id	sid	tid	token	lemma	pos
ap-2021	1	1	acta	acta	PROPN
ap-2021	1	2	polytechnica	polytechnica	PROPN
ap-2021	1	3	doi:10.14311	doi:10.14311	PROPN
ap-2021	1	4	/	/	SYM
ap-2021	1	5	ap.2013.53.0883	ap.2013.53.0883	PROPN
ap-2021	1	6	acta	acta	PROPN
ap-2021	1	7	polytechnica	polytechnica	PROPN
ap-2021	1	8	53(6):883–889	53(6):883–889	PROPN
ap-2021	1	9	,	,	PUNCT
ap-2021	1	10	2013	2013	NUM
ap-2021	1	11	©	©	PROPN
ap-2021	1	12	czech	czech	PROPN
ap-2021	1	13	technical	technical	PROPN
ap-2021	1	14	university	university	PROPN
ap-2021	1	15	in	in	ADP
ap-2021	1	16	prague	prague	PROPN
ap-2021	1	17	,	,	PUNCT
ap-2021	1	18	2013	2013	NUM
ap-2021	1	19	available	available	ADJ
ap-2021	1	20	online	online	ADV
ap-2021	1	21	at	at	ADP
ap-2021	1	22	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-2021	1	23	control	control	NOUN
ap-2021	1	24	of	of	ADP
ap-2021	1	25	the	the	DET
ap-2021	1	26	double	double	ADJ
ap-2021	1	27	inverted	inverted	ADJ
ap-2021	1	28	pendulum	pendulum	NOUN
ap-2021	1	29	on	on	ADP
ap-2021	1	30	a	a	DET
ap-2021	1	31	cart	cart	NOUN
ap-2021	1	32	using	use	VERB
ap-2021	1	33	the	the	DET
ap-2021	1	34	natural	natural	ADJ
ap-2021	1	35	motion	motion	NOUN
ap-2021	1	36	zdeněk	zdeněk	NOUN
ap-2021	1	37	neusser∗	neusser∗	VERB
ap-2021	1	38	,	,	PUNCT
ap-2021	1	39	michael	michael	PROPN
ap-2021	1	40	valášek	valášek	VERB
ap-2021	1	41	department	department	PROPN
ap-2021	1	42	of	of	ADP
ap-2021	1	43	mechanics	mechanic	NOUN
ap-2021	1	44	,	,	PUNCT
ap-2021	1	45	biomechanics	biomechanic	NOUN
ap-2021	1	46	and	and	CCONJ
ap-2021	1	47	mechatronics	mechatronic	NOUN
ap-2021	1	48	,	,	PUNCT
ap-2021	1	49	faculty	faculty	NOUN
ap-2021	1	50	of	of	ADP
ap-2021	1	51	mechanical	mechanical	ADJ
ap-2021	1	52	engineering	engineering	NOUN
ap-2021	1	53	,	,	PUNCT
ap-2021	1	54	czech	czech	PROPN
ap-2021	1	55	technical	technical	PROPN
ap-2021	1	56	university	university	PROPN
ap-2021	1	57	in	in	ADP
ap-2021	1	58	prague	prague	PROPN
ap-2021	1	59	,	,	PUNCT
ap-2021	1	60	technická	technická	VERB
ap-2021	1	61	4,166	4,166	NUM
ap-2021	1	62	07	07	NUM
ap-2021	1	63	prague	prague	PROPN
ap-2021	1	64	,	,	PUNCT
ap-2021	1	65	czech	czech	PROPN
ap-2021	1	66	republic	republic	NOUN
ap-2021	1	67	∗	∗	NOUN
ap-2021	1	68	corresponding	correspond	VERB
ap-2021	1	69	author	author	NOUN
ap-2021	1	70	:	:	PUNCT
ap-2021	1	71	zdenek.neusser@fs.cvut.cz	zdenek.neusser@fs.cvut.cz	X
ap-2021	1	72	abstract	abstract	ADJ
ap-2021	1	73	.	.	PUNCT
ap-2021	2	1	this	this	DET
ap-2021	2	2	paper	paper	NOUN
ap-2021	2	3	deals	deal	NOUN
ap-2021	2	4	with	with	ADP
ap-2021	2	5	controlling	control	VERB
ap-2021	2	6	the	the	DET
ap-2021	2	7	swing	swing	NOUN
ap-2021	2	8	-	-	PUNCT
ap-2021	2	9	up	up	ADP
ap-2021	2	10	motion	motion	NOUN
ap-2021	2	11	of	of	ADP
ap-2021	2	12	the	the	DET
ap-2021	2	13	double	double	ADJ
ap-2021	2	14	pendulum	pendulum	NOUN
ap-2021	2	15	on	on	ADP
ap-2021	2	16	a	a	DET
ap-2021	2	17	cart	cart	NOUN
ap-2021	2	18	using	use	VERB
ap-2021	2	19	a	a	DET
ap-2021	2	20	novel	novel	ADJ
ap-2021	2	21	control	control	NOUN
ap-2021	2	22	.	.	PUNCT
ap-2021	3	1	the	the	DET
ap-2021	3	2	system	system	NOUN
ap-2021	3	3	control	control	NOUN
ap-2021	3	4	is	be	AUX
ap-2021	3	5	based	base	VERB
ap-2021	3	6	on	on	ADP
ap-2021	3	7	finding	find	VERB
ap-2021	3	8	a	a	DET
ap-2021	3	9	feasible	feasible	ADJ
ap-2021	3	10	trajectory	trajectory	NOUN
ap-2021	3	11	connecting	connect	VERB
ap-2021	3	12	the	the	DET
ap-2021	3	13	equilibrium	equilibrium	NOUN
ap-2021	3	14	positions	position	NOUN
ap-2021	3	15	from	from	ADP
ap-2021	3	16	which	which	PRON
ap-2021	3	17	the	the	DET
ap-2021	3	18	eigenfrequencies	eigenfrequencie	NOUN
ap-2021	3	19	of	of	ADP
ap-2021	3	20	the	the	DET
ap-2021	3	21	system	system	NOUN
ap-2021	3	22	are	be	AUX
ap-2021	3	23	determined	determine	VERB
ap-2021	3	24	.	.	PUNCT
ap-2021	4	1	then	then	ADV
ap-2021	4	2	the	the	DET
ap-2021	4	3	system	system	NOUN
ap-2021	4	4	is	be	AUX
ap-2021	4	5	controlled	control	VERB
ap-2021	4	6	during	during	ADP
ap-2021	4	7	the	the	DET
ap-2021	4	8	motion	motion	NOUN
ap-2021	4	9	between	between	ADP
ap-2021	4	10	the	the	DET
ap-2021	4	11	equilibrium	equilibrium	NOUN
ap-2021	4	12	positions	position	NOUN
ap-2021	4	13	by	by	ADP
ap-2021	4	14	the	the	DET
ap-2021	4	15	special	special	ADJ
ap-2021	4	16	harmonic	harmonic	ADJ
ap-2021	4	17	excitation	excitation	NOUN
ap-2021	4	18	at	at	ADP
ap-2021	4	19	the	the	DET
ap-2021	4	20	system	system	NOUN
ap-2021	4	21	resonances	resonance	NOUN
ap-2021	4	22	.	.	PUNCT
ap-2021	5	1	around	around	ADP
ap-2021	5	2	the	the	DET
ap-2021	5	3	two	two	NUM
ap-2021	5	4	equilibrium	equilibrium	NOUN
ap-2021	5	5	positions	position	NOUN
ap-2021	5	6	,	,	PUNCT
ap-2021	5	7	the	the	DET
ap-2021	5	8	trajectory	trajectory	NOUN
ap-2021	5	9	is	be	AUX
ap-2021	5	10	stabilized	stabilize	VERB
ap-2021	5	11	by	by	ADP
ap-2021	5	12	the	the	DET
ap-2021	5	13	nonlinear	nonlinear	ADJ
ap-2021	5	14	quadratic	quadratic	ADJ
ap-2021	5	15	regulator	regulator	NOUN
ap-2021	5	16	nqr	nqr	PROPN
ap-2021	5	17	(	(	PUNCT
ap-2021	5	18	also	also	ADV
ap-2021	5	19	known	know	VERB
ap-2021	5	20	as	as	ADP
ap-2021	5	21	sdre	sdre	NOUN
ap-2021	5	22	–	–	PUNCT
ap-2021	5	23	the	the	DET
ap-2021	5	24	state	state	NOUN
ap-2021	5	25	dependent	dependent	ADJ
ap-2021	5	26	riccati	riccati	PROPN
ap-2021	5	27	equation	equation	NOUN
ap-2021	5	28	)	)	PUNCT
ap-2021	5	29	.	.	PUNCT
ap-2021	6	1	these	these	PRON
ap-2021	6	2	together	together	ADV
ap-2021	6	3	form	form	VERB
ap-2021	6	4	the	the	DET
ap-2021	6	5	control	control	NOUN
ap-2021	6	6	between	between	ADP
ap-2021	6	7	the	the	DET
ap-2021	6	8	equilibrium	equilibrium	NOUN
ap-2021	6	9	positions	position	NOUN
ap-2021	6	10	demonstrated	demonstrate	VERB
ap-2021	6	11	on	on	ADP
ap-2021	6	12	the	the	DET
ap-2021	6	13	double	double	ADJ
ap-2021	6	14	pendulum	pendulum	NOUN
ap-2021	6	15	on	on	ADP
ap-2021	6	16	a	a	DET
ap-2021	6	17	cart	cart	NOUN
ap-2021	6	18	.	.	PUNCT
ap-2021	7	1	keywords	keyword	NOUN
ap-2021	7	2	:	:	PUNCT
ap-2021	7	3	underactuated	underactuated	ADJ
ap-2021	7	4	systems	system	NOUN
ap-2021	7	5	,	,	PUNCT
ap-2021	7	6	nonlinear	nonlinear	ADJ
ap-2021	7	7	control	control	NOUN
ap-2021	7	8	,	,	PUNCT
ap-2021	7	9	mechanical	mechanical	ADJ
ap-2021	7	10	systems	system	NOUN
ap-2021	7	11	.	.	PUNCT
ap-2021	8	1	1	1	X
ap-2021	8	2	.	.	X
ap-2021	8	3	introduction	introduction	NOUN
ap-2021	8	4	the	the	DET
ap-2021	8	5	control	control	NOUN
ap-2021	8	6	of	of	ADP
ap-2021	8	7	systems	system	NOUN
ap-2021	8	8	with	with	ADP
ap-2021	8	9	fewer	few	ADJ
ap-2021	8	10	actuators	actuator	NOUN
ap-2021	8	11	than	than	ADP
ap-2021	8	12	degrees	degree	NOUN
ap-2021	8	13	of	of	ADP
ap-2021	8	14	freedom	freedom	NOUN
ap-2021	8	15	is	be	AUX
ap-2021	8	16	a	a	DET
ap-2021	8	17	challenging	challenging	ADJ
ap-2021	8	18	task	task	NOUN
ap-2021	8	19	.	.	PUNCT
ap-2021	9	1	systems	system	NOUN
ap-2021	9	2	of	of	ADP
ap-2021	9	3	this	this	DET
ap-2021	9	4	type	type	NOUN
ap-2021	9	5	are	be	AUX
ap-2021	9	6	called	call	VERB
ap-2021	9	7	underactuated	underactuated	ADJ
ap-2021	9	8	systems	system	NOUN
ap-2021	9	9	.	.	PUNCT
ap-2021	10	1	a	a	DET
ap-2021	10	2	more	more	ADV
ap-2021	10	3	precise	precise	ADJ
ap-2021	10	4	definition	definition	NOUN
ap-2021	10	5	of	of	ADP
ap-2021	10	6	underactuated	underactuated	ADJ
ap-2021	10	7	systems	system	NOUN
ap-2021	10	8	should	should	AUX
ap-2021	10	9	be	be	AUX
ap-2021	10	10	based	base	VERB
ap-2021	10	11	on	on	ADP
ap-2021	10	12	the	the	DET
ap-2021	10	13	number	number	NOUN
ap-2021	10	14	of	of	ADP
ap-2021	10	15	blocks	block	NOUN
ap-2021	10	16	in	in	ADP
ap-2021	10	17	the	the	DET
ap-2021	10	18	brunovsky	brunovsky	ADJ
ap-2021	10	19	canonical	canonical	ADJ
ap-2021	10	20	form	form	NOUN
ap-2021	10	21	[	[	X
ap-2021	10	22	1	1	NUM
ap-2021	10	23	]	]	PUNCT
ap-2021	10	24	.	.	PUNCT
ap-2021	11	1	our	our	PRON
ap-2021	11	2	study	study	NOUN
ap-2021	11	3	deals	deal	VERB
ap-2021	11	4	with	with	ADP
ap-2021	11	5	the	the	DET
ap-2021	11	6	double	double	ADJ
ap-2021	11	7	pendulum	pendulum	NOUN
ap-2021	11	8	on	on	ADP
ap-2021	11	9	a	a	DET
ap-2021	11	10	cart	cart	NOUN
ap-2021	11	11	in	in	ADP
ap-2021	11	12	the	the	DET
ap-2021	11	13	gravity	gravity	NOUN
ap-2021	11	14	field	field	NOUN
ap-2021	11	15	between	between	ADP
ap-2021	11	16	equilibrium	equilibrium	NOUN
ap-2021	11	17	positions	position	NOUN
ap-2021	11	18	passing	pass	VERB
ap-2021	11	19	through	through	ADP
ap-2021	11	20	singularity	singularity	NOUN
ap-2021	11	21	positions	position	NOUN
ap-2021	11	22	.	.	PUNCT
ap-2021	12	1	the	the	DET
ap-2021	12	2	mechanism	mechanism	NOUN
ap-2021	12	3	can	can	AUX
ap-2021	12	4	be	be	AUX
ap-2021	12	5	controlled	control	VERB
ap-2021	12	6	in	in	ADP
ap-2021	12	7	its	its	PRON
ap-2021	12	8	equilibrium	equilibrium	NOUN
ap-2021	12	9	positions	position	NOUN
ap-2021	12	10	(	(	PUNCT
ap-2021	12	11	see	see	VERB
ap-2021	12	12	[	[	X
ap-2021	12	13	2	2	NUM
ap-2021	12	14	]	]	NUM
ap-2021	12	15	)	)	PUNCT
ap-2021	12	16	,	,	PUNCT
ap-2021	12	17	but	but	CCONJ
ap-2021	12	18	there	there	PRON
ap-2021	12	19	are	be	VERB
ap-2021	12	20	always	always	ADV
ap-2021	12	21	singularity	singularity	NOUN
ap-2021	12	22	points	point	NOUN
ap-2021	12	23	in	in	ADP
ap-2021	12	24	between	between	ADP
ap-2021	12	25	.	.	PUNCT
ap-2021	13	1	the	the	DET
ap-2021	13	2	system	system	NOUN
ap-2021	13	3	is	be	AUX
ap-2021	13	4	not	not	PART
ap-2021	13	5	controllable	controllable	ADJ
ap-2021	13	6	by	by	ADP
ap-2021	13	7	the	the	DET
ap-2021	13	8	nqr	nqr	PROPN
ap-2021	13	9	control	control	NOUN
ap-2021	13	10	[	[	X
ap-2021	13	11	3	3	NUM
ap-2021	13	12	,	,	PUNCT
ap-2021	13	13	4	4	NUM
ap-2021	13	14	]	]	PUNCT
ap-2021	13	15	)	)	PUNCT
ap-2021	13	16	with	with	ADP
ap-2021	13	17	zero	zero	NUM
ap-2021	13	18	velocity	velocity	NOUN
ap-2021	13	19	.	.	PUNCT
ap-2021	14	1	the	the	DET
ap-2021	14	2	main	main	ADJ
ap-2021	14	3	aim	aim	NOUN
ap-2021	14	4	of	of	ADP
ap-2021	14	5	our	our	PRON
ap-2021	14	6	work	work	NOUN
ap-2021	14	7	is	be	AUX
ap-2021	14	8	to	to	PART
ap-2021	14	9	determine	determine	VERB
ap-2021	14	10	the	the	DET
ap-2021	14	11	behavior	behavior	NOUN
ap-2021	14	12	of	of	ADP
ap-2021	14	13	the	the	DET
ap-2021	14	14	actuator	actuator	NOUN
ap-2021	14	15	for	for	ADP
ap-2021	14	16	utilizing	utilize	VERB
ap-2021	14	17	the	the	DET
ap-2021	14	18	swing	swing	NOUN
ap-2021	14	19	-	-	PUNCT
ap-2021	14	20	up	up	ADP
ap-2021	14	21	motion	motion	NOUN
ap-2021	14	22	.	.	PUNCT
ap-2021	15	1	it	it	PRON
ap-2021	15	2	is	be	AUX
ap-2021	15	3	a	a	DET
ap-2021	15	4	challenging	challenging	ADJ
ap-2021	15	5	task	task	NOUN
ap-2021	15	6	(	(	PUNCT
ap-2021	15	7	according	accord	VERB
ap-2021	15	8	to	to	ADP
ap-2021	15	9	[	[	X
ap-2021	15	10	5	5	NUM
ap-2021	15	11	]	]	PUNCT
ap-2021	15	12	)	)	PUNCT
ap-2021	15	13	to	to	PART
ap-2021	15	14	move	move	VERB
ap-2021	15	15	the	the	DET
ap-2021	15	16	mechanism	mechanism	NOUN
ap-2021	15	17	over	over	ADP
ap-2021	15	18	this	this	DET
ap-2021	15	19	region	region	NOUN
ap-2021	15	20	of	of	ADP
ap-2021	15	21	singular	singular	PROPN
ap-2021	15	22	positions	position	NOUN
ap-2021	15	23	,	,	PUNCT
ap-2021	15	24	or	or	CCONJ
ap-2021	15	25	even	even	ADV
ap-2021	15	26	to	to	PART
ap-2021	15	27	perform	perform	VERB
ap-2021	15	28	trajectory	trajectory	NOUN
ap-2021	15	29	tracking	tracking	NOUN
ap-2021	15	30	.	.	PUNCT
ap-2021	16	1	this	this	DET
ap-2021	16	2	problem	problem	NOUN
ap-2021	16	3	has	have	AUX
ap-2021	16	4	already	already	ADV
ap-2021	16	5	been	be	AUX
ap-2021	16	6	investigated	investigate	VERB
ap-2021	16	7	by	by	ADP
ap-2021	16	8	many	many	ADJ
ap-2021	16	9	authors	author	NOUN
ap-2021	16	10	.	.	PUNCT
ap-2021	17	1	the	the	DET
ap-2021	17	2	energy	energy	NOUN
ap-2021	17	3	based	base	VERB
ap-2021	17	4	approach	approach	NOUN
ap-2021	17	5	used	use	VERB
ap-2021	17	6	in	in	ADP
ap-2021	17	7	the	the	DET
ap-2021	17	8	design	design	NOUN
ap-2021	17	9	of	of	ADP
ap-2021	17	10	stabilizing	stabilizing	NOUN
ap-2021	17	11	controllers	controller	NOUN
ap-2021	17	12	constitutes	constitute	VERB
ap-2021	17	13	the	the	DET
ap-2021	17	14	basis	basis	NOUN
ap-2021	17	15	of	of	ADP
ap-2021	17	16	the	the	DET
ap-2021	17	17	control	control	NOUN
ap-2021	17	18	applied	apply	VERB
ap-2021	17	19	in	in	ADP
ap-2021	17	20	[	[	X
ap-2021	17	21	6	6	NUM
ap-2021	17	22	]	]	PUNCT
ap-2021	17	23	and	and	CCONJ
ap-2021	17	24	in	in	ADP
ap-2021	17	25	[	[	X
ap-2021	17	26	7	7	NUM
ap-2021	17	27	]	]	PUNCT
ap-2021	17	28	,	,	PUNCT
ap-2021	17	29	and	and	CCONJ
ap-2021	17	30	this	this	PRON
ap-2021	17	31	is	be	AUX
ap-2021	17	32	another	another	DET
ap-2021	17	33	type	type	NOUN
ap-2021	17	34	of	of	ADP
ap-2021	17	35	energy	energy	NOUN
ap-2021	17	36	-	-	PUNCT
ap-2021	17	37	based	base	VERB
ap-2021	17	38	approach	approach	NOUN
ap-2021	17	39	applied	apply	VERB
ap-2021	17	40	to	to	ADP
ap-2021	17	41	the	the	DET
ap-2021	17	42	double	double	ADJ
ap-2021	17	43	inverted	inverted	ADJ
ap-2021	17	44	pendulum	pendulum	NOUN
ap-2021	17	45	on	on	ADP
ap-2021	17	46	a	a	DET
ap-2021	17	47	cart	cart	NOUN
ap-2021	17	48	.	.	PUNCT
ap-2021	18	1	a	a	DET
ap-2021	18	2	modified	modify	VERB
ap-2021	18	3	energy	energy	NOUN
ap-2021	18	4	control	control	NOUN
ap-2021	18	5	strategy	strategy	NOUN
ap-2021	18	6	using	use	VERB
ap-2021	18	7	friction	friction	NOUN
ap-2021	18	8	forces	force	NOUN
ap-2021	18	9	is	be	AUX
ap-2021	18	10	used	use	VERB
ap-2021	18	11	in	in	ADP
ap-2021	18	12	[	[	X
ap-2021	18	13	10	10	NUM
ap-2021	18	14	]	]	PUNCT
ap-2021	18	15	.	.	PUNCT
ap-2021	19	1	a	a	DET
ap-2021	19	2	method	method	NOUN
ap-2021	19	3	adding	add	VERB
ap-2021	19	4	the	the	DET
ap-2021	19	5	actuators	actuator	NOUN
ap-2021	19	6	to	to	ADP
ap-2021	19	7	the	the	DET
ap-2021	19	8	underactuated	underactuated	ADJ
ap-2021	19	9	joints	joint	NOUN
ap-2021	19	10	and	and	CCONJ
ap-2021	19	11	running	run	VERB
ap-2021	19	12	the	the	DET
ap-2021	19	13	swing	swing	NOUN
ap-2021	19	14	-	-	PUNCT
ap-2021	19	15	up	up	ADP
ap-2021	19	16	motion	motion	NOUN
ap-2021	19	17	with	with	ADP
ap-2021	19	18	optimization	optimization	NOUN
ap-2021	19	19	that	that	PRON
ap-2021	19	20	minimizes	minimize	VERB
ap-2021	19	21	the	the	DET
ap-2021	19	22	action	action	NOUN
ap-2021	19	23	of	of	ADP
ap-2021	19	24	the	the	DET
ap-2021	19	25	added	add	VERB
ap-2021	19	26	actuators	actuator	NOUN
ap-2021	19	27	is	be	AUX
ap-2021	19	28	used	use	VERB
ap-2021	19	29	in	in	ADP
ap-2021	19	30	[	[	X
ap-2021	19	31	8	8	NUM
ap-2021	19	32	]	]	PUNCT
ap-2021	19	33	.	.	PUNCT
ap-2021	20	1	partly	partly	ADV
ap-2021	20	2	stable	stable	ADJ
ap-2021	20	3	controllers	controller	NOUN
ap-2021	20	4	derived	derive	VERB
ap-2021	20	5	using	use	VERB
ap-2021	20	6	the	the	DET
ap-2021	20	7	dynamic	dynamic	ADJ
ap-2021	20	8	model	model	NOUN
ap-2021	20	9	of	of	ADP
ap-2021	20	10	the	the	DET
ap-2021	20	11	manipulator	manipulator	NOUN
ap-2021	20	12	in	in	ADP
ap-2021	20	13	order	order	NOUN
ap-2021	20	14	to	to	PART
ap-2021	20	15	employ	employ	VERB
ap-2021	20	16	them	they	PRON
ap-2021	20	17	under	under	ADP
ap-2021	20	18	an	an	DET
ap-2021	20	19	optimal	optimal	ADJ
ap-2021	20	20	switching	switching	NOUN
ap-2021	20	21	sequence	sequence	NOUN
ap-2021	20	22	is	be	AUX
ap-2021	20	23	presented	present	VERB
ap-2021	20	24	in	in	ADP
ap-2021	20	25	[	[	X
ap-2021	20	26	9	9	NUM
ap-2021	20	27	]	]	PUNCT
ap-2021	20	28	.	.	PUNCT
ap-2021	21	1	another	another	DET
ap-2021	21	2	approach	approach	NOUN
ap-2021	21	3	is	be	AUX
ap-2021	21	4	to	to	PART
ap-2021	21	5	use	use	VERB
ap-2021	21	6	exact	exact	ADJ
ap-2021	21	7	input	input	NOUN
ap-2021	21	8	-	-	PUNCT
ap-2021	21	9	output	output	NOUN
ap-2021	21	10	linearization	linearization	NOUN
ap-2021	21	11	within	within	ADP
ap-2021	21	12	a	a	DET
ap-2021	21	13	certain	certain	ADJ
ap-2021	21	14	submanifold	submanifold	NOUN
ap-2021	21	15	(	(	PUNCT
ap-2021	21	16	direction	direction	NOUN
ap-2021	21	17	)	)	PUNCT
ap-2021	21	18	in	in	ADP
ap-2021	21	19	which	which	PRON
ap-2021	21	20	the	the	DET
ap-2021	21	21	system	system	NOUN
ap-2021	21	22	is	be	AUX
ap-2021	21	23	controllable	controllable	ADJ
ap-2021	21	24	and	and	CCONJ
ap-2021	21	25	the	the	DET
ap-2021	21	26	zero	zero	NUM
ap-2021	21	27	-	-	PUNCT
ap-2021	21	28	dynamics	dynamic	NOUN
ap-2021	21	29	is	be	AUX
ap-2021	21	30	stable	stable	ADJ
ap-2021	21	31	[	[	X
ap-2021	21	32	10	10	NUM
ap-2021	21	33	]	]	PUNCT
ap-2021	21	34	.	.	PUNCT
ap-2021	22	1	this	this	DET
ap-2021	22	2	approach	approach	NOUN
ap-2021	22	3	is	be	AUX
ap-2021	22	4	used	use	VERB
ap-2021	22	5	in	in	ADP
ap-2021	22	6	[	[	X
ap-2021	22	7	11	11	NUM
ap-2021	22	8	]	]	PUNCT
ap-2021	22	9	,	,	PUNCT
ap-2021	22	10	where	where	SCONJ
ap-2021	22	11	the	the	DET
ap-2021	22	12	feedforward	feedforward	NOUN
ap-2021	22	13	control	control	NOUN
ap-2021	22	14	strategy	strategy	NOUN
ap-2021	22	15	is	be	AUX
ap-2021	22	16	combined	combine	VERB
ap-2021	22	17	with	with	ADP
ap-2021	22	18	input	input	NOUN
ap-2021	22	19	-	-	PUNCT
ap-2021	22	20	output	output	NOUN
ap-2021	22	21	linearization	linearization	NOUN
ap-2021	22	22	.	.	PUNCT
ap-2021	23	1	the	the	DET
ap-2021	23	2	system	system	NOUN
ap-2021	23	3	acquires	acquire	VERB
ap-2021	23	4	new	new	ADJ
ap-2021	23	5	input	input	NOUN
ap-2021	23	6	variables	variable	NOUN
ap-2021	23	7	that	that	PRON
ap-2021	23	8	are	be	AUX
ap-2021	23	9	suitable	suitable	ADJ
ap-2021	23	10	for	for	ADP
ap-2021	23	11	controlling	control	VERB
ap-2021	23	12	the	the	DET
ap-2021	23	13	actuated	actuate	VERB
ap-2021	23	14	part	part	NOUN
ap-2021	23	15	together	together	ADV
ap-2021	23	16	with	with	ADP
ap-2021	23	17	the	the	DET
ap-2021	23	18	underactuated	underactuated	ADJ
ap-2021	23	19	part	part	NOUN
ap-2021	23	20	.	.	PUNCT
ap-2021	24	1	however	however	ADV
ap-2021	24	2	,	,	PUNCT
ap-2021	24	3	the	the	DET
ap-2021	24	4	system	system	NOUN
ap-2021	24	5	can	can	AUX
ap-2021	24	6	be	be	AUX
ap-2021	24	7	controlled	control	VERB
ap-2021	24	8	by	by	ADP
ap-2021	24	9	this	this	DET
ap-2021	24	10	new	new	ADJ
ap-2021	24	11	input	input	NOUN
ap-2021	24	12	only	only	ADV
ap-2021	24	13	if	if	SCONJ
ap-2021	24	14	the	the	DET
ap-2021	24	15	input	input	NOUN
ap-2021	24	16	functions	function	NOUN
ap-2021	24	17	are	be	AUX
ap-2021	24	18	from	from	ADP
ap-2021	24	19	a	a	DET
ap-2021	24	20	certain	certain	ADJ
ap-2021	24	21	admissible	admissible	ADJ
ap-2021	24	22	class	class	NOUN
ap-2021	24	23	of	of	ADP
ap-2021	24	24	functions	function	NOUN
ap-2021	24	25	.	.	PUNCT
ap-2021	25	1	this	this	DET
ap-2021	25	2	admissible	admissible	ADJ
ap-2021	25	3	class	class	NOUN
ap-2021	25	4	of	of	ADP
ap-2021	25	5	functions	function	NOUN
ap-2021	25	6	can	can	AUX
ap-2021	25	7	be	be	AUX
ap-2021	25	8	determined	determine	VERB
ap-2021	25	9	by	by	ADP
ap-2021	25	10	the	the	DET
ap-2021	25	11	cyclic	cyclic	PROPN
ap-2021	25	12	control	control	NOUN
ap-2021	25	13	described	describe	VERB
ap-2021	25	14	in	in	ADP
ap-2021	25	15	[	[	X
ap-2021	25	16	12	12	NUM
ap-2021	25	17	]	]	PUNCT
ap-2021	25	18	as	as	ADP
ap-2021	25	19	periodic	periodic	ADJ
ap-2021	25	20	invariant	invariant	ADJ
ap-2021	25	21	functions	function	NOUN
ap-2021	25	22	(	(	PUNCT
ap-2021	25	23	with	with	ADP
ap-2021	25	24	respect	respect	NOUN
ap-2021	25	25	to	to	ADP
ap-2021	25	26	the	the	DET
ap-2021	25	27	actuated	actuate	VERB
ap-2021	25	28	variables	variable	NOUN
ap-2021	25	29	)	)	PUNCT
ap-2021	25	30	,	,	PUNCT
ap-2021	25	31	without	without	ADP
ap-2021	25	32	details	detail	NOUN
ap-2021	25	33	.	.	PUNCT
ap-2021	26	1	another	another	DET
ap-2021	26	2	way	way	NOUN
ap-2021	26	3	to	to	PART
ap-2021	26	4	find	find	VERB
ap-2021	26	5	suitable	suitable	ADJ
ap-2021	26	6	admissible	admissible	ADJ
ap-2021	26	7	functions	function	NOUN
ap-2021	26	8	for	for	ADP
ap-2021	26	9	controlling	control	VERB
ap-2021	26	10	underactuated	underactuated	ADJ
ap-2021	26	11	mechanical	mechanical	ADJ
ap-2021	26	12	systems	system	NOUN
ap-2021	26	13	between	between	ADP
ap-2021	26	14	equilibrium	equilibrium	NOUN
ap-2021	26	15	positions	position	NOUN
ap-2021	26	16	across	across	ADP
ap-2021	26	17	a	a	DET
ap-2021	26	18	singularity	singularity	NOUN
ap-2021	26	19	area	area	NOUN
ap-2021	26	20	in	in	ADP
ap-2021	26	21	the	the	DET
ap-2021	26	22	gravity	gravity	NOUN
ap-2021	26	23	field	field	NOUN
ap-2021	26	24	is	be	AUX
ap-2021	26	25	described	describe	VERB
ap-2021	26	26	in	in	ADP
ap-2021	26	27	[	[	X
ap-2021	26	28	13	13	NUM
ap-2021	26	29	]	]	PUNCT
ap-2021	26	30	.	.	PUNCT
ap-2021	27	1	these	these	DET
ap-2021	27	2	suitable	suitable	ADJ
ap-2021	27	3	admissible	admissible	ADJ
ap-2021	27	4	functions	function	NOUN
ap-2021	27	5	are	be	AUX
ap-2021	27	6	based	base	VERB
ap-2021	27	7	on	on	ADP
ap-2021	27	8	inverting	invert	VERB
ap-2021	27	9	the	the	DET
ap-2021	27	10	so	so	ADV
ap-2021	27	11	-	-	PUNCT
ap-2021	27	12	called	call	VERB
ap-2021	27	13	natural	natural	ADJ
ap-2021	27	14	motion	motion	NOUN
ap-2021	27	15	,	,	PUNCT
ap-2021	27	16	or	or	CCONJ
ap-2021	27	17	on	on	ADP
ap-2021	27	18	reusing	reuse	VERB
ap-2021	27	19	specific	specific	ADJ
ap-2021	27	20	knowledge	knowledge	NOUN
ap-2021	27	21	gained	gain	VERB
ap-2021	27	22	from	from	ADP
ap-2021	27	23	these	these	DET
ap-2021	27	24	natural	natural	ADJ
ap-2021	27	25	motions	motion	NOUN
ap-2021	27	26	.	.	PUNCT
ap-2021	28	1	in	in	ADP
ap-2021	28	2	brief	brief	NOUN
ap-2021	28	3	,	,	PUNCT
ap-2021	28	4	the	the	DET
ap-2021	28	5	natural	natural	ADJ
ap-2021	28	6	motion	motion	NOUN
ap-2021	28	7	is	be	AUX
ap-2021	28	8	a	a	DET
ap-2021	28	9	motion	motion	NOUN
ap-2021	28	10	of	of	ADP
ap-2021	28	11	the	the	DET
ap-2021	28	12	system	system	NOUN
ap-2021	28	13	without	without	ADP
ap-2021	28	14	control	control	NOUN
ap-2021	28	15	.	.	PUNCT
ap-2021	29	1	the	the	DET
ap-2021	29	2	method	method	NOUN
ap-2021	29	3	is	be	AUX
ap-2021	29	4	shown	show	VERB
ap-2021	29	5	in	in	ADP
ap-2021	29	6	[	[	X
ap-2021	29	7	13	13	NUM
ap-2021	29	8	]	]	PUNCT
ap-2021	29	9	only	only	ADV
ap-2021	29	10	for	for	ADP
ap-2021	29	11	a	a	DET
ap-2021	29	12	double	double	ADJ
ap-2021	29	13	pendulum	pendulum	NOUN
ap-2021	29	14	and	and	CCONJ
ap-2021	29	15	a	a	DET
ap-2021	29	16	pendulum	pendulum	NOUN
ap-2021	29	17	on	on	ADP
ap-2021	29	18	a	a	DET
ap-2021	29	19	cart	cart	NOUN
ap-2021	29	20	.	.	PUNCT
ap-2021	30	1	our	our	PRON
ap-2021	30	2	paper	paper	NOUN
ap-2021	30	3	deals	deal	NOUN
ap-2021	30	4	with	with	ADP
ap-2021	30	5	the	the	DET
ap-2021	30	6	application	application	NOUN
ap-2021	30	7	of	of	ADP
ap-2021	30	8	this	this	DET
ap-2021	30	9	approach	approach	NOUN
ap-2021	30	10	also	also	ADV
ap-2021	30	11	for	for	ADP
ap-2021	30	12	the	the	DET
ap-2021	30	13	swing	swing	NOUN
ap-2021	30	14	-	-	PUNCT
ap-2021	30	15	up	up	ADP
ap-2021	30	16	motion	motion	NOUN
ap-2021	30	17	of	of	ADP
ap-2021	30	18	a	a	DET
ap-2021	30	19	double	double	ADJ
ap-2021	30	20	pendulum	pendulum	NOUN
ap-2021	30	21	on	on	ADP
ap-2021	30	22	a	a	DET
ap-2021	30	23	cart	cart	NOUN
ap-2021	30	24	as	as	ADP
ap-2021	30	25	a	a	DET
ap-2021	30	26	more	more	ADV
ap-2021	30	27	complex	complex	ADJ
ap-2021	30	28	system	system	NOUN
ap-2021	30	29	than	than	SCONJ
ap-2021	30	30	that	that	PRON
ap-2021	30	31	investigated	investigate	VERB
ap-2021	30	32	in	in	ADP
ap-2021	30	33	[	[	X
ap-2021	30	34	13	13	NUM
ap-2021	30	35	]	]	PUNCT
ap-2021	30	36	.	.	PUNCT
ap-2021	31	1	our	our	PRON
ap-2021	31	2	paper	paper	NOUN
ap-2021	31	3	describes	describe	VERB
ap-2021	31	4	this	this	DET
ap-2021	31	5	different	different	ADJ
ap-2021	31	6	approach	approach	NOUN
ap-2021	31	7	to	to	ADP
ap-2021	31	8	the	the	DET
ap-2021	31	9	control	control	NOUN
ap-2021	31	10	of	of	ADP
ap-2021	31	11	underactuated	underactuated	ADJ
ap-2021	31	12	systems	system	NOUN
ap-2021	31	13	.	.	PUNCT
ap-2021	32	1	it	it	PRON
ap-2021	32	2	demonstrates	demonstrate	VERB
ap-2021	32	3	a	a	DET
ap-2021	32	4	different	different	ADJ
ap-2021	32	5	solution	solution	NOUN
ap-2021	32	6	of	of	ADP
ap-2021	32	7	the	the	DET
ap-2021	32	8	problem	problem	NOUN
ap-2021	32	9	explored	explore	VERB
ap-2021	32	10	in	in	ADP
ap-2021	32	11	[	[	X
ap-2021	32	12	7	7	NUM
ap-2021	32	13	]	]	PUNCT
ap-2021	32	14	and	and	CCONJ
ap-2021	32	15	justifies	justify	VERB
ap-2021	32	16	the	the	DET
ap-2021	32	17	same	same	ADJ
ap-2021	32	18	results	result	NOUN
ap-2021	32	19	as	as	ADP
ap-2021	32	20	in	in	ADP
ap-2021	32	21	[	[	X
ap-2021	32	22	7	7	NUM
ap-2021	32	23	]	]	PUNCT
ap-2021	32	24	,	,	PUNCT
ap-2021	32	25	but	but	CCONJ
ap-2021	32	26	with	with	ADP
ap-2021	32	27	broader	broad	ADJ
ap-2021	32	28	validity	validity	NOUN
ap-2021	32	29	and	and	CCONJ
ap-2021	32	30	applicability	applicability	NOUN
ap-2021	32	31	.	.	PUNCT
ap-2021	33	1	2	2	X
ap-2021	33	2	.	.	NOUN
ap-2021	33	3	natural	natural	ADJ
ap-2021	33	4	motion	motion	NOUN
ap-2021	33	5	natural	natural	ADJ
ap-2021	33	6	motion	motion	NOUN
ap-2021	33	7	[	[	X
ap-2021	33	8	13	13	NUM
ap-2021	33	9	]	]	PUNCT
ap-2021	33	10	is	be	AUX
ap-2021	33	11	the	the	DET
ap-2021	33	12	motion	motion	NOUN
ap-2021	33	13	of	of	ADP
ap-2021	33	14	an	an	DET
ap-2021	33	15	investigated	investigate	VERB
ap-2021	33	16	mechanical	mechanical	ADJ
ap-2021	33	17	system	system	NOUN
ap-2021	33	18	moving	move	VERB
ap-2021	33	19	in	in	ADP
ap-2021	33	20	the	the	DET
ap-2021	33	21	gravity	gravity	NOUN
ap-2021	33	22	field	field	NOUN
ap-2021	33	23	with	with	ADP
ap-2021	33	24	zero	zero	NUM
ap-2021	33	25	or	or	CCONJ
ap-2021	33	26	constant	constant	ADJ
ap-2021	33	27	inputs	input	NOUN
ap-2021	33	28	(	(	PUNCT
ap-2021	33	29	drive	drive	ADJ
ap-2021	33	30	torques	torque	NOUN
ap-2021	33	31	caused	cause	VERB
ap-2021	33	32	by	by	ADP
ap-2021	33	33	gravity	gravity	NOUN
ap-2021	33	34	)	)	PUNCT
ap-2021	33	35	,	,	PUNCT
ap-2021	33	36	from	from	ADP
ap-2021	33	37	the	the	DET
ap-2021	33	38	unstable	unstable	ADJ
ap-2021	33	39	equilibrium	equilibrium	NOUN
ap-2021	33	40	position	position	NOUN
ap-2021	33	41	to	to	ADP
ap-2021	33	42	the	the	DET
ap-2021	33	43	stable	stable	ADJ
ap-2021	33	44	equilibrium	equilibrium	NOUN
ap-2021	33	45	position	position	NOUN
ap-2021	33	46	.	.	PUNCT
ap-2021	34	1	to	to	PART
ap-2021	34	2	reach	reach	VERB
ap-2021	34	3	the	the	DET
ap-2021	34	4	desired	desire	VERB
ap-2021	34	5	quiescent	quiescent	ADJ
ap-2021	34	6	motion	motion	NOUN
ap-2021	34	7	,	,	PUNCT
ap-2021	34	8	it	it	PRON
ap-2021	34	9	is	be	AUX
ap-2021	34	10	necessary	necessary	ADJ
ap-2021	34	11	to	to	PART
ap-2021	34	12	add	add	VERB
ap-2021	34	13	a	a	DET
ap-2021	34	14	passive	passive	ADJ
ap-2021	34	15	member	member	NOUN
ap-2021	34	16	(	(	PUNCT
ap-2021	34	17	a	a	DET
ap-2021	34	18	damper	damper	NOUN
ap-2021	34	19	)	)	PUNCT
ap-2021	34	20	into	into	ADP
ap-2021	34	21	the	the	DET
ap-2021	34	22	actuator	actuator	NOUN
ap-2021	34	23	.	.	PUNCT
ap-2021	35	1	the	the	DET
ap-2021	35	2	underactuated	underactuated	ADJ
ap-2021	35	3	part	part	NOUN
ap-2021	35	4	moves	move	VERB
ap-2021	35	5	freely	freely	ADV
ap-2021	35	6	,	,	PUNCT
ap-2021	35	7	but	but	CCONJ
ap-2021	35	8	due	due	ADP
ap-2021	35	9	to	to	ADP
ap-2021	35	10	the	the	DET
ap-2021	35	11	overall	overall	ADJ
ap-2021	35	12	energy	energy	NOUN
ap-2021	35	13	flow	flow	NOUN
ap-2021	35	14	into	into	ADP
ap-2021	35	15	883	883	NUM
ap-2021	35	16	http://dx.doi.org/10.14311/ap.2013.53.0883	http://dx.doi.org/10.14311/ap.2013.53.0883	NOUN
ap-2021	35	17	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-2021	35	18	z.	z.	PROPN
ap-2021	35	19	neusser	neusser	PROPN
ap-2021	35	20	,	,	PUNCT
ap-2021	35	21	m.	m.	NOUN
ap-2021	35	22	valášek	valášek	VERB
ap-2021	35	23	acta	acta	PROPN
ap-2021	35	24	polytechnica	polytechnica	PROPN
ap-2021	35	25	figure	figure	NOUN
ap-2021	35	26	1	1	NUM
ap-2021	35	27	.	.	X
ap-2021	35	28	double	double	ADJ
ap-2021	35	29	pendulum	pendulum	NOUN
ap-2021	35	30	on	on	ADP
ap-2021	35	31	a	a	DET
ap-2021	35	32	cart	cart	NOUN
ap-2021	35	33	;	;	PUNCT
ap-2021	35	34	left	leave	VERB
ap-2021	35	35	,	,	PUNCT
ap-2021	35	36	lower	low	ADJ
ap-2021	35	37	position	position	NOUN
ap-2021	35	38	,	,	PUNCT
ap-2021	35	39	right	right	INTJ
ap-2021	35	40	,	,	PUNCT
ap-2021	35	41	upper	upper	ADJ
ap-2021	35	42	position	position	NOUN
ap-2021	35	43	.	.	PUNCT
ap-2021	36	1	the	the	DET
ap-2021	36	2	passive	passive	ADJ
ap-2021	36	3	part	part	NOUN
ap-2021	36	4	the	the	DET
ap-2021	36	5	whole	whole	ADJ
ap-2021	36	6	system	system	NOUN
ap-2021	36	7	is	be	AUX
ap-2021	36	8	stabilized	stabilize	VERB
ap-2021	36	9	around	around	ADP
ap-2021	36	10	the	the	DET
ap-2021	36	11	stable	stable	ADJ
ap-2021	36	12	equilibrium	equilibrium	NOUN
ap-2021	36	13	point	point	NOUN
ap-2021	36	14	.	.	PUNCT
ap-2021	37	1	the	the	DET
ap-2021	37	2	damping	damp	VERB
ap-2021	37	3	term	term	NOUN
ap-2021	37	4	(	(	PUNCT
ap-2021	37	5	the	the	DET
ap-2021	37	6	added	add	VERB
ap-2021	37	7	passive	passive	ADJ
ap-2021	37	8	member	member	NOUN
ap-2021	37	9	)	)	PUNCT
ap-2021	37	10	is	be	AUX
ap-2021	37	11	chosen	choose	VERB
ap-2021	37	12	small	small	ADJ
ap-2021	37	13	,	,	PUNCT
ap-2021	37	14	in	in	ADP
ap-2021	37	15	order	order	NOUN
ap-2021	37	16	to	to	PART
ap-2021	37	17	remove	remove	VERB
ap-2021	37	18	the	the	DET
ap-2021	37	19	difference	difference	NOUN
ap-2021	37	20	in	in	ADP
ap-2021	37	21	potential	potential	ADJ
ap-2021	37	22	energy	energy	NOUN
ap-2021	37	23	between	between	ADP
ap-2021	37	24	the	the	DET
ap-2021	37	25	equilibrium	equilibrium	NOUN
ap-2021	37	26	positions	position	NOUN
ap-2021	37	27	.	.	PUNCT
ap-2021	38	1	the	the	DET
ap-2021	38	2	value	value	NOUN
ap-2021	38	3	of	of	ADP
ap-2021	38	4	the	the	DET
ap-2021	38	5	damping	damp	VERB
ap-2021	38	6	term	term	NOUN
ap-2021	38	7	is	be	AUX
ap-2021	38	8	optimized	optimize	VERB
ap-2021	38	9	with	with	ADP
ap-2021	38	10	respect	respect	NOUN
ap-2021	38	11	to	to	ADP
ap-2021	38	12	the	the	DET
ap-2021	38	13	settling	settling	NOUN
ap-2021	38	14	time	time	NOUN
ap-2021	38	15	.	.	PUNCT
ap-2021	39	1	the	the	DET
ap-2021	39	2	natural	natural	ADJ
ap-2021	39	3	motion	motion	NOUN
ap-2021	39	4	is	be	AUX
ap-2021	39	5	later	later	ADV
ap-2021	39	6	used	use	VERB
ap-2021	39	7	to	to	PART
ap-2021	39	8	determine	determine	VERB
ap-2021	39	9	the	the	DET
ap-2021	39	10	eigenfrequencies	eigenfrequencie	NOUN
ap-2021	39	11	of	of	ADP
ap-2021	39	12	the	the	DET
ap-2021	39	13	natural	natural	ADJ
ap-2021	39	14	motion	motion	NOUN
ap-2021	39	15	.	.	PUNCT
ap-2021	40	1	these	these	PRON
ap-2021	40	2	are	be	AUX
ap-2021	40	3	not	not	PART
ap-2021	40	4	influenced	influence	VERB
ap-2021	40	5	by	by	ADP
ap-2021	40	6	the	the	DET
ap-2021	40	7	damping	damp	VERB
ap-2021	40	8	if	if	SCONJ
ap-2021	40	9	it	it	PRON
ap-2021	40	10	is	be	AUX
ap-2021	40	11	small	small	ADJ
ap-2021	40	12	.	.	PUNCT
ap-2021	41	1	proposition	proposition	NOUN
ap-2021	41	2	1	1	NUM
ap-2021	41	3	.	.	PUNCT
ap-2021	42	1	the	the	DET
ap-2021	42	2	control	control	NOUN
ap-2021	42	3	described	describe	VERB
ap-2021	42	4	here	here	ADV
ap-2021	42	5	enables	enable	VERB
ap-2021	42	6	the	the	DET
ap-2021	42	7	system	system	NOUN
ap-2021	42	8	of	of	ADP
ap-2021	42	9	the	the	DET
ap-2021	42	10	cart	cart	NOUN
ap-2021	42	11	-	-	PUNCT
ap-2021	42	12	double	double	ADJ
ap-2021	42	13	-	-	PUNCT
ap-2021	42	14	pendulum	pendulum	NOUN
ap-2021	42	15	to	to	PART
ap-2021	42	16	be	be	AUX
ap-2021	42	17	moved	move	VERB
ap-2021	42	18	from	from	ADP
ap-2021	42	19	the	the	DET
ap-2021	42	20	lower	low	ADJ
ap-2021	42	21	position	position	NOUN
ap-2021	42	22	(	(	PUNCT
ap-2021	42	23	figure	figure	NOUN
ap-2021	42	24	1	1	NUM
ap-2021	42	25	left	leave	VERB
ap-2021	42	26	)	)	PUNCT
ap-2021	42	27	to	to	ADP
ap-2021	42	28	the	the	DET
ap-2021	42	29	upper	upper	ADJ
ap-2021	42	30	position	position	NOUN
ap-2021	42	31	(	(	PUNCT
ap-2021	42	32	figure	figure	NOUN
ap-2021	42	33	1	1	NUM
ap-2021	42	34	right	right	NOUN
ap-2021	42	35	)	)	PUNCT
ap-2021	42	36	.	.	PUNCT
ap-2021	43	1	justification	justification	NOUN
ap-2021	43	2	.	.	PUNCT
ap-2021	44	1	the	the	DET
ap-2021	44	2	control	control	NOUN
ap-2021	44	3	consists	consist	VERB
ap-2021	44	4	of	of	ADP
ap-2021	44	5	two	two	NUM
ap-2021	44	6	phases	phase	NOUN
ap-2021	44	7	.	.	PUNCT
ap-2021	45	1	first	first	ADV
ap-2021	45	2	,	,	PUNCT
ap-2021	45	3	the	the	DET
ap-2021	45	4	system	system	NOUN
ap-2021	45	5	is	be	AUX
ap-2021	45	6	moved	move	VERB
ap-2021	45	7	from	from	ADP
ap-2021	45	8	the	the	DET
ap-2021	45	9	lower	low	ADJ
ap-2021	45	10	position	position	NOUN
ap-2021	45	11	(	(	PUNCT
ap-2021	45	12	figure	figure	NOUN
ap-2021	45	13	1	1	NUM
ap-2021	45	14	left	leave	VERB
ap-2021	45	15	)	)	PUNCT
ap-2021	45	16	to	to	ADP
ap-2021	45	17	the	the	DET
ap-2021	45	18	vicinity	vicinity	NOUN
ap-2021	45	19	of	of	ADP
ap-2021	45	20	the	the	DET
ap-2021	45	21	upper	upper	ADJ
ap-2021	45	22	position	position	NOUN
ap-2021	45	23	(	(	PUNCT
ap-2021	45	24	figure	figure	NOUN
ap-2021	45	25	1	1	NUM
ap-2021	45	26	right	right	NOUN
ap-2021	45	27	)	)	PUNCT
ap-2021	45	28	with	with	ADP
ap-2021	45	29	small	small	ADJ
ap-2021	45	30	final	final	ADJ
ap-2021	45	31	velocities	velocity	NOUN
ap-2021	45	32	.	.	PUNCT
ap-2021	46	1	second	second	ADJ
ap-2021	46	2	,	,	PUNCT
ap-2021	46	3	the	the	DET
ap-2021	46	4	system	system	NOUN
ap-2021	46	5	is	be	AUX
ap-2021	46	6	stabilized	stabilize	VERB
ap-2021	46	7	and	and	CCONJ
ap-2021	46	8	controlled	control	VERB
ap-2021	46	9	exactly	exactly	ADV
ap-2021	46	10	into	into	ADP
ap-2021	46	11	the	the	DET
ap-2021	46	12	equilibrium	equilibrium	NOUN
ap-2021	46	13	at	at	ADP
ap-2021	46	14	the	the	DET
ap-2021	46	15	upper	upper	ADJ
ap-2021	46	16	position	position	NOUN
ap-2021	46	17	by	by	ADP
ap-2021	46	18	nqr	nqr	PROPN
ap-2021	46	19	control	control	NOUN
ap-2021	46	20	.	.	PUNCT
ap-2021	47	1	the	the	DET
ap-2021	47	2	first	first	ADJ
ap-2021	47	3	phase	phase	NOUN
ap-2021	47	4	is	be	AUX
ap-2021	47	5	realized	realize	VERB
ap-2021	47	6	by	by	ADP
ap-2021	47	7	proper	proper	ADJ
ap-2021	47	8	selection	selection	NOUN
ap-2021	47	9	of	of	ADP
ap-2021	47	10	the	the	DET
ap-2021	47	11	amplitudes	amplitude	NOUN
ap-2021	47	12	in	in	ADP
ap-2021	47	13	equation	equation	NOUN
ap-2021	47	14	(	(	PUNCT
ap-2021	47	15	9	9	NUM
ap-2021	47	16	)	)	PUNCT
ap-2021	47	17	)	)	PUNCT
ap-2021	48	1	in	in	ADP
ap-2021	48	2	order	order	NOUN
ap-2021	48	3	to	to	PART
ap-2021	48	4	achieve	achieve	VERB
ap-2021	48	5	values	value	NOUN
ap-2021	48	6	in	in	ADP
ap-2021	48	7	the	the	DET
ap-2021	48	8	vicinity	vicinity	NOUN
ap-2021	48	9	of	of	ADP
ap-2021	48	10	the	the	DET
ap-2021	48	11	upper	upper	ADJ
ap-2021	48	12	position	position	NOUN
ap-2021	48	13	and	and	CCONJ
ap-2021	48	14	small	small	ADJ
ap-2021	48	15	velocities	velocity	NOUN
ap-2021	48	16	.	.	PUNCT
ap-2021	49	1	amplitude	amplitude	NOUN
ap-2021	49	2	values	value	NOUN
ap-2021	49	3	of	of	ADP
ap-2021	49	4	this	this	DET
ap-2021	49	5	kind	kind	NOUN
ap-2021	49	6	exist	exist	VERB
ap-2021	49	7	because	because	SCONJ
ap-2021	49	8	each	each	DET
ap-2021	49	9	amplitude	amplitude	NOUN
ap-2021	49	10	influences	influence	VERB
ap-2021	49	11	the	the	DET
ap-2021	49	12	particular	particular	ADJ
ap-2021	49	13	different	different	ADJ
ap-2021	49	14	eigenmode	eigenmode	NOUN
ap-2021	49	15	,	,	PUNCT
ap-2021	49	16	and	and	CCONJ
ap-2021	49	17	because	because	SCONJ
ap-2021	49	18	the	the	DET
ap-2021	49	19	periods	period	NOUN
ap-2021	49	20	of	of	ADP
ap-2021	49	21	all	all	DET
ap-2021	49	22	eigenmodes	eigenmode	NOUN
ap-2021	49	23	meet	meet	VERB
ap-2021	49	24	at	at	ADP
ap-2021	49	25	one	one	NUM
ap-2021	49	26	time	time	NOUN
ap-2021	49	27	instant	instant	NOUN
ap-2021	49	28	.	.	PUNCT
ap-2021	50	1	the	the	DET
ap-2021	50	2	excitation	excitation	NOUN
ap-2021	50	3	at	at	ADP
ap-2021	50	4	the	the	DET
ap-2021	50	5	eigenfrequencies	eigenfrequencie	NOUN
ap-2021	50	6	guarantees	guarantee	VERB
ap-2021	50	7	sufficient	sufficient	ADJ
ap-2021	50	8	amplification	amplification	NOUN
ap-2021	50	9	of	of	ADP
ap-2021	50	10	the	the	DET
ap-2021	50	11	excitation	excitation	NOUN
ap-2021	50	12	amplitudes	amplitude	NOUN
ap-2021	50	13	to	to	ADP
ap-2021	50	14	the	the	DET
ap-2021	50	15	angular	angular	ADJ
ap-2021	50	16	amplitudes	amplitude	NOUN
ap-2021	50	17	of	of	ADP
ap-2021	50	18	the	the	DET
ap-2021	50	19	double	double	ADJ
ap-2021	50	20	-	-	PUNCT
ap-2021	50	21	pendulum	pendulum	NOUN
ap-2021	50	22	.	.	PUNCT
ap-2021	51	1	the	the	DET
ap-2021	51	2	combination	combination	NOUN
ap-2021	51	3	of	of	ADP
ap-2021	51	4	two	two	NUM
ap-2021	51	5	and	and	CCONJ
ap-2021	51	6	more	more	ADV
ap-2021	51	7	different	different	ADJ
ap-2021	51	8	eigenmodes	eigenmode	NOUN
ap-2021	51	9	enables	enable	VERB
ap-2021	51	10	any	any	DET
ap-2021	51	11	desired	desire	VERB
ap-2021	51	12	position	position	NOUN
ap-2021	51	13	to	to	PART
ap-2021	51	14	be	be	AUX
ap-2021	51	15	reached	reach	VERB
ap-2021	51	16	,	,	PUNCT
ap-2021	51	17	and	and	CCONJ
ap-2021	51	18	the	the	DET
ap-2021	51	19	meeting	meeting	NOUN
ap-2021	51	20	of	of	ADP
ap-2021	51	21	all	all	DET
ap-2021	51	22	periods	period	NOUN
ap-2021	51	23	at	at	ADP
ap-2021	51	24	one	one	NUM
ap-2021	51	25	time	time	NOUN
ap-2021	51	26	instant	instant	NOUN
ap-2021	51	27	enables	enable	VERB
ap-2021	51	28	zero	zero	NUM
ap-2021	51	29	or	or	CCONJ
ap-2021	51	30	near	near	ADP
ap-2021	51	31	zero	zero	NUM
ap-2021	51	32	velocities	velocity	NOUN
ap-2021	51	33	to	to	PART
ap-2021	51	34	be	be	AUX
ap-2021	51	35	reached	reach	VERB
ap-2021	51	36	.	.	PUNCT
ap-2021	52	1	proposition	proposition	NOUN
ap-2021	52	2	2	2	NUM
ap-2021	52	3	.	.	PUNCT
ap-2021	53	1	the	the	DET
ap-2021	53	2	cart	cart	NOUN
ap-2021	53	3	-	-	PUNCT
ap-2021	53	4	double	double	ADJ
ap-2021	53	5	-	-	PUNCT
ap-2021	53	6	pendulum	pendulum	NOUN
ap-2021	53	7	system	system	NOUN
ap-2021	53	8	can	can	AUX
ap-2021	53	9	be	be	AUX
ap-2021	53	10	moved	move	VERB
ap-2021	53	11	from	from	ADP
ap-2021	53	12	any	any	DET
ap-2021	53	13	position	position	NOUN
ap-2021	53	14	to	to	ADP
ap-2021	53	15	the	the	DET
ap-2021	53	16	upper	upper	ADJ
ap-2021	53	17	position	position	NOUN
ap-2021	53	18	(	(	PUNCT
ap-2021	53	19	figure	figure	NOUN
ap-2021	53	20	1	1	NUM
ap-2021	53	21	right	right	NOUN
ap-2021	53	22	)	)	PUNCT
ap-2021	53	23	.	.	PUNCT
ap-2021	54	1	u	u	NOUN
ap-2021	54	2	x	x	X
ap-2021	54	3	ϕ	ϕ	PROPN
ap-2021	54	4	�	�	PROPN
ap-2021	54	5	ϕ	ϕ	PROPN
ap-2021	54	6	�	�	PROPN
ap-2021	54	7	mv	mv	PROPN
ap-2021	54	8	i1	i1	PROPN
ap-2021	54	9	,	,	PUNCT
ap-2021	54	10	m1	m1	PROPN
ap-2021	54	11	,	,	PUNCT
ap-2021	54	12	l1	l1	PROPN
ap-2021	54	13	,	,	PUNCT
ap-2021	54	14	lt1	lt1	NOUN
ap-2021	54	15	i2	i2	PROPN
ap-2021	54	16	,	,	PUNCT
ap-2021	54	17	m2	m2	PROPN
ap-2021	54	18	,	,	PUNCT
ap-2021	54	19	l2	l2	NOUN
ap-2021	54	20	,	,	PUNCT
ap-2021	54	21	lt2	lt2	PROPN
ap-2021	54	22	figure	figure	NOUN
ap-2021	54	23	2	2	NUM
ap-2021	54	24	.	.	PUNCT
ap-2021	54	25	scheme	scheme	NOUN
ap-2021	54	26	of	of	ADP
ap-2021	54	27	the	the	DET
ap-2021	54	28	double	double	ADJ
ap-2021	54	29	inverted	inverted	ADJ
ap-2021	54	30	pendulum	pendulum	NOUN
ap-2021	54	31	on	on	ADP
ap-2021	54	32	a	a	DET
ap-2021	54	33	cart	cart	NOUN
ap-2021	54	34	with	with	ADP
ap-2021	54	35	coordinates	coordinate	NOUN
ap-2021	54	36	,	,	PUNCT
ap-2021	54	37	parameters	parameter	NOUN
ap-2021	54	38	and	and	CCONJ
ap-2021	54	39	external	external	ADJ
ap-2021	54	40	force	force	NOUN
ap-2021	54	41	.	.	PUNCT
ap-2021	55	1	justification	justification	NOUN
ap-2021	55	2	.	.	PUNCT
ap-2021	56	1	the	the	DET
ap-2021	56	2	control	control	NOUN
ap-2021	56	3	consists	consist	VERB
ap-2021	56	4	of	of	ADP
ap-2021	56	5	two	two	NUM
ap-2021	56	6	phases	phase	NOUN
ap-2021	56	7	.	.	PUNCT
ap-2021	57	1	first	first	ADV
ap-2021	57	2	,	,	PUNCT
ap-2021	57	3	the	the	DET
ap-2021	57	4	system	system	NOUN
ap-2021	57	5	is	be	AUX
ap-2021	57	6	moved	move	VERB
ap-2021	57	7	from	from	ADP
ap-2021	57	8	any	any	DET
ap-2021	57	9	position	position	NOUN
ap-2021	57	10	to	to	ADP
ap-2021	57	11	the	the	DET
ap-2021	57	12	lower	low	ADJ
ap-2021	57	13	position	position	NOUN
ap-2021	57	14	(	(	PUNCT
ap-2021	57	15	figure	figure	NOUN
ap-2021	57	16	1	1	NUM
ap-2021	57	17	left	left	ADJ
ap-2021	57	18	)	)	PUNCT
ap-2021	57	19	,	,	PUNCT
ap-2021	57	20	and	and	CCONJ
ap-2021	57	21	then	then	ADV
ap-2021	57	22	the	the	DET
ap-2021	57	23	system	system	NOUN
ap-2021	57	24	is	be	AUX
ap-2021	57	25	moved	move	VERB
ap-2021	57	26	to	to	ADP
ap-2021	57	27	the	the	DET
ap-2021	57	28	upper	upper	ADJ
ap-2021	57	29	position	position	NOUN
ap-2021	57	30	,	,	PUNCT
ap-2021	57	31	according	accord	VERB
ap-2021	57	32	to	to	ADP
ap-2021	57	33	1	1	NUM
ap-2021	57	34	.	.	PUNCT
ap-2021	58	1	the	the	DET
ap-2021	58	2	first	first	ADJ
ap-2021	58	3	phase	phase	NOUN
ap-2021	58	4	is	be	AUX
ap-2021	58	5	realized	realize	VERB
ap-2021	58	6	by	by	ADP
ap-2021	58	7	active	active	ADJ
ap-2021	58	8	damping	damping	NOUN
ap-2021	58	9	,	,	PUNCT
ap-2021	58	10	i.e.	i.e.	X
ap-2021	58	11	the	the	DET
ap-2021	58	12	control	control	NOUN
ap-2021	58	13	applies	apply	VERB
ap-2021	58	14	damping	damp	VERB
ap-2021	58	15	of	of	ADP
ap-2021	58	16	significant	significant	ADJ
ap-2021	58	17	value	value	NOUN
ap-2021	58	18	to	to	ADP
ap-2021	58	19	the	the	DET
ap-2021	58	20	cart	cart	NOUN
ap-2021	58	21	,	,	PUNCT
ap-2021	58	22	in	in	ADP
ap-2021	58	23	order	order	NOUN
ap-2021	58	24	to	to	PART
ap-2021	58	25	damp	damp	VERB
ap-2021	58	26	out	out	ADP
ap-2021	58	27	the	the	DET
ap-2021	58	28	energy	energy	NOUN
ap-2021	58	29	and	and	CCONJ
ap-2021	58	30	stop	stop	VERB
ap-2021	58	31	the	the	DET
ap-2021	58	32	system	system	NOUN
ap-2021	58	33	at	at	ADP
ap-2021	58	34	stable	stable	ADJ
ap-2021	58	35	equilibrium	equilibrium	NOUN
ap-2021	58	36	in	in	ADP
ap-2021	58	37	the	the	DET
ap-2021	58	38	lower	low	ADJ
ap-2021	58	39	position	position	NOUN
ap-2021	58	40	(	(	PUNCT
ap-2021	58	41	figure	figure	NOUN
ap-2021	58	42	1	1	NUM
ap-2021	58	43	left	left	ADJ
ap-2021	58	44	)	)	PUNCT
ap-2021	58	45	.	.	PUNCT
ap-2021	59	1	3	3	X
ap-2021	59	2	.	.	X
ap-2021	59	3	problem	problem	NOUN
ap-2021	59	4	formulation	formulation	NOUN
ap-2021	59	5	figure	figure	NOUN
ap-2021	59	6	2	2	NUM
ap-2021	59	7	presents	present	VERB
ap-2021	59	8	the	the	DET
ap-2021	59	9	scheme	scheme	NOUN
ap-2021	59	10	of	of	ADP
ap-2021	59	11	a	a	DET
ap-2021	59	12	double	double	ADJ
ap-2021	59	13	inverted	inverted	ADJ
ap-2021	59	14	pendulum	pendulum	NOUN
ap-2021	59	15	on	on	ADP
ap-2021	59	16	a	a	DET
ap-2021	59	17	cart	cart	NOUN
ap-2021	59	18	.	.	PUNCT
ap-2021	60	1	this	this	DET
ap-2021	60	2	mechanism	mechanism	NOUN
ap-2021	60	3	has	have	VERB
ap-2021	60	4	the	the	DET
ap-2021	60	5	cart	cart	NOUN
ap-2021	60	6	moving	move	VERB
ap-2021	60	7	horizontally	horizontally	ADV
ap-2021	60	8	,	,	PUNCT
ap-2021	60	9	with	with	SCONJ
ap-2021	60	10	two	two	NUM
ap-2021	60	11	links	link	NOUN
ap-2021	60	12	rotationally	rotationally	ADV
ap-2021	60	13	connected	connect	VERB
ap-2021	60	14	,	,	PUNCT
ap-2021	60	15	and	and	CCONJ
ap-2021	60	16	there	there	PRON
ap-2021	60	17	is	be	VERB
ap-2021	60	18	a	a	DET
ap-2021	60	19	force	force	NOUN
ap-2021	60	20	acting	act	VERB
ap-2021	60	21	on	on	ADP
ap-2021	60	22	the	the	DET
ap-2021	60	23	cart	cart	NOUN
ap-2021	60	24	.	.	PUNCT
ap-2021	61	1	using	use	VERB
ap-2021	61	2	lagrange	lagrange	NOUN
ap-2021	61	3	equations	equation	NOUN
ap-2021	61	4	of	of	ADP
ap-2021	61	5	the	the	DET
ap-2021	61	6	second	second	ADJ
ap-2021	61	7	type	type	NOUN
ap-2021	61	8	,	,	PUNCT
ap-2021	61	9	the	the	DET
ap-2021	61	10	dynamic	dynamic	ADJ
ap-2021	61	11	equations	equation	NOUN
ap-2021	61	12	of	of	ADP
ap-2021	61	13	the	the	DET
ap-2021	61	14	double	double	ADJ
ap-2021	61	15	pendulum	pendulum	NOUN
ap-2021	61	16	on	on	ADP
ap-2021	61	17	a	a	DET
ap-2021	61	18	cart	cart	NOUN
ap-2021	61	19	are	be	AUX
ap-2021	61	20	obtained	obtain	VERB
ap-2021	61	21	.	.	PUNCT
ap-2021	62	1	put	put	VERB
ap-2021	62	2	m	m	NOUN
ap-2021	62	3	=	=	NOUN
ap-2021	62	4	mv+m1+m2	mv+m1+m2	NOUN
ap-2021	62	5	a	a	DET
ap-2021	62	6	cosφ1	cosφ1	NOUN
ap-2021	62	7	m2lt2	m2lt2	ADJ
ap-2021	62	8	cosφ2	cosφ2	PROPN
ap-2021	62	9	a	a	DET
ap-2021	62	10	cosφ1	cosφ1	NOUN
ap-2021	63	1	i1+m1l	i1+m1l	ADP
ap-2021	63	2	2	2	NUM
ap-2021	63	3	t1+m2l	t1+m2l	NOUN
ap-2021	63	4	2	2	NUM
ap-2021	63	5	1	1	NUM
ap-2021	63	6	b	b	NOUN
ap-2021	63	7	cos(φ1−φ2	cos(φ1−φ2	NOUN
ap-2021	63	8	)	)	PUNCT
ap-2021	63	9	m2lt2	m2lt2	PROPN
ap-2021	63	10	cosφ2	cosφ2	PROPN
ap-2021	63	11	b	b	PROPN
ap-2021	63	12	cos(φ1−φ2	cos(φ1−φ2	NOUN
ap-2021	63	13	)	)	PUNCT
ap-2021	63	14	i2+m2l	i2+m2l	PRON
ap-2021	63	15	2	2	NUM
ap-2021	63	16	t2	t2	NOUN
ap-2021	63	17			NOUN
ap-2021	63	18	,	,	PUNCT
ap-2021	63	19	f	f	PROPN
ap-2021	63	20	=	=	SYM
ap-2021	63	21			PROPN
ap-2021	63	22	(	(	PUNCT
ap-2021	63	23	m1lt1+m2l1	m1lt1+m2l1	PROPN
ap-2021	63	24	)	)	PUNCT
ap-2021	63	25	sinφ1	sinφ1	ADJ
ap-2021	64	1	φ̇	φ̇	ADJ
ap-2021	64	2	2	2	NUM
ap-2021	64	3	1+m2lt2	1+m2lt2	NUM
ap-2021	64	4	sinφ2	sinφ2	NOUN
ap-2021	64	5	φ̇	φ̇	ADV
ap-2021	64	6	2	2	NUM
ap-2021	64	7	2	2	NUM
ap-2021	64	8	−m2l1lt2	−m2l1lt2	NOUN
ap-2021	64	9	sin(φ1−φ2)φ̇2	sin(φ1−φ2)φ̇2	PUNCT
ap-2021	64	10	2+(m1lt1+m2l1	2+(m1lt1+m2l1	NOUN
ap-2021	64	11	)	)	PUNCT
ap-2021	64	12	sinφ1	sinφ1	NOUN
ap-2021	65	1	g	g	PROPN
ap-2021	65	2	m2l1lt2	m2l1lt2	PROPN
ap-2021	65	3	sin(φ1−φ2)φ̇2	sin(φ1−φ2)φ̇2	PUNCT
ap-2021	65	4	1+m2lt2	1+m2lt2	NUM
ap-2021	65	5	sinφ2	sinφ2	NOUN
ap-2021	65	6	g	g	NOUN
ap-2021	65	7			NOUN
ap-2021	65	8	,	,	PUNCT
ap-2021	65	9	m(φ1	m(φ1	PROPN
ap-2021	65	10	,	,	PUNCT
ap-2021	65	11	φ2	φ2	PROPN
ap-2021	65	12	)	)	PUNCT
ap-2021	65	13			PROPN
ap-2021	65	14	ẍφ̈1	ẍφ̈1	SYM
ap-2021	65	15	φ̈2	φ̈2	NOUN
ap-2021	65	16			NOUN
ap-2021	65	17	=	=	SYM
ap-2021	65	18	f	f	PROPN
ap-2021	65	19	(	(	PUNCT
ap-2021	65	20	φ1	φ1	PROPN
ap-2021	65	21	,	,	PUNCT
ap-2021	65	22	φ̇1	φ̇1	PROPN
ap-2021	65	23	,	,	PUNCT
ap-2021	65	24	φ2	φ2	PROPN
ap-2021	65	25	,	,	PUNCT
ap-2021	65	26	φ̇2	φ̇2	NOUN
ap-2021	65	27	)	)	PUNCT
ap-2021	65	28	+	+	CCONJ
ap-2021	65	29	u(t	u(t	NOUN
ap-2021	65	30	)	)	PUNCT
ap-2021	65	31	1	1	NOUN
ap-2021	65	32	0	0	NUM
ap-2021	65	33	0	0	NUM
ap-2021	65	34			NOUN
ap-2021	65	35	,	,	PUNCT
ap-2021	65	36	(	(	PUNCT
ap-2021	65	37	1	1	X
ap-2021	65	38	)	)	PUNCT
ap-2021	65	39	where	where	SCONJ
ap-2021	65	40	a	a	DET
ap-2021	65	41	=	=	PUNCT
ap-2021	65	42	(	(	PUNCT
ap-2021	65	43	m1lt1	m1lt1	NOUN
ap-2021	65	44	+	+	NOUN
ap-2021	65	45	m2l1	m2l1	NOUN
ap-2021	65	46	)	)	PUNCT
ap-2021	65	47	and	and	CCONJ
ap-2021	65	48	b	b	X
ap-2021	65	49	=	=	SYM
ap-2021	65	50	m2l1lt2	m2l1lt2	PROPN
ap-2021	65	51	.	.	PROPN
ap-2021	65	52	matrix	matrix	NOUN
ap-2021	65	53	m	m	NOUN
ap-2021	65	54	is	be	AUX
ap-2021	65	55	the	the	DET
ap-2021	65	56	inertia	inertia	NOUN
ap-2021	65	57	matrix	matrix	NOUN
ap-2021	65	58	,	,	PUNCT
ap-2021	65	59	and	and	CCONJ
ap-2021	65	60	vector	vector	NOUN
ap-2021	65	61	f	f	PROPN
ap-2021	65	62	contains	contain	VERB
ap-2021	65	63	the	the	DET
ap-2021	65	64	forces	force	NOUN
ap-2021	65	65	dependent	dependent	ADJ
ap-2021	65	66	on	on	ADP
ap-2021	65	67	the	the	DET
ap-2021	65	68	velocities	velocity	NOUN
ap-2021	65	69	and	and	CCONJ
ap-2021	65	70	external	external	ADJ
ap-2021	65	71	forces	force	NOUN
ap-2021	65	72	besides	besides	SCONJ
ap-2021	65	73	the	the	DET
ap-2021	65	74	control	control	NOUN
ap-2021	65	75	inputs	input	NOUN
ap-2021	65	76	.	.	PUNCT
ap-2021	66	1	actuator	actuator	NOUN
ap-2021	66	2	u	u	PROPN
ap-2021	66	3	is	be	AUX
ap-2021	66	4	the	the	DET
ap-2021	66	5	horizontal	horizontal	ADJ
ap-2021	66	6	force	force	NOUN
ap-2021	66	7	acting	act	VERB
ap-2021	66	8	between	between	ADP
ap-2021	66	9	the	the	DET
ap-2021	66	10	base	base	NOUN
ap-2021	66	11	frame	frame	NOUN
ap-2021	66	12	and	and	CCONJ
ap-2021	66	13	the	the	DET
ap-2021	66	14	cart	cart	NOUN
ap-2021	66	15	.	.	PUNCT
ap-2021	67	1	the	the	DET
ap-2021	67	2	goal	goal	NOUN
ap-2021	67	3	is	be	AUX
ap-2021	67	4	to	to	PART
ap-2021	67	5	control	control	VERB
ap-2021	67	6	the	the	DET
ap-2021	67	7	mechanism	mechanism	NOUN
ap-2021	67	8	from	from	ADP
ap-2021	67	9	the	the	DET
ap-2021	67	10	stable	stable	ADJ
ap-2021	67	11	equilibrium	equilibrium	NOUN
ap-2021	67	12	point	point	NOUN
ap-2021	67	13	(	(	PUNCT
ap-2021	67	14	ϕ1	ϕ1	NOUN
ap-2021	67	15	=	=	SYM
ap-2021	67	16	π	π	PROPN
ap-2021	67	17	,	,	PUNCT
ap-2021	67	18	ϕ2	ϕ2	ADV
ap-2021	67	19	=	=	SYM
ap-2021	67	20	π	π	X
ap-2021	67	21	)	)	PUNCT
ap-2021	67	22	into	into	ADP
ap-2021	67	23	the	the	DET
ap-2021	67	24	upper	upper	ADJ
ap-2021	67	25	unstable	unstable	ADJ
ap-2021	67	26	equilibrium	equilibrium	NOUN
ap-2021	67	27	point	point	NOUN
ap-2021	67	28	(	(	PUNCT
ap-2021	67	29	ϕ1	ϕ1	NOUN
ap-2021	67	30	=	=	SYM
ap-2021	67	31	0	0	NUM
ap-2021	67	32	,	,	PUNCT
ap-2021	67	33	ϕ2	ϕ2	ADV
ap-2021	67	34	=	=	SYM
ap-2021	67	35	0	0	NUM
ap-2021	67	36	)	)	PUNCT
ap-2021	67	37	.	.	PUNCT
ap-2021	68	1	the	the	DET
ap-2021	68	2	procedure	procedure	NOUN
ap-2021	68	3	described	describe	VERB
ap-2021	68	4	in	in	ADP
ap-2021	68	5	detail	detail	NOUN
ap-2021	68	6	in	in	ADP
ap-2021	68	7	[	[	X
ap-2021	68	8	13	13	NUM
ap-2021	68	9	]	]	PUNCT
ap-2021	68	10	covering	cover	VERB
ap-2021	68	11	input884	input884	PROPN
ap-2021	68	12	vol	vol	NOUN
ap-2021	68	13	.	.	PUNCT
ap-2021	69	1	53	53	NUM
ap-2021	69	2	no	no	NOUN
ap-2021	69	3	.	.	PUNCT
ap-2021	70	1	6/2013	6/2013	NUM
ap-2021	70	2	control	control	NOUN
ap-2021	70	3	of	of	ADP
ap-2021	70	4	the	the	DET
ap-2021	70	5	double	double	ADJ
ap-2021	70	6	inverted	inverted	ADJ
ap-2021	70	7	pendulum	pendulum	NOUN
ap-2021	70	8	on	on	ADP
ap-2021	70	9	a	a	DET
ap-2021	70	10	cart	cart	NOUN
ap-2021	70	11	output	output	NOUN
ap-2021	70	12	feedback	feedback	NOUN
ap-2021	70	13	linearization	linearization	NOUN
ap-2021	70	14	which	which	PRON
ap-2021	70	15	forms	form	VERB
ap-2021	70	16	the	the	DET
ap-2021	70	17	basis	basis	NOUN
ap-2021	70	18	for	for	ADP
ap-2021	70	19	subsequent	subsequent	ADJ
ap-2021	70	20	adaptation	adaptation	NOUN
ap-2021	70	21	of	of	ADP
ap-2021	70	22	the	the	DET
ap-2021	70	23	system	system	NOUN
ap-2021	70	24	of	of	ADP
ap-2021	70	25	equations	equation	NOUN
ap-2021	70	26	.	.	PUNCT
ap-2021	71	1	it	it	PRON
ap-2021	71	2	is	be	AUX
ap-2021	71	3	necessary	necessary	ADJ
ap-2021	71	4	to	to	PART
ap-2021	71	5	divide	divide	VERB
ap-2021	71	6	the	the	DET
ap-2021	71	7	coordinates	coordinate	NOUN
ap-2021	71	8	of	of	ADP
ap-2021	71	9	the	the	DET
ap-2021	71	10	mechanism	mechanism	NOUN
ap-2021	71	11	in	in	ADP
ap-2021	71	12	such	such	ADJ
ap-2021	71	13	way	way	NOUN
ap-2021	71	14	that	that	PRON
ap-2021	71	15	one	one	NUM
ap-2021	71	16	part	part	NOUN
ap-2021	71	17	is	be	AUX
ap-2021	71	18	controlled	control	VERB
ap-2021	71	19	and	and	CCONJ
ap-2021	71	20	another	another	PRON
ap-2021	71	21	forms	form	VERB
ap-2021	71	22	the	the	DET
ap-2021	71	23	zero	zero	NUM
ap-2021	71	24	dynamic	dynamic	NOUN
ap-2021	71	25	.	.	PUNCT
ap-2021	72	1	it	it	PRON
ap-2021	72	2	is	be	AUX
ap-2021	72	3	used	use	VERB
ap-2021	72	4	the	the	DET
ap-2021	72	5	following	follow	VERB
ap-2021	72	6	division	division	NOUN
ap-2021	72	7	of	of	ADP
ap-2021	72	8	the	the	DET
ap-2021	72	9	coordinates	coordinate	NOUN
ap-2021	72	10	(	(	PUNCT
ap-2021	72	11	but	but	CCONJ
ap-2021	72	12	this	this	DET
ap-2021	72	13	choice	choice	NOUN
ap-2021	72	14	is	be	AUX
ap-2021	72	15	not	not	PART
ap-2021	72	16	unique	unique	ADJ
ap-2021	72	17	,	,	PUNCT
ap-2021	72	18	as	as	SCONJ
ap-2021	72	19	is	be	AUX
ap-2021	72	20	demonstrated	demonstrate	VERB
ap-2021	72	21	in	in	ADP
ap-2021	72	22	[	[	X
ap-2021	72	23	13	13	NUM
ap-2021	72	24	]	]	PUNCT
ap-2021	72	25	):	):	PUNCT
ap-2021	72	26	qm	qm	PROPN
ap-2021	72	27	=	=	SYM
ap-2021	72	28	x	x	PROPN
ap-2021	72	29	,	,	PUNCT
ap-2021	72	30	qz	qz	NOUN
ap-2021	72	31	=	=	PUNCT
ap-2021	73	1	[	[	PUNCT
ap-2021	73	2	ϕ1	ϕ1	NOUN
ap-2021	73	3	ϕ2	ϕ2	ADV
ap-2021	73	4	]	]	PUNCT
ap-2021	73	5	index	index	NOUN
ap-2021	73	6	m	m	PROPN
ap-2021	73	7	denotes	denote	VERB
ap-2021	73	8	the	the	DET
ap-2021	73	9	actuated	actuate	VERB
ap-2021	73	10	(	(	PUNCT
ap-2021	73	11	controlled	control	VERB
ap-2021	73	12	)	)	PUNCT
ap-2021	73	13	part	part	NOUN
ap-2021	73	14	,	,	PUNCT
ap-2021	73	15	and	and	CCONJ
ap-2021	73	16	index	index	NOUN
ap-2021	73	17	z	z	NOUN
ap-2021	73	18	denotes	denote	VERB
ap-2021	73	19	the	the	DET
ap-2021	73	20	zero	zero	NUM
ap-2021	73	21	dynamics	dynamic	NOUN
ap-2021	73	22	coordinates	coordinate	NOUN
ap-2021	73	23	.	.	PUNCT
ap-2021	74	1	matrix	matrix	NOUN
ap-2021	74	2	m	m	VERB
ap-2021	74	3	is	be	AUX
ap-2021	74	4	decomposed	decompose	VERB
ap-2021	74	5	in	in	ADP
ap-2021	74	6	the	the	DET
ap-2021	74	7	following	following	ADJ
ap-2021	74	8	way	way	NOUN
ap-2021	74	9	:	:	PUNCT
ap-2021	74	10	m	m	AUX
ap-2021	74	11	=	=	PUNCT
ap-2021	74	12	[	[	PUNCT
ap-2021	74	13	mmm	mmm	X
ap-2021	74	14	mmz	mmz	PROPN
ap-2021	74	15	mzm	mzm	NOUN
ap-2021	74	16	mzz	mzz	NOUN
ap-2021	74	17	]	]	PUNCT
ap-2021	74	18	,	,	PUNCT
ap-2021	74	19	where	where	SCONJ
ap-2021	74	20	mmm	mmm	INTJ
ap-2021	74	21	=	=	PUNCT
ap-2021	75	1	[	[	PUNCT
ap-2021	75	2	mv	mv	PROPN
ap-2021	75	3	+	+	PROPN
ap-2021	75	4	m1	m1	PROPN
ap-2021	75	5	+	+	PROPN
ap-2021	75	6	m2	m2	PROPN
ap-2021	75	7	]	]	PUNCT
ap-2021	75	8	,	,	PUNCT
ap-2021	75	9	mmz	mmz	PROPN
ap-2021	75	10	=	=	PUNCT
ap-2021	75	11	[	[	PUNCT
ap-2021	75	12	(	(	PUNCT
ap-2021	75	13	m1lt1	m1lt1	NOUN
ap-2021	75	14	+	+	NOUN
ap-2021	75	15	m2l1	m2l1	NOUN
ap-2021	75	16	)	)	PUNCT
ap-2021	75	17	cosφ1	cosφ1	PROPN
ap-2021	75	18	,	,	PUNCT
ap-2021	75	19	m2lt2	m2lt2	ADJ
ap-2021	75	20	cosφ2	cosφ2	PROPN
ap-2021	75	21	]	]	PUNCT
ap-2021	75	22	,	,	PUNCT
ap-2021	75	23	mzm	mzm	ADV
ap-2021	76	1	=	=	PUNCT
ap-2021	76	2	[	[	PUNCT
ap-2021	76	3	(	(	PUNCT
ap-2021	76	4	m1lt1	m1lt1	NOUN
ap-2021	76	5	+	+	NOUN
ap-2021	76	6	m2l1	m2l1	NOUN
ap-2021	76	7	)	)	PUNCT
ap-2021	76	8	cosφ1	cosφ1	NOUN
ap-2021	76	9	m2lt2	m2lt2	ADJ
ap-2021	76	10	cosφ2	cosφ2	PROPN
ap-2021	76	11	]	]	PUNCT
ap-2021	76	12	,	,	PUNCT
ap-2021	76	13	mzz	mzz	NOUN
ap-2021	76	14	=	=	SYM
ap-2021	76	15	[	[	PUNCT
ap-2021	76	16	i1	i1	NOUN
ap-2021	76	17	+	+	CCONJ
ap-2021	76	18	m1l	m1l	ADJ
ap-2021	76	19	2	2	NUM
ap-2021	76	20	t1	t1	NOUN
ap-2021	76	21	+	+	NOUN
ap-2021	76	22	m2l	m2l	NOUN
ap-2021	76	23	2	2	NUM
ap-2021	76	24	1	1	NUM
ap-2021	76	25	m2l1lt2	m2l1lt2	PROPN
ap-2021	76	26	cos(φ1	cos(φ1	PROPN
ap-2021	76	27	−	−	PROPN
ap-2021	76	28	φ2	φ2	PROPN
ap-2021	76	29	)	)	PUNCT
ap-2021	77	1	m2l1lt2	m2l1lt2	PROPN
ap-2021	78	1	cos(φ1	cos(φ1	PROPN
ap-2021	78	2	−	−	PROPN
ap-2021	78	3	φ2	φ2	PROPN
ap-2021	78	4	)	)	PUNCT
ap-2021	78	5	i2	i2	PROPN
ap-2021	78	6	+	+	PROPN
ap-2021	78	7	m2l	m2l	PROPN
ap-2021	78	8	2	2	NUM
ap-2021	78	9	t2	t2	NOUN
ap-2021	78	10	]	]	PUNCT
ap-2021	78	11	.	.	PUNCT
ap-2021	79	1	a	a	DET
ap-2021	79	2	necessary	necessary	ADJ
ap-2021	79	3	condition	condition	NOUN
ap-2021	79	4	for	for	ADP
ap-2021	79	5	matrixmzz	matrixmzz	NOUN
ap-2021	79	6	is	be	AUX
ap-2021	79	7	that	that	SCONJ
ap-2021	79	8	it	it	PRON
ap-2021	79	9	must	must	AUX
ap-2021	79	10	be	be	AUX
ap-2021	79	11	invertible	invertible	ADJ
ap-2021	79	12	,	,	PUNCT
ap-2021	79	13	and	and	CCONJ
ap-2021	79	14	for	for	ADP
ap-2021	79	15	nonzero	nonzero	PROPN
ap-2021	79	16	moments	moment	NOUN
ap-2021	79	17	of	of	ADP
ap-2021	79	18	inertia	inertia	NOUN
ap-2021	79	19	this	this	PRON
ap-2021	79	20	is	be	AUX
ap-2021	79	21	the	the	DET
ap-2021	79	22	case	case	NOUN
ap-2021	79	23	.	.	PUNCT
ap-2021	80	1	vector	vector	NOUN
ap-2021	80	2	f	f	PROPN
ap-2021	80	3	is	be	AUX
ap-2021	80	4	as	as	SCONJ
ap-2021	80	5	follows	follow	VERB
ap-2021	80	6	:	:	PUNCT
ap-2021	80	7	f	f	X
ap-2021	81	1	=	=	PUNCT
ap-2021	81	2	[	[	PUNCT
ap-2021	81	3	fm	fm	NOUN
ap-2021	81	4	fz	fz	X
ap-2021	81	5	]	]	PUNCT
ap-2021	81	6	,	,	PUNCT
ap-2021	81	7	where	where	SCONJ
ap-2021	81	8	fm	fm	NOUN
ap-2021	81	9	=	=	PUNCT
ap-2021	81	10	(	(	PUNCT
ap-2021	81	11	m1lt1	m1lt1	NOUN
ap-2021	81	12	+	+	NOUN
ap-2021	81	13	m2l1	m2l1	NOUN
ap-2021	81	14	)	)	PUNCT
ap-2021	81	15	sinφ1	sinφ1	ADJ
ap-2021	82	1	φ̇	φ̇	ADJ
ap-2021	82	2	2	2	NUM
ap-2021	82	3	1	1	NUM
ap-2021	82	4	+	+	ADJ
ap-2021	82	5	m2lt2	m2lt2	ADJ
ap-2021	82	6	sinφ2	sinφ2	NOUN
ap-2021	82	7	φ̇	φ̇	ADJ
ap-2021	82	8	2	2	NUM
ap-2021	82	9	2	2	NUM
ap-2021	82	10	,	,	PUNCT
ap-2021	82	11	fz	fz	VERB
ap-2021	83	1	=	=	X
ap-2021	83	2	[	[	PUNCT
ap-2021	83	3	−m2l1lt2	−m2l1lt2	X
ap-2021	83	4	sin(φ1−φ2)φ̇2	sin(φ1−φ2)φ̇2	SYM
ap-2021	83	5	2+(m1lt1+m2l1	2+(m1lt1+m2l1	NUM
ap-2021	83	6	)	)	PUNCT
ap-2021	83	7	sinφ1	sinφ1	NOUN
ap-2021	83	8	g	g	PROPN
ap-2021	83	9	m2l1lt2	m2l1lt2	PROPN
ap-2021	83	10	sin(φ1−φ2)φ̇2	sin(φ1−φ2)φ̇2	PUNCT
ap-2021	83	11	1+m2lt2	1+m2lt2	NUM
ap-2021	83	12	sinφ2	sinφ2	NOUN
ap-2021	83	13	g	g	X
ap-2021	83	14	]	]	PUNCT
ap-2021	83	15	.	.	PUNCT
ap-2021	84	1	the	the	DET
ap-2021	84	2	new	new	ADJ
ap-2021	84	3	control	control	PROPN
ap-2021	84	4	variable	variable	PROPN
ap-2021	84	5	w	w	PROPN
ap-2021	84	6	is	be	AUX
ap-2021	84	7	chosen	choose	VERB
ap-2021	84	8	as	as	ADP
ap-2021	84	9	a	a	DET
ap-2021	84	10	second	second	ADJ
ap-2021	84	11	derivative	derivative	NOUN
ap-2021	84	12	of	of	ADP
ap-2021	84	13	coordinate	coordinate	NOUN
ap-2021	84	14	x	x	NOUN
ap-2021	84	15	:	:	PUNCT
ap-2021	84	16	ẍ	ẍ	X
ap-2021	85	1	=	=	SYM
ap-2021	85	2	w.	w.	PROPN
ap-2021	85	3	(	(	PUNCT
ap-2021	85	4	2	2	NUM
ap-2021	85	5	)	)	PUNCT
ap-2021	85	6	the	the	DET
ap-2021	85	7	remaining	remain	VERB
ap-2021	85	8	coordinates	coordinate	NOUN
ap-2021	85	9	ϕ1	ϕ1	NOUN
ap-2021	85	10	and	and	CCONJ
ap-2021	85	11	ϕ2	ϕ2	ADV
ap-2021	85	12	can	can	AUX
ap-2021	85	13	be	be	AUX
ap-2021	85	14	expressed	express	VERB
ap-2021	85	15	directly	directly	ADV
ap-2021	85	16	from	from	ADP
ap-2021	85	17	equation	equation	NOUN
ap-2021	85	18	(	(	PUNCT
ap-2021	85	19	1	1	NUM
ap-2021	85	20	)	)	PUNCT
ap-2021	85	21	and	and	CCONJ
ap-2021	85	22	its	its	PRON
ap-2021	85	23	decomposition	decomposition	NOUN
ap-2021	85	24	.	.	PUNCT
ap-2021	86	1	the	the	DET
ap-2021	86	2	zero	zero	NUM
ap-2021	86	3	dynamics	dynamic	NOUN
ap-2021	86	4	is	be	AUX
ap-2021	86	5	represented	represent	VERB
ap-2021	86	6	by	by	ADP
ap-2021	86	7	:	:	PUNCT
ap-2021	86	8	[	[	PUNCT
ap-2021	86	9	ϕ1	ϕ1	NOUN
ap-2021	86	10	ϕ2	ϕ2	ADV
ap-2021	86	11	]	]	PUNCT
ap-2021	86	12	=	=	PUNCT
ap-2021	87	1	m−1	m−1	PROPN
ap-2021	87	2	zz	zz	PROPN
ap-2021	87	3	(	(	PUNCT
ap-2021	87	4	fz	fz	NOUN
ap-2021	87	5	−mzmw	−mzmw	NOUN
ap-2021	87	6	)	)	PUNCT
ap-2021	87	7	.	.	PUNCT
ap-2021	88	1	(	(	PUNCT
ap-2021	88	2	3	3	X
ap-2021	88	3	)	)	PUNCT
ap-2021	88	4	the	the	DET
ap-2021	88	5	expression	expression	NOUN
ap-2021	88	6	for	for	ADP
ap-2021	88	7	actuator	actuator	NOUN
ap-2021	88	8	u	u	PROPN
ap-2021	88	9	is	be	AUX
ap-2021	88	10	derived	derive	VERB
ap-2021	88	11	by	by	ADP
ap-2021	88	12	decomposing	decompose	VERB
ap-2021	88	13	equations	equation	NOUN
ap-2021	88	14	(	(	PUNCT
ap-2021	88	15	2	2	NUM
ap-2021	88	16	)	)	PUNCT
ap-2021	88	17	and	and	CCONJ
ap-2021	88	18	(	(	PUNCT
ap-2021	88	19	3	3	NUM
ap-2021	88	20	):	):	PUNCT
ap-2021	88	21	u(t	u(t	NOUN
ap-2021	88	22	)	)	PUNCT
ap-2021	89	1	=	=	SYM
ap-2021	89	2	fm	fm	PROPN
ap-2021	89	3	−mmzm	−mmzm	PUNCT
ap-2021	89	4	−1	−1	NOUN
ap-2021	89	5	zz	zz	PROPN
ap-2021	89	6	fz	fz	INTJ
ap-2021	89	7	−	−	PROPN
ap-2021	90	1	(	(	PUNCT
ap-2021	90	2	mmm	mmm	INTJ
ap-2021	90	3	−mmzm	−mmzm	PUNCT
ap-2021	90	4	−1	−1	NOUN
ap-2021	90	5	zz	zz	PROPN
ap-2021	90	6	mzm)w	mzm)w	PROPN
ap-2021	90	7	.	.	PUNCT
ap-2021	91	1	(	(	PUNCT
ap-2021	91	2	4	4	X
ap-2021	91	3	)	)	PUNCT
ap-2021	91	4	the	the	DET
ap-2021	91	5	singular	singular	ADJ
ap-2021	91	6	positions	position	NOUN
ap-2021	91	7	of	of	ADP
ap-2021	91	8	the	the	DET
ap-2021	91	9	system	system	NOUN
ap-2021	91	10	are	be	AUX
ap-2021	91	11	for	for	ADP
ap-2021	91	12	ϕ1	ϕ1	NOUN
ap-2021	91	13	=	=	SYM
ap-2021	91	14	±π/2	±π/2	NOUN
ap-2021	91	15	,	,	PUNCT
ap-2021	91	16	ϕ2	ϕ2	ADV
ap-2021	91	17	=	=	SYM
ap-2021	91	18	±π/2	±π/2	NOUN
ap-2021	91	19	,	,	PUNCT
ap-2021	91	20	and	and	CCONJ
ap-2021	91	21	other	other	ADJ
ap-2021	91	22	states	state	NOUN
ap-2021	91	23	(	(	PUNCT
ap-2021	91	24	velocities	velocity	NOUN
ap-2021	91	25	)	)	PUNCT
ap-2021	91	26	zero	zero	NUM
ap-2021	91	27	.	.	PUNCT
ap-2021	92	1	then	then	ADV
ap-2021	92	2	mzm	mzm	ADV
ap-2021	92	3	=	=	PUNCT
ap-2021	92	4	0	0	X
ap-2021	92	5	.	.	PUNCT
ap-2021	93	1	the	the	DET
ap-2021	93	2	system	system	NOUN
ap-2021	93	3	of	of	ADP
ap-2021	93	4	equations	equation	NOUN
ap-2021	93	5	(	(	PUNCT
ap-2021	93	6	2)–(3	2)–(3	NUM
ap-2021	93	7	)	)	PUNCT
ap-2021	93	8	then	then	ADV
ap-2021	93	9	takes	take	VERB
ap-2021	93	10	the	the	DET
ap-2021	93	11	following	follow	VERB
ap-2021	93	12	form	form	NOUN
ap-2021	93	13	with	with	ADP
ap-2021	93	14	zero	zero	NUM
ap-2021	93	15	velocity	velocity	NOUN
ap-2021	93	16	terms	term	NOUN
ap-2021	93	17	:	:	PUNCT
ap-2021	93	18	ẍ	ẍ	X
ap-2021	93	19	=	=	SYM
ap-2021	93	20	w	w	PROPN
ap-2021	93	21	,	,	PUNCT
ap-2021	93	22	[	[	PUNCT
ap-2021	93	23	ϕ1	ϕ1	NOUN
ap-2021	93	24	ϕ2	ϕ2	ADV
ap-2021	93	25	]	]	PUNCT
ap-2021	93	26	=	=	PUNCT
ap-2021	93	27	m−1	m−1	PROPN
ap-2021	93	28	zz	zz	NUM
ap-2021	93	29	fz	fz	PROPN
ap-2021	93	30	,	,	PUNCT
ap-2021	93	31	(	(	PUNCT
ap-2021	93	32	5	5	NUM
ap-2021	93	33	)	)	PUNCT
ap-2021	93	34	where	where	SCONJ
ap-2021	93	35	the	the	DET
ap-2021	93	36	control	control	NOUN
ap-2021	93	37	variable	variable	NOUN
ap-2021	93	38	can	can	AUX
ap-2021	93	39	not	not	PART
ap-2021	93	40	influence	influence	VERB
ap-2021	93	41	coordinates	coordinate	NOUN
ap-2021	93	42	ϕ1	ϕ1	NOUN
ap-2021	93	43	and	and	CCONJ
ap-2021	93	44	ϕ2	ϕ2	ADV
ap-2021	93	45	and	and	CCONJ
ap-2021	93	46	the	the	DET
ap-2021	93	47	system	system	NOUN
ap-2021	93	48	can	can	AUX
ap-2021	93	49	not	not	PART
ap-2021	93	50	be	be	AUX
ap-2021	93	51	controlled	control	VERB
ap-2021	93	52	.	.	PUNCT
ap-2021	94	1	4	4	X
ap-2021	94	2	.	.	X
ap-2021	94	3	how	how	SCONJ
ap-2021	94	4	to	to	PART
ap-2021	94	5	get	get	VERB
ap-2021	94	6	new	new	ADJ
ap-2021	94	7	input	input	NOUN
ap-2021	94	8	w	w	ADP
ap-2021	94	9	the	the	DET
ap-2021	94	10	problem	problem	NOUN
ap-2021	94	11	of	of	ADP
ap-2021	94	12	how	how	SCONJ
ap-2021	94	13	to	to	PART
ap-2021	94	14	get	get	VERB
ap-2021	94	15	a	a	DET
ap-2021	94	16	new	new	ADJ
ap-2021	94	17	input	input	NOUN
ap-2021	94	18	w	w	NOUN
ap-2021	94	19	to	to	PART
ap-2021	94	20	ensure	ensure	VERB
ap-2021	94	21	that	that	SCONJ
ap-2021	94	22	qz	qz	PROPN
ap-2021	94	23	ends	end	VERB
ap-2021	94	24	in	in	ADP
ap-2021	94	25	the	the	DET
ap-2021	94	26	desired	desire	VERB
ap-2021	94	27	position	position	NOUN
ap-2021	94	28	together	together	ADV
ap-2021	94	29	with	with	ADP
ap-2021	94	30	qm	qm	PROPN
ap-2021	94	31	has	have	AUX
ap-2021	94	32	been	be	AUX
ap-2021	94	33	addressed	address	VERB
ap-2021	94	34	in	in	ADP
ap-2021	94	35	[	[	X
ap-2021	94	36	13	13	NUM
ap-2021	94	37	]	]	PUNCT
ap-2021	94	38	.	.	PUNCT
ap-2021	95	1	it	it	PRON
ap-2021	95	2	is	be	AUX
ap-2021	95	3	easy	easy	ADJ
ap-2021	95	4	to	to	PART
ap-2021	95	5	find	find	VERB
ap-2021	95	6	such	such	ADJ
ap-2021	95	7	w	w	NOUN
ap-2021	95	8	,	,	PUNCT
ap-2021	95	9	which	which	PRON
ap-2021	95	10	controls	control	VERB
ap-2021	95	11	qm	qm	PROPN
ap-2021	95	12	,	,	PUNCT
ap-2021	95	13	but	but	CCONJ
ap-2021	95	14	it	it	PRON
ap-2021	95	15	is	be	AUX
ap-2021	95	16	not	not	PART
ap-2021	95	17	easy	easy	ADJ
ap-2021	95	18	to	to	PART
ap-2021	95	19	find	find	VERB
ap-2021	95	20	such	such	ADJ
ap-2021	95	21	w	w	ADP
ap-2021	95	22	which	which	PRON
ap-2021	95	23	simultaneously	simultaneously	ADV
ap-2021	95	24	controls	control	VERB
ap-2021	95	25	qm	qm	PROPN
ap-2021	95	26	and	and	CCONJ
ap-2021	95	27	qz	qz	PROPN
ap-2021	95	28	.	.	PUNCT
ap-2021	96	1	the	the	DET
ap-2021	96	2	new	new	ADJ
ap-2021	96	3	input	input	NOUN
ap-2021	96	4	w	w	NOUN
ap-2021	96	5	contains	contain	VERB
ap-2021	96	6	two	two	NUM
ap-2021	96	7	parts	part	NOUN
ap-2021	96	8	according	accord	VERB
ap-2021	96	9	to	to	ADP
ap-2021	96	10	[	[	X
ap-2021	96	11	12	12	NUM
ap-2021	96	12	]	]	PUNCT
ap-2021	96	13	.	.	PUNCT
ap-2021	97	1	it	it	PRON
ap-2021	97	2	consists	consist	VERB
ap-2021	97	3	of	of	ADP
ap-2021	97	4	the	the	DET
ap-2021	97	5	active	active	ADJ
ap-2021	97	6	part	part	NOUN
ap-2021	97	7	wa	wa	PROPN
ap-2021	97	8	,	,	PUNCT
ap-2021	97	9	which	which	PRON
ap-2021	97	10	moves	move	VERB
ap-2021	97	11	the	the	DET
ap-2021	97	12	qm	qm	PROPN
ap-2021	97	13	coordinates	coordinate	NOUN
ap-2021	97	14	from	from	ADP
ap-2021	97	15	the	the	DET
ap-2021	97	16	initial	initial	ADJ
ap-2021	97	17	position	position	NOUN
ap-2021	97	18	qm(0	qm(0	NOUN
ap-2021	97	19	)	)	PUNCT
ap-2021	97	20	to	to	ADP
ap-2021	97	21	the	the	DET
ap-2021	97	22	desired	desire	VERB
ap-2021	97	23	final	final	ADJ
ap-2021	97	24	position	position	NOUN
ap-2021	97	25	qmd(t	qmd(t	PROPN
ap-2021	97	26	)	)	PUNCT
ap-2021	97	27	in	in	ADP
ap-2021	97	28	some	some	DET
ap-2021	97	29	chosen	choose	VERB
ap-2021	97	30	time	time	NOUN
ap-2021	97	31	t	t	PROPN
ap-2021	97	32	from	from	ADP
ap-2021	97	33	equation	equation	NOUN
ap-2021	97	34	(	(	PUNCT
ap-2021	97	35	2	2	NUM
ap-2021	97	36	)	)	PUNCT
ap-2021	97	37	,	,	PUNCT
ap-2021	97	38	and	and	CCONJ
ap-2021	97	39	the	the	DET
ap-2021	97	40	invariant	invariant	ADJ
ap-2021	97	41	part	part	NOUN
ap-2021	97	42	wi	wi	PROPN
ap-2021	97	43	which	which	PRON
ap-2021	97	44	is	be	AUX
ap-2021	97	45	invariant	invariant	ADJ
ap-2021	97	46	to	to	ADP
ap-2021	97	47	the	the	DET
ap-2021	97	48	final	final	ADJ
ap-2021	97	49	position	position	NOUN
ap-2021	97	50	of	of	ADP
ap-2021	97	51	the	the	DET
ap-2021	97	52	motion	motion	NOUN
ap-2021	97	53	of	of	ADP
ap-2021	97	54	qm	qm	PROPN
ap-2021	97	55	,	,	PUNCT
ap-2021	97	56	but	but	CCONJ
ap-2021	97	57	due	due	ADP
ap-2021	97	58	to	to	ADP
ap-2021	97	59	the	the	DET
ap-2021	97	60	dynamic	dynamic	ADJ
ap-2021	97	61	connection	connection	NOUN
ap-2021	97	62	through	through	ADP
ap-2021	97	63	zero	zero	NUM
ap-2021	97	64	dynamics	dynamic	NOUN
ap-2021	97	65	influences	influence	VERB
ap-2021	97	66	qz	qz	NOUN
ap-2021	97	67	in	in	ADP
ap-2021	97	68	a	a	DET
ap-2021	97	69	way	way	NOUN
ap-2021	97	70	that	that	PRON
ap-2021	97	71	moves	move	VERB
ap-2021	97	72	qz	qz	NOUN
ap-2021	97	73	from	from	ADP
ap-2021	97	74	the	the	DET
ap-2021	97	75	initial	initial	ADJ
ap-2021	97	76	position	position	NOUN
ap-2021	97	77	qz(0	qz(0	NOUN
ap-2021	97	78	)	)	PUNCT
ap-2021	97	79	to	to	ADP
ap-2021	97	80	the	the	DET
ap-2021	97	81	desired	desire	VERB
ap-2021	97	82	final	final	ADJ
ap-2021	97	83	position	position	NOUN
ap-2021	97	84	qzd(t	qzd(t	PROPN
ap-2021	97	85	)	)	PUNCT
ap-2021	97	86	in	in	ADP
ap-2021	97	87	time	time	NOUN
ap-2021	97	88	t	t	NOUN
ap-2021	97	89	:	:	PUNCT
ap-2021	97	90	w	w	X
ap-2021	97	91	=	=	PUNCT
ap-2021	97	92	wa	wa	PROPN
ap-2021	97	93	+	+	X
ap-2021	97	94	wi	wi	PROPN
ap-2021	97	95	.	.	PUNCT
ap-2021	98	1	(	(	PUNCT
ap-2021	98	2	6	6	X
ap-2021	98	3	)	)	PUNCT
ap-2021	98	4	the	the	DET
ap-2021	98	5	invariant	invariant	ADJ
ap-2021	98	6	wi	wi	PROPN
ap-2021	98	7	is	be	AUX
ap-2021	98	8	such	such	ADJ
ap-2021	98	9	that∫	that∫	NOUN
ap-2021	98	10	t	t	NOUN
ap-2021	98	11	0	0	NUM
ap-2021	99	1	wi	wi	PROPN
ap-2021	99	2	dt	dt	PROPN
ap-2021	100	1	=	=	SYM
ap-2021	100	2	0	0	NUM
ap-2021	100	3	and	and	CCONJ
ap-2021	100	4	∫	∫	PROPN
ap-2021	101	1	t	t	PROPN
ap-2021	101	2	0	0	NUM
ap-2021	101	3	∫	∫	PROPN
ap-2021	101	4	t	t	PROPN
ap-2021	101	5	0	0	NUM
ap-2021	102	1	wi	wi	PROPN
ap-2021	102	2	dt	dt	X
ap-2021	103	1	dt	dt	PROPN
ap-2021	103	2	=	=	PUNCT
ap-2021	104	1	0	0	PROPN
ap-2021	104	2	.	.	PUNCT
ap-2021	105	1	(	(	PUNCT
ap-2021	105	2	7	7	X
ap-2021	105	3	)	)	PUNCT
ap-2021	105	4	in	in	ADP
ap-2021	105	5	our	our	PRON
ap-2021	105	6	case	case	NOUN
ap-2021	105	7	,	,	PUNCT
ap-2021	105	8	due	due	ADP
ap-2021	105	9	to	to	ADP
ap-2021	105	10	conditions	condition	NOUN
ap-2021	105	11	(	(	PUNCT
ap-2021	105	12	7	7	X
ap-2021	105	13	)	)	PUNCT
ap-2021	105	14	the	the	DET
ap-2021	105	15	motion	motion	NOUN
ap-2021	105	16	of	of	ADP
ap-2021	105	17	x	x	PUNCT
ap-2021	105	18	in	in	ADP
ap-2021	105	19	the	the	DET
ap-2021	105	20	final	final	ADJ
ap-2021	105	21	velocity	velocity	NOUN
ap-2021	105	22	and	and	CCONJ
ap-2021	105	23	position	position	NOUN
ap-2021	105	24	is	be	AUX
ap-2021	105	25	influenced	influence	VERB
ap-2021	105	26	only	only	ADV
ap-2021	105	27	by	by	ADP
ap-2021	105	28	the	the	DET
ap-2021	105	29	active	active	ADJ
ap-2021	105	30	part	part	NOUN
ap-2021	105	31	wa	wa	NOUN
ap-2021	105	32	of	of	ADP
ap-2021	105	33	the	the	DET
ap-2021	105	34	control	control	NOUN
ap-2021	105	35	(	(	PUNCT
ap-2021	105	36	6	6	NUM
ap-2021	105	37	)	)	PUNCT
ap-2021	105	38	.	.	PUNCT
ap-2021	106	1	this	this	DET
ap-2021	106	2	control	control	NOUN
ap-2021	106	3	is	be	AUX
ap-2021	106	4	chosen	choose	VERB
ap-2021	106	5	arbitrarily	arbitrarily	ADV
ap-2021	106	6	just	just	ADV
ap-2021	106	7	to	to	PART
ap-2021	106	8	fulfil	fulfil	VERB
ap-2021	106	9	the	the	DET
ap-2021	106	10	desired	desire	VERB
ap-2021	106	11	final	final	ADJ
ap-2021	106	12	values	value	NOUN
ap-2021	106	13	for	for	ADP
ap-2021	106	14	the	the	DET
ap-2021	106	15	position	position	NOUN
ap-2021	106	16	and	and	CCONJ
ap-2021	106	17	velocity	velocity	NOUN
ap-2021	106	18	of	of	ADP
ap-2021	106	19	x.	x.	NOUN
ap-2021	106	20	when	when	SCONJ
ap-2021	106	21	the	the	DET
ap-2021	106	22	active	active	ADJ
ap-2021	106	23	part	part	NOUN
ap-2021	106	24	wa	wa	ADJ
ap-2021	106	25	is	be	AUX
ap-2021	106	26	chosen	choose	VERB
ap-2021	106	27	,	,	PUNCT
ap-2021	106	28	it	it	PRON
ap-2021	106	29	is	be	AUX
ap-2021	106	30	a	a	DET
ap-2021	106	31	given	give	VERB
ap-2021	106	32	function	function	NOUN
ap-2021	106	33	of	of	ADP
ap-2021	106	34	time	time	NOUN
ap-2021	106	35	wa(t	wa(t	NOUN
ap-2021	106	36	)	)	PUNCT
ap-2021	106	37	,	,	PUNCT
ap-2021	106	38	and	and	CCONJ
ap-2021	106	39	substitution	substitution	NOUN
ap-2021	106	40	of	of	ADP
ap-2021	106	41	(	(	PUNCT
ap-2021	106	42	6	6	NUM
ap-2021	106	43	)	)	PUNCT
ap-2021	106	44	into	into	ADP
ap-2021	106	45	(	(	PUNCT
ap-2021	106	46	3	3	X
ap-2021	106	47	)	)	PUNCT
ap-2021	106	48	results	result	NOUN
ap-2021	106	49	in	in	ADP
ap-2021	106	50	[	[	PUNCT
ap-2021	106	51	ϕ1	ϕ1	NOUN
ap-2021	106	52	ϕ2	ϕ2	ADV
ap-2021	106	53	]	]	PUNCT
ap-2021	107	1	=	=	PUNCT
ap-2021	107	2	m−1	m−1	PROPN
ap-2021	107	3	zz	zz	PROPN
ap-2021	107	4	(	(	PUNCT
ap-2021	107	5	fz	fz	INTJ
ap-2021	107	6	−mzm(wa(t	−mzm(wa(t	NOUN
ap-2021	107	7	)	)	PUNCT
ap-2021	108	1	+	+	CCONJ
ap-2021	108	2	wi	wi	PROPN
ap-2021	108	3	)	)	PUNCT
ap-2021	108	4	)	)	PUNCT
ap-2021	109	1	(	(	PUNCT
ap-2021	109	2	8)	8)	NUM
ap-2021	109	3	now	now	ADV
ap-2021	109	4	the	the	DET
ap-2021	109	5	motion	motion	NOUN
ap-2021	109	6	of	of	ADP
ap-2021	109	7	ϕ1	ϕ1	NOUN
ap-2021	109	8	and	and	CCONJ
ap-2021	109	9	ϕ2	ϕ2	ADV
ap-2021	109	10	can	can	AUX
ap-2021	109	11	be	be	AUX
ap-2021	109	12	controlled	control	VERB
ap-2021	109	13	by	by	ADP
ap-2021	109	14	the	the	DET
ap-2021	109	15	choice	choice	NOUN
ap-2021	109	16	of	of	ADP
ap-2021	109	17	wi	wi	PROPN
ap-2021	109	18	just	just	ADV
ap-2021	109	19	fulfilling	fulfil	VERB
ap-2021	109	20	the	the	DET
ap-2021	109	21	conditions	condition	NOUN
ap-2021	109	22	(	(	PUNCT
ap-2021	109	23	7	7	NUM
ap-2021	109	24	)	)	PUNCT
ap-2021	109	25	.	.	PUNCT
ap-2021	110	1	for	for	ADP
ap-2021	110	2	invariant	invariant	ADJ
ap-2021	110	3	motion	motion	NOUN
ap-2021	110	4	,	,	PUNCT
ap-2021	110	5	use	use	NOUN
ap-2021	110	6	is	be	AUX
ap-2021	110	7	made	make	VERB
ap-2021	110	8	of	of	ADP
ap-2021	110	9	so	so	ADV
ap-2021	110	10	-	-	PUNCT
ap-2021	110	11	called	call	VERB
ap-2021	110	12	natural	natural	ADJ
ap-2021	110	13	motions	motion	NOUN
ap-2021	110	14	and	and	CCONJ
ap-2021	110	15	their	their	PRON
ap-2021	110	16	frequencies	frequency	NOUN
ap-2021	110	17	fi	fi	NOUN
ap-2021	110	18	,	,	PUNCT
ap-2021	110	19	wi	wi	PROPN
ap-2021	110	20	=	=	PUNCT
ap-2021	111	1	∑	∑	PROPN
ap-2021	111	2	i	i	PRON
ap-2021	111	3	ai	ai	VERB
ap-2021	111	4	sin(2πfit+	sin(2πfit+	PROPN
ap-2021	111	5	ϕi	ϕi	ADP
ap-2021	111	6	)	)	PUNCT
ap-2021	111	7	,	,	PUNCT
ap-2021	111	8	(	(	PUNCT
ap-2021	111	9	9	9	X
ap-2021	111	10	)	)	PUNCT
ap-2021	111	11	where	where	SCONJ
ap-2021	111	12	amplitudes	amplitude	NOUN
ap-2021	111	13	ai	ai	VERB
ap-2021	111	14	and	and	CCONJ
ap-2021	111	15	phases	phase	NOUN
ap-2021	111	16	ϕi	ϕi	ADP
ap-2021	111	17	are	be	AUX
ap-2021	111	18	some	some	DET
ap-2021	111	19	constants	constant	NOUN
ap-2021	111	20	as	as	ADP
ap-2021	111	21	a	a	DET
ap-2021	111	22	result	result	NOUN
ap-2021	111	23	of	of	ADP
ap-2021	111	24	optimization	optimization	NOUN
ap-2021	111	25	.	.	PUNCT
ap-2021	112	1	the	the	DET
ap-2021	112	2	frequencies	frequency	NOUN
ap-2021	112	3	fi	fi	NOUN
ap-2021	112	4	are	be	AUX
ap-2021	112	5	chosen	choose	VERB
ap-2021	112	6	and	and	CCONJ
ap-2021	112	7	the	the	DET
ap-2021	112	8	amplitudes	amplitude	NOUN
ap-2021	112	9	ai	ai	VERB
ap-2021	112	10	and	and	CCONJ
ap-2021	112	11	phases	phase	NOUN
ap-2021	112	12	ϕi	ϕi	ADP
ap-2021	112	13	are	be	AUX
ap-2021	112	14	optimized	optimize	VERB
ap-2021	112	15	for	for	ADP
ap-2021	112	16	coordinates	coordinate	NOUN
ap-2021	112	17	ϕ1	ϕ1	NOUN
ap-2021	112	18	and	and	CCONJ
ap-2021	112	19	ϕ2	ϕ2	ADV
ap-2021	112	20	to	to	PART
ap-2021	112	21	reach	reach	VERB
ap-2021	112	22	the	the	DET
ap-2021	112	23	desired	desire	VERB
ap-2021	112	24	position	position	NOUN
ap-2021	112	25	and	and	CCONJ
ap-2021	112	26	velocity	velocity	NOUN
ap-2021	112	27	at	at	ADP
ap-2021	112	28	the	the	DET
ap-2021	112	29	chosen	choose	VERB
ap-2021	112	30	settling	settling	NOUN
ap-2021	112	31	time	time	NOUN
ap-2021	112	32	t	t	PROPN
ap-2021	112	33	.	.	PUNCT
ap-2021	113	1	if	if	SCONJ
ap-2021	113	2	it	it	PRON
ap-2021	113	3	holds	hold	VERB
ap-2021	113	4	2πfit	2πfit	PROPN
ap-2021	113	5	=	=	SYM
ap-2021	113	6	2kiπ	2kiπ	NUM
ap-2021	113	7	(	(	PUNCT
ap-2021	113	8	10	10	NUM
ap-2021	113	9	)	)	PUNCT
ap-2021	113	10	for	for	ADP
ap-2021	113	11	some	some	DET
ap-2021	113	12	natural	natural	ADJ
ap-2021	113	13	number	number	NOUN
ap-2021	113	14	ki	ki	PROPN
ap-2021	113	15	,	,	PUNCT
ap-2021	113	16	then	then	ADV
ap-2021	113	17	functions	function	NOUN
ap-2021	113	18	(	(	PUNCT
ap-2021	113	19	9	9	NUM
ap-2021	113	20	)	)	PUNCT
ap-2021	113	21	satisfy	satisfy	NOUN
ap-2021	113	22	conditions	condition	NOUN
ap-2021	113	23	(	(	PUNCT
ap-2021	113	24	7	7	NUM
ap-2021	113	25	)	)	PUNCT
ap-2021	113	26	.	.	PUNCT
ap-2021	114	1	how	how	SCONJ
ap-2021	114	2	to	to	PART
ap-2021	114	3	determine	determine	VERB
ap-2021	114	4	suitable	suitable	ADJ
ap-2021	114	5	frequencies	frequency	NOUN
ap-2021	114	6	is	be	AUX
ap-2021	114	7	explained	explain	VERB
ap-2021	114	8	in	in	ADP
ap-2021	114	9	the	the	DET
ap-2021	114	10	next	next	ADJ
ap-2021	114	11	section	section	NOUN
ap-2021	114	12	.	.	PUNCT
ap-2021	115	1	5	5	X
ap-2021	115	2	.	.	X
ap-2021	115	3	simulation	simulation	NOUN
ap-2021	115	4	of	of	ADP
ap-2021	115	5	the	the	DET
ap-2021	115	6	natural	natural	ADJ
ap-2021	115	7	motion	motion	NOUN
ap-2021	115	8	during	during	ADP
ap-2021	115	9	the	the	DET
ap-2021	115	10	simulation	simulation	NOUN
ap-2021	115	11	all	all	DET
ap-2021	115	12	states	state	NOUN
ap-2021	115	13	are	be	AUX
ap-2021	115	14	recorded	record	VERB
ap-2021	115	15	.	.	PUNCT
ap-2021	116	1	fourier	fouri	ADJ
ap-2021	116	2	analysis	analysis	NOUN
ap-2021	116	3	is	be	AUX
ap-2021	116	4	applied	apply	VERB
ap-2021	116	5	to	to	ADP
ap-2021	116	6	the	the	DET
ap-2021	116	7	recorded	record	VERB
ap-2021	116	8	states	state	NOUN
ap-2021	116	9	in	in	ADP
ap-2021	116	10	order	order	NOUN
ap-2021	116	11	to	to	PART
ap-2021	116	12	determine	determine	VERB
ap-2021	116	13	the	the	DET
ap-2021	116	14	eigenfrequencies	eigenfrequencie	NOUN
ap-2021	116	15	of	of	ADP
ap-2021	116	16	the	the	DET
ap-2021	116	17	considered	considered	ADJ
ap-2021	116	18	nonlinear	nonlinear	ADJ
ap-2021	116	19	system	system	NOUN
ap-2021	116	20	.	.	PUNCT
ap-2021	117	1	the	the	DET
ap-2021	117	2	feedforward	feedforward	NOUN
ap-2021	117	3	control	control	NOUN
ap-2021	117	4	is	be	AUX
ap-2021	117	5	constructed	construct	VERB
ap-2021	117	6	885	885	NUM
ap-2021	117	7	z.	z.	PROPN
ap-2021	117	8	neusser	neusser	PROPN
ap-2021	117	9	,	,	PUNCT
ap-2021	117	10	m.	m.	NOUN
ap-2021	117	11	valášek	valášek	VERB
ap-2021	117	12	acta	acta	PROPN
ap-2021	117	13	polytechnica	polytechnica	PROPN
ap-2021	117	14	−2	−2	PROPN
ap-2021	117	15	−1.5	−1.5	PROPN
ap-2021	117	16	−1	−1	NOUN
ap-2021	118	1	−0.5	−0.5	NOUN
ap-2021	118	2	0	0	NUM
ap-2021	118	3	0.5	0.5	NUM
ap-2021	118	4	1	1	NUM
ap-2021	118	5	1.5	1.5	NUM
ap-2021	118	6	2	2	NUM
ap-2021	118	7	−2	−2	NOUN
ap-2021	118	8	−1.5	−1.5	NOUN
ap-2021	118	9	−1	−1	NOUN
ap-2021	118	10	−0.5	−0.5	NOUN
ap-2021	118	11	0	0	NUM
ap-2021	118	12	0.5	0.5	NUM
ap-2021	118	13	1	1	NUM
ap-2021	118	14	1.5	1.5	NUM
ap-2021	118	15	2	2	NUM
ap-2021	118	16	x	x	SYM
ap-2021	119	1	[	[	X
ap-2021	119	2	m	m	X
ap-2021	119	3	]	]	X
ap-2021	119	4	y	y	PROPN
ap-2021	120	1	[	[	X
ap-2021	120	2	m	m	X
ap-2021	120	3	]	]	X
ap-2021	120	4	cart	cart	NOUN
ap-2021	120	5	motion	motion	NOUN
ap-2021	120	6	end	end	NOUN
ap-2021	120	7	of	of	ADP
ap-2021	120	8	the	the	DET
ap-2021	120	9	first	first	ADJ
ap-2021	120	10	link	link	NOUN
ap-2021	120	11	end	end	NOUN
ap-2021	120	12	of	of	ADP
ap-2021	120	13	the	the	DET
ap-2021	120	14	second	second	ADJ
ap-2021	120	15	link	link	NOUN
ap-2021	120	16	figure	figure	NOUN
ap-2021	120	17	3	3	NUM
ap-2021	120	18	.	.	PUNCT
ap-2021	120	19	motion	motion	NOUN
ap-2021	120	20	of	of	ADP
ap-2021	120	21	the	the	DET
ap-2021	120	22	double	double	ADJ
ap-2021	120	23	pendulum	pendulum	NOUN
ap-2021	120	24	on	on	ADP
ap-2021	120	25	a	a	DET
ap-2021	120	26	cart	cart	NOUN
ap-2021	120	27	from	from	ADP
ap-2021	120	28	its	its	PRON
ap-2021	120	29	upper	upper	ADJ
ap-2021	120	30	position	position	NOUN
ap-2021	120	31	into	into	ADP
ap-2021	120	32	the	the	DET
ap-2021	120	33	bottom	bottom	ADJ
ap-2021	120	34	position	position	NOUN
ap-2021	120	35	with	with	ADP
ap-2021	120	36	the	the	DET
ap-2021	120	37	damping	damp	VERB
ap-2021	120	38	force	force	NOUN
ap-2021	120	39	between	between	ADP
ap-2021	120	40	the	the	DET
ap-2021	120	41	cart	cart	NOUN
ap-2021	120	42	and	and	CCONJ
ap-2021	120	43	the	the	DET
ap-2021	120	44	base	base	NOUN
ap-2021	120	45	frame	frame	NOUN
ap-2021	120	46	.	.	PUNCT
ap-2021	121	1	using	use	VERB
ap-2021	121	2	these	these	DET
ap-2021	121	3	eigenfrequencies	eigenfrequencie	NOUN
ap-2021	121	4	and	and	CCONJ
ap-2021	121	5	from	from	ADP
ap-2021	121	6	equations	equation	NOUN
ap-2021	121	7	(	(	PUNCT
ap-2021	121	8	4	4	NUM
ap-2021	121	9	)	)	PUNCT
ap-2021	121	10	,	,	PUNCT
ap-2021	121	11	(	(	PUNCT
ap-2021	121	12	6	6	NUM
ap-2021	121	13	)	)	PUNCT
ap-2021	121	14	and	and	CCONJ
ap-2021	121	15	(	(	PUNCT
ap-2021	121	16	9	9	NUM
ap-2021	121	17	)	)	PUNCT
ap-2021	121	18	.	.	PUNCT
ap-2021	122	1	the	the	DET
ap-2021	122	2	eigenfrequencies	eigenfrequencie	NOUN
ap-2021	122	3	of	of	ADP
ap-2021	122	4	the	the	DET
ap-2021	122	5	natural	natural	ADJ
ap-2021	122	6	motion	motion	NOUN
ap-2021	122	7	describe	describe	VERB
ap-2021	122	8	the	the	DET
ap-2021	122	9	vibrational	vibrational	ADJ
ap-2021	122	10	motion	motion	NOUN
ap-2021	122	11	of	of	ADP
ap-2021	122	12	variables	variable	NOUN
ap-2021	122	13	q	q	PROPN
ap-2021	122	14	that	that	PRON
ap-2021	122	15	ends	end	VERB
ap-2021	122	16	at	at	ADP
ap-2021	122	17	equilibrium	equilibrium	NOUN
ap-2021	122	18	,	,	PUNCT
ap-2021	122	19	where	where	SCONJ
ap-2021	122	20	all	all	DET
ap-2021	122	21	swings	swing	NOUN
ap-2021	122	22	meet	meet	VERB
ap-2021	122	23	at	at	ADP
ap-2021	122	24	the	the	DET
ap-2021	122	25	final	final	ADJ
ap-2021	122	26	time	time	NOUN
ap-2021	122	27	.	.	PUNCT
ap-2021	123	1	the	the	DET
ap-2021	123	2	conditions	condition	NOUN
ap-2021	123	3	(	(	PUNCT
ap-2021	123	4	10	10	NUM
ap-2021	123	5	)	)	PUNCT
ap-2021	123	6	are	be	AUX
ap-2021	123	7	therefore	therefore	ADV
ap-2021	123	8	satisfied	satisfied	ADJ
ap-2021	123	9	.	.	PUNCT
ap-2021	124	1	at	at	ADP
ap-2021	124	2	the	the	DET
ap-2021	124	3	same	same	ADJ
ap-2021	124	4	time	time	NOUN
ap-2021	124	5	,	,	PUNCT
ap-2021	124	6	the	the	DET
ap-2021	124	7	determined	determined	ADJ
ap-2021	124	8	eigenfrequencies	eigenfrequencie	NOUN
ap-2021	124	9	are	be	AUX
ap-2021	124	10	in	in	ADP
ap-2021	124	11	fact	fact	NOUN
ap-2021	124	12	rational	rational	ADJ
ap-2021	124	13	numbers	number	NOUN
ap-2021	124	14	,	,	PUNCT
ap-2021	124	15	and	and	CCONJ
ap-2021	124	16	the	the	DET
ap-2021	124	17	natural	natural	ADJ
ap-2021	124	18	numbers	number	NOUN
ap-2021	124	19	ki	ki	PROPN
ap-2021	124	20	at	at	ADP
ap-2021	124	21	the	the	DET
ap-2021	124	22	final	final	ADJ
ap-2021	124	23	time	time	NOUN
ap-2021	124	24	t	t	NOUN
ap-2021	124	25	for	for	ADP
ap-2021	124	26	any	any	DET
ap-2021	124	27	set	set	NOUN
ap-2021	124	28	of	of	ADP
ap-2021	124	29	eigenfrequencies	eigenfrequencie	NOUN
ap-2021	124	30	fi	fi	NOUN
ap-2021	124	31	therefore	therefore	ADV
ap-2021	124	32	exist	exist	VERB
ap-2021	124	33	.	.	PUNCT
ap-2021	125	1	finally	finally	ADV
ap-2021	125	2	,	,	PUNCT
ap-2021	125	3	the	the	DET
ap-2021	125	4	conditions	condition	NOUN
ap-2021	125	5	(	(	PUNCT
ap-2021	125	6	10	10	NUM
ap-2021	125	7	)	)	PUNCT
ap-2021	125	8	from	from	ADP
ap-2021	125	9	the	the	DET
ap-2021	125	10	natural	natural	ADJ
ap-2021	125	11	motion	motion	NOUN
ap-2021	125	12	are	be	AUX
ap-2021	125	13	to	to	PART
ap-2021	125	14	be	be	AUX
ap-2021	125	15	satisfied	satisfied	ADJ
ap-2021	125	16	just	just	ADV
ap-2021	125	17	approximately	approximately	ADV
ap-2021	125	18	in	in	ADP
ap-2021	125	19	order	order	NOUN
ap-2021	125	20	to	to	PART
ap-2021	125	21	move	move	VERB
ap-2021	125	22	the	the	DET
ap-2021	125	23	mechanical	mechanical	ADJ
ap-2021	125	24	system	system	NOUN
ap-2021	125	25	into	into	ADP
ap-2021	125	26	such	such	ADJ
ap-2021	125	27	vicinity	vicinity	NOUN
ap-2021	125	28	of	of	ADP
ap-2021	125	29	the	the	DET
ap-2021	125	30	upper	upper	ADJ
ap-2021	125	31	equilibrium	equilibrium	NOUN
ap-2021	125	32	that	that	PRON
ap-2021	125	33	the	the	DET
ap-2021	125	34	nqr	nqr	PROPN
ap-2021	125	35	control	control	NOUN
ap-2021	125	36	can	can	AUX
ap-2021	125	37	stabilize	stabilize	VERB
ap-2021	125	38	the	the	DET
ap-2021	125	39	motion	motion	NOUN
ap-2021	125	40	.	.	PUNCT
ap-2021	126	1	the	the	DET
ap-2021	126	2	excitation	excitation	NOUN
ap-2021	126	3	of	of	ADP
ap-2021	126	4	the	the	DET
ap-2021	126	5	system	system	NOUN
ap-2021	126	6	at	at	ADP
ap-2021	126	7	its	its	PRON
ap-2021	126	8	eigenfrequencies	eigenfrequencie	NOUN
ap-2021	126	9	enables	enable	VERB
ap-2021	126	10	large	large	ADJ
ap-2021	126	11	motion	motion	NOUN
ap-2021	126	12	of	of	ADP
ap-2021	126	13	the	the	DET
ap-2021	126	14	system	system	NOUN
ap-2021	126	15	to	to	PART
ap-2021	126	16	be	be	AUX
ap-2021	126	17	caused	cause	VERB
ap-2021	126	18	on	on	ADP
ap-2021	126	19	the	the	DET
ap-2021	126	20	basis	basis	NOUN
ap-2021	126	21	of	of	ADP
ap-2021	126	22	resonance	resonance	NOUN
ap-2021	126	23	.	.	PUNCT
ap-2021	127	1	the	the	DET
ap-2021	127	2	eigenfrequencies	eigenfrequencie	NOUN
ap-2021	127	3	allow	allow	VERB
ap-2021	127	4	the	the	DET
ap-2021	127	5	mechanism	mechanism	NOUN
ap-2021	127	6	to	to	PART
ap-2021	127	7	be	be	AUX
ap-2021	127	8	excited	excite	VERB
ap-2021	127	9	with	with	ADP
ap-2021	127	10	less	less	ADJ
ap-2021	127	11	input	input	NOUN
ap-2021	127	12	energy	energy	NOUN
ap-2021	127	13	than	than	ADP
ap-2021	127	14	other	other	ADJ
ap-2021	127	15	frequencies	frequency	NOUN
ap-2021	127	16	,	,	PUNCT
ap-2021	127	17	as	as	SCONJ
ap-2021	127	18	excitation	excitation	NOUN
ap-2021	127	19	by	by	ADP
ap-2021	127	20	eigenfrequencies	eigenfrequencie	NOUN
ap-2021	127	21	enables	enable	VERB
ap-2021	127	22	the	the	DET
ap-2021	127	23	energy	energy	NOUN
ap-2021	127	24	to	to	PART
ap-2021	127	25	be	be	AUX
ap-2021	127	26	accumulated	accumulate	VERB
ap-2021	127	27	in	in	ADP
ap-2021	127	28	the	the	DET
ap-2021	127	29	system	system	NOUN
ap-2021	127	30	.	.	PUNCT
ap-2021	128	1	the	the	DET
ap-2021	128	2	system	system	NOUN
ap-2021	128	3	is	be	AUX
ap-2021	128	4	nonlinear	nonlinear	ADJ
ap-2021	128	5	,	,	PUNCT
ap-2021	128	6	and	and	CCONJ
ap-2021	128	7	it	it	PRON
ap-2021	128	8	is	be	AUX
ap-2021	128	9	not	not	PART
ap-2021	128	10	easy	easy	ADJ
ap-2021	128	11	to	to	PART
ap-2021	128	12	determine	determine	VERB
ap-2021	128	13	the	the	DET
ap-2021	128	14	eigenfrequencies	eigenfrequencie	NOUN
ap-2021	128	15	.	.	PUNCT
ap-2021	129	1	the	the	DET
ap-2021	129	2	usage	usage	NOUN
ap-2021	129	3	of	of	ADP
ap-2021	129	4	natural	natural	ADJ
ap-2021	129	5	motion	motion	NOUN
ap-2021	129	6	is	be	AUX
ap-2021	129	7	therefore	therefore	ADV
ap-2021	129	8	helpful	helpful	ADJ
ap-2021	129	9	.	.	PUNCT
ap-2021	130	1	the	the	DET
ap-2021	130	2	following	follow	VERB
ap-2021	130	3	parameters	parameter	NOUN
ap-2021	130	4	are	be	AUX
ap-2021	130	5	used	use	VERB
ap-2021	130	6	for	for	ADP
ap-2021	130	7	the	the	DET
ap-2021	130	8	simulation	simulation	NOUN
ap-2021	130	9	:	:	PUNCT
ap-2021	130	10	the	the	DET
ap-2021	130	11	mass	mass	NOUN
ap-2021	130	12	of	of	ADP
ap-2021	130	13	the	the	DET
ap-2021	130	14	cart	cart	NOUN
ap-2021	130	15	is	be	AUX
ap-2021	130	16	1	1	NUM
ap-2021	130	17	kg	kg	NOUN
ap-2021	130	18	,	,	PUNCT
ap-2021	130	19	the	the	DET
ap-2021	130	20	mass	mass	NOUN
ap-2021	130	21	of	of	ADP
ap-2021	130	22	the	the	DET
ap-2021	130	23	first	first	ADJ
ap-2021	130	24	and	and	CCONJ
ap-2021	130	25	second	second	ADJ
ap-2021	130	26	link	link	NOUN
ap-2021	130	27	is	be	AUX
ap-2021	130	28	0.5	0.5	NUM
ap-2021	130	29	kg	kg	NOUN
ap-2021	130	30	,	,	PUNCT
ap-2021	130	31	their	their	PRON
ap-2021	130	32	moments	moment	NOUN
ap-2021	130	33	of	of	ADP
ap-2021	130	34	inertia	inertia	NOUN
ap-2021	130	35	are	be	AUX
ap-2021	130	36	0.0417	0.0417	NUM
ap-2021	130	37	kg	kg	NOUN
ap-2021	130	38	/	/	SYM
ap-2021	130	39	m2	m2	PROPN
ap-2021	130	40	,	,	PUNCT
ap-2021	130	41	and	and	CCONJ
ap-2021	130	42	the	the	DET
ap-2021	130	43	length	length	NOUN
ap-2021	130	44	of	of	ADP
ap-2021	130	45	each	each	DET
ap-2021	130	46	part	part	NOUN
ap-2021	130	47	is	be	AUX
ap-2021	130	48	1	1	NUM
ap-2021	130	49	m	m	NOUN
ap-2021	130	50	,	,	PUNCT
ap-2021	130	51	with	with	ADP
ap-2021	130	52	the	the	DET
ap-2021	130	53	center	center	NOUN
ap-2021	130	54	of	of	ADP
ap-2021	130	55	gravity	gravity	NOUN
ap-2021	130	56	in	in	ADP
ap-2021	130	57	the	the	DET
ap-2021	130	58	middle	middle	NOUN
ap-2021	130	59	of	of	ADP
ap-2021	130	60	each	each	DET
ap-2021	130	61	part	part	NOUN
ap-2021	130	62	.	.	PUNCT
ap-2021	131	1	the	the	DET
ap-2021	131	2	natural	natural	ADJ
ap-2021	131	3	motion	motion	NOUN
ap-2021	131	4	is	be	AUX
ap-2021	131	5	illustrated	illustrate	VERB
ap-2021	131	6	in	in	ADP
ap-2021	131	7	figure	figure	NOUN
ap-2021	131	8	3	3	NUM
ap-2021	131	9	.	.	PUNCT
ap-2021	132	1	the	the	DET
ap-2021	132	2	natural	natural	ADJ
ap-2021	132	3	motion	motion	NOUN
ap-2021	132	4	is	be	AUX
ap-2021	132	5	achieved	achieve	VERB
ap-2021	132	6	by	by	ADP
ap-2021	132	7	simulating	simulate	VERB
ap-2021	132	8	the	the	DET
ap-2021	132	9	equations	equation	NOUN
ap-2021	132	10	of	of	ADP
ap-2021	132	11	motion	motion	NOUN
ap-2021	132	12	(	(	PUNCT
ap-2021	132	13	1	1	NUM
ap-2021	132	14	)	)	PUNCT
ap-2021	132	15	with	with	ADP
ap-2021	132	16	zero	zero	NUM
ap-2021	132	17	control	control	NOUN
ap-2021	132	18	and	and	CCONJ
ap-2021	132	19	with	with	ADP
ap-2021	132	20	damping	damp	VERB
ap-2021	132	21	instead	instead	ADV
ap-2021	132	22	of	of	ADP
ap-2021	132	23	it	it	PRON
ap-2021	132	24	,	,	PUNCT
ap-2021	132	25	u(t	u(t	PROPN
ap-2021	132	26	)	)	PUNCT
ap-2021	132	27	=	=	PUNCT
ap-2021	133	1	−bx	−bx	NOUN
ap-2021	133	2	from	from	ADP
ap-2021	133	3	the	the	DET
ap-2021	133	4	upper	upper	ADJ
ap-2021	133	5	position	position	NOUN
ap-2021	133	6	to	to	ADP
ap-2021	133	7	the	the	DET
ap-2021	133	8	lower	low	ADJ
ap-2021	133	9	position	position	NOUN
ap-2021	133	10	.	.	PUNCT
ap-2021	134	1	the	the	DET
ap-2021	134	2	outer	outer	ADJ
ap-2021	134	3	dotted	dotted	ADJ
ap-2021	134	4	line	line	NOUN
ap-2021	134	5	represents	represent	VERB
ap-2021	134	6	the	the	DET
ap-2021	134	7	end	end	NOUN
ap-2021	134	8	point	point	NOUN
ap-2021	134	9	of	of	ADP
ap-2021	134	10	the	the	DET
ap-2021	134	11	second	second	ADJ
ap-2021	134	12	link	link	NOUN
ap-2021	134	13	,	,	PUNCT
ap-2021	134	14	the	the	DET
ap-2021	134	15	dashed	dash	VERB
ap-2021	134	16	line	line	NOUN
ap-2021	134	17	is	be	AUX
ap-2021	134	18	the	the	DET
ap-2021	134	19	trajectory	trajectory	NOUN
ap-2021	134	20	of	of	ADP
ap-2021	134	21	the	the	DET
ap-2021	134	22	joint	joint	NOUN
ap-2021	134	23	between	between	ADP
ap-2021	134	24	links	link	NOUN
ap-2021	134	25	,	,	PUNCT
ap-2021	134	26	and	and	CCONJ
ap-2021	134	27	the	the	DET
ap-2021	134	28	straight	straight	ADJ
ap-2021	134	29	line	line	NOUN
ap-2021	134	30	represents	represent	VERB
ap-2021	134	31	the	the	DET
ap-2021	134	32	cart	cart	NOUN
ap-2021	134	33	movements	movement	NOUN
ap-2021	134	34	.	.	PUNCT
ap-2021	135	1	it	it	PRON
ap-2021	135	2	starts	start	VERB
ap-2021	135	3	in	in	ADP
ap-2021	135	4	the	the	DET
ap-2021	135	5	upper	upper	ADJ
ap-2021	135	6	position	position	NOUN
ap-2021	135	7	with	with	ADP
ap-2021	135	8	a	a	DET
ap-2021	135	9	slight	slight	ADJ
ap-2021	135	10	deflection	deflection	NOUN
ap-2021	135	11	in	in	ADP
ap-2021	135	12	the	the	DET
ap-2021	135	13	first	first	ADJ
ap-2021	135	14	and	and	CCONJ
ap-2021	135	15	second	second	ADJ
ap-2021	135	16	angle	angle	NOUN
ap-2021	135	17	ϕ1	ϕ1	NOUN
ap-2021	135	18	,	,	PUNCT
ap-2021	135	19	ϕ2	ϕ2	ADV
ap-2021	135	20	and	and	CCONJ
ap-2021	135	21	zero	zero	NUM
ap-2021	135	22	velocities	velocity	NOUN
ap-2021	135	23	.	.	PUNCT
ap-2021	136	1	it	it	PRON
ap-2021	136	2	falls	fall	VERB
ap-2021	136	3	into	into	ADP
ap-2021	136	4	the	the	DET
ap-2021	136	5	bottom	bottom	ADJ
ap-2021	136	6	stable	stable	ADJ
ap-2021	136	7	position	position	NOUN
ap-2021	136	8	with	with	ADP
ap-2021	136	9	a	a	DET
ap-2021	136	10	quiescent	quiescent	ADJ
ap-2021	136	11	motion	motion	NOUN
ap-2021	136	12	.	.	PUNCT
ap-2021	137	1	this	this	DET
ap-2021	137	2	behavior	behavior	NOUN
ap-2021	137	3	is	be	AUX
ap-2021	137	4	caused	cause	VERB
ap-2021	137	5	by	by	ADP
ap-2021	137	6	the	the	DET
ap-2021	137	7	damping	damp	VERB
ap-2021	137	8	force	force	NOUN
ap-2021	137	9	acting	act	VERB
ap-2021	137	10	between	between	ADP
ap-2021	137	11	the	the	DET
ap-2021	137	12	cart	cart	NOUN
ap-2021	137	13	and	and	CCONJ
ap-2021	137	14	the	the	DET
ap-2021	137	15	base	base	NOUN
ap-2021	137	16	frame	frame	NOUN
ap-2021	137	17	,	,	PUNCT
ap-2021	137	18	where	where	SCONJ
ap-2021	137	19	the	the	DET
ap-2021	137	20	actuator	actuator	NOUN
ap-2021	137	21	is	be	AUX
ap-2021	137	22	later	later	ADV
ap-2021	137	23	placed	place	VERB
ap-2021	137	24	.	.	PUNCT
ap-2021	138	1	the	the	DET
ap-2021	138	2	damping	damp	VERB
ap-2021	138	3	coefficient	coefficient	NOUN
ap-2021	138	4	(	(	PUNCT
ap-2021	138	5	b	b	NOUN
ap-2021	138	6	=	=	SYM
ap-2021	138	7	11.92nms	11.92nms	NUM
ap-2021	138	8	/	/	SYM
ap-2021	138	9	rad	rad	NOUN
ap-2021	138	10	)	)	PUNCT
ap-2021	138	11	is	be	AUX
ap-2021	138	12	received	receive	VERB
ap-2021	138	13	by	by	ADP
ap-2021	138	14	the	the	DET
ap-2021	138	15	optimization	optimization	NOUN
ap-2021	138	16	with	with	ADP
ap-2021	138	17	respect	respect	NOUN
ap-2021	138	18	to	to	ADP
ap-2021	138	19	the	the	DET
ap-2021	138	20	settling	settling	NOUN
ap-2021	138	21	time	time	NOUN
ap-2021	138	22	.	.	PUNCT
ap-2021	139	1	the	the	DET
ap-2021	139	2	behaviors	behavior	NOUN
ap-2021	139	3	of	of	ADP
ap-2021	139	4	all	all	DET
ap-2021	139	5	states	state	NOUN
ap-2021	139	6	,	,	PUNCT
ap-2021	139	7	including	include	VERB
ap-2021	139	8	the	the	DET
ap-2021	139	9	accelerations	acceleration	NOUN
ap-2021	139	10	,	,	PUNCT
ap-2021	139	11	are	be	AUX
ap-2021	139	12	recorded	record	VERB
ap-2021	139	13	.	.	PUNCT
ap-2021	140	1	6	6	X
ap-2021	140	2	.	.	X
ap-2021	140	3	control	control	NOUN
ap-2021	140	4	design	design	VERB
ap-2021	140	5	the	the	DET
ap-2021	140	6	data	datum	NOUN
ap-2021	140	7	from	from	ADP
ap-2021	140	8	the	the	DET
ap-2021	140	9	natural	natural	ADJ
ap-2021	140	10	fall	fall	NOUN
ap-2021	140	11	motion	motion	NOUN
ap-2021	140	12	are	be	AUX
ap-2021	140	13	now	now	ADV
ap-2021	140	14	used	use	VERB
ap-2021	140	15	.	.	PUNCT
ap-2021	141	1	the	the	DET
ap-2021	141	2	first	first	ADJ
ap-2021	141	3	frequencies	frequency	NOUN
ap-2021	141	4	from	from	ADP
ap-2021	141	5	the	the	DET
ap-2021	141	6	angular	angular	ADJ
ap-2021	141	7	acceleration	acceleration	NOUN
ap-2021	141	8	of	of	ADP
ap-2021	141	9	the	the	DET
ap-2021	141	10	first	first	ADJ
ap-2021	141	11	and	and	CCONJ
ap-2021	141	12	the	the	DET
ap-2021	141	13	second	second	ADJ
ap-2021	141	14	link	link	NOUN
ap-2021	141	15	angular	angular	ADJ
ap-2021	141	16	acceleration	acceleration	NOUN
ap-2021	141	17	form	form	NOUN
ap-2021	141	18	the	the	DET
ap-2021	141	19	basis	basis	NOUN
ap-2021	141	20	for	for	ADP
ap-2021	141	21	the	the	DET
ap-2021	141	22	new	new	ADJ
ap-2021	141	23	input	input	NOUN
ap-2021	141	24	variable	variable	NOUN
ap-2021	141	25	for	for	ADP
ap-2021	141	26	the	the	DET
ap-2021	141	27	swing	swing	NOUN
ap-2021	141	28	-	-	PUNCT
ap-2021	141	29	up	up	ADP
ap-2021	141	30	motion	motion	NOUN
ap-2021	141	31	(	(	PUNCT
ap-2021	141	32	figure	figure	NOUN
ap-2021	141	33	4	4	NUM
ap-2021	141	34	)	)	PUNCT
ap-2021	141	35	.	.	PUNCT
ap-2021	142	1	the	the	DET
ap-2021	142	2	frequencies	frequency	NOUN
ap-2021	142	3	for	for	ADP
ap-2021	142	4	the	the	DET
ap-2021	142	5	angular	angular	ADJ
ap-2021	142	6	acceleration	acceleration	NOUN
ap-2021	142	7	of	of	ADP
ap-2021	142	8	the	the	DET
ap-2021	142	9	first	first	ADJ
ap-2021	142	10	link	link	NOUN
ap-2021	142	11	are	be	AUX
ap-2021	142	12	0.4053	0.4053	NUM
ap-2021	142	13	,	,	PUNCT
ap-2021	142	14	0.5722	0.5722	NUM
ap-2021	142	15	,	,	PUNCT
ap-2021	142	16	0.8583	0.8583	NUM
ap-2021	142	17	,	,	PUNCT
ap-2021	142	18	0.9537	0.9537	NUM
ap-2021	142	19	,	,	PUNCT
ap-2021	142	20	1.0490	1.0490	NUM
ap-2021	142	21	,	,	PUNCT
ap-2021	142	22	1.1444hz	1.1444hz	NUM
ap-2021	142	23	(	(	PUNCT
ap-2021	142	24	figure	figure	NOUN
ap-2021	142	25	4	4	NUM
ap-2021	142	26	middle	middle	ADJ
ap-2021	142	27	row	row	NOUN
ap-2021	142	28	)	)	PUNCT
ap-2021	142	29	,	,	PUNCT
ap-2021	142	30	the	the	DET
ap-2021	142	31	frequencies	frequency	NOUN
ap-2021	142	32	for	for	ADP
ap-2021	142	33	angular	angular	ADJ
ap-2021	142	34	acceleration	acceleration	NOUN
ap-2021	142	35	of	of	ADP
ap-2021	142	36	the	the	DET
ap-2021	142	37	second	second	ADJ
ap-2021	142	38	link	link	NOUN
ap-2021	142	39	are	be	AUX
ap-2021	142	40	0.4053	0.4053	NUM
ap-2021	142	41	,	,	PUNCT
ap-2021	142	42	0.6437	0.6437	NUM
ap-2021	142	43	,	,	PUNCT
ap-2021	142	44	0.8345	0.8345	NUM
ap-2021	142	45	,	,	PUNCT
ap-2021	142	46	0.9537	0.9537	NUM
ap-2021	142	47	,	,	PUNCT
ap-2021	142	48	1.0490	1.0490	NUM
ap-2021	142	49	,	,	PUNCT
ap-2021	142	50	1.1206hz	1.1206hz	NUM
ap-2021	142	51	(	(	PUNCT
ap-2021	142	52	figure	figure	NOUN
ap-2021	142	53	4	4	NUM
ap-2021	142	54	last	last	ADJ
ap-2021	142	55	row	row	NOUN
ap-2021	142	56	)	)	PUNCT
ap-2021	142	57	.	.	PUNCT
ap-2021	143	1	the	the	DET
ap-2021	143	2	frequencies	frequency	NOUN
ap-2021	143	3	for	for	ADP
ap-2021	143	4	the	the	DET
ap-2021	143	5	cart	cart	NOUN
ap-2021	143	6	acceleration	acceleration	NOUN
ap-2021	143	7	are	be	AUX
ap-2021	143	8	0.4053	0.4053	NUM
ap-2021	143	9	,	,	PUNCT
ap-2021	143	10	0.5722	0.5722	NUM
ap-2021	143	11	,	,	PUNCT
ap-2021	143	12	0.7629	0.7629	NUM
ap-2021	143	13	,	,	PUNCT
ap-2021	143	14	0.9060	0.9060	NUM
ap-2021	143	15	,	,	PUNCT
ap-2021	143	16	1.0014	1.0014	NUM
ap-2021	143	17	,	,	PUNCT
ap-2021	143	18	1.0967hz	1.0967hz	NUM
ap-2021	143	19	(	(	PUNCT
ap-2021	143	20	figure	figure	VERB
ap-2021	143	21	4	4	NUM
ap-2021	143	22	first	first	ADJ
ap-2021	143	23	row	row	NOUN
ap-2021	143	24	)	)	PUNCT
ap-2021	143	25	.	.	PUNCT
ap-2021	144	1	the	the	DET
ap-2021	144	2	input	input	NOUN
ap-2021	144	3	variable	variable	NOUN
ap-2021	144	4	w	w	ADP
ap-2021	144	5	consists	consist	NOUN
ap-2021	144	6	of	of	ADP
ap-2021	144	7	the	the	DET
ap-2021	144	8	active	active	ADJ
ap-2021	144	9	part	part	NOUN
ap-2021	144	10	and	and	CCONJ
ap-2021	144	11	the	the	DET
ap-2021	144	12	invariant	invariant	ADJ
ap-2021	144	13	part	part	NOUN
ap-2021	144	14	(	(	PUNCT
ap-2021	144	15	according	accord	VERB
ap-2021	144	16	to	to	ADP
ap-2021	144	17	equation	equation	NOUN
ap-2021	144	18	(	(	PUNCT
ap-2021	144	19	6	6	NUM
ap-2021	144	20	)	)	PUNCT
ap-2021	144	21	)	)	PUNCT
ap-2021	144	22	.	.	PUNCT
ap-2021	145	1	in	in	ADP
ap-2021	145	2	this	this	DET
ap-2021	145	3	case	case	NOUN
ap-2021	145	4	,	,	PUNCT
ap-2021	145	5	the	the	DET
ap-2021	145	6	active	active	ADJ
ap-2021	145	7	part	part	NOUN
ap-2021	145	8	is	be	AUX
ap-2021	145	9	zero	zero	NUM
ap-2021	145	10	,	,	PUNCT
ap-2021	145	11	because	because	SCONJ
ap-2021	145	12	variable	variable	ADJ
ap-2021	145	13	x	x	NOUN
ap-2021	145	14	has	have	VERB
ap-2021	145	15	the	the	DET
ap-2021	145	16	same	same	ADJ
ap-2021	145	17	initial	initial	ADJ
ap-2021	145	18	and	and	CCONJ
ap-2021	145	19	final	final	ADJ
ap-2021	145	20	position	position	NOUN
ap-2021	145	21	.	.	PUNCT
ap-2021	146	1	the	the	DET
ap-2021	146	2	sinusoidal	sinusoidal	ADJ
ap-2021	146	3	behavior	behavior	NOUN
ap-2021	146	4	of	of	ADP
ap-2021	146	5	the	the	DET
ap-2021	146	6	invariant	invariant	ADJ
ap-2021	146	7	part	part	NOUN
ap-2021	146	8	has	have	VERB
ap-2021	146	9	frequencies	frequency	NOUN
ap-2021	146	10	from	from	ADP
ap-2021	146	11	the	the	DET
ap-2021	146	12	movement	movement	NOUN
ap-2021	146	13	of	of	ADP
ap-2021	146	14	the	the	DET
ap-2021	146	15	two	two	NUM
ap-2021	146	16	links	link	NOUN
ap-2021	146	17	,	,	PUNCT
ap-2021	146	18	because	because	SCONJ
ap-2021	146	19	w	w	NOUN
ap-2021	146	20	directly	directly	ADV
ap-2021	146	21	influences	influence	VERB
ap-2021	146	22	ϕ1	ϕ1	NOUN
ap-2021	146	23	and	and	CCONJ
ap-2021	146	24	ϕ2	ϕ2	ADV
ap-2021	146	25	through	through	ADP
ap-2021	146	26	the	the	DET
ap-2021	146	27	zero	zero	NUM
ap-2021	146	28	dynamics	dynamic	NOUN
ap-2021	146	29	in	in	ADP
ap-2021	146	30	equation	equation	NOUN
ap-2021	146	31	(	(	PUNCT
ap-2021	146	32	3	3	NUM
ap-2021	146	33	)	)	PUNCT
ap-2021	146	34	)	)	PUNCT
ap-2021	146	35	.	.	PUNCT
ap-2021	147	1	the	the	DET
ap-2021	147	2	amplitudes	amplitude	NOUN
ap-2021	147	3	are	be	AUX
ap-2021	147	4	proportional	proportional	ADJ
ap-2021	147	5	to	to	ADP
ap-2021	147	6	the	the	DET
ap-2021	147	7	difference	difference	NOUN
ap-2021	147	8	in	in	ADP
ap-2021	147	9	potential	potential	ADJ
ap-2021	147	10	energy	energy	NOUN
ap-2021	147	11	between	between	ADP
ap-2021	147	12	the	the	DET
ap-2021	147	13	initial	initial	ADJ
ap-2021	147	14	and	and	CCONJ
ap-2021	147	15	final	final	ADJ
ap-2021	147	16	position	position	NOUN
ap-2021	147	17	of	of	ADP
ap-2021	147	18	the	the	DET
ap-2021	147	19	mechanism	mechanism	NOUN
ap-2021	147	20	,	,	PUNCT
ap-2021	147	21	but	but	CCONJ
ap-2021	147	22	their	their	PRON
ap-2021	147	23	values	value	NOUN
ap-2021	147	24	are	be	AUX
ap-2021	147	25	the	the	DET
ap-2021	147	26	result	result	NOUN
ap-2021	147	27	of	of	ADP
ap-2021	147	28	optimization	optimization	NOUN
ap-2021	147	29	.	.	PUNCT
ap-2021	148	1	the	the	DET
ap-2021	148	2	difference	difference	NOUN
ap-2021	148	3	of	of	ADP
ap-2021	148	4	the	the	DET
ap-2021	148	5	potential	potential	ADJ
ap-2021	148	6	energy	energy	NOUN
ap-2021	148	7	is	be	AUX
ap-2021	148	8	ep	ep	PROPN
ap-2021	148	9	=	=	PUNCT
ap-2021	148	10	m1lt1	m1lt1	VERB
ap-2021	148	11	g	g	PROPN
ap-2021	148	12	+	+	NOUN
ap-2021	148	13	m2(l1	m2(l1	PRON
ap-2021	148	14	+	+	NUM
ap-2021	148	15	lt2)g	lt2)g	NOUN
ap-2021	148	16	.	.	PUNCT
ap-2021	149	1	(	(	PUNCT
ap-2021	149	2	11	11	NUM
ap-2021	149	3	)	)	PUNCT
ap-2021	149	4	all	all	DET
ap-2021	149	5	parameters	parameter	NOUN
ap-2021	149	6	and	and	CCONJ
ap-2021	149	7	behaviors	behavior	NOUN
ap-2021	149	8	of	of	ADP
ap-2021	149	9	the	the	DET
ap-2021	149	10	control	control	NOUN
ap-2021	149	11	variable	variable	PROPN
ap-2021	149	12	w	w	PROPN
ap-2021	149	13	are	be	AUX
ap-2021	149	14	included	include	VERB
ap-2021	149	15	in	in	ADP
ap-2021	149	16	the	the	DET
ap-2021	149	17	following	follow	VERB
ap-2021	149	18	system	system	NOUN
ap-2021	149	19	:	:	PUNCT
ap-2021	149	20	a	a	DET
ap-2021	149	21	=	=	X
ap-2021	149	22	[	[	PUNCT
ap-2021	149	23	5	5	NUM
ap-2021	149	24	6	6	NUM
ap-2021	149	25	,	,	PUNCT
ap-2021	149	26	1	1	NUM
ap-2021	149	27	12	12	NUM
ap-2021	149	28	,	,	PUNCT
ap-2021	149	29	1	1	NUM
ap-2021	149	30	12	12	NUM
ap-2021	149	31	]	]	PUNCT
ap-2021	149	32	(	(	PUNCT
ap-2021	149	33	m1lt1	m1lt1	VERB
ap-2021	149	34	g	g	NOUN
ap-2021	149	35	+	+	NOUN
ap-2021	149	36	m2(l1	m2(l1	PRON
ap-2021	149	37	+	+	NUM
ap-2021	149	38	lt2)g	lt2)g	NOUN
ap-2021	149	39	)	)	PUNCT
ap-2021	149	40	,	,	PUNCT
ap-2021	149	41	ϕ	ϕ	X
ap-2021	150	1	=	=	PUNCT
ap-2021	150	2	[	[	PUNCT
ap-2021	150	3	−π	−π	NUM
ap-2021	150	4	2	2	NUM
ap-2021	150	5	,	,	PUNCT
ap-2021	150	6	π2	π2	PROPN
ap-2021	150	7	,	,	PUNCT
ap-2021	150	8	π	π	PROPN
ap-2021	150	9	2	2	NUM
ap-2021	150	10	]	]	PUNCT
ap-2021	150	11	,	,	PUNCT
ap-2021	150	12	f	f	X
ap-2021	150	13	=	=	X
ap-2021	150	14	[	[	PUNCT
ap-2021	150	15	0.4053	0.4053	NUM
ap-2021	150	16	,	,	PUNCT
ap-2021	150	17	0.6437	0.6437	NUM
ap-2021	150	18	,	,	PUNCT
ap-2021	150	19	0.8345	0.8345	NUM
ap-2021	150	20	]	]	PUNCT
ap-2021	150	21	,	,	PUNCT
ap-2021	150	22	ẍ1	ẍ1	PROPN
ap-2021	150	23	=	=	SYM
ap-2021	150	24	w	w	PROPN
ap-2021	150	25	,	,	PUNCT
ap-2021	150	26	wa	wa	NOUN
ap-2021	150	27	=	=	PROPN
ap-2021	150	28	0	0	PROPN
ap-2021	150	29	,	,	PUNCT
ap-2021	150	30	wi	wi	PROPN
ap-2021	150	31	=	=	SYM
ap-2021	150	32	3∑	3∑	NUM
ap-2021	150	33	i=1	i=1	NOUN
ap-2021	151	1	ai	ai	VERB
ap-2021	151	2	sin(2πfit+	sin(2πfit+	PROPN
ap-2021	151	3	ϕi	ϕi	ADP
ap-2021	151	4	)	)	PUNCT
ap-2021	151	5	,	,	PUNCT
ap-2021	151	6	w	w	NOUN
ap-2021	151	7	=	=	PUNCT
ap-2021	151	8	wa	wa	PROPN
ap-2021	151	9	+	+	X
ap-2021	151	10	wi	wi	PROPN
ap-2021	151	11	.	.	PUNCT
ap-2021	152	1	(	(	PUNCT
ap-2021	152	2	12	12	NUM
ap-2021	152	3	)	)	PUNCT
ap-2021	152	4	the	the	DET
ap-2021	152	5	conditions	condition	NOUN
ap-2021	152	6	(	(	PUNCT
ap-2021	152	7	10	10	NUM
ap-2021	152	8	)	)	PUNCT
ap-2021	152	9	are	be	AUX
ap-2021	152	10	fulfilled	fulfil	VERB
ap-2021	152	11	only	only	ADV
ap-2021	152	12	approximately	approximately	ADV
ap-2021	152	13	(	(	PUNCT
ap-2021	152	14	2/0.4053	2/0.4053	NUM
ap-2021	152	15	=	=	SYM
ap-2021	152	16	4.93	4.93	NUM
ap-2021	152	17	,	,	PUNCT
ap-2021	152	18	3/0.6437	3/0.6437	NUM
ap-2021	152	19	=	=	SYM
ap-2021	152	20	4.66	4.66	NUM
ap-2021	152	21	and	and	CCONJ
ap-2021	152	22	4/0.8345	4/0.8345	NUM
ap-2021	152	23	=	=	SYM
ap-2021	152	24	4.79	4.79	NUM
ap-2021	152	25	)	)	PUNCT
ap-2021	152	26	,	,	PUNCT
ap-2021	152	27	but	but	CCONJ
ap-2021	152	28	near	near	ADP
ap-2021	152	29	the	the	DET
ap-2021	152	30	upper	upper	ADJ
ap-2021	152	31	position	position	NOUN
ap-2021	152	32	the	the	DET
ap-2021	152	33	control	control	NOUN
ap-2021	152	34	is	be	AUX
ap-2021	152	35	switched	switch	VERB
ap-2021	152	36	to	to	ADP
ap-2021	152	37	nqr	nqr	PROPN
ap-2021	152	38	.	.	PUNCT
ap-2021	153	1	the	the	DET
ap-2021	153	2	usage	usage	NOUN
ap-2021	153	3	of	of	ADP
ap-2021	153	4	these	these	DET
ap-2021	153	5	frequencies	frequency	NOUN
ap-2021	153	6	is	be	AUX
ap-2021	153	7	886	886	NUM
ap-2021	153	8	vol	vol	NOUN
ap-2021	153	9	.	.	PUNCT
ap-2021	154	1	53	53	NUM
ap-2021	154	2	no	no	NOUN
ap-2021	154	3	.	.	PUNCT
ap-2021	155	1	6/2013	6/2013	NUM
ap-2021	155	2	control	control	NOUN
ap-2021	155	3	of	of	ADP
ap-2021	155	4	the	the	DET
ap-2021	155	5	double	double	ADJ
ap-2021	155	6	inverted	inverted	ADJ
ap-2021	155	7	pendulum	pendulum	NOUN
ap-2021	155	8	on	on	ADP
ap-2021	155	9	a	a	DET
ap-2021	155	10	cart	cart	NOUN
ap-2021	155	11	0	0	NUM
ap-2021	155	12	5	5	NUM
ap-2021	155	13	10	10	NUM
ap-2021	155	14	15	15	NUM
ap-2021	155	15	−40	−40	NOUN
ap-2021	155	16	−20	−20	NOUN
ap-2021	155	17	0	0	NUM
ap-2021	156	1	20	20	NUM
ap-2021	156	2	40	40	NUM
ap-2021	156	3	t	t	NOUN
ap-2021	156	4	[	[	X
ap-2021	156	5	s	s	X
ap-2021	156	6	]	]	PUNCT
ap-2021	156	7	ẍ	ẍ	PUNCT
ap-2021	157	1	[	[	X
ap-2021	157	2	m	m	X
ap-2021	157	3	s−	s−	NOUN
ap-2021	157	4	2	2	NUM
ap-2021	157	5	]	]	SYM
ap-2021	157	6	0	0	NUM
ap-2021	157	7	1	1	NUM
ap-2021	157	8	2	2	NUM
ap-2021	157	9	3	3	NUM
ap-2021	157	10	0	0	NUM
ap-2021	157	11	0.1	0.1	NUM
ap-2021	157	12	0.2	0.2	NUM
ap-2021	157	13	0.3	0.3	NUM
ap-2021	157	14	0.4	0.4	NUM
ap-2021	157	15	f	f	PROPN
ap-2021	158	1	[	[	X
ap-2021	158	2	hz	hz	X
ap-2021	158	3	]	]	X
ap-2021	158	4	|ẍ	|ẍ	PROPN
ap-2021	158	5	|	|	ADV
ap-2021	158	6	[	[	PUNCT
ap-2021	158	7	m	m	NOUN
ap-2021	158	8	s−	s−	NOUN
ap-2021	158	9	2	2	NUM
ap-2021	158	10	]	]	SYM
ap-2021	158	11	0	0	NUM
ap-2021	158	12	5	5	NUM
ap-2021	158	13	10	10	NUM
ap-2021	158	14	15	15	NUM
ap-2021	158	15	−200	−200	NOUN
ap-2021	158	16	−100	−100	ADP
ap-2021	158	17	0	0	NUM
ap-2021	158	18	100	100	NUM
ap-2021	158	19	200	200	NUM
ap-2021	158	20	t	t	NOUN
ap-2021	159	1	[	[	X
ap-2021	159	2	s	s	X
ap-2021	159	3	]	]	X
ap-2021	159	4	ϕ̈	ϕ̈	PROPN
ap-2021	159	5	1	1	NUM
ap-2021	160	1	[	[	X
ap-2021	160	2	r	r	X
ap-2021	160	3	a	a	X
ap-2021	160	4	d	d	X
ap-2021	160	5	·	·	SYM
ap-2021	160	6	s	s	PART
ap-2021	160	7	−	−	NOUN
ap-2021	160	8	2	2	NUM
ap-2021	160	9	]	]	SYM
ap-2021	160	10	0	0	NUM
ap-2021	160	11	1	1	NUM
ap-2021	160	12	2	2	NUM
ap-2021	160	13	3	3	NUM
ap-2021	160	14	0	0	NUM
ap-2021	160	15	1	1	NUM
ap-2021	160	16	2	2	NUM
ap-2021	160	17	3	3	NUM
ap-2021	160	18	f	f	NOUN
ap-2021	161	1	[	[	X
ap-2021	161	2	hz	hz	X
ap-2021	161	3	]	]	X
ap-2021	161	4	|ϕ̈	|ϕ̈	VERB
ap-2021	161	5	1	1	NUM
ap-2021	161	6	|	|	NOUN
ap-2021	161	7	[	[	PUNCT
ap-2021	161	8	ra	ra	NOUN
ap-2021	161	9	d	d	PROPN
ap-2021	161	10	·	·	SYM
ap-2021	161	11	s	s	PART
ap-2021	161	12	−	−	NOUN
ap-2021	161	13	2	2	NUM
ap-2021	161	14	]	]	SYM
ap-2021	161	15	0	0	NUM
ap-2021	161	16	5	5	NUM
ap-2021	161	17	10	10	NUM
ap-2021	161	18	15	15	NUM
ap-2021	161	19	−200	−200	NOUN
ap-2021	161	20	−100	−100	ADP
ap-2021	161	21	0	0	NUM
ap-2021	161	22	100	100	NUM
ap-2021	161	23	200	200	NUM
ap-2021	161	24	t	t	NOUN
ap-2021	162	1	[	[	X
ap-2021	162	2	s	s	X
ap-2021	162	3	]	]	X
ap-2021	162	4	ϕ̈	ϕ̈	PROPN
ap-2021	162	5	2	2	NUM
ap-2021	163	1	[	[	X
ap-2021	163	2	r	r	X
ap-2021	163	3	a	a	X
ap-2021	163	4	d	d	X
ap-2021	163	5	·	·	SYM
ap-2021	163	6	s	s	PART
ap-2021	163	7	−	−	NOUN
ap-2021	163	8	2	2	NUM
ap-2021	163	9	]	]	SYM
ap-2021	163	10	0	0	NUM
ap-2021	163	11	1	1	NUM
ap-2021	163	12	2	2	NUM
ap-2021	163	13	3	3	NUM
ap-2021	163	14	0	0	NUM
ap-2021	163	15	2	2	NUM
ap-2021	163	16	4	4	NUM
ap-2021	163	17	6	6	NUM
ap-2021	163	18	f	f	NOUN
ap-2021	164	1	[	[	X
ap-2021	164	2	hz	hz	X
ap-2021	164	3	]	]	X
ap-2021	164	4	|ϕ̈	|ϕ̈	VERB
ap-2021	164	5	2	2	NUM
ap-2021	164	6	|	|	NOUN
ap-2021	164	7	[	[	PUNCT
ap-2021	164	8	ra	ra	NOUN
ap-2021	164	9	d	d	PROPN
ap-2021	164	10	·	·	SYM
ap-2021	164	11	s	s	PART
ap-2021	164	12	−	−	NOUN
ap-2021	164	13	2	2	NUM
ap-2021	164	14	]	]	PUNCT
ap-2021	164	15	figure	figure	NOUN
ap-2021	164	16	4	4	NUM
ap-2021	164	17	.	.	PUNCT
ap-2021	165	1	accelerations	acceleration	NOUN
ap-2021	165	2	(	(	PUNCT
ap-2021	165	3	left	leave	VERB
ap-2021	165	4	)	)	PUNCT
ap-2021	165	5	and	and	CCONJ
ap-2021	165	6	their	their	PRON
ap-2021	165	7	fourier	fourier	NOUN
ap-2021	165	8	transformations	transformation	NOUN
ap-2021	165	9	.	.	PUNCT
ap-2021	166	1	efficient	efficient	ADJ
ap-2021	166	2	,	,	PUNCT
ap-2021	166	3	because	because	SCONJ
ap-2021	166	4	they	they	PRON
ap-2021	166	5	are	be	AUX
ap-2021	166	6	the	the	DET
ap-2021	166	7	eigenfrequencies	eigenfrequencie	NOUN
ap-2021	166	8	and	and	CCONJ
ap-2021	166	9	the	the	DET
ap-2021	166	10	system	system	NOUN
ap-2021	166	11	is	be	AUX
ap-2021	166	12	sensitive	sensitive	ADJ
ap-2021	166	13	to	to	ADP
ap-2021	166	14	the	the	DET
ap-2021	166	15	input	input	NOUN
ap-2021	166	16	on	on	ADP
ap-2021	166	17	these	these	DET
ap-2021	166	18	frequencies	frequency	NOUN
ap-2021	166	19	.	.	PUNCT
ap-2021	167	1	in	in	ADP
ap-2021	167	2	the	the	DET
ap-2021	167	3	surroundings	surrounding	NOUN
ap-2021	167	4	of	of	ADP
ap-2021	167	5	the	the	DET
ap-2021	167	6	desired	desire	VERB
ap-2021	167	7	position	position	NOUN
ap-2021	167	8	it	it	PRON
ap-2021	167	9	is	be	AUX
ap-2021	167	10	required	require	VERB
ap-2021	167	11	to	to	PART
ap-2021	167	12	use	use	VERB
ap-2021	167	13	the	the	DET
ap-2021	167	14	local	local	ADJ
ap-2021	167	15	stabilization	stabilization	NOUN
ap-2021	167	16	control	control	NOUN
ap-2021	167	17	.	.	PUNCT
ap-2021	168	1	in	in	ADP
ap-2021	168	2	our	our	PRON
ap-2021	168	3	case	case	NOUN
ap-2021	168	4	,	,	PUNCT
ap-2021	168	5	we	we	PRON
ap-2021	168	6	use	use	VERB
ap-2021	168	7	the	the	DET
ap-2021	168	8	nonlinear	nonlinear	ADJ
ap-2021	168	9	quadratic	quadratic	ADJ
ap-2021	168	10	regulator	regulator	NOUN
ap-2021	168	11	(	(	PUNCT
ap-2021	168	12	nqr	nqr	PROPN
ap-2021	168	13	or	or	CCONJ
ap-2021	168	14	sdre	sdre	NOUN
ap-2021	168	15	,	,	PUNCT
ap-2021	168	16	see	see	VERB
ap-2021	168	17	[	[	X
ap-2021	168	18	3	3	NUM
ap-2021	168	19	,	,	PUNCT
ap-2021	168	20	4	4	NUM
ap-2021	168	21	]	]	NUM
ap-2021	168	22	)	)	PUNCT
ap-2021	168	23	.	.	PUNCT
ap-2021	169	1	however	however	ADV
ap-2021	169	2	,	,	PUNCT
ap-2021	169	3	the	the	DET
ap-2021	169	4	region	region	NOUN
ap-2021	169	5	of	of	ADP
ap-2021	169	6	attraction	attraction	NOUN
ap-2021	169	7	of	of	ADP
ap-2021	169	8	this	this	DET
ap-2021	169	9	control	control	NOUN
ap-2021	169	10	is	be	AUX
ap-2021	169	11	also	also	ADV
ap-2021	169	12	limited	limited	ADJ
ap-2021	169	13	.	.	PUNCT
ap-2021	170	1	in	in	ADP
ap-2021	170	2	each	each	DET
ap-2021	170	3	time	time	NOUN
ap-2021	170	4	step	step	NOUN
ap-2021	170	5	,	,	PUNCT
ap-2021	170	6	the	the	DET
ap-2021	170	7	nqr	nqr	ADJ
ap-2021	170	8	controller	controller	NOUN
ap-2021	170	9	calculates	calculate	VERB
ap-2021	170	10	the	the	DET
ap-2021	170	11	input	input	NOUN
ap-2021	170	12	torque	torque	NOUN
ap-2021	170	13	u	u	NOUN
ap-2021	170	14	at	at	ADP
ap-2021	170	15	the	the	DET
ap-2021	170	16	cart	cart	NOUN
ap-2021	170	17	.	.	PUNCT
ap-2021	171	1	the	the	DET
ap-2021	171	2	input	input	NOUN
ap-2021	171	3	variable	variable	NOUN
ap-2021	171	4	u	u	NOUN
ap-2021	171	5	is	be	AUX
ap-2021	171	6	therefore	therefore	ADV
ap-2021	171	7	plotted	plot	VERB
ap-2021	171	8	in	in	ADP
ap-2021	171	9	the	the	DET
ap-2021	171	10	same	same	ADJ
ap-2021	171	11	figure	figure	NOUN
ap-2021	171	12	,	,	PUNCT
ap-2021	171	13	based	base	VERB
ap-2021	171	14	on	on	ADP
ap-2021	171	15	the	the	DET
ap-2021	171	16	acceleration	acceleration	NOUN
ap-2021	171	17	of	of	ADP
ap-2021	171	18	the	the	DET
ap-2021	171	19	cart	cart	NOUN
ap-2021	171	20	(	(	PUNCT
ap-2021	171	21	4	4	NUM
ap-2021	171	22	)	)	PUNCT
ap-2021	171	23	when	when	SCONJ
ap-2021	171	24	using	use	VERB
ap-2021	171	25	nqr	nqr	PROPN
ap-2021	171	26	control	control	NOUN
ap-2021	171	27	and	and	CCONJ
ap-2021	171	28	based	base	VERB
ap-2021	171	29	on	on	ADP
ap-2021	171	30	the	the	DET
ap-2021	171	31	nqr	nqr	ADJ
ap-2021	171	32	algorithm	algorithm	NOUN
ap-2021	171	33	in	in	ADP
ap-2021	171	34	the	the	DET
ap-2021	171	35	vicinity	vicinity	NOUN
ap-2021	171	36	of	of	ADP
ap-2021	171	37	the	the	DET
ap-2021	171	38	unstable	unstable	ADJ
ap-2021	171	39	equilibrium	equilibrium	NOUN
ap-2021	171	40	.	.	PUNCT
ap-2021	172	1	7	7	X
ap-2021	172	2	.	.	X
ap-2021	172	3	simulation	simulation	NOUN
ap-2021	172	4	of	of	ADP
ap-2021	172	5	the	the	DET
ap-2021	172	6	double	double	ADJ
ap-2021	172	7	inverted	inverted	ADJ
ap-2021	172	8	pendulum	pendulum	NOUN
ap-2021	172	9	on	on	ADP
ap-2021	172	10	the	the	DET
ap-2021	172	11	cart	cart	NOUN
ap-2021	172	12	the	the	DET
ap-2021	172	13	control	control	NOUN
ap-2021	172	14	is	be	AUX
ap-2021	172	15	designed	design	VERB
ap-2021	172	16	,	,	PUNCT
ap-2021	172	17	and	and	CCONJ
ap-2021	172	18	is	be	AUX
ap-2021	172	19	used	use	VERB
ap-2021	172	20	for	for	ADP
ap-2021	172	21	the	the	DET
ap-2021	172	22	simulation	simulation	NOUN
ap-2021	172	23	of	of	ADP
ap-2021	172	24	the	the	DET
ap-2021	172	25	system	system	NOUN
ap-2021	172	26	described	describe	VERB
ap-2021	172	27	by	by	ADP
ap-2021	172	28	equations	equation	NOUN
ap-2021	172	29	(	(	PUNCT
ap-2021	172	30	2)–(3	2)–(3	NUM
ap-2021	172	31	)	)	PUNCT
ap-2021	172	32	.	.	PUNCT
ap-2021	173	1	the	the	DET
ap-2021	173	2	simulated	simulated	ADJ
ap-2021	173	3	swing	swing	NOUN
ap-2021	173	4	-	-	PUNCT
ap-2021	173	5	up	up	ADP
ap-2021	173	6	motion	motion	NOUN
ap-2021	173	7	guided	guide	VERB
ap-2021	173	8	by	by	ADP
ap-2021	173	9	the	the	DET
ap-2021	173	10	cart	cart	NOUN
ap-2021	173	11	acceleration	acceleration	NOUN
ap-2021	173	12	ẍ1	ẍ1	PUNCT
ap-2021	174	1	=	=	PUNCT
ap-2021	174	2	w	w	AUX
ap-2021	174	3	described	describe	VERB
ap-2021	174	4	in	in	ADP
ap-2021	174	5	equation	equation	NOUN
ap-2021	174	6	(	(	PUNCT
ap-2021	174	7	12	12	NUM
ap-2021	174	8	)	)	PUNCT
ap-2021	174	9	reaches	reach	VERB
ap-2021	174	10	the	the	DET
ap-2021	174	11	surroundings	surrounding	NOUN
ap-2021	174	12	of	of	ADP
ap-2021	174	13	the	the	DET
ap-2021	174	14	unstable	unstable	ADJ
ap-2021	174	15	equilibrium	equilibrium	NOUN
ap-2021	174	16	position	position	NOUN
ap-2021	174	17	(	(	PUNCT
ap-2021	174	18	see	see	VERB
ap-2021	174	19	figure	figure	NOUN
ap-2021	174	20	5	5	NUM
ap-2021	174	21	)	)	PUNCT
ap-2021	174	22	.	.	PUNCT
ap-2021	175	1	the	the	DET
ap-2021	175	2	nqr	nqr	PROPN
ap-2021	175	3	algorithm	algorithm	NOUN
ap-2021	175	4	is	be	AUX
ap-2021	175	5	used	use	VERB
ap-2021	175	6	for	for	ADP
ap-2021	175	7	the	the	DET
ap-2021	175	8	stabilization	stabilization	NOUN
ap-2021	175	9	around	around	ADP
ap-2021	175	10	the	the	DET
ap-2021	175	11	upper	upper	ADJ
ap-2021	175	12	equilibrium	equilibrium	NOUN
ap-2021	175	13	.	.	PUNCT
ap-2021	176	1	this	this	DET
ap-2021	176	2	algorithm	algorithm	NOUN
ap-2021	176	3	controls	control	VERB
ap-2021	176	4	the	the	DET
ap-2021	176	5	system	system	NOUN
ap-2021	176	6	from	from	ADP
ap-2021	176	7	the	the	DET
ap-2021	176	8	position	position	NOUN
ap-2021	176	9	in	in	ADP
ap-2021	176	10	the	the	DET
ap-2021	176	11	surroundings	surrounding	NOUN
ap-2021	176	12	of	of	ADP
ap-2021	176	13	the	the	DET
ap-2021	176	14	upper	upper	ADJ
ap-2021	176	15	unstable	unstable	ADJ
ap-2021	176	16	position	position	NOUN
ap-2021	176	17	to	to	ADP
ap-2021	176	18	this	this	DET
ap-2021	176	19	unstable	unstable	ADJ
ap-2021	176	20	equilibrium	equilibrium	NOUN
ap-2021	176	21	.	.	PUNCT
ap-2021	177	1	when	when	SCONJ
ap-2021	177	2	the	the	DET
ap-2021	177	3	pendulum	pendulum	NOUN
ap-2021	177	4	reaches	reach	VERB
ap-2021	177	5	the	the	DET
ap-2021	177	6	position	position	NOUN
ap-2021	177	7	where	where	SCONJ
ap-2021	177	8	it	it	PRON
ap-2021	177	9	can	can	AUX
ap-2021	177	10	be	be	AUX
ap-2021	177	11	controlled	control	VERB
ap-2021	177	12	by	by	ADP
ap-2021	177	13	nqr	nqr	PROPN
ap-2021	177	14	,	,	PUNCT
ap-2021	177	15	it	it	PRON
ap-2021	177	16	is	be	AUX
ap-2021	177	17	switched	switch	VERB
ap-2021	177	18	on	on	ADP
ap-2021	177	19	and	and	CCONJ
ap-2021	177	20	it	it	PRON
ap-2021	177	21	leads	lead	VERB
ap-2021	177	22	the	the	DET
ap-2021	177	23	mechanism	mechanism	NOUN
ap-2021	177	24	to	to	ADP
ap-2021	177	25	equilibrium	equilibrium	NOUN
ap-2021	177	26	.	.	PUNCT
ap-2021	178	1	the	the	DET
ap-2021	178	2	entire	entire	ADJ
ap-2021	178	3	trajectory	trajectory	NOUN
ap-2021	178	4	of	of	ADP
ap-2021	178	5	the	the	DET
ap-2021	178	6	end	end	NOUN
ap-2021	178	7	point	point	NOUN
ap-2021	178	8	of	of	ADP
ap-2021	178	9	the	the	DET
ap-2021	178	10	pendulum	pendulum	NOUN
ap-2021	178	11	and	and	CCONJ
ap-2021	178	12	the	the	DET
ap-2021	178	13	cart	cart	NOUN
ap-2021	178	14	is	be	AUX
ap-2021	178	15	shown	show	VERB
ap-2021	178	16	in	in	ADP
ap-2021	178	17	figure	figure	NOUN
ap-2021	178	18	5	5	NUM
ap-2021	178	19	left	leave	VERB
ap-2021	178	20	,	,	PUNCT
ap-2021	178	21	with	with	ADP
ap-2021	178	22	the	the	DET
ap-2021	178	23	starting	starting	NOUN
ap-2021	178	24	position	position	NOUN
ap-2021	178	25	and	and	CCONJ
ap-2021	178	26	the	the	DET
ap-2021	178	27	final	final	ADJ
ap-2021	178	28	position	position	NOUN
ap-2021	178	29	marked	mark	VERB
ap-2021	178	30	.	.	PUNCT
ap-2021	179	1	figure	figure	NOUN
ap-2021	179	2	5	5	NUM
ap-2021	179	3	right	right	ADJ
ap-2021	179	4	depicts	depict	VERB
ap-2021	179	5	the	the	DET
ap-2021	179	6	behavior	behavior	NOUN
ap-2021	179	7	of	of	ADP
ap-2021	179	8	the	the	DET
ap-2021	179	9	input	input	NOUN
ap-2021	179	10	force	force	NOUN
ap-2021	179	11	acting	act	VERB
ap-2021	179	12	on	on	ADP
ap-2021	179	13	the	the	DET
ap-2021	179	14	cart	cart	NOUN
ap-2021	179	15	.	.	PUNCT
ap-2021	180	1	the	the	DET
ap-2021	180	2	control	control	PROPN
ap-2021	180	3	algorithm	algorithm	PROPN
ap-2021	180	4	nqr	nqr	PROPN
ap-2021	180	5	starts	start	VERB
ap-2021	180	6	at	at	ADP
ap-2021	180	7	time	time	NOUN
ap-2021	180	8	2.715	2.715	NUM
ap-2021	180	9	s.	s.	PROPN
ap-2021	180	10	a	a	DET
ap-2021	180	11	big	big	ADJ
ap-2021	180	12	step	step	NOUN
ap-2021	180	13	in	in	ADP
ap-2021	180	14	the	the	DET
ap-2021	180	15	input	input	NOUN
ap-2021	180	16	torque	torque	NOUN
ap-2021	180	17	is	be	AUX
ap-2021	180	18	shown	show	VERB
ap-2021	180	19	in	in	ADP
ap-2021	180	20	figure	figure	NOUN
ap-2021	180	21	6	6	NUM
ap-2021	180	22	right	right	ADV
ap-2021	180	23	,	,	PUNCT
ap-2021	180	24	when	when	SCONJ
ap-2021	180	25	the	the	DET
ap-2021	180	26	change	change	NOUN
ap-2021	180	27	in	in	ADP
ap-2021	180	28	the	the	DET
ap-2021	180	29	control	control	NOUN
ap-2021	180	30	strategies	strategy	NOUN
ap-2021	180	31	is	be	AUX
ap-2021	180	32	made	make	VERB
ap-2021	180	33	.	.	PUNCT
ap-2021	181	1	for	for	ADP
ap-2021	181	2	illustration	illustration	NOUN
ap-2021	181	3	,	,	PUNCT
ap-2021	181	4	the	the	DET
ap-2021	181	5	behavior	behavior	NOUN
ap-2021	181	6	of	of	ADP
ap-2021	181	7	the	the	DET
ap-2021	181	8	ϕ1	ϕ1	NOUN
ap-2021	181	9	,	,	PUNCT
ap-2021	181	10	ϕ2	ϕ2	ADV
ap-2021	181	11	and	and	CCONJ
ap-2021	181	12	x	x	PRON
ap-2021	181	13	coordinates	coordinate	NOUN
ap-2021	181	14	and	and	CCONJ
ap-2021	181	15	their	their	PRON
ap-2021	181	16	velocities	velocity	NOUN
ap-2021	181	17	are	be	AUX
ap-2021	181	18	shown	show	VERB
ap-2021	181	19	in	in	ADP
ap-2021	181	20	figure	figure	NOUN
ap-2021	181	21	7	7	NUM
ap-2021	181	22	.	.	NOUN
ap-2021	181	23	8	8	NUM
ap-2021	181	24	.	.	PUNCT
ap-2021	182	1	conclusions	conclusion	NOUN
ap-2021	182	2	this	this	DET
ap-2021	182	3	paper	paper	NOUN
ap-2021	182	4	has	have	AUX
ap-2021	182	5	described	describe	VERB
ap-2021	182	6	a	a	DET
ap-2021	182	7	novel	novel	ADJ
ap-2021	182	8	control	control	NOUN
ap-2021	182	9	for	for	ADP
ap-2021	182	10	the	the	DET
ap-2021	182	11	bottom	bottom	ADJ
ap-2021	182	12	-	-	PUNCT
ap-2021	182	13	up	up	ADP
ap-2021	182	14	motion	motion	NOUN
ap-2021	182	15	of	of	ADP
ap-2021	182	16	a	a	DET
ap-2021	182	17	double	double	ADJ
ap-2021	182	18	pendulum	pendulum	NOUN
ap-2021	182	19	on	on	ADP
ap-2021	182	20	a	a	DET
ap-2021	182	21	cart	cart	NOUN
ap-2021	182	22	using	use	VERB
ap-2021	182	23	eigenfrequencies	eigenfrequencie	NOUN
ap-2021	182	24	determined	determine	VERB
ap-2021	182	25	from	from	ADP
ap-2021	182	26	the	the	DET
ap-2021	182	27	natural	natural	ADJ
ap-2021	182	28	motion	motion	NOUN
ap-2021	182	29	.	.	PUNCT
ap-2021	183	1	the	the	DET
ap-2021	183	2	set	set	NOUN
ap-2021	183	3	of	of	ADP
ap-2021	183	4	equations	equation	NOUN
ap-2021	183	5	describing	describe	VERB
ap-2021	183	6	the	the	DET
ap-2021	183	7	mechanical	mechanical	ADJ
ap-2021	183	8	system	system	NOUN
ap-2021	183	9	is	be	AUX
ap-2021	183	10	transformed	transform	VERB
ap-2021	183	11	using	use	VERB
ap-2021	183	12	exact	exact	ADJ
ap-2021	183	13	input	input	NOUN
ap-2021	183	14	-	-	PUNCT
ap-2021	183	15	output	output	NOUN
ap-2021	183	16	feedback	feedback	NOUN
ap-2021	183	17	linearization	linearization	NOUN
ap-2021	183	18	.	.	PUNCT
ap-2021	184	1	the	the	DET
ap-2021	184	2	control	control	NOUN
ap-2021	184	3	is	be	AUX
ap-2021	184	4	based	base	VERB
ap-2021	184	5	on	on	ADP
ap-2021	184	6	the	the	DET
ap-2021	184	7	feedforward	feedforward	NOUN
ap-2021	184	8	control	control	NOUN
ap-2021	184	9	strategy	strategy	NOUN
ap-2021	184	10	,	,	PUNCT
ap-2021	184	11	using	use	VERB
ap-2021	184	12	sinusoids	sinusoid	NOUN
ap-2021	184	13	with	with	ADP
ap-2021	184	14	frequencies	frequency	NOUN
ap-2021	184	15	obtained	obtain	VERB
ap-2021	184	16	from	from	ADP
ap-2021	184	17	the	the	DET
ap-2021	184	18	falling	fall	VERB
ap-2021	184	19	trajectory	trajectory	NOUN
ap-2021	184	20	(	(	PUNCT
ap-2021	184	21	natural	natural	ADJ
ap-2021	184	22	motion	motion	NOUN
ap-2021	184	23	)	)	PUNCT
ap-2021	184	24	.	.	PUNCT
ap-2021	185	1	the	the	DET
ap-2021	185	2	frequencies	frequency	NOUN
ap-2021	185	3	of	of	ADP
ap-2021	185	4	the	the	DET
ap-2021	185	5	sinusoids	sinusoid	NOUN
ap-2021	185	6	are	be	AUX
ap-2021	185	7	eigenfrequencies	eigenfrequencie	NOUN
ap-2021	185	8	of	of	ADP
ap-2021	185	9	this	this	DET
ap-2021	185	10	underactuated	underactuated	ADJ
ap-2021	185	11	system	system	NOUN
ap-2021	185	12	.	.	PUNCT
ap-2021	186	1	the	the	DET
ap-2021	186	2	amplitudes	amplitude	NOUN
ap-2021	186	3	of	of	ADP
ap-2021	186	4	this	this	DET
ap-2021	186	5	control	control	NOUN
ap-2021	186	6	are	be	AUX
ap-2021	186	7	related	relate	VERB
ap-2021	186	8	to	to	ADP
ap-2021	186	9	the	the	DET
ap-2021	186	10	potential	potential	ADJ
ap-2021	186	11	energy	energy	NOUN
ap-2021	186	12	needed	need	VERB
ap-2021	186	13	for	for	SCONJ
ap-2021	186	14	the	the	DET
ap-2021	186	15	system	system	NOUN
ap-2021	186	16	to	to	PART
ap-2021	186	17	change	change	VERB
ap-2021	186	18	its	its	PRON
ap-2021	186	19	position	position	NOUN
ap-2021	186	20	in	in	ADP
ap-2021	186	21	the	the	DET
ap-2021	186	22	field	field	NOUN
ap-2021	186	23	of	of	ADP
ap-2021	186	24	gravity	gravity	NOUN
ap-2021	186	25	.	.	PUNCT
ap-2021	187	1	the	the	DET
ap-2021	187	2	zero	zero	NUM
ap-2021	187	3	dynamics	dynamic	NOUN
ap-2021	187	4	integrated	integrate	VERB
ap-2021	187	5	in	in	ADP
ap-2021	187	6	the	the	DET
ap-2021	187	7	underactuated	underactuated	ADJ
ap-2021	187	8	mechanisms	mechanism	NOUN
ap-2021	187	9	can	can	AUX
ap-2021	187	10	be	be	AUX
ap-2021	187	11	controlled	control	VERB
ap-2021	187	12	by	by	ADP
ap-2021	187	13	frequencies	frequency	NOUN
ap-2021	187	14	added	add	VERB
ap-2021	187	15	to	to	ADP
ap-2021	187	16	the	the	DET
ap-2021	187	17	signal	signal	NOUN
ap-2021	187	18	of	of	ADP
ap-2021	187	19	the	the	DET
ap-2021	187	20	control	control	NOUN
ap-2021	187	21	variable	variable	NOUN
ap-2021	187	22	.	.	PUNCT
ap-2021	188	1	the	the	DET
ap-2021	188	2	approach	approach	NOUN
ap-2021	188	3	described	describe	VERB
ap-2021	188	4	here	here	ADV
ap-2021	188	5	has	have	VERB
ap-2021	188	6	great	great	ADJ
ap-2021	188	7	potential	potential	NOUN
ap-2021	188	8	for	for	ADP
ap-2021	188	9	extending	extend	VERB
ap-2021	188	10	this	this	DET
ap-2021	188	11	control	control	NOUN
ap-2021	188	12	into	into	ADP
ap-2021	188	13	the	the	DET
ap-2021	188	14	field	field	NOUN
ap-2021	188	15	of	of	ADP
ap-2021	188	16	underactuated	underactuated	ADJ
ap-2021	188	17	systems	system	NOUN
ap-2021	188	18	.	.	PUNCT
ap-2021	189	1	887	887	NUM
ap-2021	189	2	z.	z.	PROPN
ap-2021	189	3	neusser	neusser	PROPN
ap-2021	189	4	,	,	PUNCT
ap-2021	189	5	m.	m.	NOUN
ap-2021	189	6	valášek	valášek	VERB
ap-2021	189	7	acta	acta	PROPN
ap-2021	189	8	polytechnica	polytechnica	PROPN
ap-2021	189	9	−3	−3	PROPN
ap-2021	189	10	−2	−2	PROPN
ap-2021	189	11	−1	−1	NOUN
ap-2021	189	12	0	0	NUM
ap-2021	189	13	1	1	NUM
ap-2021	189	14	−3	−3	NOUN
ap-2021	189	15	−2	−2	NOUN
ap-2021	189	16	−1	−1	NOUN
ap-2021	189	17	0	0	NUM
ap-2021	189	18	1	1	NUM
ap-2021	189	19	2	2	NUM
ap-2021	189	20	x	x	SYM
ap-2021	190	1	[	[	X
ap-2021	190	2	m	m	X
ap-2021	190	3	]	]	X
ap-2021	190	4	y	y	PROPN
ap-2021	191	1	[	[	X
ap-2021	191	2	m	m	X
ap-2021	191	3	]	]	X
ap-2021	191	4	0	0	NUM
ap-2021	191	5	1	1	NUM
ap-2021	191	6	2	2	NUM
ap-2021	191	7	3	3	NUM
ap-2021	191	8	−10	−10	NOUN
ap-2021	191	9	−5	−5	ADV
ap-2021	191	10	0	0	NUM
ap-2021	191	11	5	5	NUM
ap-2021	191	12	10	10	NUM
ap-2021	191	13	t	t	NOUN
ap-2021	192	1	[	[	X
ap-2021	192	2	s	s	X
ap-2021	192	3	]	]	PUNCT
ap-2021	192	4	ẍ	ẍ	PUNCT
ap-2021	193	1	[	[	X
ap-2021	193	2	m	m	X
ap-2021	193	3	s−	s−	NOUN
ap-2021	193	4	2	2	NUM
ap-2021	193	5	]	]	PUNCT
ap-2021	193	6	figure	figure	NOUN
ap-2021	193	7	5	5	NUM
ap-2021	193	8	.	.	PUNCT
ap-2021	194	1	swing	swing	NOUN
ap-2021	194	2	-	-	PUNCT
ap-2021	194	3	up	up	ADP
ap-2021	194	4	motion	motion	NOUN
ap-2021	194	5	controlled	control	VERB
ap-2021	194	6	by	by	ADP
ap-2021	194	7	cart	cart	NOUN
ap-2021	194	8	acceleration	acceleration	NOUN
ap-2021	194	9	;	;	PUNCT
ap-2021	194	10	left	leave	VERB
ap-2021	194	11	,	,	PUNCT
ap-2021	194	12	mechanism	mechanism	NOUN
ap-2021	194	13	end	end	NOUN
ap-2021	194	14	points	point	NOUN
ap-2021	194	15	in	in	ADP
ap-2021	194	16	the	the	DET
ap-2021	194	17	working	work	VERB
ap-2021	194	18	plane	plane	NOUN
ap-2021	194	19	;	;	PUNCT
ap-2021	194	20	right	right	ADJ
ap-2021	194	21	,	,	PUNCT
ap-2021	194	22	input	input	NOUN
ap-2021	194	23	acceleration	acceleration	NOUN
ap-2021	194	24	behavior	behavior	NOUN
ap-2021	194	25	.	.	PUNCT
ap-2021	195	1	−2	−2	NOUN
ap-2021	195	2	0	0	NUM
ap-2021	195	3	2	2	NUM
ap-2021	195	4	4	4	NUM
ap-2021	195	5	−5	−5	NOUN
ap-2021	195	6	−4	−4	X
ap-2021	195	7	−3	−3	NOUN
ap-2021	195	8	−2	−2	PROPN
ap-2021	195	9	−1	−1	NOUN
ap-2021	195	10	0	0	NUM
ap-2021	195	11	1	1	NUM
ap-2021	195	12	2	2	NUM
ap-2021	195	13	3	3	NUM
ap-2021	195	14	4	4	NUM
ap-2021	195	15	5	5	NUM
ap-2021	195	16	x	x	SYM
ap-2021	196	1	[	[	X
ap-2021	196	2	m	m	X
ap-2021	196	3	]	]	X
ap-2021	196	4	y	y	PROPN
ap-2021	197	1	[	[	X
ap-2021	197	2	m	m	X
ap-2021	197	3	]	]	X
ap-2021	197	4	0	0	NUM
ap-2021	197	5	5	5	NUM
ap-2021	197	6	10	10	NUM
ap-2021	197	7	15	15	NUM
ap-2021	197	8	−20	−20	NOUN
ap-2021	197	9	0	0	NUM
ap-2021	197	10	20	20	NUM
ap-2021	197	11	40	40	NUM
ap-2021	197	12	60	60	NUM
ap-2021	197	13	80	80	NUM
ap-2021	197	14	t	t	NOUN
ap-2021	198	1	[	[	X
ap-2021	198	2	s	s	X
ap-2021	198	3	]	]	X
ap-2021	198	4	u	u	NOUN
ap-2021	198	5	[	[	X
ap-2021	198	6	n	n	X
ap-2021	198	7	]	]	PUNCT
ap-2021	198	8	figure	figure	NOUN
ap-2021	198	9	6	6	NUM
ap-2021	198	10	.	.	PUNCT
ap-2021	198	11	final	final	ADJ
ap-2021	198	12	swing	swing	NOUN
ap-2021	198	13	up	up	ADP
ap-2021	198	14	motion	motion	NOUN
ap-2021	198	15	for	for	ADP
ap-2021	198	16	the	the	DET
ap-2021	198	17	double	double	ADJ
ap-2021	198	18	pendulum	pendulum	NOUN
ap-2021	198	19	on	on	ADP
ap-2021	198	20	the	the	DET
ap-2021	198	21	cart	cart	NOUN
ap-2021	198	22	;	;	PUNCT
ap-2021	198	23	left	leave	VERB
ap-2021	198	24	,	,	PUNCT
ap-2021	198	25	motion	motion	NOUN
ap-2021	198	26	in	in	ADP
ap-2021	198	27	the	the	DET
ap-2021	198	28	plane	plane	NOUN
ap-2021	198	29	;	;	PUNCT
ap-2021	198	30	right	right	ADV
ap-2021	198	31	,	,	PUNCT
ap-2021	198	32	the	the	DET
ap-2021	198	33	input	input	NOUN
ap-2021	198	34	torque	torque	NOUN
ap-2021	198	35	acting	act	VERB
ap-2021	198	36	on	on	ADP
ap-2021	198	37	the	the	DET
ap-2021	198	38	cart	cart	NOUN
ap-2021	198	39	.	.	PUNCT
ap-2021	199	1	our	our	PRON
ap-2021	199	2	work	work	NOUN
ap-2021	199	3	forms	form	VERB
ap-2021	199	4	the	the	DET
ap-2021	199	5	basis	basis	NOUN
ap-2021	199	6	for	for	ADP
ap-2021	199	7	the	the	DET
ap-2021	199	8	control	control	NOUN
ap-2021	199	9	of	of	ADP
ap-2021	199	10	systems	system	NOUN
ap-2021	199	11	with	with	ADP
ap-2021	199	12	flexible	flexible	ADJ
ap-2021	199	13	parts	part	NOUN
ap-2021	199	14	to	to	PART
ap-2021	199	15	reduce	reduce	VERB
ap-2021	199	16	unintentional	unintentional	ADJ
ap-2021	199	17	residual	residual	ADJ
ap-2021	199	18	structural	structural	ADJ
ap-2021	199	19	vibrations	vibration	NOUN
ap-2021	199	20	during	during	ADP
ap-2021	199	21	the	the	DET
ap-2021	199	22	motion	motion	NOUN
ap-2021	199	23	.	.	PUNCT
ap-2021	200	1	this	this	DET
ap-2021	200	2	kind	kind	NOUN
ap-2021	200	3	of	of	ADP
ap-2021	200	4	control	control	NOUN
ap-2021	200	5	is	be	AUX
ap-2021	200	6	useful	useful	ADJ
ap-2021	200	7	in	in	ADP
ap-2021	200	8	controlling	control	VERB
ap-2021	200	9	flexible	flexible	ADJ
ap-2021	200	10	robots	robot	NOUN
ap-2021	200	11	.	.	PUNCT
ap-2021	201	1	acknowledgements	acknowledgement	NOUN
ap-2021	201	2	this	this	DET
ap-2021	201	3	work	work	NOUN
ap-2021	201	4	was	be	AUX
ap-2021	201	5	partially	partially	ADV
ap-2021	201	6	supported	support	VERB
ap-2021	201	7	by	by	ADP
ap-2021	201	8	project	project	NOUN
ap-2021	201	9	msm	msm	NOUN
ap-2021	201	10	6840770003	6840770003	NUM
ap-2021	201	11	‘	'	PUNCT
ap-2021	201	12	algorithms	algorithm	NOUN
ap-2021	201	13	for	for	ADP
ap-2021	201	14	computer	computer	NOUN
ap-2021	201	15	simulation	simulation	NOUN
ap-2021	201	16	and	and	CCONJ
ap-2021	201	17	application	application	NOUN
ap-2021	201	18	in	in	ADP
ap-2021	201	19	engineering	engineering	NOUN
ap-2021	201	20	’	'	PUNCT
ap-2021	201	21	.	.	PUNCT
ap-2021	202	1	references	reference	NOUN
ap-2021	202	2	[	[	X
ap-2021	202	3	1	1	NUM
ap-2021	202	4	]	]	PUNCT
ap-2021	202	5	valášek	valášek	NOUN
ap-2021	202	6	,	,	PUNCT
ap-2021	202	7	m.	m.	NOUN
ap-2021	202	8	:	:	PUNCT
ap-2021	202	9	design	design	NOUN
ap-2021	202	10	and	and	CCONJ
ap-2021	202	11	control	control	NOUN
ap-2021	202	12	of	of	ADP
ap-2021	202	13	under	under	ADV
ap-2021	202	14	-	-	PUNCT
ap-2021	202	15	actuated	actuate	VERB
ap-2021	202	16	and	and	CCONJ
ap-2021	202	17	over	over	ADV
ap-2021	202	18	-	-	PUNCT
ap-2021	202	19	actuated	actuate	VERB
ap-2021	202	20	mechanical	mechanical	ADJ
ap-2021	202	21	systems	system	NOUN
ap-2021	202	22	challenges	challenge	NOUN
ap-2021	202	23	of	of	ADP
ap-2021	202	24	mechanics	mechanic	NOUN
ap-2021	202	25	and	and	CCONJ
ap-2021	202	26	mechatronics	mechatronic	NOUN
ap-2021	202	27	.	.	PUNCT
ap-2021	203	1	supplement	supplement	NOUN
ap-2021	203	2	to	to	ADP
ap-2021	203	3	vehicle	vehicle	NOUN
ap-2021	203	4	system	system	NOUN
ap-2021	203	5	dynamics	dynamic	NOUN
ap-2021	203	6	,	,	PUNCT
ap-2021	203	7	40	40	NUM
ap-2021	203	8	,	,	PUNCT
ap-2021	203	9	2004	2004	NUM
ap-2021	203	10	,	,	PUNCT
ap-2021	203	11	p.	p.	NOUN
ap-2021	203	12	37–50	37–50	NUM
ap-2021	203	13	.	.	PUNCT
ap-2021	204	1	[	[	X
ap-2021	204	2	2	2	NUM
ap-2021	204	3	]	]	PUNCT
ap-2021	204	4	olfati	olfati	NOUN
ap-2021	204	5	-	-	PUNCT
ap-2021	204	6	saber	saber	NOUN
ap-2021	204	7	,	,	PUNCT
ap-2021	204	8	r.	r.	PROPN
ap-2021	204	9	:	:	PUNCT
ap-2021	204	10	nonlinear	nonlinear	ADJ
ap-2021	204	11	control	control	NOUN
ap-2021	204	12	of	of	ADP
ap-2021	204	13	underactuated	underactuated	ADJ
ap-2021	204	14	mechanical	mechanical	ADJ
ap-2021	204	15	systems	system	NOUN
ap-2021	204	16	with	with	ADP
ap-2021	204	17	application	application	NOUN
ap-2021	204	18	to	to	ADP
ap-2021	204	19	robotics	robotic	NOUN
ap-2021	204	20	and	and	CCONJ
ap-2021	204	21	aerospace	aerospace	NOUN
ap-2021	204	22	vehicles	vehicle	NOUN
ap-2021	204	23	.	.	PUNCT
ap-2021	205	1	phd	phd	NOUN
ap-2021	205	2	thesis	thesis	PROPN
ap-2021	205	3	,	,	PUNCT
ap-2021	205	4	mit	mit	PROPN
ap-2021	205	5	,	,	PUNCT
ap-2021	205	6	boston	boston	PROPN
ap-2021	205	7	,	,	PUNCT
ap-2021	205	8	2001	2001	NUM
ap-2021	205	9	.	.	PUNCT
ap-2021	206	1	[	[	X
ap-2021	206	2	3	3	NUM
ap-2021	206	3	]	]	X
ap-2021	206	4	steinbauer	steinbauer	NOUN
ap-2021	206	5	,	,	PUNCT
ap-2021	206	6	p.	p.	NOUN
ap-2021	206	7	:	:	PUNCT
ap-2021	206	8	nonlinear	nonlinear	ADJ
ap-2021	206	9	control	control	NOUN
ap-2021	206	10	of	of	ADP
ap-2021	206	11	nonlinear	nonlinear	ADJ
ap-2021	206	12	mechanical	mechanical	ADJ
ap-2021	206	13	systems	system	NOUN
ap-2021	206	14	.	.	PUNCT
ap-2021	207	1	phd	phd	NOUN
ap-2021	207	2	thesis	thesis	PROPN
ap-2021	207	3	,	,	PUNCT
ap-2021	207	4	czech	czech	PROPN
ap-2021	207	5	technical	technical	PROPN
ap-2021	207	6	university	university	PROPN
ap-2021	207	7	in	in	ADP
ap-2021	207	8	prague	prague	PROPN
ap-2021	207	9	,	,	PUNCT
ap-2021	207	10	prague	prague	PROPN
ap-2021	207	11	,	,	PUNCT
ap-2021	207	12	2002	2002	NUM
ap-2021	207	13	.	.	PUNCT
ap-2021	208	1	(	(	PUNCT
ap-2021	208	2	in	in	ADP
ap-2021	208	3	czech	czech	PROPN
ap-2021	208	4	)	)	PUNCT
ap-2021	209	1	[	[	X
ap-2021	209	2	4	4	X
ap-2021	209	3	]	]	PUNCT
ap-2021	209	4	valášek	valášek	PROPN
ap-2021	209	5	,	,	PUNCT
ap-2021	209	6	m.	m.	NOUN
ap-2021	209	7	,	,	PUNCT
ap-2021	209	8	steinbauer	steinbauer	NOUN
ap-2021	209	9	,	,	PUNCT
ap-2021	209	10	p.	p.	NOUN
ap-2021	209	11	:	:	PUNCT
ap-2021	210	1	nonlinear	nonlinear	ADJ
ap-2021	210	2	control	control	NOUN
ap-2021	210	3	of	of	ADP
ap-2021	210	4	multibody	multibody	ADJ
ap-2021	210	5	systems	system	NOUN
ap-2021	210	6	.	.	PUNCT
ap-2021	211	1	in	in	ADP
ap-2021	211	2	:	:	PUNCT
ap-2021	211	3	“	"	PUNCT
ap-2021	211	4	euromech	euromech	NOUN
ap-2021	211	5	colloquium	colloquium	NOUN
ap-2021	211	6	404	404	NUM
ap-2021	211	7	,	,	PUNCT
ap-2021	211	8	advances	advance	NOUN
ap-2021	211	9	in	in	ADP
ap-2021	211	10	computational	computational	ADJ
ap-2021	211	11	multibody	multibody	ADJ
ap-2021	211	12	dynamics	dynamic	NOUN
ap-2021	211	13	”	"	PUNCT
ap-2021	211	14	,	,	PUNCT
ap-2021	211	15	lisboa	lisboa	PROPN
ap-2021	211	16	:	:	PUNCT
ap-2021	211	17	instituto	instituto	PROPN
ap-2021	211	18	technico	technico	PROPN
ap-2021	211	19	superior	superior	PROPN
ap-2021	211	20	,	,	PUNCT
ap-2021	211	21	av	av	PROPN
ap-2021	211	22	.	.	PUNCT
ap-2021	211	23	rovisco	rovisco	PROPN
ap-2021	211	24	pais	pais	PROPN
ap-2021	211	25	,	,	PUNCT
ap-2021	211	26	1999	1999	NUM
ap-2021	211	27	,	,	PUNCT
ap-2021	211	28	p.	p.	NOUN
ap-2021	211	29	437–444	437–444	NUM
ap-2021	211	30	.	.	PUNCT
ap-2021	212	1	[	[	X
ap-2021	212	2	5	5	NUM
ap-2021	212	3	]	]	X
ap-2021	212	4	aneke	aneke	ADJ
ap-2021	212	5	,	,	PUNCT
ap-2021	212	6	n.	n.	PROPN
ap-2021	212	7	p.	p.	PROPN
ap-2021	212	8	i.	i.	PROPN
ap-2021	212	9	:	:	PUNCT
ap-2021	212	10	control	control	NOUN
ap-2021	212	11	of	of	ADP
ap-2021	212	12	underactuated	underactuated	ADJ
ap-2021	212	13	mechanical	mechanical	ADJ
ap-2021	212	14	systems	system	NOUN
ap-2021	212	15	.	.	PUNCT
ap-2021	213	1	phd	phd	NOUN
ap-2021	213	2	thesis	thesis	PROPN
ap-2021	213	3	,	,	PUNCT
ap-2021	213	4	tu	tu	PROPN
ap-2021	213	5	eindhoven	eindhoven	PROPN
ap-2021	213	6	,	,	PUNCT
ap-2021	213	7	eindhoven	eindhoven	NOUN
ap-2021	213	8	,	,	PUNCT
ap-2021	213	9	2002	2002	NUM
ap-2021	213	10	.	.	PUNCT
ap-2021	214	1	[	[	X
ap-2021	214	2	6	6	NUM
ap-2021	214	3	]	]	X
ap-2021	214	4	fantoni	fantoni	PROPN
ap-2021	214	5	,	,	PUNCT
ap-2021	214	6	i.	i.	PROPN
ap-2021	214	7	,	,	PUNCT
ap-2021	214	8	lozano	lozano	PROPN
ap-2021	214	9	,	,	PUNCT
ap-2021	214	10	r.	r.	PROPN
ap-2021	214	11	:	:	PUNCT
ap-2021	214	12	non	non	ADJ
ap-2021	214	13	-	-	ADJ
ap-2021	214	14	linear	linear	ADJ
ap-2021	214	15	control	control	NOUN
ap-2021	214	16	for	for	ADP
ap-2021	214	17	888	888	NUM
ap-2021	214	18	vol	vol	NOUN
ap-2021	214	19	.	.	PUNCT
ap-2021	215	1	53	53	NUM
ap-2021	215	2	no	no	NOUN
ap-2021	215	3	.	.	PUNCT
ap-2021	216	1	6/2013	6/2013	NUM
ap-2021	216	2	control	control	NOUN
ap-2021	216	3	of	of	ADP
ap-2021	216	4	the	the	DET
ap-2021	216	5	double	double	ADJ
ap-2021	216	6	inverted	inverted	ADJ
ap-2021	216	7	pendulum	pendulum	NOUN
ap-2021	216	8	on	on	ADP
ap-2021	216	9	a	a	DET
ap-2021	216	10	cart	cart	NOUN
ap-2021	216	11	0	0	NUM
ap-2021	216	12	5	5	NUM
ap-2021	216	13	10	10	NUM
ap-2021	216	14	15	15	NUM
ap-2021	216	15	−3	−3	ADJ
ap-2021	216	16	−2	−2	NOUN
ap-2021	216	17	−1	−1	NOUN
ap-2021	216	18	0	0	NUM
ap-2021	216	19	1	1	NUM
ap-2021	216	20	2	2	NUM
ap-2021	216	21	3	3	NUM
ap-2021	216	22	4	4	NUM
ap-2021	216	23	5	5	NUM
ap-2021	216	24	6	6	NUM
ap-2021	216	25	7	7	NUM
ap-2021	216	26	t	t	NOUN
ap-2021	217	1	[	[	X
ap-2021	217	2	s	s	X
ap-2021	217	3	]	]	X
ap-2021	217	4	x	x	PUNCT
ap-2021	218	1	[	[	X
ap-2021	218	2	m	m	X
ap-2021	218	3	]	]	X
ap-2021	218	4	ϕ	ϕ	X
ap-2021	218	5	1	1	NUM
ap-2021	219	1	[	[	X
ap-2021	219	2	r	r	NOUN
ap-2021	219	3	a	a	X
ap-2021	219	4	d	d	X
ap-2021	219	5	]	]	X
ap-2021	219	6	ϕ	ϕ	X
ap-2021	219	7	2	2	NUM
ap-2021	220	1	[	[	X
ap-2021	220	2	r	r	NOUN
ap-2021	220	3	a	a	X
ap-2021	220	4	d	d	X
ap-2021	220	5	]	]	X
ap-2021	220	6	x	x	SYM
ap-2021	220	7	ϕ1	ϕ1	NOUN
ap-2021	220	8	ϕ2	ϕ2	ADV
ap-2021	220	9	0	0	NUM
ap-2021	220	10	5	5	NUM
ap-2021	220	11	10	10	NUM
ap-2021	220	12	15	15	NUM
ap-2021	220	13	−10	−10	NOUN
ap-2021	220	14	−5	−5	ADV
ap-2021	220	15	0	0	NUM
ap-2021	220	16	5	5	NUM
ap-2021	220	17	10	10	NUM
ap-2021	220	18	15	15	NUM
ap-2021	220	19	t	t	NOUN
ap-2021	221	1	[	[	X
ap-2021	221	2	s	s	X
ap-2021	221	3	]	]	X
ap-2021	221	4	ẋ	ẋ	PROPN
ap-2021	222	1	[	[	X
ap-2021	222	2	m	m	X
ap-2021	222	3	s−	s−	NOUN
ap-2021	222	4	1	1	NUM
ap-2021	222	5	]	]	PUNCT
ap-2021	223	1	ϕ̇	ϕ̇	PRON
ap-2021	223	2	1	1	NUM
ap-2021	224	1	[	[	X
ap-2021	224	2	r	r	X
ap-2021	224	3	a	a	X
ap-2021	224	4	d	d	X
ap-2021	224	5	·	·	SYM
ap-2021	224	6	s	s	PART
ap-2021	224	7	−	−	NOUN
ap-2021	224	8	1	1	NUM
ap-2021	224	9	]	]	PUNCT
ap-2021	224	10	ϕ̇	ϕ̇	PRON
ap-2021	224	11	2	2	NUM
ap-2021	225	1	[	[	X
ap-2021	225	2	r	r	X
ap-2021	225	3	a	a	X
ap-2021	225	4	d	d	X
ap-2021	225	5	·	·	SYM
ap-2021	225	6	s	s	PART
ap-2021	225	7	−	−	NOUN
ap-2021	225	8	1	1	NUM
ap-2021	225	9	]	]	PUNCT
ap-2021	225	10	x	x	PUNCT
ap-2021	225	11	ϕ1	ϕ1	NOUN
ap-2021	225	12	ϕ2	ϕ2	ADV
ap-2021	225	13	figure	figure	VERB
ap-2021	225	14	7	7	NUM
ap-2021	225	15	.	.	PUNCT
ap-2021	225	16	upward	upward	ADJ
ap-2021	225	17	movement	movement	NOUN
ap-2021	225	18	of	of	ADP
ap-2021	225	19	the	the	DET
ap-2021	225	20	double	double	ADJ
ap-2021	225	21	inverted	inverted	ADJ
ap-2021	225	22	pendulum	pendulum	NOUN
ap-2021	225	23	on	on	ADP
ap-2021	225	24	the	the	DET
ap-2021	225	25	cart	cart	NOUN
ap-2021	225	26	,	,	PUNCT
ap-2021	225	27	positions	position	NOUN
ap-2021	225	28	and	and	CCONJ
ap-2021	225	29	velocities	velocity	NOUN
ap-2021	225	30	.	.	PUNCT
ap-2021	226	1	underactuated	underactuated	ADJ
ap-2021	226	2	mechanical	mechanical	ADJ
ap-2021	226	3	systems	system	NOUN
ap-2021	226	4	.	.	PUNCT
ap-2021	227	1	london	london	PROPN
ap-2021	227	2	:	:	PUNCT
ap-2021	227	3	springer	springer	NOUN
ap-2021	227	4	-	-	PUNCT
ap-2021	227	5	verlag	verlag	PROPN
ap-2021	227	6	,	,	PUNCT
ap-2021	227	7	2002	2002	NUM
ap-2021	227	8	.	.	PUNCT
ap-2021	228	1	[	[	X
ap-2021	228	2	7	7	X
ap-2021	228	3	]	]	X
ap-2021	228	4	xin	xin	PROPN
ap-2021	228	5	,	,	PUNCT
ap-2021	228	6	x.	x.	NOUN
ap-2021	228	7	:	:	PUNCT
ap-2021	228	8	analysis	analysis	NOUN
ap-2021	228	9	of	of	ADP
ap-2021	228	10	the	the	DET
ap-2021	228	11	energy	energy	NOUN
ap-2021	228	12	-	-	PUNCT
ap-2021	228	13	based	base	VERB
ap-2021	228	14	swing	swing	NOUN
ap-2021	228	15	-	-	PUNCT
ap-2021	228	16	up	up	ADP
ap-2021	228	17	control	control	NOUN
ap-2021	228	18	for	for	ADP
ap-2021	228	19	the	the	DET
ap-2021	228	20	double	double	ADJ
ap-2021	228	21	pendulum	pendulum	NOUN
ap-2021	228	22	on	on	ADP
ap-2021	228	23	a	a	DET
ap-2021	228	24	cart	cart	NOUN
ap-2021	228	25	.	.	PUNCT
ap-2021	229	1	international	international	ADJ
ap-2021	229	2	journal	journal	NOUN
ap-2021	229	3	of	of	ADP
ap-2021	229	4	robust	robust	ADJ
ap-2021	229	5	and	and	CCONJ
ap-2021	229	6	nonlinear	nonlinear	ADJ
ap-2021	229	7	control	control	NOUN
ap-2021	229	8	,	,	PUNCT
ap-2021	229	9	21	21	NUM
ap-2021	229	10	,	,	PUNCT
ap-2021	229	11	2011	2011	NUM
ap-2021	229	12	,	,	PUNCT
ap-2021	229	13	p.	p.	NOUN
ap-2021	229	14	387–403	387–403	NUM
ap-2021	229	15	.	.	PUNCT
ap-2021	230	1	[	[	X
ap-2021	230	2	8	8	NUM
ap-2021	230	3	]	]	SYM
ap-2021	230	4	rubi	rubi	NOUN
ap-2021	230	5	,	,	PUNCT
ap-2021	230	6	j.	j.	PROPN
ap-2021	230	7	,	,	PUNCT
ap-2021	230	8	rubio	rubio	PROPN
ap-2021	230	9	,	,	PUNCT
ap-2021	230	10	a.	a.	PROPN
ap-2021	230	11	,	,	PUNCT
ap-2021	230	12	avello	avello	PROPN
ap-2021	230	13	,	,	PUNCT
ap-2021	230	14	a.	a.	NOUN
ap-2021	230	15	:	:	PUNCT
ap-2021	230	16	swing	swing	NOUN
ap-2021	230	17	-	-	PUNCT
ap-2021	230	18	up	up	ADP
ap-2021	230	19	control	control	NOUN
ap-2021	230	20	problem	problem	NOUN
ap-2021	230	21	for	for	ADP
ap-2021	230	22	a	a	DET
ap-2021	230	23	self	self	NOUN
ap-2021	230	24	-	-	PUNCT
ap-2021	230	25	erecting	erect	VERB
ap-2021	230	26	double	double	ADJ
ap-2021	230	27	inverted	inverted	ADJ
ap-2021	230	28	pendulum	pendulum	NOUN
ap-2021	230	29	.	.	PUNCT
ap-2021	231	1	iee	iee	PROPN
ap-2021	231	2	proc.–control	proc.–control	PROPN
ap-2021	231	3	theory	theory	PROPN
ap-2021	231	4	app	app	PROPN
ap-2021	231	5	.	.	PROPN
ap-2021	231	6	,	,	PUNCT
ap-2021	231	7	149	149	NUM
ap-2021	231	8	(	(	PUNCT
ap-2021	231	9	2	2	NUM
ap-2021	231	10	)	)	PUNCT
ap-2021	231	11	,	,	PUNCT
ap-2021	231	12	2002	2002	NUM
ap-2021	231	13	,	,	PUNCT
ap-2021	231	14	p.	p.	NOUN
ap-2021	231	15	169–175	169–175	NUM
ap-2021	231	16	.	.	PUNCT
ap-2021	232	1	[	[	X
ap-2021	232	2	9	9	NUM
ap-2021	232	3	]	]	SYM
ap-2021	232	4	udawatta	udawatta	PROPN
ap-2021	232	5	,	,	PUNCT
ap-2021	232	6	l.	l.	PROPN
ap-2021	232	7	,	,	PUNCT
ap-2021	232	8	watanabe	watanabe	PROPN
ap-2021	232	9	,	,	PUNCT
ap-2021	232	10	k.	k.	PROPN
ap-2021	232	11	,	,	PUNCT
ap-2021	232	12	izumi	izumi	PROPN
ap-2021	232	13	,	,	PUNCT
ap-2021	232	14	k.	k.	PROPN
ap-2021	232	15	,	,	PUNCT
ap-2021	232	16	kuguchi	kuguchi	PROPN
ap-2021	232	17	,	,	PUNCT
ap-2021	232	18	k.	k.	PROPN
ap-2021	232	19	:	:	PUNCT
ap-2021	232	20	control	control	NOUN
ap-2021	232	21	of	of	ADP
ap-2021	232	22	underactuated	underactuated	ADJ
ap-2021	232	23	robot	robot	NOUN
ap-2021	232	24	manipulators	manipulator	NOUN
ap-2021	232	25	using	use	VERB
ap-2021	232	26	switching	switch	VERB
ap-2021	232	27	computed	compute	VERB
ap-2021	232	28	torque	torque	NOUN
ap-2021	232	29	method	method	NOUN
ap-2021	232	30	:	:	PUNCT
ap-2021	232	31	ga	ga	PROPN
ap-2021	232	32	based	base	VERB
ap-2021	232	33	approach	approach	NOUN
ap-2021	232	34	.	.	PUNCT
ap-2021	233	1	soft	soft	ADJ
ap-2021	233	2	computing	computing	NOUN
ap-2021	233	3	,	,	PUNCT
ap-2021	233	4	8	8	NUM
ap-2021	233	5	,	,	PUNCT
ap-2021	233	6	2003	2003	NUM
ap-2021	233	7	,	,	PUNCT
ap-2021	233	8	p.	p.	NOUN
ap-2021	233	9	51–60	51–60	NUM
ap-2021	233	10	.	.	PUNCT
ap-2021	234	1	[	[	X
ap-2021	234	2	10	10	NUM
ap-2021	234	3	]	]	X
ap-2021	234	4	mahindrakar	mahindrakar	NOUN
ap-2021	234	5	,	,	PUNCT
ap-2021	234	6	a.	a.	PROPN
ap-2021	234	7	d.	d.	PROPN
ap-2021	234	8	,	,	PUNCT
ap-2021	234	9	rao	rao	PROPN
ap-2021	234	10	,	,	PUNCT
ap-2021	234	11	s.	s.	PROPN
ap-2021	234	12	,	,	PUNCT
ap-2021	234	13	banavar	banavar	PROPN
ap-2021	234	14	,	,	PUNCT
ap-2021	234	15	r.	r.	PROPN
ap-2021	234	16	n.	n.	PROPN
ap-2021	234	17	:	:	PUNCT
ap-2021	234	18	a	a	DET
ap-2021	234	19	point	point	NOUN
ap-2021	234	20	-	-	PUNCT
ap-2021	234	21	to	to	ADP
ap-2021	234	22	-	-	PUNCT
ap-2021	234	23	point	point	NOUN
ap-2021	234	24	control	control	NOUN
ap-2021	234	25	of	of	ADP
ap-2021	234	26	a	a	DET
ap-2021	234	27	2r	2r	NUM
ap-2021	234	28	planar	planar	PROPN
ap-2021	234	29	horizontal	horizontal	ADJ
ap-2021	234	30	underactuated	underactuated	ADJ
ap-2021	234	31	manipulator	manipulator	NOUN
ap-2021	234	32	.	.	PUNCT
ap-2021	234	33	mechanism	mechanism	NOUN
ap-2021	234	34	and	and	CCONJ
ap-2021	234	35	machine	machine	NOUN
ap-2021	234	36	theory	theory	NOUN
ap-2021	234	37	,	,	PUNCT
ap-2021	234	38	41	41	NUM
ap-2021	234	39	,	,	PUNCT
ap-2021	234	40	2006	2006	NUM
ap-2021	234	41	,	,	PUNCT
ap-2021	234	42	p.	p.	NOUN
ap-2021	234	43	838–844	838–844	NUM
ap-2021	234	44	.	.	PUNCT
ap-2021	235	1	[	[	X
ap-2021	235	2	11	11	NUM
ap-2021	235	3	]	]	PUNCT
ap-2021	235	4	valášek	valášek	NOUN
ap-2021	235	5	,	,	PUNCT
ap-2021	235	6	m.	m.	NOUN
ap-2021	235	7	:	:	PUNCT
ap-2021	235	8	exact	exact	ADJ
ap-2021	235	9	input	input	NOUN
ap-2021	235	10	-	-	PUNCT
ap-2021	235	11	output	output	NOUN
ap-2021	235	12	linearization	linearization	NOUN
ap-2021	235	13	of	of	ADP
ap-2021	235	14	general	general	ADJ
ap-2021	235	15	multibody	multibody	ADJ
ap-2021	235	16	system	system	NOUN
ap-2021	235	17	by	by	ADP
ap-2021	235	18	dynamic	dynamic	ADJ
ap-2021	235	19	feedback	feedback	NOUN
ap-2021	235	20	.	.	PUNCT
ap-2021	236	1	eccomas	eccomas	PROPN
ap-2021	236	2	conference	conference	PROPN
ap-2021	236	3	madrid	madrid	PROPN
ap-2021	236	4	:	:	PUNCT
ap-2021	236	5	multibody	multibody	ADJ
ap-2021	236	6	dynamics	dynamic	NOUN
ap-2021	236	7	,	,	PUNCT
ap-2021	236	8	2005	2005	NUM
ap-2021	236	9	.	.	PUNCT
ap-2021	237	1	[	[	X
ap-2021	237	2	12	12	NUM
ap-2021	237	3	]	]	PUNCT
ap-2021	237	4	valášek	valášek	NOUN
ap-2021	237	5	,	,	PUNCT
ap-2021	237	6	m.	m.	NOUN
ap-2021	237	7	:	:	PUNCT
ap-2021	237	8	control	control	NOUN
ap-2021	237	9	of	of	ADP
ap-2021	237	10	elastic	elastic	ADJ
ap-2021	237	11	industrial	industrial	ADJ
ap-2021	237	12	robots	robot	NOUN
ap-2021	237	13	by	by	ADP
ap-2021	237	14	nonlinear	nonlinear	ADJ
ap-2021	237	15	dynamic	dynamic	ADJ
ap-2021	237	16	compensation	compensation	NOUN
ap-2021	237	17	.	.	PUNCT
ap-2021	238	1	acta	acta	PROPN
ap-2021	238	2	polytechnica	polytechnica	PROPN
ap-2021	238	3	,	,	PUNCT
ap-2021	238	4	33	33	NUM
ap-2021	238	5	(	(	PUNCT
ap-2021	238	6	1	1	NUM
ap-2021	238	7	)	)	PUNCT
ap-2021	238	8	,	,	PUNCT
ap-2021	238	9	1993	1993	NUM
ap-2021	238	10	,	,	PUNCT
ap-2021	238	11	p.	p.	NOUN
ap-2021	238	12	15–30	15–30	NUM
ap-2021	238	13	.	.	PUNCT
ap-2021	239	1	[	[	X
ap-2021	239	2	13	13	NUM
ap-2021	239	3	]	]	SYM
ap-2021	239	4	neusser	neusser	NOUN
ap-2021	239	5	,	,	PUNCT
ap-2021	239	6	z.	z.	PROPN
ap-2021	239	7	,	,	PUNCT
ap-2021	239	8	valášek	valášek	PROPN
ap-2021	239	9	,	,	PUNCT
ap-2021	239	10	m.	m.	NOUN
ap-2021	239	11	:	:	PUNCT
ap-2021	239	12	control	control	NOUN
ap-2021	239	13	of	of	ADP
ap-2021	239	14	the	the	DET
ap-2021	239	15	underactuated	underactuated	ADJ
ap-2021	239	16	mechanical	mechanical	ADJ
ap-2021	239	17	systems	system	NOUN
ap-2021	239	18	using	use	VERB
ap-2021	239	19	natural	natural	ADJ
ap-2021	239	20	motion	motion	NOUN
ap-2021	239	21	.	.	PUNCT
ap-2021	239	22	kybernetika	kybernetika	NOUN
ap-2021	239	23	;	;	PUNCT
ap-2021	239	24	48	48	NUM
ap-2021	239	25	(	(	PUNCT
ap-2021	239	26	2	2	NUM
ap-2021	239	27	)	)	PUNCT
ap-2021	239	28	,	,	PUNCT
ap-2021	239	29	2012	2012	NUM
ap-2021	239	30	,	,	PUNCT
ap-2021	239	31	p.	p.	NOUN
ap-2021	239	32	223–241	223–241	NUM
ap-2021	239	33	.	.	PUNCT
ap-2021	240	1	889	889	NUM
ap-2021	240	2	acta	acta	PROPN
ap-2021	240	3	polytechnica	polytechnica	PROPN
ap-2021	240	4	53(6):883–889	53(6):883–889	PROPN
ap-2021	240	5	,	,	PUNCT
ap-2021	240	6	2013	2013	NUM
ap-2021	240	7	1	1	NUM
ap-2021	240	8	introduction	introduction	NOUN
ap-2021	240	9	2	2	NUM
ap-2021	240	10	natural	natural	ADJ
ap-2021	240	11	motion	motion	NOUN
ap-2021	240	12	3	3	NUM
ap-2021	240	13	problem	problem	NOUN
ap-2021	240	14	formulation	formulation	NOUN
ap-2021	240	15	4	4	NUM
ap-2021	240	16	how	how	SCONJ
ap-2021	240	17	to	to	PART
ap-2021	240	18	get	get	VERB
ap-2021	240	19	new	new	ADJ
ap-2021	240	20	input	input	NOUN
ap-2021	240	21	w	w	PROPN
ap-2021	240	22	5	5	NUM
ap-2021	240	23	simulation	simulation	NOUN
ap-2021	240	24	of	of	ADP
ap-2021	240	25	the	the	DET
ap-2021	240	26	natural	natural	ADJ
ap-2021	240	27	motion	motion	NOUN
ap-2021	240	28	6	6	NUM
ap-2021	240	29	control	control	NOUN
ap-2021	240	30	design	design	VERB
ap-2021	240	31	7	7	NUM
ap-2021	240	32	simulation	simulation	NOUN
ap-2021	240	33	of	of	ADP
ap-2021	240	34	the	the	DET
ap-2021	240	35	double	double	ADJ
ap-2021	240	36	inverted	inverted	ADJ
ap-2021	240	37	pendulum	pendulum	NOUN
ap-2021	240	38	on	on	ADP
ap-2021	240	39	the	the	DET
ap-2021	240	40	cart	cart	NOUN
ap-2021	240	41	8	8	NUM
ap-2021	240	42	conclusions	conclusion	NOUN
ap-2021	240	43	acknowledgements	acknowledgement	NOUN
ap-2021	240	44	references	reference	NOUN