282	2	.	.	PUNCT
ap-4605	283	1	lösungsmethoden	lösungsmethoden	PROPN
ap-4605	283	2	und	und	PROPN
ap-4605	283	3	lösungen	lösungen	PROPN
ap-4605	283	4	.	.	PUNCT
ap-4605	284	1	band	band	PROPN
ap-4605	284	2	ii	ii	PROPN
ap-4605	284	3	.	.	PUNCT
ap-4605	285	1	akademische	akademische	PROPN
ap-4605	285	2	verlagsgesellschaft	verlagsgesellschaft	PROPN
ap-4605	285	3	,	,	PUNCT
ap-4605	285	4	leipzig	leipzig	NOUN
ap-4605	285	5	,	,	PUNCT
ap-4605	285	6	1962	1962	NUM
ap-4605	285	7	.	.	PUNCT
ap-4605	286	1	[	[	X
ap-4605	286	2	14	14	NUM
ap-4605	286	3	]	]	X
ap-4605	286	4	e.	e.	PROPN
ap-4605	286	5	kamke	kamke	PROPN
ap-4605	286	6	.	.	PUNCT
ap-4605	287	1	differentialgleichungen	differentialgleichungen	PROPN
ap-4605	287	2	.	.	PUNCT
ap-4605	288	1	lösungsmethoden	lösungsmethoden	PROPN
ap-4605	288	2	und	und	PROPN
ap-4605	288	3	lösungen	lösungen	PROPN
ap-4605	288	4	.	.	PUNCT
ap-4605	289	1	band	band	PROPN
ap-4605	289	2	i.	i.	PROPN
ap-4605	289	3	akademische	akademische	PROPN
ap-4605	289	4	verlagsgesellschaft	verlagsgesellschaft	PROPN
ap-4605	289	5	,	,	PUNCT
ap-4605	289	6	leipzig	leipzig	NOUN
ap-4605	289	7	,	,	PUNCT
ap-4605	289	8	1962	1962	NUM
ap-4605	289	9	.	.	PUNCT
ap-4605	290	1	[	[	X
ap-4605	290	2	15	15	NUM
ap-4605	290	3	]	]	X
ap-4605	290	4	l.	l.	PROPN
ap-4605	290	5	karpathopoulos	karpathopoulos	PROPN
ap-4605	290	6	,	,	PUNCT
ap-4605	290	7	a.	a.	NOUN
ap-4605	290	8	paliathanasis	paliathanasis	NOUN
ap-4605	290	9	,	,	PUNCT
ap-4605	290	10	m.	m.	NOUN
ap-4605	290	11	tsamparlis	tsamparlis	PROPN
ap-4605	290	12	.	.	PUNCT
ap-4605	291	1	lie	lie	NOUN
ap-4605	291	2	and	and	CCONJ
ap-4605	291	3	noether	noether	ADJ
ap-4605	291	4	point	point	NOUN
ap-4605	291	5	symmetries	symmetry	NOUN
ap-4605	291	6	for	for	ADP
ap-4605	291	7	a	a	DET
ap-4605	291	8	class	class	NOUN
ap-4605	291	9	of	of	ADP
ap-4605	291	10	nonautonomous	nonautonomous	ADJ
ap-4605	291	11	dynamical	dynamical	ADJ
ap-4605	291	12	systems	system	NOUN
ap-4605	291	13	.	.	PUNCT
ap-4605	292	1	j	j	PROPN
ap-4605	292	2	math	math	PROPN
ap-4605	292	3	phys	phy	NOUN
ap-4605	292	4	58:082901	58:082901	NUM
ap-4605	292	5	,	,	PUNCT
ap-4605	292	6	2017	2017	NUM
ap-4605	292	7	.	.	PUNCT
ap-4605	293	1	doi:10.1063/1.4998715	doi:10.1063/1.4998715	NOUN
ap-4605	293	2	.	.	PUNCT
ap-4605	294	1	[	[	X
ap-4605	294	2	16	16	NUM
ap-4605	294	3	]	]	X
ap-4605	294	4	y.	y.	PROPN
ap-4605	294	5	fuji	fuji	PROPN
ap-4605	294	6	,	,	PUNCT
ap-4605	294	7	k.	k.	PROPN
ap-4605	294	8	yamagishi	yamagishi	PROPN
ap-4605	294	9	.	.	PUNCT
ap-4605	295	1	killing	kill	VERB
ap-4605	295	2	spinors	spinor	NOUN
ap-4605	295	3	on	on	ADP
ap-4605	295	4	spheres	sphere	NOUN
ap-4605	295	5	and	and	CCONJ
ap-4605	295	6	hyperbolic	hyperbolic	ADJ
ap-4605	295	7	manifolds	manifold	NOUN
ap-4605	295	8	.	.	PUNCT
ap-4605	296	1	j	j	PROPN
ap-4605	296	2	math	math	PROPN
ap-4605	296	3	phys	phy	NOUN
ap-4605	296	4	27:979–981	27:979–981	PROPN
ap-4605	296	5	,	,	PUNCT
ap-4605	296	6	1986	1986	NUM
ap-4605	296	7	.	.	PUNCT
ap-4605	297	1	doi:10.1063/1.527118	doi:10.1063/1.527118	PROPN
ap-4605	297	2	.	.	PUNCT
ap-4605	298	1	[	[	X
ap-4605	298	2	17	17	NUM
ap-4605	298	3	]	]	PUNCT
ap-4605	298	4	m.	m.	NOUN
ap-4605	298	5	tsamparlis	tsamparlis	PROPN
ap-4605	298	6	,	,	PUNCT
ap-4605	298	7	a.	a.	NOUN
ap-4605	298	8	paliathanasis	paliathanasis	NOUN
ap-4605	298	9	,	,	PUNCT
ap-4605	298	10	a.	a.	PROPN
ap-4605	298	11	qadir	qadir	PROPN
ap-4605	298	12	.	.	PUNCT
ap-4605	299	1	noether	noether	ADJ
ap-4605	299	2	symmetries	symmetry	NOUN
ap-4605	299	3	and	and	CCONJ
ap-4605	299	4	isometries	isometry	NOUN
ap-4605	299	5	of	of	ADP
ap-4605	299	6	the	the	DET
ap-4605	299	7	minimal	minimal	ADJ
ap-4605	299	8	surface	surface	NOUN
ap-4605	299	9	lagrangian	lagrangian	ADJ
ap-4605	299	10	under	under	ADP
ap-4605	299	11	constant	constant	ADJ
ap-4605	299	12	volume	volume	NOUN
ap-4605	299	13	in	in	ADP
ap-4605	299	14	a	a	DET
ap-4605	299	15	riemannian	riemannian	ADJ
ap-4605	299	16	space	space	NOUN
ap-4605	299	17	.	.	PUNCT
ap-4605	300	1	int	int	PROPN
ap-4605	300	2	j	j	PROPN
ap-4605	300	3	geom	geom	PROPN
ap-4605	300	4	methods	method	NOUN
ap-4605	300	5	mod	mod	PROPN
ap-4605	300	6	phys	phy	NOUN
ap-4605	300	7	12:1550033	12:1550033	NUM
ap-4605	300	8	,	,	PUNCT
ap-4605	300	9	2015	2015	NUM
ap-4605	300	10	.	.	PUNCT
ap-4605	301	1	[	[	X
ap-4605	301	2	18	18	NUM
ap-4605	301	3	]	]	X
ap-4605	301	4	r.	r.	PROPN
ap-4605	301	5	campoamor	campoamor	PROPN
ap-4605	301	6	-	-	PUNCT
ap-4605	301	7	stursberg	stursberg	PROPN
ap-4605	301	8	.	.	PUNCT
ap-4605	302	1	an	an	DET
ap-4605	302	2	alternative	alternative	ADJ
ap-4605	302	3	approach	approach	NOUN
ap-4605	302	4	to	to	ADP
ap-4605	302	5	systems	system	NOUN
ap-4605	302	6	of	of	ADP
ap-4605	302	7	second	second	ADJ
ap-4605	302	8	-	-	PUNCT
ap-4605	302	9	order	order	NOUN
ap-4605	302	10	ordinary	ordinary	ADJ
ap-4605	302	11	differential	differential	ADJ
ap-4605	302	12	equations	equation	NOUN
ap-4605	302	13	with	with	ADP
ap-4605	302	14	maximal	maximal	ADJ
ap-4605	302	15	symmetry	symmetry	NOUN
ap-4605	302	16	.	.	PUNCT
ap-4605	303	1	realizations	realization	NOUN
ap-4605	303	2	of	of	ADP
ap-4605	303	3	sl(n	sl(n	PRON
ap-4605	303	4	+	+	CCONJ
ap-4605	303	5	2,r	2,r	NUM
ap-4605	303	6	)	)	PUNCT
ap-4605	303	7	by	by	ADP
ap-4605	303	8	special	special	ADJ
ap-4605	303	9	functions	function	NOUN
ap-4605	303	10	.	.	PUNCT
ap-4605	304	1	comm	comm	NOUN
ap-4605	304	2	nonlinear	nonlinear	PROPN
ap-4605	304	3	sci	sci	PROPN
ap-4605	304	4	num	num	ADJ
ap-4605	304	5	simulat	simulat	NOUN
ap-4605	304	6	37:200–211	37:200–211	PROPN
ap-4605	304	7	,	,	PUNCT
ap-4605	304	8	2016	2016	NUM
ap-4605	304	9	.	.	PUNCT
ap-4605	305	1	doi:10.1016	doi:10.1016	PROPN
ap-4605	305	2	/	/	SYM
ap-4605	305	3	j.cnsns.2016.01.015	j.cnsns.2016.01.015	PROPN
ap-4605	305	4	.	.	PROPN
ap-4605	306	1	378	378	NUM
ap-4605	307	1	http://dx.doi.org/10.1007/bf01177044	http://dx.doi.org/10.1007/bf01177044	PROPN
ap-4605	307	2	http://dx.doi.org/10.1080/16073606.1988.9631946	http://dx.doi.org/10.1080/16073606.1988.9631946	PROPN
ap-4605	307	3	http://dx.doi.org/10.1016/j.cnsns.2014.01.006	http://dx.doi.org/10.1016/j.cnsns.2014.01.006	PROPN
ap-4605	307	4	http://dx.doi.org/10.1016/s0022-247x(03)00147-1	http://dx.doi.org/10.1016/s0022-247x(03)00147-1	NOUN
ap-4605	307	5	http://dx.doi.org/10.1016/j.physletb.2007.07.012	http://dx.doi.org/10.1016/j.physletb.2007.07.012	PROPN
ap-4605	307	6	http://dx.doi.org/10.1063/1.4974264	http://dx.doi.org/10.1063/1.4974264	PROPN
ap-4605	307	7	http://dx.doi.org/10.1007/s0070	http://dx.doi.org/10.1007/s0070	PROPN
ap-4605	307	8	http://dx.doi.org/10.1063/1.4998715	http://dx.doi.org/10.1063/1.4998715	NOUN
ap-4605	307	9	http://dx.doi.org/10.1063/1.527118	http://dx.doi.org/10.1063/1.527118	X
ap-4605	307	10	http://dx.doi.org/10.1016/j.cnsns.2016.01.015	http://dx.doi.org/10.1016/j.cnsns.2016.01.015	PROPN
ap-4605	307	11	acta	acta	PROPN
ap-4605	307	12	polytechnica	polytechnica	PROPN
ap-4605	307	13	57(6):373–378	57(6):373–378	PROPN
ap-4605	307	14	,	,	PUNCT
ap-4605	307	15	2017	2017	NUM
ap-4605	307	16	1	1	NUM
ap-4605	307	17	introduction	introduction	NOUN
ap-4605	307	18	2	2	NUM
ap-4605	307	19	lie	lie	NOUN
ap-4605	307	20	and	and	CCONJ
ap-4605	307	21	noether	noether	ADJ
ap-4605	307	22	point	point	NOUN
ap-4605	307	23	symmetries	symmetry	NOUN
ap-4605	307	24	of	of	ADP
ap-4605	307	25	systems	system	NOUN
ap-4605	307	26	2.1	2.1	NUM
ap-4605	307	27	perturbations	perturbation	NOUN
ap-4605	307	28	that	that	PRON
ap-4605	307	29	preserve	preserve	VERB
ap-4605	307	30	symmetry	symmetry	NOUN
ap-4605	307	31	subalgebras	subalgebras	PROPN
ap-4605	307	32	3	3	NUM
ap-4605	307	33	functional	functional	ADJ
ap-4605	307	34	realizations	realization	NOUN
ap-4605	307	35	of	of	ADP
ap-4605	307	36	sl(2,r	sl(2,r	NOUN
ap-4605	307	37	)	)	PUNCT
ap-4605	307	38	as	as	SCONJ
ap-4605	307	39	noether	noether	ADJ
ap-4605	307	40	symmetry	symmetry	NOUN
ap-4605	307	41	algebra	algebra	VERB
ap-4605	307	42	3.1	3.1	NUM
ap-4605	307	43	separable	separable	ADJ
ap-4605	307	44	kinetic	kinetic	NOUN
ap-4605	307	45	lagrangians	lagrangian	VERB
ap-4605	307	46	3.2	3.2	NUM
ap-4605	307	47	systems	system	NOUN
ap-4605	307	48	with	with	ADP
ap-4605	307	49	fixed	fix	VERB
ap-4605	307	50	symmetry	symmetry	NOUN
ap-4605	307	51	4	4	NUM
ap-4605	307	52	time	time	NOUN
ap-4605	307	53	-	-	PUNCT
ap-4605	307	54	dependent	dependent	ADJ
ap-4605	307	55	lagrangians	lagrangians	ADJ
ap-4605	307	56	5	5	NUM
ap-4605	307	57	conclusions	conclusion	NOUN
ap-4605	307	58	acknowledgements	acknowledgement	NOUN
ap-4605	307	59	references	reference	NOUN