id	sid	tid	token	lemma	pos
ap-2970	1	1	acta	acta	PROPN
ap-2970	1	2	polytechnica	polytechnica	PROPN
ap-2970	1	3	doi:10.14311	doi:10.14311	PROPN
ap-2970	1	4	/	/	SYM
ap-2970	1	5	ap.2015.55.0407	ap.2015.55.0407	PROPN
ap-2970	1	6	acta	acta	PROPN
ap-2970	1	7	polytechnica	polytechnica	PROPN
ap-2970	1	8	55(6):407–414	55(6):407–414	PROPN
ap-2970	1	9	,	,	PUNCT
ap-2970	1	10	2015	2015	NUM
ap-2970	1	11	©	©	PROPN
ap-2970	1	12	czech	czech	PROPN
ap-2970	1	13	technical	technical	PROPN
ap-2970	1	14	university	university	PROPN
ap-2970	1	15	in	in	ADP
ap-2970	1	16	prague	prague	PROPN
ap-2970	1	17	,	,	PUNCT
ap-2970	1	18	2015	2015	NUM
ap-2970	1	19	available	available	ADJ
ap-2970	1	20	online	online	ADV
ap-2970	1	21	at	at	ADP
ap-2970	1	22	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-2970	1	23	an	an	DET
ap-2970	1	24	interpolation	interpolation	NOUN
ap-2970	1	25	method	method	NOUN
ap-2970	1	26	for	for	ADP
ap-2970	1	27	determining	determine	VERB
ap-2970	1	28	the	the	DET
ap-2970	1	29	frequencies	frequency	NOUN
ap-2970	1	30	of	of	ADP
ap-2970	1	31	parameterized	parameterized	ADJ
ap-2970	1	32	large	large	ADJ
ap-2970	1	33	-	-	PUNCT
ap-2970	1	34	scale	scale	NOUN
ap-2970	1	35	structures	structure	NOUN
ap-2970	1	36	s.	s.	PROPN
ap-2970	1	37	nasisi∗	nasisi∗	PROPN
ap-2970	1	38	,	,	PUNCT
ap-2970	1	39	m.	m.	NOUN
ap-2970	1	40	valášek	valášek	PROPN
ap-2970	1	41	,	,	PUNCT
ap-2970	1	42	t.	t.	PROPN
ap-2970	1	43	vampola	vampola	PROPN
ap-2970	1	44	faculty	faculty	NOUN
ap-2970	1	45	of	of	ADP
ap-2970	1	46	mechanical	mechanical	ADJ
ap-2970	1	47	engineering	engineering	NOUN
ap-2970	1	48	,	,	PUNCT
ap-2970	1	49	ctvu	ctvu	VERB
ap-2970	1	50	in	in	ADP
ap-2970	1	51	prague	prague	NOUN
ap-2970	1	52	,	,	PUNCT
ap-2970	1	53	technická	technická	NOUN
ap-2970	1	54	4	4	NUM
ap-2970	1	55	,	,	PUNCT
ap-2970	1	56	16607	16607	NUM
ap-2970	1	57	,	,	PUNCT
ap-2970	1	58	prague	prague	PROPN
ap-2970	1	59	,	,	PUNCT
ap-2970	1	60	czech	czech	PROPN
ap-2970	1	61	republic	republic	NOUN
ap-2970	1	62	∗	∗	NOUN
ap-2970	1	63	corresponding	correspond	VERB
ap-2970	1	64	author	author	NOUN
ap-2970	1	65	:	:	PUNCT
ap-2970	1	66	salvatore.nasisi@fs.cvut.cz	salvatore.nasisi@fs.cvut.cz	NOUN
ap-2970	1	67	abstract	abstract	NOUN
ap-2970	1	68	.	.	PUNCT
ap-2970	2	1	parametric	parametric	ADJ
ap-2970	2	2	model	model	NOUN
ap-2970	2	3	order	order	NOUN
ap-2970	2	4	reduction	reduction	NOUN
ap-2970	2	5	(	(	PUNCT
ap-2970	2	6	pmor	pmor	PROPN
ap-2970	2	7	)	)	PUNCT
ap-2970	2	8	is	be	AUX
ap-2970	2	9	an	an	DET
ap-2970	2	10	emerging	emerge	VERB
ap-2970	2	11	category	category	NOUN
ap-2970	2	12	of	of	ADP
ap-2970	2	13	models	model	NOUN
ap-2970	2	14	developed	develop	VERB
ap-2970	2	15	with	with	ADP
ap-2970	2	16	the	the	DET
ap-2970	2	17	aim	aim	NOUN
ap-2970	2	18	of	of	ADP
ap-2970	2	19	describing	describe	VERB
ap-2970	2	20	reduced	reduce	VERB
ap-2970	2	21	first	first	ADV
ap-2970	2	22	and	and	CCONJ
ap-2970	2	23	second	second	ADJ
ap-2970	2	24	-	-	PUNCT
ap-2970	2	25	order	order	NOUN
ap-2970	2	26	dynamical	dynamical	ADJ
ap-2970	2	27	systems	system	NOUN
ap-2970	2	28	.	.	PUNCT
ap-2970	3	1	the	the	DET
ap-2970	3	2	use	use	NOUN
ap-2970	3	3	of	of	ADP
ap-2970	3	4	a	a	DET
ap-2970	3	5	prom	prom	NOUN
ap-2970	3	6	turns	turn	VERB
ap-2970	3	7	out	out	ADP
ap-2970	3	8	useful	useful	ADJ
ap-2970	3	9	in	in	ADP
ap-2970	3	10	a	a	DET
ap-2970	3	11	variety	variety	NOUN
ap-2970	3	12	of	of	ADP
ap-2970	3	13	applications	application	NOUN
ap-2970	3	14	ranging	range	VERB
ap-2970	3	15	from	from	ADP
ap-2970	3	16	the	the	DET
ap-2970	3	17	analysis	analysis	NOUN
ap-2970	3	18	of	of	ADP
ap-2970	3	19	micro	micro	ADJ
ap-2970	3	20	-	-	ADJ
ap-2970	3	21	electro	electro	ADJ
ap-2970	3	22	-	-	PUNCT
ap-2970	3	23	mechanical	mechanical	ADJ
ap-2970	3	24	systems	system	NOUN
ap-2970	3	25	(	(	PUNCT
ap-2970	3	26	mems	mem	NOUN
ap-2970	3	27	)	)	PUNCT
ap-2970	3	28	to	to	ADP
ap-2970	3	29	the	the	DET
ap-2970	3	30	optimization	optimization	NOUN
ap-2970	3	31	of	of	ADP
ap-2970	3	32	complex	complex	ADJ
ap-2970	3	33	mechanical	mechanical	ADJ
ap-2970	3	34	systems	system	NOUN
ap-2970	3	35	because	because	SCONJ
ap-2970	3	36	they	they	PRON
ap-2970	3	37	allow	allow	VERB
ap-2970	3	38	predicting	predict	VERB
ap-2970	3	39	the	the	DET
ap-2970	3	40	dynamical	dynamical	ADJ
ap-2970	3	41	behavior	behavior	NOUN
ap-2970	3	42	to	to	PART
ap-2970	3	43	be	be	AUX
ap-2970	3	44	predicted	predict	VERB
ap-2970	3	45	at	at	ADP
ap-2970	3	46	any	any	DET
ap-2970	3	47	values	value	NOUN
ap-2970	3	48	of	of	ADP
ap-2970	3	49	the	the	DET
ap-2970	3	50	quantities	quantity	NOUN
ap-2970	3	51	of	of	ADP
ap-2970	3	52	interest	interest	NOUN
ap-2970	3	53	within	within	ADP
ap-2970	3	54	the	the	DET
ap-2970	3	55	design	design	NOUN
ap-2970	3	56	space	space	NOUN
ap-2970	3	57	,	,	PUNCT
ap-2970	3	58	e.g.	e.g.	ADV
ap-2970	3	59	material	material	NOUN
ap-2970	3	60	properties	property	NOUN
ap-2970	3	61	,	,	PUNCT
ap-2970	3	62	geometric	geometric	ADJ
ap-2970	3	63	features	feature	NOUN
ap-2970	3	64	or	or	CCONJ
ap-2970	3	65	loading	loading	NOUN
ap-2970	3	66	conditions	condition	NOUN
ap-2970	3	67	.	.	PUNCT
ap-2970	4	1	the	the	DET
ap-2970	4	2	process	process	NOUN
ap-2970	4	3	underlying	underlie	VERB
ap-2970	4	4	the	the	DET
ap-2970	4	5	construction	construction	NOUN
ap-2970	4	6	of	of	ADP
ap-2970	4	7	a	a	DET
ap-2970	4	8	prom	prom	NOUN
ap-2970	4	9	using	use	VERB
ap-2970	4	10	an	an	DET
ap-2970	4	11	svd	svd	PROPN
ap-2970	4	12	-	-	PUNCT
ap-2970	4	13	based	base	VERB
ap-2970	4	14	method	method	NOUN
ap-2970	4	15	accounts	account	VERB
ap-2970	4	16	for	for	ADP
ap-2970	4	17	three	three	NUM
ap-2970	4	18	basic	basic	ADJ
ap-2970	4	19	phases	phase	NOUN
ap-2970	4	20	:	:	PUNCT
ap-2970	4	21	a	a	X
ap-2970	4	22	)	)	PUNCT
ap-2970	4	23	construction	construction	NOUN
ap-2970	4	24	of	of	ADP
ap-2970	4	25	several	several	ADJ
ap-2970	4	26	local	local	ADJ
ap-2970	4	27	roms	rom	NOUN
ap-2970	4	28	(	(	PUNCT
ap-2970	4	29	reduced	reduce	VERB
ap-2970	4	30	order	order	NOUN
ap-2970	4	31	models	model	NOUN
ap-2970	4	32	)	)	PUNCT
ap-2970	4	33	;	;	PUNCT
ap-2970	4	34	b	b	X
ap-2970	4	35	)	)	PUNCT
ap-2970	4	36	projection	projection	NOUN
ap-2970	4	37	of	of	ADP
ap-2970	4	38	the	the	DET
ap-2970	4	39	state	state	NOUN
ap-2970	4	40	-	-	PUNCT
ap-2970	4	41	space	space	NOUN
ap-2970	4	42	vector	vector	NOUN
ap-2970	4	43	onto	onto	ADP
ap-2970	4	44	a	a	DET
ap-2970	4	45	common	common	ADJ
ap-2970	4	46	subspace	subspace	NOUN
ap-2970	4	47	spanned	span	VERB
ap-2970	4	48	by	by	ADP
ap-2970	4	49	several	several	ADJ
ap-2970	4	50	transformation	transformation	NOUN
ap-2970	4	51	matrices	matrix	NOUN
ap-2970	4	52	derived	derive	VERB
ap-2970	4	53	in	in	ADP
ap-2970	4	54	the	the	DET
ap-2970	4	55	first	first	ADJ
ap-2970	4	56	step	step	NOUN
ap-2970	4	57	;	;	PUNCT
ap-2970	4	58	c	c	X
ap-2970	4	59	)	)	PUNCT
ap-2970	4	60	use	use	NOUN
ap-2970	4	61	of	of	ADP
ap-2970	4	62	an	an	DET
ap-2970	4	63	interpolation	interpolation	NOUN
ap-2970	4	64	method	method	NOUN
ap-2970	4	65	capable	capable	ADJ
ap-2970	4	66	of	of	ADP
ap-2970	4	67	capturing	capture	VERB
ap-2970	4	68	the	the	DET
ap-2970	4	69	values	value	NOUN
ap-2970	4	70	of	of	ADP
ap-2970	4	71	the	the	DET
ap-2970	4	72	quantity	quantity	NOUN
ap-2970	4	73	of	of	ADP
ap-2970	4	74	interest	interest	NOUN
ap-2970	4	75	for	for	ADP
ap-2970	4	76	one	one	NUM
ap-2970	4	77	or	or	CCONJ
ap-2970	4	78	more	more	ADJ
ap-2970	4	79	parameters	parameter	NOUN
ap-2970	4	80	.	.	PUNCT
ap-2970	5	1	one	one	NUM
ap-2970	5	2	of	of	ADP
ap-2970	5	3	the	the	DET
ap-2970	5	4	major	major	ADJ
ap-2970	5	5	difficulties	difficulty	NOUN
ap-2970	5	6	encountered	encounter	VERB
ap-2970	5	7	in	in	ADP
ap-2970	5	8	this	this	DET
ap-2970	5	9	process	process	NOUN
ap-2970	5	10	has	have	AUX
ap-2970	5	11	been	be	AUX
ap-2970	5	12	identified	identify	VERB
ap-2970	5	13	at	at	ADP
ap-2970	5	14	the	the	DET
ap-2970	5	15	level	level	NOUN
ap-2970	5	16	of	of	ADP
ap-2970	5	17	the	the	DET
ap-2970	5	18	interpolation	interpolation	NOUN
ap-2970	5	19	method	method	NOUN
ap-2970	5	20	and	and	CCONJ
ap-2970	5	21	can	can	AUX
ap-2970	5	22	be	be	AUX
ap-2970	5	23	encapsulated	encapsulate	VERB
ap-2970	5	24	in	in	ADP
ap-2970	5	25	the	the	DET
ap-2970	5	26	following	following	ADJ
ap-2970	5	27	contradiction	contradiction	NOUN
ap-2970	5	28	:	:	PUNCT
ap-2970	5	29	if	if	SCONJ
ap-2970	5	30	the	the	DET
ap-2970	5	31	number	number	NOUN
ap-2970	5	32	of	of	ADP
ap-2970	5	33	detailed	detailed	ADJ
ap-2970	5	34	finite	finite	ADJ
ap-2970	5	35	element	element	NOUN
ap-2970	5	36	analyses	analysis	NOUN
ap-2970	5	37	is	be	AUX
ap-2970	5	38	high	high	ADJ
ap-2970	5	39	then	then	ADV
ap-2970	5	40	an	an	DET
ap-2970	5	41	interpolation	interpolation	NOUN
ap-2970	5	42	method	method	NOUN
ap-2970	5	43	can	can	AUX
ap-2970	5	44	better	well	ADV
ap-2970	5	45	describe	describe	VERB
ap-2970	5	46	the	the	DET
ap-2970	5	47	system	system	NOUN
ap-2970	5	48	for	for	ADP
ap-2970	5	49	a	a	DET
ap-2970	5	50	given	give	VERB
ap-2970	5	51	choice	choice	NOUN
ap-2970	5	52	of	of	ADP
ap-2970	5	53	a	a	DET
ap-2970	5	54	parameter	parameter	NOUN
ap-2970	5	55	,	,	PUNCT
ap-2970	5	56	but	but	CCONJ
ap-2970	5	57	the	the	DET
ap-2970	5	58	computation	computation	NOUN
ap-2970	5	59	time	time	NOUN
ap-2970	5	60	is	be	AUX
ap-2970	5	61	higher	high	ADJ
ap-2970	5	62	.	.	PUNCT
ap-2970	6	1	in	in	ADP
ap-2970	6	2	this	this	DET
ap-2970	6	3	paper	paper	NOUN
ap-2970	6	4	,	,	PUNCT
ap-2970	6	5	a	a	DET
ap-2970	6	6	method	method	NOUN
ap-2970	6	7	is	be	AUX
ap-2970	6	8	proposed	propose	VERB
ap-2970	6	9	for	for	ADP
ap-2970	6	10	removing	remove	VERB
ap-2970	6	11	this	this	DET
ap-2970	6	12	contradiction	contradiction	NOUN
ap-2970	6	13	by	by	ADP
ap-2970	6	14	introducing	introduce	VERB
ap-2970	6	15	a	a	DET
ap-2970	6	16	new	new	ADJ
ap-2970	6	17	interpolation	interpolation	NOUN
ap-2970	6	18	method	method	NOUN
ap-2970	6	19	(	(	PUNCT
ap-2970	6	20	rsdm	rsdm	NOUN
ap-2970	6	21	)	)	PUNCT
ap-2970	6	22	.	.	PUNCT
ap-2970	7	1	this	this	DET
ap-2970	7	2	method	method	NOUN
ap-2970	7	3	allows	allow	VERB
ap-2970	7	4	us	we	PRON
ap-2970	7	5	to	to	PART
ap-2970	7	6	restore	restore	VERB
ap-2970	7	7	and	and	CCONJ
ap-2970	7	8	make	make	VERB
ap-2970	7	9	available	available	ADJ
ap-2970	7	10	to	to	ADP
ap-2970	7	11	the	the	DET
ap-2970	7	12	interpolation	interpolation	NOUN
ap-2970	7	13	tool	tool	NOUN
ap-2970	7	14	certain	certain	ADJ
ap-2970	7	15	natural	natural	ADJ
ap-2970	7	16	components	component	NOUN
ap-2970	7	17	belonging	belong	VERB
ap-2970	7	18	to	to	ADP
ap-2970	7	19	the	the	DET
ap-2970	7	20	matrices	matrix	NOUN
ap-2970	7	21	of	of	ADP
ap-2970	7	22	the	the	DET
ap-2970	7	23	full	full	ADJ
ap-2970	7	24	fe	fe	NOUN
ap-2970	7	25	model	model	NOUN
ap-2970	7	26	that	that	PRON
ap-2970	7	27	are	be	AUX
ap-2970	7	28	related	relate	VERB
ap-2970	7	29	,	,	PUNCT
ap-2970	7	30	on	on	ADP
ap-2970	7	31	one	one	NUM
ap-2970	7	32	hand	hand	NOUN
ap-2970	7	33	to	to	ADP
ap-2970	7	34	the	the	DET
ap-2970	7	35	process	process	NOUN
ap-2970	7	36	of	of	ADP
ap-2970	7	37	reduction	reduction	NOUN
ap-2970	7	38	and	and	CCONJ
ap-2970	7	39	,	,	PUNCT
ap-2970	7	40	on	on	ADP
ap-2970	7	41	the	the	DET
ap-2970	7	42	other	other	ADJ
ap-2970	7	43	to	to	ADP
ap-2970	7	44	the	the	DET
ap-2970	7	45	characteristics	characteristic	NOUN
ap-2970	7	46	of	of	ADP
ap-2970	7	47	a	a	DET
ap-2970	7	48	solid	solid	NOUN
ap-2970	7	49	in	in	ADP
ap-2970	7	50	the	the	DET
ap-2970	7	51	fe	fe	PROPN
ap-2970	7	52	theory	theory	NOUN
ap-2970	7	53	.	.	PUNCT
ap-2970	8	1	this	this	DET
ap-2970	8	2	approach	approach	NOUN
ap-2970	8	3	shows	show	VERB
ap-2970	8	4	higher	high	ADJ
ap-2970	8	5	accuracy	accuracy	NOUN
ap-2970	8	6	than	than	ADP
ap-2970	8	7	methods	method	NOUN
ap-2970	8	8	used	use	VERB
ap-2970	8	9	for	for	ADP
ap-2970	8	10	assessing	assess	VERB
ap-2970	8	11	the	the	DET
ap-2970	8	12	eigenbehavior	eigenbehavior	NOUN
ap-2970	8	13	of	of	ADP
ap-2970	8	14	the	the	DET
ap-2970	8	15	system	system	NOUN
ap-2970	8	16	.	.	PUNCT
ap-2970	9	1	a	a	DET
ap-2970	9	2	hexapod	hexapod	NOUN
ap-2970	9	3	will	will	AUX
ap-2970	9	4	be	be	AUX
ap-2970	9	5	analyzed	analyze	VERB
ap-2970	9	6	to	to	PART
ap-2970	9	7	confirm	confirm	VERB
ap-2970	9	8	the	the	DET
ap-2970	9	9	usefulness	usefulness	NOUN
ap-2970	9	10	of	of	ADP
ap-2970	9	11	the	the	DET
ap-2970	9	12	rsdm	rsdm	NOUN
ap-2970	9	13	.	.	PUNCT
ap-2970	10	1	keywords	keyword	NOUN
ap-2970	10	2	:	:	PUNCT
ap-2970	10	3	prom	prom	NOUN
ap-2970	10	4	;	;	PUNCT
ap-2970	10	5	singular	singular	NOUN
ap-2970	10	6	value	value	NOUN
ap-2970	10	7	decomposition	decomposition	NOUN
ap-2970	10	8	;	;	PUNCT
ap-2970	10	9	interpolation	interpolation	NOUN
ap-2970	10	10	method	method	NOUN
ap-2970	10	11	;	;	PUNCT
ap-2970	10	12	large	large	ADJ
ap-2970	10	13	-	-	PUNCT
ap-2970	10	14	scale	scale	NOUN
ap-2970	10	15	hexapod	hexapod	NOUN
ap-2970	10	16	;	;	PUNCT
ap-2970	10	17	structural	structural	ADJ
ap-2970	10	18	optimization	optimization	NOUN
ap-2970	10	19	.	.	PUNCT
ap-2970	11	1	1	1	X
ap-2970	11	2	.	.	X
ap-2970	11	3	introduction	introduction	NOUN
ap-2970	11	4	1.1	1.1	NUM
ap-2970	11	5	.	.	PUNCT
ap-2970	12	1	parametric	parametric	ADJ
ap-2970	12	2	model	model	NOUN
ap-2970	12	3	order	order	NOUN
ap-2970	12	4	reduction	reduction	NOUN
ap-2970	12	5	and	and	CCONJ
ap-2970	12	6	its	its	PRON
ap-2970	12	7	interpolation	interpolation	NOUN
ap-2970	12	8	within	within	ADP
ap-2970	12	9	the	the	DET
ap-2970	12	10	engineering	engineering	NOUN
ap-2970	12	11	community	community	NOUN
ap-2970	12	12	increasing	increase	VERB
ap-2970	12	13	efforts	effort	NOUN
ap-2970	12	14	have	have	AUX
ap-2970	12	15	been	be	AUX
ap-2970	12	16	focusing	focus	VERB
ap-2970	12	17	on	on	ADP
ap-2970	12	18	parametric	parametric	ADJ
ap-2970	12	19	models	model	NOUN
ap-2970	12	20	order	order	NOUN
ap-2970	12	21	reduction	reduction	NOUN
ap-2970	12	22	(	(	PUNCT
ap-2970	12	23	pmor	pmor	PROPN
ap-2970	12	24	)	)	PUNCT
ap-2970	12	25	as	as	ADP
ap-2970	12	26	a	a	DET
ap-2970	12	27	way	way	NOUN
ap-2970	12	28	of	of	ADP
ap-2970	12	29	diminishing	diminish	VERB
ap-2970	12	30	the	the	DET
ap-2970	12	31	computation	computation	NOUN
ap-2970	12	32	time	time	NOUN
ap-2970	12	33	for	for	ADP
ap-2970	12	34	simulating	simulate	VERB
ap-2970	12	35	large	large	ADJ
ap-2970	12	36	systems	system	NOUN
ap-2970	12	37	.	.	PUNCT
ap-2970	13	1	by	by	ADP
ap-2970	13	2	interpolating	interpolate	VERB
ap-2970	13	3	among	among	ADP
ap-2970	13	4	the	the	DET
ap-2970	13	5	reduced	reduce	VERB
ap-2970	13	6	matrices	matrix	NOUN
ap-2970	13	7	obtained	obtain	VERB
ap-2970	13	8	at	at	ADP
ap-2970	13	9	specific	specific	ADJ
ap-2970	13	10	values	value	NOUN
ap-2970	13	11	of	of	ADP
ap-2970	13	12	1	1	NUM
ap-2970	13	13	or	or	CCONJ
ap-2970	13	14	more	more	ADJ
ap-2970	13	15	parameters	parameter	NOUN
ap-2970	13	16	–	–	PUNCT
ap-2970	13	17	where	where	SCONJ
ap-2970	13	18	a	a	DET
ap-2970	13	19	parameters	parameter	NOUN
ap-2970	13	20	refers	refer	VERB
ap-2970	13	21	,	,	PUNCT
ap-2970	13	22	for	for	ADP
ap-2970	13	23	example	example	NOUN
ap-2970	13	24	,	,	PUNCT
ap-2970	13	25	to	to	ADP
ap-2970	13	26	the	the	DET
ap-2970	13	27	length	length	NOUN
ap-2970	13	28	of	of	ADP
ap-2970	13	29	a	a	DET
ap-2970	13	30	plate	plate	NOUN
ap-2970	13	31	,	,	PUNCT
ap-2970	13	32	the	the	DET
ap-2970	13	33	magnitude	magnitude	NOUN
ap-2970	13	34	of	of	ADP
ap-2970	13	35	an	an	DET
ap-2970	13	36	externally	externally	ADV
ap-2970	13	37	applied	apply	VERB
ap-2970	13	38	force	force	NOUN
ap-2970	13	39	,	,	PUNCT
ap-2970	13	40	a	a	DET
ap-2970	13	41	material	material	NOUN
ap-2970	13	42	property	property	NOUN
ap-2970	13	43	,	,	PUNCT
ap-2970	13	44	or	or	CCONJ
ap-2970	13	45	specific	specific	ADJ
ap-2970	13	46	boundary	boundary	ADJ
ap-2970	13	47	or	or	CCONJ
ap-2970	13	48	initial	initial	ADJ
ap-2970	13	49	conditions	condition	NOUN
ap-2970	13	50	–	–	PUNCT
ap-2970	13	51	the	the	DET
ap-2970	13	52	analyst	analyst	NOUN
ap-2970	13	53	is	be	AUX
ap-2970	13	54	able	able	ADJ
ap-2970	13	55	to	to	PART
ap-2970	13	56	obtain	obtain	VERB
ap-2970	13	57	very	very	ADV
ap-2970	13	58	fast	fast	ADJ
ap-2970	13	59	and	and	CCONJ
ap-2970	13	60	accurate	accurate	ADJ
ap-2970	13	61	models	model	NOUN
ap-2970	13	62	that	that	PRON
ap-2970	13	63	can	can	AUX
ap-2970	13	64	then	then	ADV
ap-2970	13	65	be	be	AUX
ap-2970	13	66	used	use	VERB
ap-2970	13	67	for	for	ADP
ap-2970	13	68	a	a	DET
ap-2970	13	69	number	number	NOUN
ap-2970	13	70	of	of	ADP
ap-2970	13	71	purposes	purpose	NOUN
ap-2970	13	72	.	.	PUNCT
ap-2970	14	1	one	one	NUM
ap-2970	14	2	indicator	indicator	NOUN
ap-2970	14	3	showing	show	VERB
ap-2970	14	4	how	how	SCONJ
ap-2970	14	5	increasing	increase	VERB
ap-2970	14	6	attention	attention	NOUN
ap-2970	14	7	has	have	AUX
ap-2970	14	8	been	be	AUX
ap-2970	14	9	spreading	spread	VERB
ap-2970	14	10	throughout	throughout	ADP
ap-2970	14	11	the	the	DET
ap-2970	14	12	scientific	scientific	ADJ
ap-2970	14	13	community	community	NOUN
ap-2970	14	14	is	be	AUX
ap-2970	14	15	shown	show	VERB
ap-2970	14	16	by	by	ADP
ap-2970	14	17	the	the	DET
ap-2970	14	18	application	application	NOUN
ap-2970	14	19	of	of	ADP
ap-2970	14	20	the	the	DET
ap-2970	14	21	parametric	parametric	ADJ
ap-2970	14	22	order	order	NOUN
ap-2970	14	23	reduction	reduction	NOUN
ap-2970	14	24	for	for	ADP
ap-2970	14	25	solving	solve	VERB
ap-2970	14	26	electrochemical	electrochemical	ADJ
ap-2970	14	27	models	model	NOUN
ap-2970	14	28	for	for	ADP
ap-2970	14	29	simulating	simulate	VERB
ap-2970	14	30	cyclic	cyclic	ADJ
ap-2970	14	31	voltammograms	voltammogram	NOUN
ap-2970	14	32	in	in	ADP
ap-2970	14	33	the	the	DET
ap-2970	14	34	field	field	NOUN
ap-2970	14	35	of	of	ADP
ap-2970	14	36	polarography	polarography	NOUN
ap-2970	14	37	[	[	X
ap-2970	14	38	8	8	NUM
ap-2970	14	39	]	]	PUNCT
ap-2970	14	40	;	;	PUNCT
ap-2970	14	41	for	for	ADP
ap-2970	14	42	simulating	simulate	VERB
ap-2970	14	43	3d	3d	PROPN
ap-2970	14	44	micro	micro	ADJ
ap-2970	14	45	-	-	ADJ
ap-2970	14	46	electro	electro	ADJ
ap-2970	14	47	-	-	PUNCT
ap-2970	14	48	mechanicalsystems	mechanicalsystem	NOUN
ap-2970	14	49	(	(	PUNCT
ap-2970	14	50	mems	mem	NOUN
ap-2970	14	51	)	)	PUNCT
ap-2970	15	1	[	[	X
ap-2970	15	2	19	19	NUM
ap-2970	15	3	]	]	X
ap-2970	15	4	;	;	PUNCT
ap-2970	15	5	for	for	ADP
ap-2970	15	6	design	design	NOUN
ap-2970	15	7	optimization	optimization	NOUN
ap-2970	15	8	[	[	X
ap-2970	15	9	9	9	NUM
ap-2970	15	10	]	]	PUNCT
ap-2970	15	11	,	,	PUNCT
ap-2970	15	12	and	and	CCONJ
ap-2970	15	13	also	also	ADV
ap-2970	15	14	for	for	ADP
ap-2970	15	15	control	control	NOUN
ap-2970	15	16	[	[	X
ap-2970	15	17	18	18	NUM
ap-2970	15	18	]	]	PUNCT
ap-2970	15	19	.	.	PUNCT
ap-2970	16	1	in	in	ADP
ap-2970	16	2	these	these	DET
ap-2970	16	3	studies	study	NOUN
ap-2970	16	4	,	,	PUNCT
ap-2970	16	5	ordinary	ordinary	ADJ
ap-2970	16	6	first	first	ADJ
ap-2970	16	7	and	and	CCONJ
ap-2970	16	8	second	second	ADJ
ap-2970	16	9	order	order	NOUN
ap-2970	16	10	differential	differential	ADJ
ap-2970	16	11	equations	equation	NOUN
ap-2970	16	12	are	be	AUX
ap-2970	16	13	solved	solve	VERB
ap-2970	16	14	to	to	PART
ap-2970	16	15	estimate	estimate	VERB
ap-2970	16	16	the	the	DET
ap-2970	16	17	frequency	frequency	NOUN
ap-2970	16	18	response	response	NOUN
ap-2970	16	19	of	of	ADP
ap-2970	16	20	the	the	DET
ap-2970	16	21	system	system	NOUN
ap-2970	16	22	within	within	ADP
ap-2970	16	23	a	a	DET
ap-2970	16	24	range	range	NOUN
ap-2970	16	25	of	of	ADP
ap-2970	16	26	frequencies	frequency	NOUN
ap-2970	16	27	of	of	ADP
ap-2970	16	28	interest	interest	NOUN
ap-2970	16	29	.	.	PUNCT
ap-2970	17	1	to	to	PART
ap-2970	17	2	reduce	reduce	VERB
ap-2970	17	3	these	these	DET
ap-2970	17	4	equations	equation	NOUN
ap-2970	17	5	,	,	PUNCT
ap-2970	17	6	most	most	ADJ
ap-2970	17	7	works	work	NOUN
ap-2970	17	8	employ	employ	VERB
ap-2970	17	9	mor	mor	PROPN
ap-2970	17	10	techniques	technique	NOUN
ap-2970	17	11	spanning	span	VERB
ap-2970	17	12	from	from	ADP
ap-2970	17	13	the	the	DET
ap-2970	17	14	truncated	truncate	VERB
ap-2970	17	15	balanced	balanced	ADJ
ap-2970	17	16	realization	realization	NOUN
ap-2970	17	17	method	method	NOUN
ap-2970	17	18	[	[	X
ap-2970	17	19	2	2	NUM
ap-2970	17	20	–	–	PUNCT
ap-2970	17	21	4	4	NUM
ap-2970	17	22	]	]	PUNCT
ap-2970	17	23	to	to	ADP
ap-2970	17	24	the	the	DET
ap-2970	17	25	krylov	krylov	PROPN
ap-2970	17	26	subspace	subspace	NOUN
ap-2970	17	27	method	method	NOUN
ap-2970	17	28	[	[	X
ap-2970	17	29	5–7	5–7	NOUN
ap-2970	17	30	,	,	PUNCT
ap-2970	17	31	10	10	NUM
ap-2970	17	32	]	]	PUNCT
ap-2970	17	33	.	.	PUNCT
ap-2970	18	1	1.2	1.2	NUM
ap-2970	18	2	.	.	PUNCT
ap-2970	18	3	problems	problem	NOUN
ap-2970	18	4	related	relate	VERB
ap-2970	18	5	to	to	ADP
ap-2970	18	6	the	the	DET
ap-2970	18	7	interpolation	interpolation	NOUN
ap-2970	18	8	method	method	VERB
ap-2970	18	9	the	the	DET
ap-2970	18	10	construction	construction	NOUN
ap-2970	18	11	of	of	ADP
ap-2970	18	12	a	a	DET
ap-2970	18	13	prom	prom	NOUN
ap-2970	18	14	is	be	AUX
ap-2970	18	15	accompanied	accompany	VERB
ap-2970	18	16	by	by	ADP
ap-2970	18	17	the	the	DET
ap-2970	18	18	use	use	NOUN
ap-2970	18	19	of	of	ADP
ap-2970	18	20	an	an	DET
ap-2970	18	21	interpolation	interpolation	NOUN
ap-2970	18	22	method	method	NOUN
ap-2970	18	23	for	for	ADP
ap-2970	18	24	predicting	predict	VERB
ap-2970	18	25	the	the	DET
ap-2970	18	26	values	value	NOUN
ap-2970	18	27	of	of	ADP
ap-2970	18	28	the	the	DET
ap-2970	18	29	quantity	quantity	NOUN
ap-2970	18	30	of	of	ADP
ap-2970	18	31	interest	interest	NOUN
ap-2970	18	32	for	for	ADP
ap-2970	18	33	one	one	NUM
ap-2970	18	34	or	or	CCONJ
ap-2970	18	35	more	more	ADJ
ap-2970	18	36	parameters	parameter	NOUN
ap-2970	18	37	at	at	ADP
ap-2970	18	38	any	any	DET
ap-2970	18	39	point	point	NOUN
ap-2970	18	40	in	in	ADP
ap-2970	18	41	the	the	DET
ap-2970	18	42	design	design	NOUN
ap-2970	18	43	space	space	NOUN
ap-2970	18	44	.	.	PUNCT
ap-2970	19	1	computing	compute	VERB
ap-2970	19	2	of	of	ADP
ap-2970	19	3	parametric	parametric	ADJ
ap-2970	19	4	stiffness	stiffness	NOUN
ap-2970	19	5	and	and	CCONJ
ap-2970	19	6	mass	mass	ADJ
ap-2970	19	7	matrices	matrix	NOUN
ap-2970	19	8	requires	require	VERB
ap-2970	19	9	the	the	DET
ap-2970	19	10	application	application	NOUN
ap-2970	19	11	of	of	ADP
ap-2970	19	12	a	a	DET
ap-2970	19	13	suitable	suitable	ADJ
ap-2970	19	14	interpolation	interpolation	NOUN
ap-2970	19	15	scheme	scheme	NOUN
ap-2970	19	16	to	to	PART
ap-2970	19	17	deliver	deliver	VERB
ap-2970	19	18	accurate	accurate	ADJ
ap-2970	19	19	results	result	NOUN
ap-2970	19	20	.	.	PUNCT
ap-2970	20	1	an	an	DET
ap-2970	20	2	interpolation	interpolation	NOUN
ap-2970	20	3	scheme	scheme	NOUN
ap-2970	20	4	for	for	ADP
ap-2970	20	5	the	the	DET
ap-2970	20	6	computation	computation	NOUN
ap-2970	20	7	of	of	ADP
ap-2970	20	8	parametric	parametric	ADJ
ap-2970	20	9	matrices	matrix	NOUN
ap-2970	20	10	is	be	AUX
ap-2970	20	11	suitable	suitable	ADJ
ap-2970	20	12	when	when	SCONJ
ap-2970	20	13	it	it	PRON
ap-2970	20	14	:	:	PUNCT
ap-2970	20	15	(	(	PUNCT
ap-2970	20	16	1	1	X
ap-2970	20	17	.	.	PUNCT
ap-2970	20	18	)	)	PUNCT
ap-2970	20	19	preserves	preserve	VERB
ap-2970	20	20	the	the	DET
ap-2970	20	21	property	property	NOUN
ap-2970	20	22	of	of	ADP
ap-2970	20	23	positive	positive	ADJ
ap-2970	20	24	definiteness	definiteness	NOUN
ap-2970	20	25	of	of	ADP
ap-2970	20	26	the	the	DET
ap-2970	20	27	parametric	parametric	ADJ
ap-2970	20	28	roms	rom	NOUN
ap-2970	20	29	;	;	PUNCT
ap-2970	20	30	407	407	NUM
ap-2970	20	31	http://dx.doi.org/10.14311/ap.2015.55.0407	http://dx.doi.org/10.14311/ap.2015.55.0407	NOUN
ap-2970	20	32	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-2970	20	33	s.	s.	PROPN
ap-2970	20	34	nasisi	nasisi	VERB
ap-2970	20	35	,	,	PUNCT
ap-2970	20	36	m.	m.	NOUN
ap-2970	20	37	valášek	valášek	PROPN
ap-2970	20	38	,	,	PUNCT
ap-2970	20	39	t.	t.	PROPN
ap-2970	20	40	vampola	vampola	PROPN
ap-2970	20	41	acta	acta	PROPN
ap-2970	20	42	polytechnica	polytechnica	PROPN
ap-2970	20	43	(	(	PUNCT
ap-2970	20	44	2	2	NUM
ap-2970	20	45	.	.	PUNCT
ap-2970	20	46	)	)	PUNCT
ap-2970	20	47	preserves	preserve	VERB
ap-2970	20	48	the	the	DET
ap-2970	20	49	quantity	quantity	NOUN
ap-2970	20	50	of	of	ADP
ap-2970	20	51	interest	interest	NOUN
ap-2970	20	52	within	within	ADP
ap-2970	20	53	the	the	DET
ap-2970	20	54	design	design	NOUN
ap-2970	20	55	space	space	NOUN
ap-2970	20	56	with	with	ADP
ap-2970	20	57	the	the	DET
ap-2970	20	58	least	least	ADJ
ap-2970	20	59	error	error	NOUN
ap-2970	20	60	;	;	PUNCT
ap-2970	20	61	(	(	PUNCT
ap-2970	20	62	3	3	NUM
ap-2970	20	63	.	.	PUNCT
ap-2970	20	64	)	)	PUNCT
ap-2970	20	65	requires	require	VERB
ap-2970	20	66	the	the	DET
ap-2970	20	67	lowest	low	ADJ
ap-2970	20	68	computational	computational	ADJ
ap-2970	20	69	cost	cost	NOUN
ap-2970	20	70	with	with	ADP
ap-2970	20	71	the	the	DET
ap-2970	20	72	simplest	simple	ADJ
ap-2970	20	73	or	or	CCONJ
ap-2970	20	74	minimal	minimal	ADJ
ap-2970	20	75	mathematical	mathematical	ADJ
ap-2970	20	76	apparatus	apparatus	NOUN
ap-2970	20	77	.	.	PUNCT
ap-2970	21	1	the	the	DET
ap-2970	21	2	first	first	ADJ
ap-2970	21	3	property	property	NOUN
ap-2970	21	4	is	be	AUX
ap-2970	21	5	essential	essential	ADJ
ap-2970	21	6	because	because	SCONJ
ap-2970	21	7	if	if	SCONJ
ap-2970	21	8	it	it	PRON
ap-2970	21	9	is	be	AUX
ap-2970	21	10	violated	violate	VERB
ap-2970	21	11	then	then	ADV
ap-2970	21	12	the	the	DET
ap-2970	21	13	computation	computation	NOUN
ap-2970	21	14	of	of	ADP
ap-2970	21	15	,	,	PUNCT
ap-2970	21	16	for	for	ADP
ap-2970	21	17	example	example	NOUN
ap-2970	21	18	,	,	PUNCT
ap-2970	21	19	the	the	DET
ap-2970	21	20	eigenfrequencies	eigenfrequencie	NOUN
ap-2970	21	21	of	of	ADP
ap-2970	21	22	the	the	DET
ap-2970	21	23	system	system	NOUN
ap-2970	21	24	under	under	ADP
ap-2970	21	25	investigation	investigation	NOUN
ap-2970	21	26	yields	yield	VERB
ap-2970	21	27	complex	complex	ADJ
ap-2970	21	28	numbers	number	NOUN
ap-2970	21	29	.	.	PUNCT
ap-2970	22	1	an	an	DET
ap-2970	22	2	intuitive	intuitive	ADJ
ap-2970	22	3	approach	approach	NOUN
ap-2970	22	4	used	use	VERB
ap-2970	22	5	for	for	ADP
ap-2970	22	6	interpolating	interpolate	VERB
ap-2970	22	7	between	between	ADP
ap-2970	22	8	two	two	NUM
ap-2970	22	9	or	or	CCONJ
ap-2970	22	10	more	more	ADJ
ap-2970	22	11	precomputed	precompute	VERB
ap-2970	22	12	roms	rom	NOUN
ap-2970	22	13	would	would	AUX
ap-2970	22	14	consist	consist	VERB
ap-2970	22	15	of	of	ADP
ap-2970	22	16	lettin	lettin	NOUN
ap-2970	22	17	a	a	DET
ap-2970	22	18	first	first	ADJ
ap-2970	22	19	,	,	PUNCT
ap-2970	22	20	second	second	ADJ
ap-2970	22	21	or	or	CCONJ
ap-2970	22	22	higher	high	ADJ
ap-2970	22	23	order	order	NOUN
ap-2970	22	24	interpolating	interpolate	VERB
ap-2970	22	25	polynomial	polynomial	ADJ
ap-2970	22	26	passing	pass	VERB
ap-2970	22	27	through	through	ADP
ap-2970	22	28	the	the	DET
ap-2970	22	29	values	value	NOUN
ap-2970	22	30	of	of	ADP
ap-2970	22	31	the	the	DET
ap-2970	22	32	k	k	PROPN
ap-2970	22	33	or	or	CCONJ
ap-2970	22	34	m	m	PROPN
ap-2970	22	35	entries	entry	NOUN
ap-2970	22	36	for	for	ADP
ap-2970	22	37	different	different	ADJ
ap-2970	22	38	values	value	NOUN
ap-2970	22	39	of	of	ADP
ap-2970	22	40	the	the	DET
ap-2970	22	41	parameter	parameter	NOUN
ap-2970	22	42	of	of	ADP
ap-2970	22	43	interest	interest	NOUN
ap-2970	22	44	.	.	PUNCT
ap-2970	23	1	therefore	therefore	ADV
ap-2970	23	2	,	,	PUNCT
ap-2970	23	3	if	if	SCONJ
ap-2970	23	4	the	the	DET
ap-2970	23	5	parameter	parameter	NOUN
ap-2970	23	6	that	that	PRON
ap-2970	23	7	is	be	AUX
ap-2970	23	8	used	use	VERB
ap-2970	23	9	is	be	AUX
ap-2970	23	10	,	,	PUNCT
ap-2970	23	11	for	for	ADP
ap-2970	23	12	example	example	NOUN
ap-2970	23	13	,	,	PUNCT
ap-2970	23	14	the	the	DET
ap-2970	23	15	length	length	NOUN
ap-2970	23	16	of	of	ADP
ap-2970	23	17	a	a	DET
ap-2970	23	18	cantilever	cantilever	NOUN
ap-2970	23	19	,	,	PUNCT
ap-2970	23	20	and	and	CCONJ
ap-2970	23	21	three	three	NUM
ap-2970	23	22	points	point	NOUN
ap-2970	23	23	have	have	AUX
ap-2970	23	24	been	be	AUX
ap-2970	23	25	chosen	choose	VERB
ap-2970	23	26	to	to	PART
ap-2970	23	27	explore	explore	VERB
ap-2970	23	28	the	the	DET
ap-2970	23	29	design	design	NOUN
ap-2970	23	30	space	space	NOUN
ap-2970	23	31	spanning	span	VERB
ap-2970	23	32	from	from	ADP
ap-2970	23	33	the	the	DET
ap-2970	23	34	first	first	ADJ
ap-2970	23	35	length	length	NOUN
ap-2970	23	36	,	,	PUNCT
ap-2970	23	37	say	say	VERB
ap-2970	23	38	l1	l1	PROPN
ap-2970	23	39	=	=	PROPN
ap-2970	23	40	200	200	NUM
ap-2970	23	41	mm	mm	NOUN
ap-2970	23	42	to	to	ADP
ap-2970	23	43	the	the	DET
ap-2970	23	44	third	third	ADJ
ap-2970	23	45	length	length	NOUN
ap-2970	23	46	l3	l3	PROPN
ap-2970	23	47	=	=	SYM
ap-2970	23	48	300	300	NUM
ap-2970	23	49	mm	mm	NOUN
ap-2970	23	50	through	through	ADP
ap-2970	23	51	l2	l2	NOUN
ap-2970	23	52	=	=	PUNCT
ap-2970	23	53	250	250	NUM
ap-2970	23	54	mm	mm	NOUN
ap-2970	23	55	,	,	PUNCT
ap-2970	23	56	a	a	DET
ap-2970	23	57	quadratic	quadratic	ADJ
ap-2970	23	58	polynomial	polynomial	NOUN
ap-2970	23	59	could	could	AUX
ap-2970	23	60	be	be	AUX
ap-2970	23	61	used	use	VERB
ap-2970	23	62	to	to	PART
ap-2970	23	63	interpolate	interpolate	VERB
ap-2970	23	64	between	between	ADP
ap-2970	23	65	points	point	NOUN
ap-2970	23	66	:	:	PUNCT
ap-2970	23	67	(	(	PUNCT
ap-2970	23	68	l1,k	l1,k	PROPN
ap-2970	23	69	(	(	PUNCT
ap-2970	23	70	1	1	NUM
ap-2970	23	71	)	)	PUNCT
ap-2970	23	72	ij	ij	NOUN
ap-2970	23	73	)	)	PUNCT
ap-2970	23	74	,	,	PUNCT
ap-2970	23	75	(	(	PUNCT
ap-2970	23	76	l2,k	l2,k	PROPN
ap-2970	23	77	(	(	PUNCT
ap-2970	23	78	2	2	NUM
ap-2970	23	79	)	)	PUNCT
ap-2970	23	80	ij	ij	NOUN
ap-2970	23	81	)	)	PUNCT
ap-2970	23	82	,	,	PUNCT
ap-2970	23	83	(	(	PUNCT
ap-2970	23	84	l3,k	l3,k	ADV
ap-2970	23	85	(	(	PUNCT
ap-2970	23	86	3	3	NUM
ap-2970	23	87	)	)	PUNCT
ap-2970	23	88	ij	ij	NOUN
ap-2970	23	89	)	)	PUNCT
ap-2970	23	90	and	and	CCONJ
ap-2970	23	91	(	(	PUNCT
ap-2970	23	92	l1,m	l1,m	PROPN
ap-2970	23	93	(	(	PUNCT
ap-2970	23	94	1	1	NUM
ap-2970	23	95	)	)	PUNCT
ap-2970	23	96	ij	ij	NOUN
ap-2970	23	97	)	)	PUNCT
ap-2970	23	98	,	,	PUNCT
ap-2970	23	99	(	(	PUNCT
ap-2970	23	100	l2,m	l2,m	PROPN
ap-2970	23	101	(	(	PUNCT
ap-2970	23	102	2	2	NUM
ap-2970	23	103	)	)	PUNCT
ap-2970	23	104	ij	ij	NOUN
ap-2970	23	105	)	)	PUNCT
ap-2970	23	106	,	,	PUNCT
ap-2970	23	107	(	(	PUNCT
ap-2970	23	108	l3,m	l3,m	PROPN
ap-2970	23	109	(	(	PUNCT
ap-2970	23	110	3	3	NUM
ap-2970	23	111	)	)	PUNCT
ap-2970	23	112	ij	ij	NOUN
ap-2970	23	113	)	)	PUNCT
ap-2970	23	114	,	,	PUNCT
ap-2970	23	115	where	where	SCONJ
ap-2970	23	116	the	the	DET
ap-2970	23	117	superscript	superscript	NOUN
ap-2970	23	118	indicates	indicate	VERB
ap-2970	23	119	at	at	ADP
ap-2970	23	120	what	what	PRON
ap-2970	23	121	length	length	NOUN
ap-2970	23	122	value	value	NOUN
ap-2970	23	123	the	the	DET
ap-2970	23	124	matrix	matrix	NOUN
ap-2970	23	125	has	have	AUX
ap-2970	23	126	been	be	AUX
ap-2970	23	127	computed	compute	VERB
ap-2970	23	128	.	.	PUNCT
ap-2970	24	1	although	although	SCONJ
ap-2970	24	2	this	this	DET
ap-2970	24	3	scheme	scheme	NOUN
ap-2970	24	4	seems	seem	VERB
ap-2970	24	5	attractive	attractive	ADJ
ap-2970	24	6	due	due	ADP
ap-2970	24	7	to	to	ADP
ap-2970	24	8	the	the	DET
ap-2970	24	9	use	use	NOUN
ap-2970	24	10	of	of	ADP
ap-2970	24	11	reduced	reduce	VERB
ap-2970	24	12	matrices	matrix	NOUN
ap-2970	24	13	and	and	CCONJ
ap-2970	24	14	available	available	ADJ
ap-2970	24	15	functions	function	NOUN
ap-2970	24	16	for	for	ADP
ap-2970	24	17	computing	compute	VERB
ap-2970	24	18	interpolating	interpolate	VERB
ap-2970	24	19	polynomials	polynomial	NOUN
ap-2970	24	20	,	,	PUNCT
ap-2970	24	21	it	it	PRON
ap-2970	24	22	produces	produce	VERB
ap-2970	24	23	ineffective	ineffective	ADJ
ap-2970	24	24	results	result	NOUN
ap-2970	24	25	.	.	PUNCT
ap-2970	25	1	the	the	DET
ap-2970	25	2	reason	reason	NOUN
ap-2970	25	3	is	be	AUX
ap-2970	25	4	that	that	DET
ap-2970	25	5	homologous	homologous	ADJ
ap-2970	25	6	entries	entry	NOUN
ap-2970	25	7	,	,	PUNCT
ap-2970	25	8	e.g.	e.g.	ADV
ap-2970	25	9	,	,	PUNCT
ap-2970	25	10	of	of	ADP
ap-2970	25	11	a	a	DET
ap-2970	25	12	stiffness	stiffness	ADJ
ap-2970	25	13	matrix	matrix	NOUN
ap-2970	25	14	calculated	calculate	VERB
ap-2970	25	15	at	at	ADP
ap-2970	25	16	different	different	ADJ
ap-2970	25	17	length	length	NOUN
ap-2970	25	18	values	value	NOUN
ap-2970	25	19	exhibits	exhibit	VERB
ap-2970	25	20	a	a	DET
ap-2970	25	21	highly	highly	ADV
ap-2970	25	22	nonlinear	nonlinear	ADJ
ap-2970	25	23	behavior	behavior	NOUN
ap-2970	25	24	.	.	PUNCT
ap-2970	26	1	therefore	therefore	ADV
ap-2970	26	2	,	,	PUNCT
ap-2970	26	3	one	one	NUM
ap-2970	26	4	consequence	consequence	NOUN
ap-2970	26	5	of	of	ADP
ap-2970	26	6	applying	apply	VERB
ap-2970	26	7	this	this	DET
ap-2970	26	8	method	method	NOUN
ap-2970	26	9	is	be	AUX
ap-2970	26	10	that	that	SCONJ
ap-2970	26	11	the	the	DET
ap-2970	26	12	property	property	NOUN
ap-2970	26	13	(	(	PUNCT
ap-2970	26	14	1	1	NUM
ap-2970	26	15	)	)	PUNCT
ap-2970	26	16	above	above	ADV
ap-2970	26	17	is	be	AUX
ap-2970	26	18	violated	violate	VERB
ap-2970	26	19	.	.	PUNCT
ap-2970	27	1	there	there	PRON
ap-2970	27	2	is	be	VERB
ap-2970	27	3	a	a	DET
ap-2970	27	4	possible	possible	ADJ
ap-2970	27	5	way	way	NOUN
ap-2970	27	6	out	out	ADV
ap-2970	27	7	;	;	PUNCT
ap-2970	27	8	it	it	PRON
ap-2970	27	9	would	would	AUX
ap-2970	27	10	entail	entail	VERB
ap-2970	27	11	calculating	calculate	VERB
ap-2970	27	12	the	the	DET
ap-2970	27	13	matrices	matrix	NOUN
ap-2970	27	14	for	for	ADP
ap-2970	27	15	length	length	NOUN
ap-2970	27	16	values	value	NOUN
ap-2970	27	17	very	very	ADV
ap-2970	27	18	close	close	ADV
ap-2970	27	19	to	to	ADP
ap-2970	27	20	each	each	DET
ap-2970	27	21	other	other	ADJ
ap-2970	27	22	.	.	PUNCT
ap-2970	28	1	in	in	ADP
ap-2970	28	2	this	this	DET
ap-2970	28	3	case	case	NOUN
ap-2970	28	4	,	,	PUNCT
ap-2970	28	5	the	the	DET
ap-2970	28	6	parametric	parametric	ADJ
ap-2970	28	7	matrix	matrix	NOUN
ap-2970	28	8	would	would	AUX
ap-2970	28	9	be	be	AUX
ap-2970	28	10	readily	readily	ADV
ap-2970	28	11	available	available	ADJ
ap-2970	28	12	for	for	ADP
ap-2970	28	13	any	any	DET
ap-2970	28	14	length	length	NOUN
ap-2970	28	15	value	value	NOUN
ap-2970	28	16	.	.	PUNCT
ap-2970	29	1	the	the	DET
ap-2970	29	2	problem	problem	NOUN
ap-2970	29	3	is	be	AUX
ap-2970	29	4	that	that	SCONJ
ap-2970	29	5	this	this	DET
ap-2970	29	6	procedure	procedure	NOUN
ap-2970	29	7	would	would	AUX
ap-2970	29	8	require	require	VERB
ap-2970	29	9	the	the	DET
ap-2970	29	10	interval	interval	NOUN
ap-2970	29	11	between	between	ADP
ap-2970	29	12	two	two	NUM
ap-2970	29	13	adjacent	adjacent	ADJ
ap-2970	29	14	matrices	matrix	NOUN
ap-2970	29	15	be	be	AUX
ap-2970	29	16	so	so	ADV
ap-2970	29	17	narrow	narrow	ADJ
ap-2970	29	18	that	that	SCONJ
ap-2970	29	19	it	it	PRON
ap-2970	29	20	would	would	AUX
ap-2970	29	21	discourage	discourage	VERB
ap-2970	29	22	the	the	DET
ap-2970	29	23	use	use	NOUN
ap-2970	29	24	of	of	ADP
ap-2970	29	25	a	a	DET
ap-2970	29	26	prom	prom	NOUN
ap-2970	29	27	,	,	PUNCT
ap-2970	29	28	and	and	CCONJ
ap-2970	29	29	would	would	AUX
ap-2970	29	30	therefore	therefore	ADV
ap-2970	29	31	find	find	VERB
ap-2970	29	32	no	no	DET
ap-2970	29	33	application	application	NOUN
ap-2970	29	34	at	at	ADV
ap-2970	29	35	all	all	ADV
ap-2970	29	36	for	for	ADP
ap-2970	29	37	engineering	engineering	NOUN
ap-2970	29	38	purposes	purpose	NOUN
ap-2970	29	39	.	.	PUNCT
ap-2970	30	1	a	a	DET
ap-2970	30	2	simple	simple	ADJ
ap-2970	30	3	way	way	NOUN
ap-2970	30	4	to	to	PART
ap-2970	30	5	obtain	obtain	VERB
ap-2970	30	6	a	a	DET
ap-2970	30	7	parametric	parametric	ADJ
ap-2970	30	8	rom	rom	NOUN
ap-2970	30	9	for	for	ADP
ap-2970	30	10	a	a	DET
ap-2970	30	11	given	give	VERB
ap-2970	30	12	set	set	NOUN
ap-2970	30	13	of	of	ADP
ap-2970	30	14	parameters	parameter	NOUN
ap-2970	30	15	entails	entail	VERB
ap-2970	30	16	performing	perform	VERB
ap-2970	30	17	a	a	DET
ap-2970	30	18	linear	linear	ADJ
ap-2970	30	19	approximation	approximation	NOUN
ap-2970	30	20	of	of	ADP
ap-2970	30	21	a	a	DET
ap-2970	30	22	rom	rom	NOUN
ap-2970	30	23	that	that	PRON
ap-2970	30	24	lies	lie	VERB
ap-2970	30	25	between	between	ADP
ap-2970	30	26	two	two	NUM
ap-2970	30	27	precomputed	precompute	VERB
ap-2970	30	28	roms	rom	NOUN
ap-2970	30	29	obtained	obtain	VERB
ap-2970	30	30	for	for	ADP
ap-2970	30	31	different	different	ADJ
ap-2970	30	32	values	value	NOUN
ap-2970	30	33	of	of	ADP
ap-2970	30	34	the	the	DET
ap-2970	30	35	parameters	parameter	NOUN
ap-2970	30	36	.	.	PUNCT
ap-2970	31	1	these	these	DET
ap-2970	31	2	precomputed	precompute	VERB
ap-2970	31	3	roms	rom	NOUN
ap-2970	31	4	are	be	AUX
ap-2970	31	5	weighted	weight	VERB
ap-2970	31	6	by	by	ADP
ap-2970	31	7	appropriately	appropriately	ADV
ap-2970	31	8	chosen	choose	VERB
ap-2970	31	9	functions	function	NOUN
ap-2970	31	10	and	and	CCONJ
ap-2970	31	11	the	the	DET
ap-2970	31	12	final	final	ADJ
ap-2970	31	13	,	,	PUNCT
ap-2970	31	14	parametric	parametric	ADJ
ap-2970	31	15	matrix	matrix	NOUN
ap-2970	31	16	is	be	AUX
ap-2970	31	17	generated	generate	VERB
ap-2970	31	18	by	by	ADP
ap-2970	31	19	superimposing	superimpose	VERB
ap-2970	31	20	system	system	NOUN
ap-2970	31	21	matrices	matrix	NOUN
ap-2970	31	22	,	,	PUNCT
ap-2970	31	23	as	as	SCONJ
ap-2970	31	24	shown	show	VERB
ap-2970	31	25	in	in	ADP
ap-2970	31	26	[	[	X
ap-2970	31	27	16	16	NUM
ap-2970	31	28	]	]	PUNCT
ap-2970	31	29	.	.	PUNCT
ap-2970	32	1	in	in	ADP
ap-2970	32	2	order	order	NOUN
ap-2970	32	3	to	to	PART
ap-2970	32	4	improve	improve	VERB
ap-2970	32	5	the	the	DET
ap-2970	32	6	effectiveness	effectiveness	NOUN
ap-2970	32	7	of	of	ADP
ap-2970	32	8	the	the	DET
ap-2970	32	9	interpolation	interpolation	NOUN
ap-2970	32	10	tool	tool	NOUN
ap-2970	32	11	,	,	PUNCT
ap-2970	32	12	and	and	CCONJ
ap-2970	32	13	due	due	ADP
ap-2970	32	14	to	to	ADP
ap-2970	32	15	the	the	DET
ap-2970	32	16	difficulty	difficulty	NOUN
ap-2970	32	17	arising	arise	VERB
ap-2970	32	18	from	from	ADP
ap-2970	32	19	describing	describe	VERB
ap-2970	32	20	the	the	DET
ap-2970	32	21	parametric	parametric	ADJ
ap-2970	32	22	effects	effect	NOUN
ap-2970	32	23	for	for	ADP
ap-2970	32	24	nonlinear	nonlinear	ADJ
ap-2970	32	25	systems	system	NOUN
ap-2970	32	26	a	a	DET
ap-2970	32	27	spline	spline	NOUN
ap-2970	32	28	-	-	PUNCT
ap-2970	32	29	based	base	VERB
ap-2970	32	30	interpolation	interpolation	NOUN
ap-2970	32	31	method	method	NOUN
ap-2970	32	32	is	be	AUX
ap-2970	32	33	introduced	introduce	VERB
ap-2970	32	34	in	in	ADP
ap-2970	32	35	[	[	X
ap-2970	32	36	17	17	NUM
ap-2970	32	37	]	]	PUNCT
ap-2970	32	38	and	and	CCONJ
ap-2970	32	39	also	also	ADV
ap-2970	32	40	in	in	ADP
ap-2970	32	41	[	[	X
ap-2970	32	42	15	15	NUM
ap-2970	32	43	]	]	SYM
ap-2970	32	44	,	,	PUNCT
ap-2970	32	45	where	where	SCONJ
ap-2970	32	46	element	element	NOUN
ap-2970	32	47	-	-	ADJ
ap-2970	32	48	wise	wise	ADJ
ap-2970	32	49	interpolation	interpolation	NOUN
ap-2970	32	50	in	in	ADP
ap-2970	32	51	the	the	DET
ap-2970	32	52	tangent	tangent	ADJ
ap-2970	32	53	space	space	NOUN
ap-2970	32	54	of	of	ADP
ap-2970	32	55	the	the	DET
ap-2970	32	56	matrix	matrix	NOUN
ap-2970	32	57	manifold	manifold	NOUN
ap-2970	32	58	is	be	AUX
ap-2970	32	59	employed	employ	VERB
ap-2970	32	60	.	.	PUNCT
ap-2970	33	1	[	[	X
ap-2970	33	2	15	15	NUM
ap-2970	33	3	]	]	PUNCT
ap-2970	33	4	also	also	ADV
ap-2970	33	5	addresses	address	VERB
ap-2970	33	6	the	the	DET
ap-2970	33	7	mode	mode	NOUN
ap-2970	33	8	-	-	PUNCT
ap-2970	33	9	veering	veer	VERB
ap-2970	33	10	problem	problem	NOUN
ap-2970	33	11	and	and	CCONJ
ap-2970	33	12	shows	show	VERB
ap-2970	33	13	how	how	SCONJ
ap-2970	33	14	the	the	DET
ap-2970	33	15	method	method	NOUN
ap-2970	33	16	can	can	AUX
ap-2970	33	17	detect	detect	VERB
ap-2970	33	18	the	the	DET
ap-2970	33	19	narrowing	narrowing	NOUN
ap-2970	33	20	of	of	ADP
ap-2970	33	21	the	the	DET
ap-2970	33	22	frequency	frequency	NOUN
ap-2970	33	23	gaps	gap	NOUN
ap-2970	33	24	between	between	ADP
ap-2970	33	25	two	two	NUM
ap-2970	33	26	adjacent	adjacent	ADJ
ap-2970	33	27	mode	mode	NOUN
ap-2970	33	28	shapes	shape	NOUN
ap-2970	33	29	.	.	PUNCT
ap-2970	34	1	in	in	ADP
ap-2970	34	2	[	[	X
ap-2970	34	3	18	18	NUM
ap-2970	34	4	]	]	PUNCT
ap-2970	34	5	,	,	PUNCT
ap-2970	34	6	the	the	DET
ap-2970	34	7	interpolation	interpolation	NOUN
ap-2970	34	8	method	method	NOUN
ap-2970	34	9	that	that	PRON
ap-2970	34	10	is	be	AUX
ap-2970	34	11	used	use	VERB
ap-2970	34	12	is	be	AUX
ap-2970	34	13	based	base	VERB
ap-2970	34	14	on	on	ADP
ap-2970	34	15	the	the	DET
ap-2970	34	16	direct	direct	ADJ
ap-2970	34	17	matrix	matrix	NOUN
ap-2970	34	18	interpolation	interpolation	NOUN
ap-2970	34	19	method	method	NOUN
ap-2970	34	20	–	–	PUNCT
ap-2970	34	21	in	in	ADP
ap-2970	34	22	this	this	DET
ap-2970	34	23	paper	paper	NOUN
ap-2970	34	24	indicated	indicate	VERB
ap-2970	34	25	as	as	ADP
ap-2970	34	26	dmm	dmm	PROPN
ap-2970	34	27	–	–	PUNCT
ap-2970	34	28	which	which	PRON
ap-2970	34	29	consists	consist	VERB
ap-2970	34	30	of	of	ADP
ap-2970	34	31	the	the	DET
ap-2970	34	32	weighted	weighted	ADJ
ap-2970	34	33	sum	sum	NOUN
ap-2970	34	34	of	of	ADP
ap-2970	34	35	the	the	DET
ap-2970	34	36	reduced	reduce	VERB
ap-2970	34	37	matrices	matrix	NOUN
ap-2970	34	38	calculated	calculate	VERB
ap-2970	34	39	in	in	ADP
ap-2970	34	40	correspondence	correspondence	NOUN
ap-2970	34	41	with	with	ADP
ap-2970	34	42	specific	specific	ADJ
ap-2970	34	43	values	value	NOUN
ap-2970	34	44	of	of	ADP
ap-2970	34	45	the	the	DET
ap-2970	34	46	chosen	choose	VERB
ap-2970	34	47	parameter(s	parameter(s	PROPN
ap-2970	34	48	)	)	PUNCT
ap-2970	34	49	.	.	PUNCT
ap-2970	35	1	the	the	DET
ap-2970	35	2	typical	typical	ADJ
ap-2970	35	3	form	form	NOUN
ap-2970	35	4	of	of	ADP
ap-2970	35	5	,	,	PUNCT
ap-2970	35	6	for	for	ADP
ap-2970	35	7	example	example	NOUN
ap-2970	35	8	,	,	PUNCT
ap-2970	35	9	a	a	DET
ap-2970	35	10	parametric	parametric	ADJ
ap-2970	35	11	reduced	reduce	VERB
ap-2970	35	12	stiffness	stiffness	ADJ
ap-2970	35	13	matrix	matrix	NOUN
ap-2970	35	14	is	be	AUX
ap-2970	35	15	given	give	VERB
ap-2970	35	16	by	by	ADP
ap-2970	35	17	k(p1	k(p1	NOUN
ap-2970	35	18	,	,	PUNCT
ap-2970	35	19	p2	p2	PROPN
ap-2970	35	20	,	,	PUNCT
ap-2970	35	21	.	.	PUNCT
ap-2970	35	22	.	.	PUNCT
ap-2970	35	23	.	.	PUNCT
ap-2970	35	24	)	)	PUNCT
ap-2970	36	1	=	=	PUNCT
ap-2970	36	2	k∑	k∑	PROPN
ap-2970	37	1	j=1	j=1	PROPN
ap-2970	37	2	αj(p1	αj(p1	NOUN
ap-2970	37	3	,	,	PUNCT
ap-2970	37	4	p2	p2	NOUN
ap-2970	37	5	,	,	PUNCT
ap-2970	37	6	.	.	PUNCT
ap-2970	37	7	.	.	PUNCT
ap-2970	37	8	.	.	PUNCT
ap-2970	37	9	)	)	PUNCT
ap-2970	38	1	kj	kj	PROPN
ap-2970	38	2	,	,	PUNCT
ap-2970	38	3	(	(	PUNCT
ap-2970	38	4	1	1	X
ap-2970	38	5	)	)	PUNCT
ap-2970	38	6	where	where	SCONJ
ap-2970	38	7	∑k	∑k	PROPN
ap-2970	38	8	j=1	j=1	PROPN
ap-2970	38	9	αj(p1	αj(p1	NOUN
ap-2970	38	10	,	,	PUNCT
ap-2970	38	11	p2	p2	NOUN
ap-2970	38	12	,	,	PUNCT
ap-2970	38	13	.	.	PUNCT
ap-2970	38	14	.	.	PUNCT
ap-2970	38	15	.	.	PUNCT
ap-2970	38	16	)	)	PUNCT
ap-2970	39	1	=	=	SYM
ap-2970	39	2	1	1	NUM
ap-2970	39	3	,	,	PUNCT
ap-2970	39	4	αj(pi	αj(pi	NOUN
ap-2970	39	5	)	)	PUNCT
ap-2970	39	6	=	=	SYM
ap-2970	39	7	δij	δij	NOUN
ap-2970	39	8	for	for	ADP
ap-2970	39	9	i	i	PROPN
ap-2970	39	10	,	,	PUNCT
ap-2970	39	11	j	j	PROPN
ap-2970	39	12	=	=	SYM
ap-2970	39	13	1	1	NUM
ap-2970	39	14	,	,	PUNCT
ap-2970	39	15	.	.	PUNCT
ap-2970	39	16	.	.	PUNCT
ap-2970	39	17	.	.	PUNCT
ap-2970	40	1	,	,	PUNCT
ap-2970	40	2	k	k	NOUN
ap-2970	40	3	,	,	PUNCT
ap-2970	40	4	p	p	PROPN
ap-2970	40	5	∈	∈	PROPN
ap-2970	40	6	π	π	X
ap-2970	40	7	.	.	PUNCT
ap-2970	41	1	here	here	ADV
ap-2970	41	2	,	,	PUNCT
ap-2970	41	3	αj(p1	αj(p1	NOUN
ap-2970	41	4	,	,	PUNCT
ap-2970	41	5	p2	p2	NOUN
ap-2970	41	6	,	,	PUNCT
ap-2970	41	7	.	.	PUNCT
ap-2970	41	8	.	.	PUNCT
ap-2970	41	9	.	.	PUNCT
ap-2970	41	10	)	)	PUNCT
ap-2970	41	11	are	be	AUX
ap-2970	41	12	the	the	DET
ap-2970	41	13	coefficients	coefficient	NOUN
ap-2970	41	14	depending	depend	VERB
ap-2970	41	15	on	on	ADP
ap-2970	41	16	the	the	DET
ap-2970	41	17	selected	select	VERB
ap-2970	41	18	parameters	parameter	NOUN
ap-2970	41	19	while	while	SCONJ
ap-2970	41	20	kj	kj	PROPN
ap-2970	41	21	are	be	AUX
ap-2970	41	22	the	the	DET
ap-2970	41	23	reduced	reduce	VERB
ap-2970	41	24	local	local	ADJ
ap-2970	41	25	stiffness	stiffness	NOUN
ap-2970	41	26	matrices	matrix	NOUN
ap-2970	41	27	.	.	PUNCT
ap-2970	42	1	in	in	ADP
ap-2970	42	2	[	[	X
ap-2970	42	3	18	18	NUM
ap-2970	42	4	]	]	PUNCT
ap-2970	42	5	,	,	PUNCT
ap-2970	42	6	the	the	DET
ap-2970	42	7	dmm	dmm	PROPN
ap-2970	42	8	is	be	AUX
ap-2970	42	9	employed	employ	VERB
ap-2970	42	10	for	for	ADP
ap-2970	42	11	computating	computate	VERB
ap-2970	42	12	of	of	ADP
ap-2970	42	13	the	the	DET
ap-2970	42	14	frequency	frequency	NOUN
ap-2970	42	15	response	response	NOUN
ap-2970	42	16	of	of	ADP
ap-2970	42	17	first	first	ADJ
ap-2970	42	18	-	-	PUNCT
ap-2970	42	19	order	order	NOUN
ap-2970	42	20	linear	linear	ADJ
ap-2970	42	21	time	time	NOUN
ap-2970	42	22	invariant	invariant	ADJ
ap-2970	42	23	dynamical	dynamical	ADJ
ap-2970	42	24	systems	system	NOUN
ap-2970	42	25	,	,	PUNCT
ap-2970	42	26	and	and	CCONJ
ap-2970	42	27	two	two	NUM
ap-2970	42	28	local	local	ADJ
ap-2970	42	29	models	model	NOUN
ap-2970	42	30	–	–	PUNCT
ap-2970	42	31	i.e.	i.e.	X
ap-2970	42	32	,	,	PUNCT
ap-2970	42	33	two	two	NUM
ap-2970	42	34	pairs	pair	NOUN
ap-2970	42	35	of	of	ADP
ap-2970	42	36	reduced	reduce	VERB
ap-2970	42	37	k	k	PROPN
ap-2970	42	38	and	and	CCONJ
ap-2970	42	39	m	m	PROPN
ap-2970	42	40	–	–	PUNCT
ap-2970	42	41	are	be	AUX
ap-2970	42	42	used	use	VERB
ap-2970	42	43	for	for	ADP
ap-2970	42	44	1	1	NUM
ap-2970	42	45	or	or	CCONJ
ap-2970	42	46	2	2	NUM
ap-2970	42	47	parameters	parameter	NOUN
ap-2970	42	48	.	.	PUNCT
ap-2970	43	1	unfortunately	unfortunately	ADV
ap-2970	43	2	,	,	PUNCT
ap-2970	43	3	the	the	DET
ap-2970	43	4	application	application	NOUN
ap-2970	43	5	of	of	ADP
ap-2970	43	6	this	this	DET
ap-2970	43	7	superposition	superposition	NOUN
ap-2970	43	8	of	of	ADP
ap-2970	43	9	weighted	weight	VERB
ap-2970	43	10	matrices	matrix	NOUN
ap-2970	43	11	relies	rely	VERB
ap-2970	43	12	on	on	ADP
ap-2970	43	13	the	the	DET
ap-2970	43	14	use	use	NOUN
ap-2970	43	15	of	of	ADP
ap-2970	43	16	only	only	ADV
ap-2970	43	17	1	1	NUM
ap-2970	43	18	parameter	parameter	NOUN
ap-2970	43	19	for	for	ADP
ap-2970	43	20	a	a	DET
ap-2970	43	21	linear	linear	ADJ
ap-2970	43	22	interpolation	interpolation	NOUN
ap-2970	43	23	,	,	PUNCT
ap-2970	43	24	which	which	PRON
ap-2970	43	25	implies	imply	VERB
ap-2970	43	26	the	the	DET
ap-2970	43	27	use	use	NOUN
ap-2970	43	28	of	of	ADP
ap-2970	43	29	only	only	ADV
ap-2970	43	30	two	two	NUM
ap-2970	43	31	precomputed	precompute	VERB
ap-2970	43	32	roms	rom	NOUN
ap-2970	43	33	.	.	PUNCT
ap-2970	44	1	this	this	PRON
ap-2970	44	2	can	can	AUX
ap-2970	44	3	strongly	strongly	ADV
ap-2970	44	4	affect	affect	VERB
ap-2970	44	5	the	the	DET
ap-2970	44	6	precision	precision	NOUN
ap-2970	44	7	with	with	ADP
ap-2970	44	8	which	which	PRON
ap-2970	44	9	the	the	DET
ap-2970	44	10	final	final	ADJ
ap-2970	44	11	parametric	parametric	ADJ
ap-2970	44	12	matrices	matrix	NOUN
ap-2970	44	13	can	can	AUX
ap-2970	44	14	be	be	AUX
ap-2970	44	15	employed	employ	VERB
ap-2970	44	16	with	with	ADP
ap-2970	44	17	success	success	NOUN
ap-2970	44	18	in	in	ADP
ap-2970	44	19	assessing	assess	VERB
ap-2970	44	20	the	the	DET
ap-2970	44	21	eigenbehavior	eigenbehavior	NOUN
ap-2970	44	22	of	of	ADP
ap-2970	44	23	the	the	DET
ap-2970	44	24	system	system	NOUN
ap-2970	44	25	.	.	PUNCT
ap-2970	45	1	in	in	ADP
ap-2970	45	2	[	[	X
ap-2970	45	3	15	15	NUM
ap-2970	45	4	]	]	X
ap-2970	45	5	,	,	PUNCT
ap-2970	45	6	a	a	DET
ap-2970	45	7	wing	wing	NOUN
ap-2970	45	8	with	with	ADP
ap-2970	45	9	store	store	NOUN
ap-2970	45	10	configuration	configuration	NOUN
ap-2970	45	11	is	be	AUX
ap-2970	45	12	presented	present	VERB
ap-2970	45	13	,	,	PUNCT
ap-2970	45	14	and	and	CCONJ
ap-2970	45	15	first	first	ADJ
ap-2970	45	16	8	8	NUM
ap-2970	45	17	frequencies	frequency	NOUN
ap-2970	45	18	are	be	AUX
ap-2970	45	19	calculated	calculate	VERB
ap-2970	45	20	,	,	PUNCT
ap-2970	45	21	but	but	CCONJ
ap-2970	45	22	there	there	PRON
ap-2970	45	23	is	be	VERB
ap-2970	45	24	error	error	NOUN
ap-2970	45	25	frequency	frequency	NOUN
ap-2970	45	26	of	of	ADP
ap-2970	45	27	up	up	ADV
ap-2970	45	28	10	10	NUM
ap-2970	45	29	%	%	NOUN
ap-2970	45	30	.	.	PUNCT
ap-2970	46	1	furthermore	furthermore	ADV
ap-2970	46	2	,	,	PUNCT
ap-2970	46	3	in	in	ADP
ap-2970	46	4	the	the	DET
ap-2970	46	5	aforementioned	aforementioned	ADJ
ap-2970	46	6	works	work	NOUN
ap-2970	46	7	it	it	PRON
ap-2970	46	8	have	have	AUX
ap-2970	46	9	not	not	PART
ap-2970	46	10	yet	yet	ADV
ap-2970	46	11	pointed	point	VERB
ap-2970	46	12	out	out	ADP
ap-2970	46	13	the	the	DET
ap-2970	46	14	importance	importance	NOUN
ap-2970	46	15	of	of	ADP
ap-2970	46	16	recovering	recover	VERB
ap-2970	46	17	the	the	DET
ap-2970	46	18	components	component	NOUN
ap-2970	46	19	of	of	ADP
ap-2970	46	20	the	the	DET
ap-2970	46	21	fe	fe	NOUN
ap-2970	46	22	matrices	matrix	NOUN
ap-2970	46	23	associated	associate	VERB
ap-2970	46	24	to	to	ADP
ap-2970	46	25	the	the	DET
ap-2970	46	26	process	process	NOUN
ap-2970	46	27	of	of	ADP
ap-2970	46	28	reduction	reduction	NOUN
ap-2970	46	29	and	and	CCONJ
ap-2970	46	30	the	the	DET
ap-2970	46	31	deformation	deformation	NOUN
ap-2970	46	32	of	of	ADP
ap-2970	46	33	the	the	DET
ap-2970	46	34	solid	solid	NOUN
ap-2970	46	35	.	.	PUNCT
ap-2970	47	1	in	in	ADP
ap-2970	47	2	order	order	NOUN
ap-2970	47	3	to	to	PART
ap-2970	47	4	take	take	VERB
ap-2970	47	5	these	these	DET
ap-2970	47	6	components	component	NOUN
ap-2970	47	7	into	into	ADP
ap-2970	47	8	account	account	NOUN
ap-2970	47	9	,	,	PUNCT
ap-2970	47	10	it	it	PRON
ap-2970	47	11	is	be	AUX
ap-2970	47	12	necessary	necessary	ADJ
ap-2970	47	13	to	to	PART
ap-2970	47	14	use	use	VERB
ap-2970	47	15	a	a	DET
ap-2970	47	16	different	different	ADJ
ap-2970	47	17	viewpoint	viewpoint	NOUN
ap-2970	47	18	,	,	PUNCT
ap-2970	47	19	i.e.	i.e.	X
ap-2970	47	20	to	to	PART
ap-2970	47	21	proceed	proceed	VERB
ap-2970	47	22	backwards	backwards	ADV
ap-2970	47	23	from	from	ADP
ap-2970	47	24	the	the	DET
ap-2970	47	25	roms	rom	NOUN
ap-2970	47	26	to	to	ADP
ap-2970	47	27	the	the	DET
ap-2970	47	28	mathematical	mathematical	ADJ
ap-2970	47	29	structure	structure	NOUN
ap-2970	47	30	that	that	PRON
ap-2970	47	31	characterizes	characterize	VERB
ap-2970	47	32	the	the	DET
ap-2970	47	33	computation	computation	NOUN
ap-2970	47	34	of	of	ADP
ap-2970	47	35	the	the	DET
ap-2970	47	36	matrices	matrix	NOUN
ap-2970	47	37	of	of	ADP
ap-2970	47	38	an	an	DET
ap-2970	47	39	fe	fe	X
ap-2970	47	40	assemblage	assemblage	NOUN
ap-2970	47	41	.	.	PUNCT
ap-2970	48	1	2	2	X
ap-2970	48	2	.	.	X
ap-2970	48	3	aims	aim	VERB
ap-2970	48	4	the	the	DET
ap-2970	48	5	first	first	ADJ
ap-2970	48	6	objective	objective	NOUN
ap-2970	48	7	of	of	ADP
ap-2970	48	8	this	this	DET
ap-2970	48	9	paper	paper	NOUN
ap-2970	48	10	is	be	AUX
ap-2970	48	11	to	to	PART
ap-2970	48	12	introduce	introduce	VERB
ap-2970	48	13	a	a	DET
ap-2970	48	14	new	new	ADJ
ap-2970	48	15	interpolation	interpolation	NOUN
ap-2970	48	16	method	method	NOUN
ap-2970	48	17	named	name	VERB
ap-2970	48	18	rsdm	rsdm	NOUN
ap-2970	48	19	for	for	ADP
ap-2970	48	20	adapting	adapt	VERB
ap-2970	48	21	the	the	DET
ap-2970	48	22	framework	framework	NOUN
ap-2970	48	23	of	of	ADP
ap-2970	48	24	the	the	DET
ap-2970	48	25	dmm	dmm	PROPN
ap-2970	48	26	to	to	ADP
ap-2970	48	27	a	a	DET
ap-2970	48	28	different	different	ADJ
ap-2970	48	29	structure	structure	NOUN
ap-2970	48	30	of	of	ADP
ap-2970	48	31	stiffness	stiffness	NOUN
ap-2970	48	32	and	and	CCONJ
ap-2970	48	33	mass	mass	NOUN
ap-2970	48	34	matrices	matrix	NOUN
ap-2970	48	35	.	.	PUNCT
ap-2970	49	1	instead	instead	ADV
ap-2970	49	2	of	of	ADP
ap-2970	49	3	performing	perform	VERB
ap-2970	49	4	element	element	ADJ
ap-2970	49	5	-	-	ADJ
ap-2970	49	6	wise	wise	ADJ
ap-2970	49	7	interpolation	interpolation	NOUN
ap-2970	49	8	of	of	ADP
ap-2970	49	9	precomputed	precompute	VERB
ap-2970	49	10	roms	rom	NOUN
ap-2970	49	11	,	,	PUNCT
ap-2970	49	12	the	the	DET
ap-2970	49	13	proposed	propose	VERB
ap-2970	49	14	method	method	NOUN
ap-2970	49	15	transforms	transform	VERB
ap-2970	49	16	the	the	DET
ap-2970	49	17	interpolating	interpolate	VERB
ap-2970	49	18	matrices	matrix	NOUN
ap-2970	49	19	into	into	ADP
ap-2970	49	20	a	a	DET
ap-2970	49	21	form	form	NOUN
ap-2970	49	22	that	that	PRON
ap-2970	49	23	allows	allow	VERB
ap-2970	49	24	interpolation	interpolation	NOUN
ap-2970	49	25	among	among	ADP
ap-2970	49	26	these	these	DET
ap-2970	49	27	deformation	deformation	NOUN
ap-2970	49	28	components	component	NOUN
ap-2970	49	29	,	,	PUNCT
ap-2970	49	30	and	and	CCONJ
ap-2970	49	31	changes	change	NOUN
ap-2970	49	32	in	in	ADP
ap-2970	49	33	the	the	DET
ap-2970	49	34	coordinates	coordinate	NOUN
ap-2970	49	35	of	of	ADP
ap-2970	49	36	the	the	DET
ap-2970	49	37	system	system	NOUN
ap-2970	49	38	,	,	PUNCT
ap-2970	49	39	which	which	PRON
ap-2970	49	40	are	be	AUX
ap-2970	49	41	made	make	VERB
ap-2970	49	42	visible	visible	ADJ
ap-2970	49	43	by	by	ADP
ap-2970	49	44	appropriate	appropriate	ADJ
ap-2970	49	45	factorization	factorization	NOUN
ap-2970	49	46	.	.	PUNCT
ap-2970	50	1	this	this	DET
ap-2970	50	2	process	process	NOUN
ap-2970	50	3	seems	seem	VERB
ap-2970	50	4	essential	essential	ADJ
ap-2970	50	5	,	,	PUNCT
ap-2970	50	6	because	because	SCONJ
ap-2970	50	7	certain	certain	ADJ
ap-2970	50	8	components	component	NOUN
ap-2970	50	9	describing	describe	VERB
ap-2970	50	10	the	the	DET
ap-2970	50	11	matrices	matrix	NOUN
ap-2970	50	12	of	of	ADP
ap-2970	50	13	an	an	DET
ap-2970	50	14	fe	fe	X
ap-2970	50	15	assemblage	assemblage	NOUN
ap-2970	50	16	have	have	AUX
ap-2970	50	17	remained	remained	AUX
ap-2970	50	18	encapsulated	encapsulate	VERB
ap-2970	50	19	after	after	ADP
ap-2970	50	20	the	the	DET
ap-2970	50	21	process	process	NOUN
ap-2970	50	22	of	of	ADP
ap-2970	50	23	reduction	reduction	NOUN
ap-2970	50	24	,	,	PUNCT
ap-2970	50	25	and	and	CCONJ
ap-2970	50	26	have	have	VERB
ap-2970	50	27	blent	blent	NOUN
ap-2970	50	28	with	with	ADP
ap-2970	50	29	the	the	DET
ap-2970	50	30	components	component	NOUN
ap-2970	50	31	of	of	ADP
ap-2970	50	32	the	the	DET
ap-2970	50	33	transformation	transformation	NOUN
ap-2970	50	34	matrix	matrix	NOUN
ap-2970	50	35	;	;	PUNCT
ap-2970	50	36	while	while	SCONJ
ap-2970	50	37	other	other	ADJ
ap-2970	50	38	components	component	NOUN
ap-2970	50	39	,	,	PUNCT
ap-2970	50	40	e.g.	e.g.	ADV
ap-2970	50	41	those	those	PRON
ap-2970	50	42	pertaining	pertain	VERB
ap-2970	50	43	to	to	ADP
ap-2970	50	44	the	the	DET
ap-2970	50	45	rigid	rigid	ADJ
ap-2970	50	46	rotation	rotation	NOUN
ap-2970	50	47	,	,	PUNCT
ap-2970	50	48	which	which	PRON
ap-2970	50	49	do	do	AUX
ap-2970	50	50	not	not	PART
ap-2970	50	51	participate	participate	VERB
ap-2970	50	52	in	in	ADP
ap-2970	50	53	the	the	DET
ap-2970	50	54	deformation	deformation	NOUN
ap-2970	50	55	of	of	ADP
ap-2970	50	56	the	the	DET
ap-2970	50	57	solid	solid	ADJ
ap-2970	50	58	,	,	PUNCT
ap-2970	50	59	are	be	AUX
ap-2970	50	60	not	not	PART
ap-2970	50	61	removed	remove	VERB
ap-2970	50	62	.	.	PUNCT
ap-2970	51	1	as	as	ADP
ap-2970	51	2	result	result	NOUN
ap-2970	51	3	,	,	PUNCT
ap-2970	51	4	the	the	DET
ap-2970	51	5	application	application	NOUN
ap-2970	51	6	of	of	ADP
ap-2970	51	7	a	a	DET
ap-2970	51	8	matrix	matrix	NOUN
ap-2970	51	9	interpolation	interpolation	NOUN
ap-2970	51	10	based	base	VERB
ap-2970	51	11	method	method	NOUN
ap-2970	51	12	without	without	ADP
ap-2970	51	13	this	this	DET
ap-2970	51	14	step	step	NOUN
ap-2970	51	15	remains	remain	VERB
ap-2970	51	16	,	,	PUNCT
ap-2970	51	17	so	so	ADV
ap-2970	51	18	to	to	PART
ap-2970	51	19	say	say	VERB
ap-2970	51	20	,	,	PUNCT
ap-2970	51	21	“	"	PUNCT
ap-2970	51	22	blind	blind	ADJ
ap-2970	51	23	”	"	PUNCT
ap-2970	51	24	and	and	CCONJ
ap-2970	51	25	incapable	incapable	ADJ
ap-2970	51	26	of	of	ADP
ap-2970	51	27	discerning	discern	VERB
ap-2970	51	28	between	between	ADP
ap-2970	51	29	the	the	DET
ap-2970	51	30	useful	useful	ADJ
ap-2970	51	31	components	component	NOUN
ap-2970	51	32	.	.	PUNCT
ap-2970	52	1	in	in	ADP
ap-2970	52	2	the	the	DET
ap-2970	52	3	first	first	ADJ
ap-2970	52	4	step	step	NOUN
ap-2970	52	5	of	of	ADP
ap-2970	52	6	the	the	DET
ap-2970	52	7	method	method	NOUN
ap-2970	52	8	,	,	PUNCT
ap-2970	52	9	two	two	NUM
ap-2970	52	10	pairs	pair	NOUN
ap-2970	52	11	of	of	ADP
ap-2970	52	12	matrices	matrix	NOUN
ap-2970	52	13	–	–	PUNCT
ap-2970	52	14	the	the	DET
ap-2970	52	15	stiffness	stiffness	NOUN
ap-2970	52	16	and	and	CCONJ
ap-2970	52	17	mass	mass	ADJ
ap-2970	52	18	matrices	matrix	NOUN
ap-2970	52	19	–	–	PUNCT
ap-2970	52	20	are	be	AUX
ap-2970	52	21	factorized	factorize	VERB
ap-2970	52	22	in	in	ADP
ap-2970	52	23	such	such	DET
ap-2970	52	24	a	a	DET
ap-2970	52	25	way	way	NOUN
ap-2970	52	26	as	as	SCONJ
ap-2970	52	27	to	to	PART
ap-2970	52	28	rule	rule	VERB
ap-2970	52	29	out	out	ADP
ap-2970	52	30	the	the	DET
ap-2970	52	31	useless	useless	ADJ
ap-2970	52	32	408	408	NUM
ap-2970	52	33	vol	vol	NOUN
ap-2970	52	34	.	.	PUNCT
ap-2970	53	1	55	55	NUM
ap-2970	53	2	no	no	NOUN
ap-2970	53	3	.	.	PUNCT
ap-2970	54	1	6/2015	6/2015	NUM
ap-2970	54	2	an	an	DET
ap-2970	54	3	interpolation	interpolation	NOUN
ap-2970	54	4	method	method	NOUN
ap-2970	54	5	for	for	ADP
ap-2970	54	6	determining	determine	VERB
ap-2970	54	7	the	the	DET
ap-2970	54	8	frequencies	frequency	NOUN
ap-2970	54	9	figure	figure	VERB
ap-2970	54	10	1	1	NUM
ap-2970	54	11	.	.	PUNCT
ap-2970	55	1	normalized	normalize	VERB
ap-2970	55	2	relative	relative	ADJ
ap-2970	55	3	frequency	frequency	NOUN
ap-2970	55	4	difference	difference	NOUN
ap-2970	55	5	(	(	PUNCT
ap-2970	55	6	nrfd	nrfd	NOUN
ap-2970	55	7	)	)	PUNCT
ap-2970	55	8	vs	vs	ADP
ap-2970	55	9	mode	mode	NOUN
ap-2970	55	10	number	number	NOUN
ap-2970	55	11	for	for	ADP
ap-2970	55	12	a	a	DET
ap-2970	55	13	comparison	comparison	NOUN
ap-2970	55	14	between	between	ADP
ap-2970	55	15	the	the	DET
ap-2970	55	16	proposed	propose	VERB
ap-2970	55	17	rsdm	rsdm	NOUN
ap-2970	55	18	and	and	CCONJ
ap-2970	55	19	the	the	DET
ap-2970	55	20	direct	direct	ADJ
ap-2970	55	21	matrix	matrix	NOUN
ap-2970	55	22	method	method	NOUN
ap-2970	55	23	(	(	PUNCT
ap-2970	55	24	dmm	dmm	PROPN
ap-2970	55	25	)	)	PUNCT
ap-2970	55	26	.	.	PUNCT
ap-2970	56	1	the	the	DET
ap-2970	56	2	proposed	propose	VERB
ap-2970	56	3	method	method	NOUN
ap-2970	56	4	preserves	preserve	VERB
ap-2970	56	5	the	the	DET
ap-2970	56	6	first	first	ADJ
ap-2970	56	7	three	three	NUM
ap-2970	56	8	frequencies	frequency	NOUN
ap-2970	56	9	better	well	ADJ
ap-2970	56	10	than	than	ADP
ap-2970	56	11	dmm	dmm	PROPN
ap-2970	56	12	.	.	PUNCT
ap-2970	56	13	components	component	NOUN
ap-2970	56	14	and	and	CCONJ
ap-2970	56	15	restore	restore	VERB
ap-2970	56	16	those	those	DET
ap-2970	56	17	components	component	NOUN
ap-2970	56	18	that	that	PRON
ap-2970	56	19	have	have	AUX
ap-2970	56	20	been	be	AUX
ap-2970	56	21	blended	blend	VERB
ap-2970	56	22	after	after	ADP
ap-2970	56	23	the	the	DET
ap-2970	56	24	process	process	NOUN
ap-2970	56	25	of	of	ADP
ap-2970	56	26	reduction	reduction	NOUN
ap-2970	56	27	.	.	PUNCT
ap-2970	57	1	the	the	DET
ap-2970	57	2	overall	overall	ADJ
ap-2970	57	3	computational	computational	ADJ
ap-2970	57	4	complexity	complexity	NOUN
ap-2970	57	5	and	and	CCONJ
ap-2970	57	6	the	the	DET
ap-2970	57	7	numerical	numerical	ADJ
ap-2970	57	8	properties	property	NOUN
ap-2970	57	9	take	take	VERB
ap-2970	57	10	advantage	advantage	NOUN
ap-2970	57	11	of	of	ADP
ap-2970	57	12	this	this	DET
ap-2970	57	13	procedure	procedure	NOUN
ap-2970	57	14	.	.	PUNCT
ap-2970	58	1	in	in	ADP
ap-2970	58	2	fact	fact	NOUN
ap-2970	58	3	,	,	PUNCT
ap-2970	58	4	in	in	ADP
ap-2970	58	5	order	order	NOUN
ap-2970	58	6	to	to	PART
ap-2970	58	7	obtain	obtain	VERB
ap-2970	58	8	very	very	ADV
ap-2970	58	9	accurate	accurate	ADJ
ap-2970	58	10	prom	prom	NOUN
ap-2970	58	11	,	,	PUNCT
ap-2970	58	12	especially	especially	ADV
ap-2970	58	13	within	within	ADP
ap-2970	58	14	the	the	DET
ap-2970	58	15	broad	broad	ADJ
ap-2970	58	16	design	design	NOUN
ap-2970	58	17	space	space	NOUN
ap-2970	58	18	of	of	ADP
ap-2970	58	19	the	the	DET
ap-2970	58	20	chosen	choose	VERB
ap-2970	58	21	parameters	parameter	NOUN
ap-2970	58	22	,	,	PUNCT
ap-2970	58	23	it	it	PRON
ap-2970	58	24	might	might	AUX
ap-2970	58	25	be	be	AUX
ap-2970	58	26	necessary	necessary	ADJ
ap-2970	58	27	to	to	PART
ap-2970	58	28	run	run	VERB
ap-2970	58	29	several	several	ADJ
ap-2970	58	30	detailed	detailed	ADJ
ap-2970	58	31	finite	finite	NOUN
ap-2970	58	32	element	element	NOUN
ap-2970	58	33	analyses	analysis	NOUN
ap-2970	58	34	.	.	PUNCT
ap-2970	59	1	consequently	consequently	ADV
ap-2970	59	2	,	,	PUNCT
ap-2970	59	3	it	it	PRON
ap-2970	59	4	might	might	AUX
ap-2970	59	5	be	be	AUX
ap-2970	59	6	time	time	NOUN
ap-2970	59	7	-	-	PUNCT
ap-2970	59	8	consuming	consume	VERB
ap-2970	59	9	to	to	PART
ap-2970	59	10	run	run	VERB
ap-2970	59	11	several	several	ADJ
ap-2970	59	12	simulations	simulation	NOUN
ap-2970	59	13	in	in	ADP
ap-2970	59	14	order	order	NOUN
ap-2970	59	15	to	to	PART
ap-2970	59	16	keep	keep	VERB
ap-2970	59	17	the	the	DET
ap-2970	59	18	accuracy	accuracy	NOUN
ap-2970	59	19	within	within	ADP
ap-2970	59	20	a	a	DET
ap-2970	59	21	given	give	VERB
ap-2970	59	22	tolerance	tolerance	NOUN
ap-2970	59	23	.	.	PUNCT
ap-2970	60	1	this	this	DET
ap-2970	60	2	problem	problem	NOUN
ap-2970	60	3	can	can	AUX
ap-2970	60	4	be	be	AUX
ap-2970	60	5	condensed	condense	VERB
ap-2970	60	6	in	in	ADP
ap-2970	60	7	the	the	DET
ap-2970	60	8	following	following	ADJ
ap-2970	60	9	contradiction	contradiction	NOUN
ap-2970	60	10	:	:	PUNCT
ap-2970	60	11	if	if	SCONJ
ap-2970	60	12	the	the	DET
ap-2970	60	13	number	number	NOUN
ap-2970	60	14	of	of	ADP
ap-2970	60	15	detailed	detailed	ADJ
ap-2970	60	16	finite	finite	ADJ
ap-2970	60	17	element	element	NOUN
ap-2970	60	18	analyses	analysis	NOUN
ap-2970	60	19	is	be	AUX
ap-2970	60	20	high	high	ADJ
ap-2970	60	21	(	(	PUNCT
ap-2970	60	22	3	3	NUM
ap-2970	60	23	or	or	CCONJ
ap-2970	60	24	more	more	ADJ
ap-2970	60	25	)	)	PUNCT
ap-2970	60	26	,	,	PUNCT
ap-2970	60	27	then	then	ADV
ap-2970	60	28	an	an	DET
ap-2970	60	29	interpolation	interpolation	NOUN
ap-2970	60	30	method	method	NOUN
ap-2970	60	31	can	can	AUX
ap-2970	60	32	better	well	ADV
ap-2970	60	33	describe	describe	VERB
ap-2970	60	34	the	the	DET
ap-2970	60	35	system	system	NOUN
ap-2970	60	36	because	because	SCONJ
ap-2970	60	37	it	it	PRON
ap-2970	60	38	can	can	AUX
ap-2970	60	39	more	more	ADV
ap-2970	60	40	effectively	effectively	ADV
ap-2970	60	41	predict	predict	VERB
ap-2970	60	42	the	the	DET
ap-2970	60	43	frequencies	frequency	NOUN
ap-2970	60	44	pertaining	pertain	VERB
ap-2970	60	45	to	to	ADP
ap-2970	60	46	intermediate	intermediate	ADJ
ap-2970	60	47	values	value	NOUN
ap-2970	60	48	of	of	ADP
ap-2970	60	49	the	the	DET
ap-2970	60	50	chosen	choose	VERB
ap-2970	60	51	parameter(s	parameter(s	PROPN
ap-2970	60	52	)	)	PUNCT
ap-2970	60	53	,	,	PUNCT
ap-2970	60	54	but	but	CCONJ
ap-2970	60	55	the	the	DET
ap-2970	60	56	computation	computation	NOUN
ap-2970	60	57	time	time	NOUN
ap-2970	60	58	becomes	become	VERB
ap-2970	60	59	higher	high	ADJ
ap-2970	60	60	.	.	PUNCT
ap-2970	61	1	as	as	SCONJ
ap-2970	61	2	it	it	PRON
ap-2970	61	3	will	will	AUX
ap-2970	61	4	be	be	AUX
ap-2970	61	5	shown	show	VERB
ap-2970	61	6	,	,	PUNCT
ap-2970	61	7	instead	instead	ADV
ap-2970	61	8	of	of	ADP
ap-2970	61	9	searching	search	VERB
ap-2970	61	10	for	for	ADP
ap-2970	61	11	a	a	DET
ap-2970	61	12	trade	trade	NOUN
ap-2970	61	13	-	-	PUNCT
ap-2970	61	14	off	off	NOUN
ap-2970	61	15	between	between	ADP
ap-2970	61	16	these	these	DET
ap-2970	61	17	two	two	NUM
ap-2970	61	18	conflicting	conflict	VERB
ap-2970	61	19	requirements	requirement	NOUN
ap-2970	61	20	–	–	PUNCT
ap-2970	61	21	computation	computation	NOUN
ap-2970	61	22	time	time	NOUN
ap-2970	61	23	and	and	CCONJ
ap-2970	61	24	computation	computation	NOUN
ap-2970	61	25	accuracy	accuracy	NOUN
ap-2970	61	26	–	–	PUNCT
ap-2970	61	27	it	it	PRON
ap-2970	61	28	is	be	AUX
ap-2970	61	29	possible	possible	ADJ
ap-2970	61	30	to	to	PART
ap-2970	61	31	improve	improve	VERB
ap-2970	61	32	the	the	DET
ap-2970	61	33	effectiveness	effectiveness	NOUN
ap-2970	61	34	of	of	ADP
ap-2970	61	35	the	the	DET
ap-2970	61	36	method	method	NOUN
ap-2970	61	37	and	and	CCONJ
ap-2970	61	38	to	to	PART
ap-2970	61	39	remove	remove	VERB
ap-2970	61	40	the	the	DET
ap-2970	61	41	above	above	ADJ
ap-2970	61	42	contradiction	contradiction	NOUN
ap-2970	61	43	by	by	ADP
ap-2970	61	44	making	make	VERB
ap-2970	61	45	minimal	minimal	ADJ
ap-2970	61	46	changes	change	NOUN
ap-2970	61	47	to	to	ADP
ap-2970	61	48	the	the	DET
ap-2970	61	49	direct	direct	ADJ
ap-2970	61	50	matrix	matrix	NOUN
ap-2970	61	51	method	method	NOUN
ap-2970	61	52	for	for	ADP
ap-2970	61	53	the	the	DET
ap-2970	61	54	system	system	NOUN
ap-2970	61	55	.	.	PUNCT
ap-2970	62	1	since	since	SCONJ
ap-2970	62	2	this	this	DET
ap-2970	62	3	solution	solution	NOUN
ap-2970	62	4	to	to	ADP
ap-2970	62	5	the	the	DET
ap-2970	62	6	above	above	ADJ
ap-2970	62	7	problem	problem	NOUN
ap-2970	62	8	involves	involve	VERB
ap-2970	62	9	minimal	minimal	ADJ
ap-2970	62	10	changes	change	NOUN
ap-2970	62	11	,	,	PUNCT
ap-2970	62	12	it	it	PRON
ap-2970	62	13	is	be	AUX
ap-2970	62	14	more	more	ADV
ap-2970	62	15	ideal	ideal	ADJ
ap-2970	62	16	because	because	SCONJ
ap-2970	62	17	it	it	PRON
ap-2970	62	18	provides	provide	VERB
ap-2970	62	19	an	an	DET
ap-2970	62	20	easier	easy	ADJ
ap-2970	62	21	way	way	NOUN
ap-2970	62	22	to	to	PART
ap-2970	62	23	introduce	introduce	VERB
ap-2970	62	24	fewer	few	ADJ
ap-2970	62	25	resources	resource	NOUN
ap-2970	62	26	(	(	PUNCT
ap-2970	62	27	only	only	ADV
ap-2970	62	28	a	a	DET
ap-2970	62	29	carefully	carefully	ADV
ap-2970	62	30	manipulated	manipulate	VERB
ap-2970	62	31	svd	svd	PROPN
ap-2970	62	32	)	)	PUNCT
ap-2970	62	33	,	,	PUNCT
ap-2970	62	34	while	while	SCONJ
ap-2970	62	35	reducing	reduce	VERB
ap-2970	62	36	the	the	DET
ap-2970	62	37	expenses	expense	NOUN
ap-2970	62	38	(	(	PUNCT
ap-2970	62	39	the	the	DET
ap-2970	62	40	computational	computational	ADJ
ap-2970	62	41	time	time	NOUN
ap-2970	62	42	and	and	CCONJ
ap-2970	62	43	the	the	DET
ap-2970	62	44	mathematical	mathematical	ADJ
ap-2970	62	45	apparatus	apparatus	NOUN
ap-2970	62	46	required	require	VERB
ap-2970	62	47	by	by	ADP
ap-2970	62	48	the	the	DET
ap-2970	62	49	rsdm	rsdm	NOUN
ap-2970	62	50	)	)	PUNCT
ap-2970	62	51	as	as	ADV
ap-2970	62	52	much	much	ADV
ap-2970	62	53	as	as	ADP
ap-2970	62	54	possible	possible	ADJ
ap-2970	62	55	.	.	PUNCT
ap-2970	63	1	the	the	DET
ap-2970	63	2	intuitive	intuitive	ADJ
ap-2970	63	3	promise	promise	NOUN
ap-2970	63	4	of	of	ADP
ap-2970	63	5	the	the	DET
ap-2970	63	6	proposed	propose	VERB
ap-2970	63	7	method	method	NOUN
ap-2970	63	8	is	be	AUX
ap-2970	63	9	illustrated	illustrate	VERB
ap-2970	63	10	in	in	ADP
ap-2970	63	11	figure	figure	NOUN
ap-2970	63	12	1	1	NUM
ap-2970	63	13	.	.	PUNCT
ap-2970	64	1	the	the	DET
ap-2970	64	2	second	second	ADJ
ap-2970	64	3	objective	objective	NOUN
ap-2970	64	4	of	of	ADP
ap-2970	64	5	the	the	DET
ap-2970	64	6	paper	paper	NOUN
ap-2970	64	7	is	be	AUX
ap-2970	64	8	to	to	PART
ap-2970	64	9	show	show	VERB
ap-2970	64	10	the	the	DET
ap-2970	64	11	performance	performance	NOUN
ap-2970	64	12	of	of	ADP
ap-2970	64	13	rsdm	rsdm	NOUN
ap-2970	64	14	in	in	ADP
ap-2970	64	15	terms	term	NOUN
ap-2970	64	16	of	of	ADP
ap-2970	64	17	accuracy	accuracy	NOUN
ap-2970	64	18	.	.	PUNCT
ap-2970	65	1	a	a	DET
ap-2970	65	2	numerical	numerical	ADJ
ap-2970	65	3	application	application	NOUN
ap-2970	65	4	to	to	ADP
ap-2970	65	5	a	a	DET
ap-2970	65	6	hexapod	hexapod	NOUN
ap-2970	65	7	discretized	discretize	VERB
ap-2970	65	8	with	with	ADP
ap-2970	65	9	almost	almost	ADV
ap-2970	65	10	200	200	NUM
ap-2970	65	11	thousand	thousand	NUM
ap-2970	65	12	degrees	degree	NOUN
ap-2970	65	13	of	of	ADP
ap-2970	65	14	freedom	freedom	NOUN
ap-2970	65	15	will	will	AUX
ap-2970	65	16	be	be	AUX
ap-2970	65	17	presented	present	VERB
ap-2970	65	18	.	.	PUNCT
ap-2970	66	1	3	3	X
ap-2970	66	2	.	.	X
ap-2970	66	3	description	description	NOUN
ap-2970	66	4	of	of	ADP
ap-2970	66	5	the	the	DET
ap-2970	66	6	interpolation	interpolation	NOUN
ap-2970	66	7	method	method	NOUN
ap-2970	66	8	3.1	3.1	NUM
ap-2970	66	9	.	.	PUNCT
ap-2970	67	1	foundations	foundation	NOUN
ap-2970	67	2	and	and	CCONJ
ap-2970	67	3	derivation	derivation	NOUN
ap-2970	67	4	of	of	ADP
ap-2970	67	5	the	the	DET
ap-2970	67	6	proposed	propose	VERB
ap-2970	67	7	interpolation	interpolation	NOUN
ap-2970	67	8	method	method	NOUN
ap-2970	67	9	.	.	PUNCT
ap-2970	68	1	an	an	DET
ap-2970	68	2	analogy	analogy	NOUN
ap-2970	68	3	with	with	ADP
ap-2970	68	4	continuum	continuum	ADJ
ap-2970	68	5	mechanics	mechanic	NOUN
ap-2970	68	6	solid	solid	ADJ
ap-2970	68	7	mechanics	mechanic	NOUN
ap-2970	68	8	is	be	AUX
ap-2970	68	9	a	a	DET
ap-2970	68	10	branch	branch	NOUN
ap-2970	68	11	of	of	ADP
ap-2970	68	12	continuum	continuum	ADJ
ap-2970	68	13	mechanics	mechanic	NOUN
ap-2970	68	14	that	that	PRON
ap-2970	68	15	has	have	AUX
ap-2970	68	16	been	be	AUX
ap-2970	68	17	developed	develop	VERB
ap-2970	68	18	to	to	PART
ap-2970	68	19	predict	predict	VERB
ap-2970	68	20	the	the	DET
ap-2970	68	21	behavior	behavior	NOUN
ap-2970	68	22	of	of	ADP
ap-2970	68	23	solids	solid	NOUN
ap-2970	68	24	e.g.	e.g.	ADV
ap-2970	68	25	changes	change	VERB
ap-2970	68	26	in	in	ADP
ap-2970	68	27	shape	shape	NOUN
ap-2970	68	28	,	,	PUNCT
ap-2970	68	29	internal	internal	ADJ
ap-2970	68	30	forces	force	NOUN
ap-2970	68	31	subjected	subject	VERB
ap-2970	68	32	to	to	ADP
ap-2970	68	33	the	the	DET
ap-2970	68	34	action	action	NOUN
ap-2970	68	35	of	of	ADP
ap-2970	68	36	mechanical	mechanical	ADJ
ap-2970	68	37	and	and	CCONJ
ap-2970	68	38	thermal	thermal	ADJ
ap-2970	68	39	loads	load	NOUN
ap-2970	68	40	.	.	PUNCT
ap-2970	69	1	a	a	DET
ap-2970	69	2	general	general	ADJ
ap-2970	69	3	deformation	deformation	NOUN
ap-2970	69	4	of	of	ADP
ap-2970	69	5	a	a	DET
ap-2970	69	6	solid	solid	ADJ
ap-2970	69	7	–	–	PUNCT
ap-2970	69	8	using	use	VERB
ap-2970	69	9	the	the	DET
ap-2970	69	10	idealization	idealization	NOUN
ap-2970	69	11	often	often	ADV
ap-2970	69	12	considered	consider	VERB
ap-2970	69	13	in	in	ADP
ap-2970	69	14	engineering	engineering	NOUN
ap-2970	69	15	dynamics	dynamic	NOUN
ap-2970	69	16	that	that	PRON
ap-2970	69	17	a	a	DET
ap-2970	69	18	body	body	NOUN
ap-2970	69	19	is	be	AUX
ap-2970	69	20	rigid	rigid	ADJ
ap-2970	69	21	can	can	AUX
ap-2970	69	22	be	be	AUX
ap-2970	69	23	defined	define	VERB
ap-2970	69	24	as	as	ADP
ap-2970	69	25	a	a	DET
ap-2970	69	26	combination	combination	NOUN
ap-2970	69	27	of	of	ADP
ap-2970	69	28	a	a	DET
ap-2970	69	29	rigid	rigid	ADJ
ap-2970	69	30	rotation	rotation	NOUN
ap-2970	69	31	and	and	CCONJ
ap-2970	69	32	a	a	DET
ap-2970	69	33	stretch	stretch	NOUN
ap-2970	69	34	(	(	PUNCT
ap-2970	69	35	or	or	CCONJ
ap-2970	69	36	contraction	contraction	NOUN
ap-2970	69	37	)	)	PUNCT
ap-2970	70	1	[	[	X
ap-2970	70	2	13	13	NUM
ap-2970	70	3	]	]	PUNCT
ap-2970	70	4	.	.	PUNCT
ap-2970	71	1	once	once	SCONJ
ap-2970	71	2	the	the	DET
ap-2970	71	3	deformation	deformation	NOUN
ap-2970	71	4	is	be	AUX
ap-2970	71	5	known	know	VERB
ap-2970	71	6	,	,	PUNCT
ap-2970	71	7	the	the	DET
ap-2970	71	8	stresses	stress	NOUN
ap-2970	71	9	induced	induce	VERB
ap-2970	71	10	by	by	ADP
ap-2970	71	11	external	external	ADJ
ap-2970	71	12	mechanical	mechanical	ADJ
ap-2970	71	13	and/or	and/or	CCONJ
ap-2970	71	14	thermal	thermal	ADJ
ap-2970	71	15	loads	load	NOUN
ap-2970	71	16	can	can	AUX
ap-2970	71	17	be	be	AUX
ap-2970	71	18	calculated	calculate	VERB
ap-2970	71	19	.	.	PUNCT
ap-2970	72	1	however	however	ADV
ap-2970	72	2	,	,	PUNCT
ap-2970	72	3	these	these	DET
ap-2970	72	4	stresses	stress	NOUN
ap-2970	72	5	are	be	AUX
ap-2970	72	6	generated	generate	VERB
ap-2970	72	7	by	by	ADP
ap-2970	72	8	the	the	DET
ap-2970	72	9	deformational	deformational	ADJ
ap-2970	72	10	component	component	NOUN
ap-2970	72	11	of	of	ADP
ap-2970	72	12	the	the	DET
ap-2970	72	13	stretch	stretch	NOUN
ap-2970	72	14	and	and	CCONJ
ap-2970	72	15	not	not	PART
ap-2970	72	16	of	of	ADP
ap-2970	72	17	the	the	DET
ap-2970	72	18	rigid	rigid	ADJ
ap-2970	72	19	rotation	rotation	NOUN
ap-2970	72	20	.	.	PUNCT
ap-2970	73	1	therefore	therefore	ADV
ap-2970	73	2	,	,	PUNCT
ap-2970	73	3	in	in	ADP
ap-2970	73	4	order	order	NOUN
ap-2970	73	5	to	to	PART
ap-2970	73	6	define	define	VERB
ap-2970	73	7	the	the	DET
ap-2970	73	8	deformation	deformation	NOUN
ap-2970	73	9	gradient	gradient	NOUN
ap-2970	73	10	for	for	ADP
ap-2970	73	11	a	a	DET
ap-2970	73	12	solid	solid	ADJ
ap-2970	73	13	,	,	PUNCT
ap-2970	73	14	the	the	DET
ap-2970	73	15	stretch	stretch	NOUN
ap-2970	73	16	component	component	NOUN
ap-2970	73	17	is	be	AUX
ap-2970	73	18	separated	separate	VERB
ap-2970	73	19	from	from	ADP
ap-2970	73	20	the	the	DET
ap-2970	73	21	rigid	rigid	ADJ
ap-2970	73	22	rotation	rotation	NOUN
ap-2970	73	23	component	component	NOUN
ap-2970	73	24	by	by	ADP
ap-2970	73	25	means	mean	NOUN
ap-2970	73	26	of	of	ADP
ap-2970	73	27	a	a	DET
ap-2970	73	28	mathematical	mathematical	ADJ
ap-2970	73	29	factorization	factorization	NOUN
ap-2970	73	30	known	know	VERB
ap-2970	73	31	as	as	ADP
ap-2970	73	32	polar	polar	ADJ
ap-2970	73	33	decomposition	decomposition	NOUN
ap-2970	73	34	[	[	X
ap-2970	73	35	10	10	NUM
ap-2970	73	36	]	]	PUNCT
ap-2970	73	37	.	.	PUNCT
ap-2970	74	1	in	in	ADP
ap-2970	74	2	order	order	NOUN
ap-2970	74	3	to	to	PART
ap-2970	74	4	predict	predict	VERB
ap-2970	74	5	the	the	DET
ap-2970	74	6	deformation	deformation	NOUN
ap-2970	74	7	and	and	CCONJ
ap-2970	74	8	the	the	DET
ap-2970	74	9	stress	stress	NOUN
ap-2970	74	10	fields	field	NOUN
ap-2970	74	11	,	,	PUNCT
ap-2970	74	12	most	most	ADJ
ap-2970	74	13	of	of	ADP
ap-2970	74	14	the	the	DET
ap-2970	74	15	engineering	engineering	NOUN
ap-2970	74	16	design	design	NOUN
ap-2970	74	17	calculations	calculation	NOUN
ap-2970	74	18	make	make	VERB
ap-2970	74	19	use	use	NOUN
ap-2970	74	20	of	of	ADP
ap-2970	74	21	finite	finite	ADJ
ap-2970	74	22	element	element	NOUN
ap-2970	74	23	techniques	technique	NOUN
ap-2970	74	24	that	that	PRON
ap-2970	74	25	are	be	AUX
ap-2970	74	26	employed	employ	VERB
ap-2970	74	27	to	to	PART
ap-2970	74	28	solve	solve	VERB
ap-2970	74	29	the	the	DET
ap-2970	74	30	governing	govern	VERB
ap-2970	74	31	equations	equation	NOUN
ap-2970	74	32	of	of	ADP
ap-2970	74	33	a	a	DET
ap-2970	74	34	solid	solid	ADJ
ap-2970	74	35	,	,	PUNCT
ap-2970	74	36	both	both	PRON
ap-2970	74	37	for	for	ADP
ap-2970	74	38	static	static	ADJ
ap-2970	74	39	analysis	analysis	NOUN
ap-2970	74	40	and	and	CCONJ
ap-2970	74	41	for	for	ADP
ap-2970	74	42	dynamic	dynamic	ADJ
ap-2970	74	43	analysis	analysis	NOUN
ap-2970	74	44	,	,	PUNCT
ap-2970	74	45	.	.	PUNCT
ap-2970	75	1	with	with	SCONJ
ap-2970	75	2	reference	reference	NOUN
ap-2970	75	3	to	to	PART
ap-2970	75	4	figure	figure	VERB
ap-2970	75	5	2	2	NUM
ap-2970	75	6	and	and	CCONJ
ap-2970	75	7	using	use	VERB
ap-2970	75	8	the	the	DET
ap-2970	75	9	principle	principle	NOUN
ap-2970	75	10	of	of	ADP
ap-2970	75	11	virtual	virtual	ADJ
ap-2970	75	12	work	work	NOUN
ap-2970	75	13	the	the	DET
ap-2970	75	14	equations	equation	NOUN
ap-2970	75	15	of	of	ADP
ap-2970	75	16	motion	motion	NOUN
ap-2970	75	17	for	for	ADP
ap-2970	75	18	linear	linear	ADJ
ap-2970	75	19	elastic	elastic	ADJ
ap-2970	75	20	solids	solid	NOUN
ap-2970	75	21	are	be	AUX
ap-2970	75	22	described	describe	VERB
ap-2970	75	23	as	as	ADP
ap-2970	75	24	follows	follow	VERB
ap-2970	75	25	(	(	PUNCT
ap-2970	75	26	[	[	X
ap-2970	75	27	11	11	NUM
ap-2970	75	28	]	]	PUNCT
ap-2970	75	29	,	,	PUNCT
ap-2970	75	30	p.492	p.492	PROPN
ap-2970	75	31	):	):	PUNCT
ap-2970	75	32	∫	∫	PROPN
ap-2970	75	33	r	r	NOUN
ap-2970	75	34	%	%	NOUN
ap-2970	75	35	n	n	CCONJ
ap-2970	75	36	bna	bna	PROPN
ap-2970	75	37	∂2ub	∂2ub	NOUN
ap-2970	75	38	i	i	PRON
ap-2970	75	39	∂t2	∂t2	VERB
ap-2970	75	40	δv	δv	ADP
ap-2970	75	41	a	a	DET
ap-2970	75	42	i	i	NOUN
ap-2970	75	43	dv	dv	PROPN
ap-2970	76	1	+	+	CCONJ
ap-2970	76	2	∫	∫	PROPN
ap-2970	76	3	r	r	NOUN
ap-2970	76	4	cijkl	cijkl	NOUN
ap-2970	76	5	∂nb	∂nb	PROPN
ap-2970	76	6	∂xl	∂xl	PROPN
ap-2970	76	7	∂na	∂na	PROPN
ap-2970	76	8	∂xj	∂xj	PROPN
ap-2970	76	9	ub	ub	ADP
ap-2970	76	10	kδv	kδv	PROPN
ap-2970	76	11	a	a	PRON
ap-2970	76	12	i	i	PROPN
ap-2970	76	13	dv	dv	PROPN
ap-2970	76	14	409	409	NUM
ap-2970	76	15	s.	s.	PROPN
ap-2970	76	16	nasisi	nasisi	VERB
ap-2970	76	17	,	,	PUNCT
ap-2970	76	18	m.	m.	NOUN
ap-2970	76	19	valášek	valášek	PROPN
ap-2970	76	20	,	,	PUNCT
ap-2970	76	21	t.	t.	PROPN
ap-2970	76	22	vampola	vampola	PROPN
ap-2970	76	23	acta	acta	PROPN
ap-2970	76	24	polytechnica	polytechnica	PROPN
ap-2970	76	25	−	−	PROPN
ap-2970	77	1	∫	∫	PROPN
ap-2970	78	1	r	r	NOUN
ap-2970	78	2	bin	bin	NOUN
ap-2970	78	3	aδva	aδva	PROPN
ap-2970	79	1	i	i	PRON
ap-2970	79	2	dv	dv	PROPN
ap-2970	80	1	−	−	PROPN
ap-2970	80	2	∫	∫	PROPN
ap-2970	80	3	∂2r	∂2r	PROPN
ap-2970	80	4	tin	tin	NOUN
ap-2970	80	5	aδva	aδva	NOUN
ap-2970	81	1	i	i	NOUN
ap-2970	81	2	da	da	NOUN
ap-2970	81	3	=	=	PUNCT
ap-2970	81	4	0	0	X
ap-2970	81	5	.	.	PUNCT
ap-2970	82	1	(	(	PUNCT
ap-2970	82	2	2	2	X
ap-2970	82	3	)	)	PUNCT
ap-2970	82	4	this	this	PRON
ap-2970	82	5	can	can	AUX
ap-2970	82	6	be	be	AUX
ap-2970	82	7	in	in	ADP
ap-2970	82	8	turns	turn	NOUN
ap-2970	82	9	be	be	AUX
ap-2970	82	10	written	write	VERB
ap-2970	82	11	in	in	ADP
ap-2970	82	12	the	the	DET
ap-2970	82	13	compact	compact	ADJ
ap-2970	82	14	form	form	NOUN
ap-2970	82	15	(	(	PUNCT
ap-2970	82	16	mabüb	mabüb	PROPN
ap-2970	82	17	i	i	PROPN
ap-2970	82	18	+	+	CCONJ
ap-2970	82	19	kaibkub	kaibkub	VERB
ap-2970	83	1	k	k	NOUN
ap-2970	83	2	−	−	X
ap-2970	84	1	f	f	PROPN
ap-2970	84	2	a	a	DET
ap-2970	84	3	i	i	NOUN
ap-2970	84	4	)	)	PUNCT
ap-2970	84	5	δva	δva	VERB
ap-2970	84	6	i	i	NOUN
ap-2970	84	7	=	=	NOUN
ap-2970	84	8	0	0	NUM
ap-2970	84	9	,	,	PUNCT
ap-2970	84	10	(	(	PUNCT
ap-2970	84	11	3	3	X
ap-2970	84	12	)	)	PUNCT
ap-2970	84	13	where	where	SCONJ
ap-2970	84	14	ua	ua	PROPN
ap-2970	84	15	i	i	PROPN
ap-2970	84	16	,	,	PUNCT
ap-2970	84	17	is	be	AUX
ap-2970	84	18	the	the	DET
ap-2970	84	19	displacement	displacement	ADJ
ap-2970	84	20	vector	vector	NOUN
ap-2970	84	21	at	at	ADP
ap-2970	84	22	each	each	DET
ap-2970	84	23	nodal	nodal	NOUN
ap-2970	84	24	point	point	NOUN
ap-2970	84	25	,	,	PUNCT
ap-2970	84	26	while	while	SCONJ
ap-2970	84	27	bi	bi	NOUN
ap-2970	84	28	and	and	CCONJ
ap-2970	84	29	ti	ti	NOUN
ap-2970	84	30	are	be	AUX
ap-2970	84	31	respectively	respectively	ADV
ap-2970	84	32	the	the	DET
ap-2970	84	33	vectors	vector	NOUN
ap-2970	84	34	of	of	ADP
ap-2970	84	35	body	body	NOUN
ap-2970	84	36	and	and	CCONJ
ap-2970	84	37	traction	traction	NOUN
ap-2970	84	38	forces	force	NOUN
ap-2970	84	39	.	.	PUNCT
ap-2970	85	1	this	this	DET
ap-2970	85	2	set	set	NOUN
ap-2970	85	3	of	of	ADP
ap-2970	85	4	linear	linear	PROPN
ap-2970	85	5	equations	equation	NOUN
ap-2970	85	6	can	can	AUX
ap-2970	85	7	also	also	ADV
ap-2970	85	8	be	be	AUX
ap-2970	85	9	used	use	VERB
ap-2970	85	10	to	to	PART
ap-2970	85	11	study	study	VERB
ap-2970	85	12	the	the	DET
ap-2970	85	13	eigenbehavior	eigenbehavior	NOUN
ap-2970	85	14	of	of	ADP
ap-2970	85	15	the	the	DET
ap-2970	85	16	system	system	NOUN
ap-2970	85	17	.	.	PUNCT
ap-2970	86	1	in	in	ADP
ap-2970	86	2	order	order	NOUN
ap-2970	86	3	to	to	PART
ap-2970	86	4	calculate	calculate	VERB
ap-2970	86	5	the	the	DET
ap-2970	86	6	frequencies	frequency	NOUN
ap-2970	86	7	and	and	CCONJ
ap-2970	86	8	the	the	DET
ap-2970	86	9	mode	mode	NOUN
ap-2970	86	10	shapes	shape	NOUN
ap-2970	86	11	of	of	ADP
ap-2970	86	12	this	this	DET
ap-2970	86	13	structure	structure	NOUN
ap-2970	86	14	,	,	PUNCT
ap-2970	86	15	it	it	PRON
ap-2970	86	16	is	be	AUX
ap-2970	86	17	necessary	necessary	ADJ
ap-2970	86	18	then	then	ADV
ap-2970	86	19	to	to	PART
ap-2970	86	20	solve	solve	VERB
ap-2970	86	21	the	the	DET
ap-2970	86	22	eigenproblem	eigenproblem	NOUN
ap-2970	86	23	of	of	ADP
ap-2970	86	24	the	the	DET
ap-2970	86	25	type	type	NOUN
ap-2970	86	26	kaibkφnxp	kaibkφnxp	NOUN
ap-2970	86	27	=	=	NOUN
ap-2970	86	28	maibkφnxpλpxp	maibkφnxpλpxp	NOUN
ap-2970	86	29	(	(	PUNCT
ap-2970	86	30	4	4	NUM
ap-2970	86	31	)	)	PUNCT
ap-2970	86	32	that	that	PRON
ap-2970	86	33	stems	stem	VERB
ap-2970	86	34	from	from	ADP
ap-2970	86	35	solving	solve	VERB
ap-2970	86	36	the	the	DET
ap-2970	86	37	characteristic	characteristic	ADJ
ap-2970	86	38	equation	equation	NOUN
ap-2970	86	39	obtained	obtain	VERB
ap-2970	86	40	after	after	ADP
ap-2970	86	41	introducing	introduce	VERB
ap-2970	86	42	the	the	DET
ap-2970	86	43	trial	trial	NOUN
ap-2970	86	44	solution	solution	NOUN
ap-2970	86	45	,	,	PUNCT
ap-2970	86	46	ui	ui	NOUN
ap-2970	87	1	=	=	PUNCT
ap-2970	87	2	<	<	X
ap-2970	87	3	(	(	PUNCT
ap-2970	87	4	bφnx1eiωt	bφnx1eiωt	NOUN
ap-2970	87	5	)	)	PUNCT
ap-2970	87	6	,	,	PUNCT
ap-2970	87	7	(	(	PUNCT
ap-2970	87	8	5	5	X
ap-2970	87	9	)	)	PUNCT
ap-2970	87	10	within	within	ADP
ap-2970	87	11	the	the	DET
ap-2970	87	12	system	system	NOUN
ap-2970	87	13	of	of	ADP
ap-2970	87	14	equations	equation	NOUN
ap-2970	87	15	(	(	PUNCT
ap-2970	87	16	3	3	NUM
ap-2970	87	17	)	)	PUNCT
ap-2970	87	18	.	.	PUNCT
ap-2970	88	1	the	the	DET
ap-2970	88	2	calculation	calculation	NOUN
ap-2970	88	3	of	of	ADP
ap-2970	88	4	the	the	DET
ap-2970	88	5	eigensolution	eigensolution	NOUN
ap-2970	88	6	pertaining	pertain	VERB
ap-2970	88	7	to	to	ADP
ap-2970	88	8	this	this	DET
ap-2970	88	9	set	set	NOUN
ap-2970	88	10	of	of	ADP
ap-2970	88	11	equations	equation	NOUN
ap-2970	88	12	is	be	AUX
ap-2970	88	13	therefore	therefore	ADV
ap-2970	88	14	dependent	dependent	ADJ
ap-2970	88	15	on	on	ADP
ap-2970	88	16	kaibk	kaibk	NOUN
ap-2970	88	17	and	and	CCONJ
ap-2970	88	18	maibk	maibk	NOUN
ap-2970	88	19	,	,	PUNCT
ap-2970	88	20	which	which	PRON
ap-2970	88	21	are	be	AUX
ap-2970	88	22	the	the	DET
ap-2970	88	23	stiffness	stiffness	NOUN
ap-2970	88	24	and	and	CCONJ
ap-2970	88	25	mass	mass	ADJ
ap-2970	88	26	matrices	matrix	NOUN
ap-2970	88	27	of	of	ADP
ap-2970	88	28	the	the	DET
ap-2970	88	29	finite	finite	PROPN
ap-2970	88	30	element	element	PROPN
ap-2970	88	31	assemblage	assemblage	NOUN
ap-2970	88	32	illustrated	illustrate	VERB
ap-2970	88	33	in	in	ADP
ap-2970	88	34	figure	figure	NOUN
ap-2970	88	35	2	2	NUM
ap-2970	88	36	.	.	PUNCT
ap-2970	88	37	referring	refer	VERB
ap-2970	88	38	to	to	ADP
ap-2970	88	39	(	(	PUNCT
ap-2970	88	40	2	2	NUM
ap-2970	88	41	)	)	PUNCT
ap-2970	88	42	,	,	PUNCT
ap-2970	88	43	these	these	DET
ap-2970	88	44	matrices	matrix	NOUN
ap-2970	88	45	and	and	CCONJ
ap-2970	88	46	the	the	DET
ap-2970	88	47	vector	vector	NOUN
ap-2970	88	48	of	of	ADP
ap-2970	88	49	the	the	DET
ap-2970	88	50	externally	externally	ADV
ap-2970	88	51	applied	apply	VERB
ap-2970	88	52	loads	load	NOUN
ap-2970	88	53	have	have	VERB
ap-2970	88	54	the	the	DET
ap-2970	88	55	following	following	ADJ
ap-2970	88	56	mathematical	mathematical	ADJ
ap-2970	88	57	structure	structure	NOUN
ap-2970	88	58	:	:	PUNCT
ap-2970	88	59	kaibk	kaibk	VERB
ap-2970	88	60	=	=	SYM
ap-2970	89	1	∫	∫	PROPN
ap-2970	89	2	r	r	NOUN
ap-2970	89	3	cijkl	cijkl	NOUN
ap-2970	89	4	∂na	∂na	PROPN
ap-2970	89	5	∂xj	∂xj	PROPN
ap-2970	89	6	∂n	∂n	PROPN
ap-2970	89	7	b	b	PROPN
ap-2970	89	8	∂xl	∂xl	PROPN
ap-2970	89	9	dv	dv	PROPN
ap-2970	89	10	,	,	PUNCT
ap-2970	89	11	mab	mab	PROPN
ap-2970	89	12	=	=	SYM
ap-2970	89	13	∫	∫	PROPN
ap-2970	89	14	r	r	NOUN
ap-2970	89	15	%	%	INTJ
ap-2970	89	16	nan	nan	PROPN
ap-2970	89	17	bdv	bdv	PROPN
ap-2970	89	18	,	,	PUNCT
ap-2970	89	19	(	(	PUNCT
ap-2970	89	20	6	6	NUM
ap-2970	89	21	)	)	PUNCT
ap-2970	89	22	f	f	NOUN
ap-2970	90	1	a	a	DET
ap-2970	90	2	i	i	NOUN
ap-2970	90	3	=	=	PUNCT
ap-2970	90	4	∫	∫	PROPN
ap-2970	90	5	r	r	NOUN
ap-2970	90	6	bin	bin	NOUN
ap-2970	90	7	adv	adv	PROPN
ap-2970	91	1	+	+	CCONJ
ap-2970	91	2	∫	∫	PROPN
ap-2970	91	3	∂2r	∂2r	PROPN
ap-2970	91	4	tin	tin	PROPN
ap-2970	91	5	ada	ada	PROPN
ap-2970	91	6	,	,	PUNCT
ap-2970	91	7	where	where	SCONJ
ap-2970	91	8	r	r	NOUN
ap-2970	91	9	and	and	CCONJ
ap-2970	91	10	∂2r	∂2r	NOUN
ap-2970	91	11	are	be	AUX
ap-2970	91	12	the	the	DET
ap-2970	91	13	shape	shape	NOUN
ap-2970	91	14	of	of	ADP
ap-2970	91	15	the	the	DET
ap-2970	91	16	solid	solid	ADJ
ap-2970	91	17	in	in	ADP
ap-2970	91	18	its	its	PRON
ap-2970	91	19	unloaded	unloaded	ADJ
ap-2970	91	20	condition	condition	NOUN
ap-2970	91	21	and	and	CCONJ
ap-2970	91	22	its	its	PRON
ap-2970	91	23	boundary	boundary	NOUN
ap-2970	91	24	,	,	PUNCT
ap-2970	91	25	respectively	respectively	ADV
ap-2970	91	26	.	.	PUNCT
ap-2970	92	1	analyzing	analyze	VERB
ap-2970	92	2	these	these	DET
ap-2970	92	3	relations	relation	NOUN
ap-2970	92	4	,	,	PUNCT
ap-2970	92	5	it	it	PRON
ap-2970	92	6	can	can	AUX
ap-2970	92	7	be	be	AUX
ap-2970	92	8	observed	observe	VERB
ap-2970	92	9	that	that	SCONJ
ap-2970	92	10	both	both	CCONJ
ap-2970	92	11	the	the	DET
ap-2970	92	12	finite	finite	ADJ
ap-2970	92	13	element	element	NOUN
ap-2970	92	14	stiffness	stiffness	NOUN
ap-2970	92	15	and	and	CCONJ
ap-2970	92	16	mass	mass	ADJ
ap-2970	92	17	matrices	matrix	NOUN
ap-2970	92	18	depend	depend	VERB
ap-2970	92	19	on	on	ADP
ap-2970	92	20	the	the	DET
ap-2970	92	21	material	material	NOUN
ap-2970	92	22	properties	property	NOUN
ap-2970	92	23	(	(	PUNCT
ap-2970	92	24	the	the	DET
ap-2970	92	25	density	density	NOUN
ap-2970	92	26	%	%	NOUN
ap-2970	92	27	and	and	CCONJ
ap-2970	92	28	the	the	DET
ap-2970	92	29	elastic	elastic	ADJ
ap-2970	92	30	modulus	modulus	NOUN
ap-2970	92	31	tensor	tensor	NOUN
ap-2970	92	32	cijkl	cijkl	NOUN
ap-2970	92	33	)	)	PUNCT
ap-2970	92	34	and	and	CCONJ
ap-2970	92	35	on	on	ADP
ap-2970	92	36	the	the	DET
ap-2970	92	37	element	element	NOUN
ap-2970	92	38	interpolation	interpolation	NOUN
ap-2970	92	39	functions	function	NOUN
ap-2970	92	40	or	or	CCONJ
ap-2970	92	41	shape	shape	NOUN
ap-2970	92	42	functions	function	NOUN
ap-2970	92	43	,	,	PUNCT
ap-2970	92	44	n(x1	n(x1	NOUN
ap-2970	92	45	,	,	PUNCT
ap-2970	92	46	x2	x2	PROPN
ap-2970	92	47	)	)	PUNCT
ap-2970	92	48	with	with	ADP
ap-2970	92	49	x1	x1	PROPN
ap-2970	92	50	,	,	PUNCT
ap-2970	92	51	x2	x2	PROPN
ap-2970	92	52	being	be	AUX
ap-2970	92	53	the	the	DET
ap-2970	92	54	coordinates	coordinate	NOUN
ap-2970	92	55	of	of	ADP
ap-2970	92	56	a	a	DET
ap-2970	92	57	generic	generic	ADJ
ap-2970	92	58	node	node	NOUN
ap-2970	92	59	with	with	ADP
ap-2970	92	60	respect	respect	NOUN
ap-2970	92	61	to	to	ADP
ap-2970	92	62	a	a	DET
ap-2970	92	63	reference	reference	NOUN
ap-2970	92	64	system	system	NOUN
ap-2970	92	65	o	o	NOUN
ap-2970	92	66	~	~	NOUN
ap-2970	92	67	e1	e1	NOUN
ap-2970	92	68	~e2	~e2	NUM
ap-2970	92	69	(	(	PUNCT
ap-2970	92	70	figure	figure	NOUN
ap-2970	92	71	2	2	NUM
ap-2970	92	72	)	)	PUNCT
ap-2970	92	73	;	;	PUNCT
ap-2970	92	74	while	while	SCONJ
ap-2970	92	75	,	,	PUNCT
ap-2970	92	76	indices	indice	VERB
ap-2970	92	77	a	a	PRON
ap-2970	92	78	,	,	PUNCT
ap-2970	92	79	b	b	PROPN
ap-2970	92	80	,	,	PUNCT
ap-2970	92	81	i	i	PRON
ap-2970	92	82	,	,	PUNCT
ap-2970	92	83	k	k	PROPN
ap-2970	92	84	,	,	PUNCT
ap-2970	92	85	l	l	PROPN
ap-2970	92	86	indicate	indicate	VERB
ap-2970	92	87	the	the	DET
ap-2970	92	88	directions	direction	NOUN
ap-2970	92	89	pertaining	pertain	VERB
ap-2970	92	90	to	to	ADP
ap-2970	92	91	the	the	DET
ap-2970	92	92	cartesian	cartesian	ADJ
ap-2970	92	93	basis	basis	NOUN
ap-2970	92	94	,	,	PUNCT
ap-2970	92	95	{	{	PUNCT
ap-2970	92	96	e1	e1	NOUN
ap-2970	92	97	,	,	PUNCT
ap-2970	92	98	e2	e2	PROPN
ap-2970	92	99	}	}	PUNCT
ap-2970	92	100	.	.	PUNCT
ap-2970	93	1	in	in	ADP
ap-2970	93	2	turns	turn	NOUN
ap-2970	93	3	,	,	PUNCT
ap-2970	93	4	the	the	DET
ap-2970	93	5	shape	shape	NOUN
ap-2970	93	6	functions	function	NOUN
ap-2970	93	7	depend	depend	VERB
ap-2970	93	8	on	on	ADP
ap-2970	93	9	the	the	DET
ap-2970	93	10	type	type	NOUN
ap-2970	93	11	of	of	ADP
ap-2970	93	12	finite	finite	ADJ
ap-2970	93	13	element	element	NOUN
ap-2970	93	14	and	and	CCONJ
ap-2970	93	15	on	on	ADP
ap-2970	93	16	the	the	DET
ap-2970	93	17	reciprocal	reciprocal	ADJ
ap-2970	93	18	displacement	displacement	NOUN
ap-2970	93	19	of	of	ADP
ap-2970	93	20	the	the	DET
ap-2970	93	21	nodes	node	NOUN
ap-2970	93	22	of	of	ADP
ap-2970	93	23	the	the	DET
ap-2970	93	24	discretized	discretized	ADJ
ap-2970	93	25	structure	structure	NOUN
ap-2970	93	26	.	.	PUNCT
ap-2970	94	1	that	that	PRON
ap-2970	94	2	is	is	ADV
ap-2970	94	3	,	,	PUNCT
ap-2970	94	4	the	the	DET
ap-2970	94	5	entries	entry	NOUN
ap-2970	94	6	of	of	ADP
ap-2970	94	7	the	the	DET
ap-2970	94	8	stiffness	stiffness	NOUN
ap-2970	94	9	and	and	CCONJ
ap-2970	94	10	mass	mass	ADJ
ap-2970	94	11	matrices	matrix	NOUN
ap-2970	94	12	of	of	ADP
ap-2970	94	13	a	a	DET
ap-2970	94	14	finite	finite	ADJ
ap-2970	94	15	element	element	NOUN
ap-2970	94	16	assemblage	assemblage	NOUN
ap-2970	94	17	contain	contain	VERB
ap-2970	94	18	information	information	NOUN
ap-2970	94	19	related	relate	VERB
ap-2970	94	20	to	to	ADP
ap-2970	94	21	the	the	DET
ap-2970	94	22	material	material	NOUN
ap-2970	94	23	and	and	CCONJ
ap-2970	94	24	the	the	DET
ap-2970	94	25	deformation	deformation	NOUN
ap-2970	94	26	of	of	ADP
ap-2970	94	27	the	the	DET
ap-2970	94	28	solid	solid	NOUN
ap-2970	94	29	.	.	PUNCT
ap-2970	95	1	the	the	DET
ap-2970	95	2	general	general	ADJ
ap-2970	95	3	deformation	deformation	NOUN
ap-2970	95	4	of	of	ADP
ap-2970	95	5	a	a	DET
ap-2970	95	6	solid	solid	ADJ
ap-2970	95	7	can	can	AUX
ap-2970	95	8	be	be	AUX
ap-2970	95	9	defined	define	VERB
ap-2970	95	10	as	as	ADP
ap-2970	95	11	combination	combination	NOUN
ap-2970	95	12	of	of	ADP
ap-2970	95	13	a	a	DET
ap-2970	95	14	rigid	rigid	ADJ
ap-2970	95	15	rotation	rotation	NOUN
ap-2970	95	16	and	and	CCONJ
ap-2970	95	17	a	a	DET
ap-2970	95	18	stretch	stretch	NOUN
ap-2970	95	19	(	(	PUNCT
ap-2970	95	20	or	or	CCONJ
ap-2970	95	21	contraction	contraction	NOUN
ap-2970	95	22	)	)	PUNCT
ap-2970	96	1	[	[	X
ap-2970	96	2	13	13	NUM
ap-2970	96	3	]	]	PUNCT
ap-2970	96	4	.	.	PUNCT
ap-2970	97	1	the	the	DET
ap-2970	97	2	process	process	NOUN
ap-2970	97	3	of	of	ADP
ap-2970	97	4	general	general	ADJ
ap-2970	97	5	deformation	deformation	NOUN
ap-2970	97	6	undergone	undergo	VERB
ap-2970	97	7	by	by	ADP
ap-2970	97	8	a	a	DET
ap-2970	97	9	finite	finite	ADJ
ap-2970	97	10	element	element	NOUN
ap-2970	97	11	is	be	AUX
ap-2970	97	12	illustrated	illustrate	VERB
ap-2970	97	13	in	in	ADP
ap-2970	97	14	part	part	NOUN
ap-2970	97	15	(	(	PUNCT
ap-2970	97	16	b	b	NOUN
ap-2970	97	17	)	)	PUNCT
ap-2970	97	18	of	of	ADP
ap-2970	97	19	figure	figure	NOUN
ap-2970	97	20	2	2	NUM
ap-2970	98	1	and	and	CCONJ
ap-2970	98	2	it	it	PRON
ap-2970	98	3	is	be	AUX
ap-2970	98	4	described	describe	VERB
ap-2970	98	5	as	as	ADP
ap-2970	98	6	a	a	DET
ap-2970	98	7	stretch	stretch	NOUN
ap-2970	98	8	followed	follow	VERB
ap-2970	98	9	by	by	ADP
ap-2970	98	10	a	a	DET
ap-2970	98	11	rigid	rigid	ADJ
ap-2970	98	12	rotation	rotation	NOUN
ap-2970	98	13	or	or	CCONJ
ap-2970	98	14	,	,	PUNCT
ap-2970	98	15	which	which	PRON
ap-2970	98	16	is	be	AUX
ap-2970	98	17	the	the	DET
ap-2970	98	18	same	same	ADJ
ap-2970	98	19	thing	thing	NOUN
ap-2970	98	20	,	,	PUNCT
ap-2970	98	21	by	by	ADP
ap-2970	98	22	a	a	DET
ap-2970	98	23	rigid	rigid	ADJ
ap-2970	98	24	rotation	rotation	NOUN
ap-2970	98	25	followed	follow	VERB
ap-2970	98	26	by	by	ADP
ap-2970	98	27	a	a	DET
ap-2970	98	28	stretch	stretch	NOUN
ap-2970	98	29	.	.	PUNCT
ap-2970	99	1	once	once	SCONJ
ap-2970	99	2	the	the	DET
ap-2970	99	3	deformation	deformation	NOUN
ap-2970	99	4	is	be	AUX
ap-2970	99	5	known	know	VERB
ap-2970	99	6	,	,	PUNCT
ap-2970	99	7	the	the	DET
ap-2970	99	8	stresses	stress	NOUN
ap-2970	99	9	can	can	AUX
ap-2970	99	10	be	be	AUX
ap-2970	99	11	derived	derive	VERB
ap-2970	99	12	.	.	PUNCT
ap-2970	100	1	figure	figure	NOUN
ap-2970	100	2	2	2	NUM
ap-2970	100	3	.	.	PUNCT
ap-2970	101	1	an	an	DET
ap-2970	101	2	example	example	NOUN
ap-2970	101	3	of	of	ADP
ap-2970	101	4	a	a	DET
ap-2970	101	5	finite	finite	ADJ
ap-2970	101	6	element	element	NOUN
ap-2970	101	7	mesh	mesh	NOUN
ap-2970	101	8	(	(	PUNCT
ap-2970	101	9	a	a	NOUN
ap-2970	101	10	)	)	PUNCT
ap-2970	102	1	;	;	PUNCT
ap-2970	102	2	a	a	DET
ap-2970	102	3	general	general	ADJ
ap-2970	102	4	deformation	deformation	NOUN
ap-2970	102	5	can	can	AUX
ap-2970	102	6	be	be	AUX
ap-2970	102	7	decomposed	decompose	VERB
ap-2970	102	8	into	into	ADP
ap-2970	102	9	a	a	DET
ap-2970	102	10	rotation	rotation	NOUN
ap-2970	102	11	and	and	CCONJ
ap-2970	102	12	a	a	DET
ap-2970	102	13	stretch	stretch	NOUN
ap-2970	102	14	(	(	PUNCT
ap-2970	102	15	b	b	NOUN
ap-2970	102	16	)	)	PUNCT
ap-2970	102	17	.	.	PUNCT
ap-2970	103	1	the	the	DET
ap-2970	103	2	gradient	gradient	NOUN
ap-2970	103	3	of	of	ADP
ap-2970	103	4	deformation	deformation	NOUN
ap-2970	103	5	is	be	AUX
ap-2970	103	6	defined	define	VERB
ap-2970	103	7	in	in	ADP
ap-2970	103	8	continuum	continuum	ADJ
ap-2970	103	9	mechanics	mechanic	NOUN
ap-2970	103	10	as	as	ADP
ap-2970	103	11	,	,	PUNCT
ap-2970	103	12	f	f	PROPN
ap-2970	103	13	=	=	PUNCT
ap-2970	103	14	rs	rs	NOUN
ap-2970	103	15	.	.	PUNCT
ap-2970	104	1	the	the	DET
ap-2970	104	2	analogy	analogy	NOUN
ap-2970	104	3	with	with	ADP
ap-2970	104	4	continuum	continuum	ADJ
ap-2970	104	5	mechanics	mechanic	NOUN
ap-2970	104	6	is	be	AUX
ap-2970	104	7	used	use	VERB
ap-2970	104	8	to	to	PART
ap-2970	104	9	show	show	VERB
ap-2970	104	10	the	the	DET
ap-2970	104	11	importance	importance	NOUN
ap-2970	104	12	of	of	ADP
ap-2970	104	13	recovering	recover	VERB
ap-2970	104	14	those	those	DET
ap-2970	104	15	components	component	NOUN
ap-2970	104	16	of	of	ADP
ap-2970	104	17	stretch	stretch	NOUN
ap-2970	104	18	that	that	SCONJ
ap-2970	104	19	,	,	PUNCT
ap-2970	104	20	more	more	ADJ
ap-2970	104	21	than	than	ADP
ap-2970	104	22	a	a	DET
ap-2970	104	23	rigid	rigid	ADJ
ap-2970	104	24	rotation	rotation	NOUN
ap-2970	104	25	,	,	PUNCT
ap-2970	104	26	contribute	contribute	VERB
ap-2970	104	27	to	to	ADP
ap-2970	104	28	the	the	DET
ap-2970	104	29	change	change	NOUN
ap-2970	104	30	in	in	ADP
ap-2970	104	31	the	the	DET
ap-2970	104	32	shape	shape	NOUN
ap-2970	104	33	of	of	ADP
ap-2970	104	34	the	the	DET
ap-2970	104	35	solid	solid	NOUN
ap-2970	104	36	.	.	PUNCT
ap-2970	105	1	however	however	ADV
ap-2970	105	2	,	,	PUNCT
ap-2970	105	3	these	these	DET
ap-2970	105	4	stresses	stress	NOUN
ap-2970	105	5	are	be	AUX
ap-2970	105	6	generated	generate	VERB
ap-2970	105	7	only	only	ADV
ap-2970	105	8	by	by	ADP
ap-2970	105	9	the	the	DET
ap-2970	105	10	deformation	deformation	NOUN
ap-2970	105	11	component	component	NOUN
ap-2970	105	12	of	of	ADP
ap-2970	105	13	the	the	DET
ap-2970	105	14	stretch	stretch	NOUN
ap-2970	105	15	and	and	CCONJ
ap-2970	105	16	not	not	PART
ap-2970	105	17	of	of	ADP
ap-2970	105	18	the	the	DET
ap-2970	105	19	rigid	rigid	ADJ
ap-2970	105	20	rotation	rotation	NOUN
ap-2970	105	21	;	;	PUNCT
ap-2970	105	22	that	that	PRON
ap-2970	105	23	is	is	ADV
ap-2970	105	24	,	,	PUNCT
ap-2970	105	25	a	a	DET
ap-2970	105	26	rigid	rigid	ADJ
ap-2970	105	27	rotation	rotation	NOUN
ap-2970	105	28	does	do	AUX
ap-2970	105	29	not	not	PART
ap-2970	105	30	participates	participate	VERB
ap-2970	105	31	actively	actively	ADV
ap-2970	105	32	in	in	ADP
ap-2970	105	33	the	the	DET
ap-2970	105	34	stretch	stretch	NOUN
ap-2970	105	35	or	or	CCONJ
ap-2970	105	36	contraction	contraction	NOUN
ap-2970	105	37	of	of	ADP
ap-2970	105	38	the	the	DET
ap-2970	105	39	solid	solid	NOUN
ap-2970	105	40	.	.	PUNCT
ap-2970	106	1	as	as	ADP
ap-2970	106	2	a	a	DET
ap-2970	106	3	result	result	NOUN
ap-2970	106	4	,	,	PUNCT
ap-2970	106	5	the	the	DET
ap-2970	106	6	matrices	matrix	NOUN
ap-2970	106	7	kaibk	kaibk	VERB
ap-2970	106	8	and	and	CCONJ
ap-2970	106	9	maibk	maibk	NOUN
ap-2970	106	10	are	be	AUX
ap-2970	106	11	dependent	dependent	ADJ
ap-2970	106	12	only	only	ADV
ap-2970	106	13	on	on	ADP
ap-2970	106	14	the	the	DET
ap-2970	106	15	two	two	NUM
ap-2970	106	16	components	component	NOUN
ap-2970	106	17	of	of	ADP
ap-2970	106	18	rigid	rigid	ADJ
ap-2970	106	19	rotation	rotation	NOUN
ap-2970	106	20	and	and	CCONJ
ap-2970	106	21	stretch	stretch	NOUN
ap-2970	106	22	.	.	PUNCT
ap-2970	107	1	now	now	ADV
ap-2970	107	2	,	,	PUNCT
ap-2970	107	3	without	without	ADP
ap-2970	107	4	loss	loss	NOUN
ap-2970	107	5	of	of	ADP
ap-2970	107	6	generality	generality	NOUN
ap-2970	107	7	,	,	PUNCT
ap-2970	107	8	let	let	VERB
ap-2970	107	9	us	we	PRON
ap-2970	107	10	suppose	suppose	VERB
ap-2970	107	11	that	that	SCONJ
ap-2970	107	12	the	the	DET
ap-2970	107	13	finite	finite	PROPN
ap-2970	107	14	element	element	NOUN
ap-2970	107	15	assemblage	assemblage	NOUN
ap-2970	107	16	of	of	ADP
ap-2970	107	17	figure	figure	NOUN
ap-2970	107	18	2(a	2(a	NUM
ap-2970	107	19	)	)	PUNCT
ap-2970	107	20	has	have	VERB
ap-2970	107	21	a	a	DET
ap-2970	107	22	large	large	ADJ
ap-2970	107	23	number	number	NOUN
ap-2970	107	24	of	of	ADP
ap-2970	107	25	elements	element	NOUN
ap-2970	107	26	,	,	PUNCT
ap-2970	107	27	and	and	CCONJ
ap-2970	107	28	that	that	SCONJ
ap-2970	107	29	we	we	PRON
ap-2970	107	30	desire	desire	VERB
ap-2970	107	31	to	to	PART
ap-2970	107	32	reduce	reduce	VERB
ap-2970	107	33	the	the	DET
ap-2970	107	34	size	size	NOUN
ap-2970	107	35	of	of	ADP
ap-2970	107	36	kaibk	kaibk	NOUN
ap-2970	107	37	and	and	CCONJ
ap-2970	107	38	maibk	maibk	NOUN
ap-2970	107	39	by	by	ADP
ap-2970	107	40	means	mean	NOUN
ap-2970	107	41	of	of	ADP
ap-2970	107	42	a	a	DET
ap-2970	107	43	transformation	transformation	NOUN
ap-2970	107	44	matrix	matrix	NOUN
ap-2970	107	45	t	t	X
ap-2970	107	46	which	which	PRON
ap-2970	107	47	,	,	PUNCT
ap-2970	107	48	by	by	ADP
ap-2970	107	49	definition	definition	NOUN
ap-2970	107	50	,	,	PUNCT
ap-2970	107	51	is	be	AUX
ap-2970	107	52	a	a	DET
ap-2970	107	53	rotation	rotation	NOUN
ap-2970	107	54	matrix	matrix	NOUN
ap-2970	107	55	.	.	PUNCT
ap-2970	108	1	therefore	therefore	ADV
ap-2970	108	2	,	,	PUNCT
ap-2970	108	3	the	the	DET
ap-2970	108	4	full	full	ADJ
ap-2970	108	5	stiffness	stiffness	NOUN
ap-2970	108	6	and	and	CCONJ
ap-2970	108	7	mass	mass	ADJ
ap-2970	108	8	matrices	matrix	NOUN
ap-2970	108	9	,	,	PUNCT
ap-2970	108	10	in	in	ADP
ap-2970	108	11	addition	addition	NOUN
ap-2970	108	12	to	to	ADP
ap-2970	108	13	containing	contain	VERB
ap-2970	108	14	information	information	NOUN
ap-2970	108	15	related	relate	VERB
ap-2970	108	16	to	to	ADP
ap-2970	108	17	the	the	DET
ap-2970	108	18	rigid	rigid	ADJ
ap-2970	108	19	rotation	rotation	NOUN
ap-2970	108	20	and	and	CCONJ
ap-2970	108	21	the	the	DET
ap-2970	108	22	stretch	stretch	NOUN
ap-2970	108	23	of	of	ADP
ap-2970	108	24	the	the	DET
ap-2970	108	25	solid	solid	ADJ
ap-2970	108	26	,	,	PUNCT
ap-2970	108	27	also	also	ADV
ap-2970	108	28	retain	retain	VERB
ap-2970	108	29	information	information	NOUN
ap-2970	108	30	related	relate	VERB
ap-2970	108	31	to	to	ADP
ap-2970	108	32	the	the	DET
ap-2970	108	33	change	change	NOUN
ap-2970	108	34	in	in	ADP
ap-2970	108	35	the	the	DET
ap-2970	108	36	coordinates	coordinate	NOUN
ap-2970	108	37	system	system	NOUN
ap-2970	108	38	undergone	undergo	VERB
ap-2970	108	39	after	after	ADP
ap-2970	108	40	the	the	DET
ap-2970	108	41	process	process	NOUN
ap-2970	108	42	of	of	ADP
ap-2970	108	43	reduction	reduction	NOUN
ap-2970	108	44	.	.	PUNCT
ap-2970	109	1	it	it	PRON
ap-2970	109	2	then	then	ADV
ap-2970	109	3	appears	appear	VERB
ap-2970	109	4	evident	evident	ADJ
ap-2970	109	5	then	then	ADV
ap-2970	109	6	that	that	SCONJ
ap-2970	109	7	,	,	PUNCT
ap-2970	109	8	whenever	whenever	SCONJ
ap-2970	109	9	a	a	DET
ap-2970	109	10	large	large	ADJ
ap-2970	109	11	-	-	PUNCT
ap-2970	109	12	scale	scale	NOUN
ap-2970	109	13	system	system	NOUN
ap-2970	109	14	is	be	AUX
ap-2970	109	15	reduced	reduce	VERB
ap-2970	109	16	and	and	CCONJ
ap-2970	109	17	then	then	ADV
ap-2970	109	18	analyzed	analyze	VERB
ap-2970	109	19	for	for	ADP
ap-2970	109	20	modal	modal	ADJ
ap-2970	109	21	analysis	analysis	NOUN
ap-2970	109	22	by	by	ADP
ap-2970	109	23	means	mean	NOUN
ap-2970	109	24	of	of	ADP
ap-2970	109	25	kr	kr	PROPN
ap-2970	109	26	=	=	SYM
ap-2970	109	27	t	t	PROPN
ap-2970	109	28	t	t	PROPN
ap-2970	109	29	kt	kt	PROPN
ap-2970	109	30	,	,	PUNCT
ap-2970	109	31	mr	mr	PROPN
ap-2970	109	32	=	=	PROPN
ap-2970	109	33	t	t	PROPN
ap-2970	109	34	t	t	PROPN
ap-2970	109	35	mt	mt	PROPN
ap-2970	109	36	,	,	PUNCT
ap-2970	109	37	three	three	NUM
ap-2970	109	38	types	type	NOUN
ap-2970	109	39	of	of	ADP
ap-2970	109	40	components	component	NOUN
ap-2970	109	41	are	be	AUX
ap-2970	109	42	blended	blend	VERB
ap-2970	109	43	to	to	ADP
ap-2970	109	44	one	one	NUM
ap-2970	109	45	another	another	DET
ap-2970	109	46	.	.	PUNCT
ap-2970	110	1	consequently	consequently	ADV
ap-2970	110	2	,	,	PUNCT
ap-2970	110	3	these	these	DET
ap-2970	110	4	components	component	NOUN
ap-2970	110	5	are	be	AUX
ap-2970	110	6	not	not	PART
ap-2970	110	7	actively	actively	ADV
ap-2970	110	8	exploited	exploit	VERB
ap-2970	110	9	when	when	SCONJ
ap-2970	110	10	applying	apply	VERB
ap-2970	110	11	the	the	DET
ap-2970	110	12	standard	standard	ADJ
ap-2970	110	13	matrix	matrix	NOUN
ap-2970	110	14	interpolation	interpolation	NOUN
ap-2970	110	15	method	method	NOUN
ap-2970	110	16	,	,	PUNCT
ap-2970	110	17	because	because	SCONJ
ap-2970	110	18	the	the	DET
ap-2970	110	19	weights	weight	NOUN
ap-2970	110	20	that	that	PRON
ap-2970	110	21	are	be	AUX
ap-2970	110	22	used	use	VERB
ap-2970	110	23	can	can	AUX
ap-2970	110	24	never	never	ADV
ap-2970	110	25	distinguish	distinguish	VERB
ap-2970	110	26	between	between	ADP
ap-2970	110	27	them	they	PRON
ap-2970	110	28	.	.	PUNCT
ap-2970	111	1	a	a	DET
ap-2970	111	2	direct	direct	ADJ
ap-2970	111	3	consequence	consequence	NOUN
ap-2970	111	4	of	of	ADP
ap-2970	111	5	this	this	DET
ap-2970	111	6	situation	situation	NOUN
ap-2970	111	7	is	be	AUX
ap-2970	111	8	that	that	SCONJ
ap-2970	111	9	the	the	DET
ap-2970	111	10	resulting	result	VERB
ap-2970	111	11	roms	rom	NOUN
ap-2970	111	12	can	can	AUX
ap-2970	111	13	not	not	PART
ap-2970	111	14	guarantee	guarantee	VERB
ap-2970	111	15	satisfactory	satisfactory	ADJ
ap-2970	111	16	accuracy	accuracy	NOUN
ap-2970	111	17	.	.	PUNCT
ap-2970	112	1	the	the	DET
ap-2970	112	2	question	question	NOUN
ap-2970	112	3	that	that	PRON
ap-2970	112	4	emerges	emerge	VERB
ap-2970	112	5	is	be	AUX
ap-2970	112	6	therefore	therefore	ADV
ap-2970	112	7	:	:	PUNCT
ap-2970	112	8	how	how	SCONJ
ap-2970	112	9	can	can	AUX
ap-2970	112	10	these	these	DET
ap-2970	112	11	three	three	NUM
ap-2970	112	12	components	component	NOUN
ap-2970	112	13	be	be	AUX
ap-2970	112	14	taken	take	VERB
ap-2970	112	15	out	out	ADP
ap-2970	112	16	of	of	ADP
ap-2970	112	17	kr	kr	PROPN
ap-2970	112	18	and	and	CCONJ
ap-2970	112	19	mr	mr	PROPN
ap-2970	112	20	in	in	ADP
ap-2970	112	21	order	order	NOUN
ap-2970	112	22	to	to	PART
ap-2970	112	23	make	make	VERB
ap-2970	112	24	them	they	PRON
ap-2970	112	25	visible	visible	ADJ
ap-2970	112	26	to	to	ADP
ap-2970	112	27	the	the	DET
ap-2970	112	28	interpolation	interpolation	NOUN
ap-2970	112	29	tool	tool	NOUN
ap-2970	112	30	?	?	PUNCT
ap-2970	113	1	the	the	DET
ap-2970	113	2	next	next	ADJ
ap-2970	113	3	section	section	NOUN
ap-2970	113	4	introduces	introduce	VERB
ap-2970	113	5	the	the	DET
ap-2970	113	6	important	important	ADJ
ap-2970	113	7	concept	concept	NOUN
ap-2970	113	8	of	of	ADP
ap-2970	113	9	polar	polar	ADJ
ap-2970	113	10	decomposition	decomposition	NOUN
ap-2970	113	11	,	,	PUNCT
ap-2970	113	12	which	which	PRON
ap-2970	113	13	allows	allow	VERB
ap-2970	113	14	the	the	DET
ap-2970	113	15	useless	useless	ADJ
ap-2970	113	16	component	component	NOUN
ap-2970	113	17	of	of	ADP
ap-2970	113	18	rigid	rigid	ADJ
ap-2970	113	19	rotation	rotation	NOUN
ap-2970	113	20	to	to	PART
ap-2970	113	21	be	be	AUX
ap-2970	113	22	ruled	rule	VERB
ap-2970	113	23	out	out	ADP
ap-2970	113	24	,	,	PUNCT
ap-2970	113	25	and	and	CCONJ
ap-2970	113	26	brings	bring	VERB
ap-2970	113	27	out	out	ADP
ap-2970	113	28	the	the	DET
ap-2970	113	29	useful	useful	ADJ
ap-2970	113	30	component	component	NOUN
ap-2970	113	31	associated	associate	VERB
ap-2970	113	32	to	to	ADP
ap-2970	113	33	the	the	DET
ap-2970	113	34	deformation	deformation	NOUN
ap-2970	113	35	.	.	PUNCT
ap-2970	114	1	3.2	3.2	NUM
ap-2970	114	2	.	.	PUNCT
ap-2970	115	1	polar	polar	ADJ
ap-2970	115	2	decomposition	decomposition	NOUN
ap-2970	115	3	the	the	DET
ap-2970	115	4	polar	polar	ADJ
ap-2970	115	5	decomposition	decomposition	NOUN
ap-2970	115	6	can	can	AUX
ap-2970	115	7	be	be	AUX
ap-2970	115	8	defined	define	VERB
ap-2970	115	9	as	as	ADP
ap-2970	115	10	the	the	DET
ap-2970	115	11	analogous	analogous	NOUN
ap-2970	115	12	,	,	PUNCT
ap-2970	115	13	for	for	ADP
ap-2970	115	14	matrices	matrix	NOUN
ap-2970	115	15	,	,	PUNCT
ap-2970	115	16	of	of	ADP
ap-2970	115	17	a	a	DET
ap-2970	115	18	complex	complex	ADJ
ap-2970	115	19	number	number	NOUN
ap-2970	115	20	z	z	NOUN
ap-2970	115	21	=	=	SYM
ap-2970	115	22	reiϑ	reiϑ	NOUN
ap-2970	115	23	,	,	PUNCT
ap-2970	115	24	r	r	NOUN
ap-2970	115	25	≥	≥	NOUN
ap-2970	115	26	0	0	NUM
ap-2970	115	27	.	.	PUNCT
ap-2970	115	28	410	410	NUM
ap-2970	115	29	vol	vol	NOUN
ap-2970	115	30	.	.	PUNCT
ap-2970	116	1	55	55	NUM
ap-2970	116	2	no	no	NOUN
ap-2970	116	3	.	.	PUNCT
ap-2970	117	1	6/2015	6/2015	NUM
ap-2970	117	2	an	an	DET
ap-2970	117	3	interpolation	interpolation	NOUN
ap-2970	117	4	method	method	NOUN
ap-2970	117	5	for	for	ADP
ap-2970	117	6	determining	determine	VERB
ap-2970	117	7	the	the	DET
ap-2970	117	8	frequencies	frequency	NOUN
ap-2970	117	9	figure	figure	VERB
ap-2970	117	10	3	3	NUM
ap-2970	117	11	.	.	PUNCT
ap-2970	118	1	correspondence	correspondence	NOUN
ap-2970	118	2	between	between	ADP
ap-2970	118	3	the	the	DET
ap-2970	118	4	process	process	NOUN
ap-2970	118	5	of	of	ADP
ap-2970	118	6	reducing	reduce	VERB
ap-2970	118	7	the	the	DET
ap-2970	118	8	stiffness	stiffness	ADJ
ap-2970	118	9	matrix	matrix	NOUN
ap-2970	118	10	and	and	CCONJ
ap-2970	118	11	the	the	DET
ap-2970	118	12	factors	factor	NOUN
ap-2970	118	13	calculated	calculate	VERB
ap-2970	118	14	by	by	ADP
ap-2970	118	15	svd	svd	PROPN
ap-2970	118	16	,	,	PUNCT
ap-2970	118	17	a	a	DET
ap-2970	118	18	singular	singular	ADJ
ap-2970	118	19	value	value	NOUN
ap-2970	118	20	decomposition	decomposition	NOUN
ap-2970	118	21	method	method	NOUN
ap-2970	118	22	.	.	PUNCT
ap-2970	119	1	these	these	DET
ap-2970	119	2	factors	factor	NOUN
ap-2970	119	3	have	have	AUX
ap-2970	119	4	been	be	AUX
ap-2970	119	5	identified	identify	VERB
ap-2970	119	6	after	after	ADP
ap-2970	119	7	using	use	VERB
ap-2970	119	8	polar	polar	ADJ
ap-2970	119	9	decomposition	decomposition	NOUN
ap-2970	119	10	to	to	PART
ap-2970	119	11	rule	rule	VERB
ap-2970	119	12	out	out	ADP
ap-2970	119	13	the	the	DET
ap-2970	119	14	part	part	NOUN
ap-2970	119	15	associated	associate	VERB
ap-2970	119	16	with	with	ADP
ap-2970	119	17	rigid	rigid	ADJ
ap-2970	119	18	rotation	rotation	NOUN
ap-2970	119	19	.	.	PUNCT
ap-2970	120	1	theorem	theorem	NOUN
ap-2970	120	2	1	1	NUM
ap-2970	120	3	.	.	PUNCT
ap-2970	121	1	let	let	VERB
ap-2970	121	2	a	a	DET
ap-2970	121	3	∈	∈	PROPN
ap-2970	121	4	rm×n	rm×n	NOUN
ap-2970	121	5	,	,	PUNCT
ap-2970	121	6	m	m	PRON
ap-2970	121	7	≥	≥	NOUN
ap-2970	121	8	n.	n.	NOUN
ap-2970	121	9	then	then	ADV
ap-2970	121	10	there	there	PRON
ap-2970	121	11	exists	exist	VERB
ap-2970	121	12	a	a	DET
ap-2970	121	13	matrix	matrix	NOUN
ap-2970	121	14	r	r	NOUN
ap-2970	121	15	∈	∈	NOUN
ap-2970	121	16	rm×n	rm×n	NOUN
ap-2970	121	17	and	and	CCONJ
ap-2970	121	18	a	a	DET
ap-2970	121	19	unique	unique	ADJ
ap-2970	121	20	positive	positive	ADJ
ap-2970	121	21	semi	semi	ADJ
ap-2970	121	22	-	-	ADJ
ap-2970	121	23	definite	definite	ADJ
ap-2970	121	24	matrix	matrix	NOUN
ap-2970	121	25	s	s	PART
ap-2970	121	26	∈	∈	NOUN
ap-2970	121	27	rm×n	rm×n	NOUN
ap-2970	121	28	such	such	ADJ
ap-2970	121	29	that	that	SCONJ
ap-2970	121	30	a	a	DET
ap-2970	121	31	=	=	NOUN
ap-2970	121	32	rs	rs	NOUN
ap-2970	121	33	,	,	PUNCT
ap-2970	121	34	rt	rt	NOUN
ap-2970	121	35	r	r	NOUN
ap-2970	121	36	=	=	PUNCT
ap-2970	121	37	in	in	ADP
ap-2970	121	38	.	.	PUNCT
ap-2970	122	1	(	(	PUNCT
ap-2970	122	2	7	7	X
ap-2970	122	3	)	)	PUNCT
ap-2970	122	4	if	if	SCONJ
ap-2970	122	5	rank	rank	VERB
ap-2970	122	6	a	a	DET
ap-2970	122	7	=	=	PUNCT
ap-2970	122	8	n	n	CCONJ
ap-2970	122	9	,	,	PUNCT
ap-2970	122	10	then	then	ADV
ap-2970	122	11	s	s	VERB
ap-2970	122	12	is	be	AUX
ap-2970	122	13	positive	positive	ADJ
ap-2970	122	14	definite	definite	ADJ
ap-2970	122	15	and	and	CCONJ
ap-2970	122	16	r	r	NOUN
ap-2970	122	17	is	be	AUX
ap-2970	122	18	uniquely	uniquely	ADV
ap-2970	122	19	determined.1	determined.1	VERB
ap-2970	122	20	considering	consider	VERB
ap-2970	122	21	the	the	DET
ap-2970	122	22	partition	partition	NOUN
ap-2970	122	23	u	u	NOUN
ap-2970	123	1	=	=	PUNCT
ap-2970	123	2	[	[	X
ap-2970	123	3	u1	u1	NOUN
ap-2970	123	4	u2	u2	NOUN
ap-2970	123	5	]	]	PUNCT
ap-2970	123	6	,	,	PUNCT
ap-2970	123	7	ut	ut	PROPN
ap-2970	123	8	1	1	NUM
ap-2970	123	9	u1	u1	NOUN
ap-2970	123	10	=	=	PUNCT
ap-2970	123	11	in	in	ADV
ap-2970	123	12	.	.	PUNCT
ap-2970	124	1	it	it	PRON
ap-2970	124	2	follows	follow	VERB
ap-2970	124	3	that	that	SCONJ
ap-2970	124	4	the	the	DET
ap-2970	124	5	polar	polar	ADJ
ap-2970	124	6	decomposition	decomposition	NOUN
ap-2970	124	7	of	of	ADP
ap-2970	124	8	a	a	PRON
ap-2970	124	9	is	be	AUX
ap-2970	124	10	[	[	X
ap-2970	124	11	12	12	NUM
ap-2970	124	12	]	]	PUNCT
ap-2970	124	13	a	a	DET
ap-2970	124	14	=	=	NOUN
ap-2970	124	15	rs	rs	NOUN
ap-2970	124	16	,	,	PUNCT
ap-2970	124	17	r	r	NOUN
ap-2970	124	18	=	=	SYM
ap-2970	124	19	u1v	u1v	PROPN
ap-2970	124	20	t	t	NOUN
ap-2970	124	21	,	,	PUNCT
ap-2970	124	22	s	s	NOUN
ap-2970	124	23	=	=	X
ap-2970	124	24	v	v	PROPN
ap-2970	124	25	dv	dv	PROPN
ap-2970	124	26	t	t	PROPN
ap-2970	124	27	,	,	PUNCT
ap-2970	124	28	(	(	PUNCT
ap-2970	124	29	8)	8)	NUM
ap-2970	124	30	where	where	SCONJ
ap-2970	124	31	the	the	DET
ap-2970	124	32	factor	factor	NOUN
ap-2970	124	33	v	v	NOUN
ap-2970	124	34	,	,	PUNCT
ap-2970	124	35	known	know	VERB
ap-2970	124	36	as	as	ADP
ap-2970	124	37	the	the	DET
ap-2970	124	38	right	right	ADJ
ap-2970	124	39	-	-	PUNCT
ap-2970	124	40	hand	hand	NOUN
ap-2970	124	41	singular	singular	NOUN
ap-2970	124	42	vector	vector	NOUN
ap-2970	124	43	of	of	ADP
ap-2970	124	44	s	s	NOUN
ap-2970	124	45	[	[	X
ap-2970	124	46	12	12	NUM
ap-2970	124	47	]	]	PUNCT
ap-2970	124	48	,	,	PUNCT
ap-2970	124	49	is	be	AUX
ap-2970	124	50	an	an	DET
ap-2970	124	51	orthogonal	orthogonal	ADJ
ap-2970	124	52	matrix	matrix	NOUN
ap-2970	124	53	.	.	PUNCT
ap-2970	125	1	in	in	ADP
ap-2970	125	2	continuum	continuum	ADJ
ap-2970	125	3	mechanics	mechanic	NOUN
ap-2970	125	4	,	,	PUNCT
ap-2970	125	5	the	the	DET
ap-2970	125	6	gradient	gradient	NOUN
ap-2970	125	7	of	of	ADP
ap-2970	125	8	deformation	deformation	NOUN
ap-2970	125	9	is	be	AUX
ap-2970	125	10	expressed	express	VERB
ap-2970	125	11	in	in	ADP
ap-2970	125	12	terms	term	NOUN
ap-2970	125	13	of	of	ADP
ap-2970	125	14	r	r	NOUN
ap-2970	125	15	and	and	CCONJ
ap-2970	125	16	s	s	PROPN
ap-2970	125	17	,	,	PUNCT
ap-2970	125	18	which	which	PRON
ap-2970	125	19	describe	describe	VERB
ap-2970	125	20	the	the	DET
ap-2970	125	21	rotation	rotation	NOUN
ap-2970	125	22	and	and	CCONJ
ap-2970	125	23	the	the	DET
ap-2970	125	24	stretch	stretch	NOUN
ap-2970	125	25	of	of	ADP
ap-2970	125	26	a	a	DET
ap-2970	125	27	solid	solid	ADJ
ap-2970	125	28	,	,	PUNCT
ap-2970	125	29	respectively	respectively	ADV
ap-2970	125	30	.	.	PUNCT
ap-2970	126	1	this	this	PRON
ap-2970	126	2	is	be	AUX
ap-2970	126	3	the	the	DET
ap-2970	126	4	feature	feature	NOUN
ap-2970	126	5	that	that	PRON
ap-2970	126	6	is	be	AUX
ap-2970	126	7	exploited	exploit	VERB
ap-2970	126	8	by	by	ADP
ap-2970	126	9	the	the	DET
ap-2970	126	10	proposed	propose	VERB
ap-2970	126	11	interpolation	interpolation	NOUN
ap-2970	126	12	method	method	NOUN
ap-2970	126	13	.	.	PUNCT
ap-2970	127	1	the	the	DET
ap-2970	127	2	two	two	NUM
ap-2970	127	3	matrices	matrix	NOUN
ap-2970	127	4	kr	kr	PROPN
ap-2970	127	5	and	and	CCONJ
ap-2970	127	6	mr	mr	PROPN
ap-2970	127	7	are	be	AUX
ap-2970	127	8	decomposed	decompose	VERB
ap-2970	127	9	in	in	ADP
ap-2970	127	10	terms	term	NOUN
ap-2970	127	11	of	of	ADP
ap-2970	127	12	r	r	NOUN
ap-2970	127	13	and	and	CCONJ
ap-2970	127	14	s	s	NOUN
ap-2970	127	15	,	,	PUNCT
ap-2970	127	16	and	and	CCONJ
ap-2970	127	17	since	since	SCONJ
ap-2970	127	18	the	the	DET
ap-2970	127	19	matrix	matrix	NOUN
ap-2970	127	20	r	r	NOUN
ap-2970	127	21	does	do	AUX
ap-2970	127	22	not	not	PART
ap-2970	127	23	participate	participate	VERB
ap-2970	127	24	in	in	ADP
ap-2970	127	25	the	the	DET
ap-2970	127	26	deformation	deformation	NOUN
ap-2970	127	27	of	of	ADP
ap-2970	127	28	the	the	DET
ap-2970	127	29	solid	solid	NOUN
ap-2970	127	30	,	,	PUNCT
ap-2970	127	31	it	it	PRON
ap-2970	127	32	can	can	AUX
ap-2970	127	33	be	be	AUX
ap-2970	127	34	ruled	rule	VERB
ap-2970	127	35	out	out	ADP
ap-2970	127	36	.	.	PUNCT
ap-2970	128	1	matrices	matrix	NOUN
ap-2970	128	2	kr	kr	PROPN
ap-2970	128	3	and	and	CCONJ
ap-2970	128	4	mr	mr	PROPN
ap-2970	128	5	can	can	AUX
ap-2970	128	6	therefore	therefore	ADV
ap-2970	128	7	be	be	AUX
ap-2970	128	8	expressed	express	VERB
ap-2970	128	9	in	in	ADP
ap-2970	128	10	terms	term	NOUN
ap-2970	128	11	of	of	ADP
ap-2970	128	12	the	the	DET
ap-2970	128	13	s	s	NOUN
ap-2970	128	14	-	-	NOUN
ap-2970	128	15	component	component	NOUN
ap-2970	128	16	only	only	ADV
ap-2970	128	17	.	.	PUNCT
ap-2970	129	1	as	as	SCONJ
ap-2970	129	2	several	several	ADJ
ap-2970	129	3	numerical	numerical	ADJ
ap-2970	129	4	experiments	experiment	NOUN
ap-2970	129	5	have	have	AUX
ap-2970	129	6	shown	show	VERB
ap-2970	129	7	,	,	PUNCT
ap-2970	129	8	ruling	rule	VERB
ap-2970	129	9	out	out	ADP
ap-2970	129	10	the	the	DET
ap-2970	129	11	rotational	rotational	ADJ
ap-2970	129	12	component	component	NOUN
ap-2970	129	13	of	of	ADP
ap-2970	129	14	deformation	deformation	NOUN
ap-2970	129	15	improves	improve	VERB
ap-2970	129	16	the	the	DET
ap-2970	129	17	accuracy	accuracy	NOUN
ap-2970	129	18	of	of	ADP
ap-2970	129	19	results	result	NOUN
ap-2970	129	20	.	.	PUNCT
ap-2970	130	1	therefore	therefore	ADV
ap-2970	130	2	,	,	PUNCT
ap-2970	130	3	the	the	DET
ap-2970	130	4	term	term	NOUN
ap-2970	130	5	rsdm2	rsdm2	PROPN
ap-2970	130	6	stems	stem	VERB
ap-2970	130	7	from	from	ADP
ap-2970	130	8	the	the	DET
ap-2970	130	9	process	process	NOUN
ap-2970	130	10	that	that	PRON
ap-2970	130	11	separates	separate	VERB
ap-2970	130	12	the	the	DET
ap-2970	130	13	rigid	rigid	ADJ
ap-2970	130	14	rotation	rotation	NOUN
ap-2970	130	15	from	from	ADP
ap-2970	130	16	stretch	stretch	NOUN
ap-2970	130	17	by	by	ADP
ap-2970	130	18	means	mean	NOUN
ap-2970	130	19	of	of	ADP
ap-2970	130	20	a	a	DET
ap-2970	130	21	decomposition	decomposition	NOUN
ap-2970	130	22	method	method	NOUN
ap-2970	130	23	in	in	ADP
ap-2970	130	24	order	order	NOUN
ap-2970	130	25	to	to	PART
ap-2970	130	26	bring	bring	VERB
ap-2970	130	27	out	out	ADP
ap-2970	130	28	the	the	DET
ap-2970	130	29	components	component	NOUN
ap-2970	130	30	of	of	ADP
ap-2970	130	31	transformation	transformation	NOUN
ap-2970	130	32	and	and	CCONJ
ap-2970	130	33	deformation	deformation	NOUN
ap-2970	130	34	.	.	PUNCT
ap-2970	131	1	1the	1the	ADJ
ap-2970	131	2	concepts	concept	NOUN
ap-2970	131	3	explained	explain	VERB
ap-2970	131	4	in	in	ADP
ap-2970	131	5	this	this	DET
ap-2970	131	6	paper	paper	NOUN
ap-2970	131	7	deal	deal	NOUN
ap-2970	131	8	with	with	ADP
ap-2970	131	9	real	real	ADJ
ap-2970	131	10	matrices	matrix	NOUN
ap-2970	131	11	.	.	PUNCT
ap-2970	132	1	consequently	consequently	ADV
ap-2970	132	2	,	,	PUNCT
ap-2970	132	3	the	the	DET
ap-2970	132	4	complex	complex	ADJ
ap-2970	132	5	matrices	matrix	NOUN
ap-2970	132	6	that	that	PRON
ap-2970	132	7	appear	appear	VERB
ap-2970	132	8	in	in	ADP
ap-2970	132	9	the	the	DET
ap-2970	132	10	referenced	reference	VERB
ap-2970	132	11	scientific	scientific	ADJ
ap-2970	132	12	literature	literature	NOUN
ap-2970	132	13	are	be	AUX
ap-2970	132	14	converted	convert	VERB
ap-2970	132	15	into	into	ADP
ap-2970	132	16	real	real	ADJ
ap-2970	132	17	matrices	matrix	NOUN
ap-2970	132	18	.	.	PUNCT
ap-2970	133	1	2here	2here	X
ap-2970	133	2	,	,	PUNCT
ap-2970	133	3	different	different	ADJ
ap-2970	133	4	letters	letter	NOUN
ap-2970	133	5	have	have	AUX
ap-2970	133	6	been	be	AUX
ap-2970	133	7	used	use	VERB
ap-2970	133	8	from	from	ADP
ap-2970	133	9	those	those	PRON
ap-2970	133	10	adopted	adopt	VERB
ap-2970	133	11	in	in	ADP
ap-2970	133	12	[	[	X
ap-2970	133	13	12	12	NUM
ap-2970	133	14	]	]	PUNCT
ap-2970	133	15	,	,	PUNCT
ap-2970	133	16	which	which	PRON
ap-2970	133	17	are	be	AUX
ap-2970	133	18	u	u	NOUN
ap-2970	133	19	and	and	CCONJ
ap-2970	133	20	h	h	NOUN
ap-2970	133	21	;	;	PUNCT
ap-2970	133	22	they	they	PRON
ap-2970	133	23	are	be	AUX
ap-2970	133	24	also	also	ADV
ap-2970	133	25	different	different	ADJ
ap-2970	133	26	from	from	ADP
ap-2970	133	27	those	those	PRON
ap-2970	133	28	employed	employ	VERB
ap-2970	133	29	by	by	ADP
ap-2970	133	30	[	[	X
ap-2970	133	31	14	14	NUM
ap-2970	133	32	]	]	PUNCT
ap-2970	133	33	,	,	PUNCT
ap-2970	133	34	which	which	PRON
ap-2970	133	35	are	be	AUX
ap-2970	133	36	q	q	ADJ
ap-2970	133	37	and	and	CCONJ
ap-2970	133	38	s	s	VERB
ap-2970	133	39	figure	figure	NOUN
ap-2970	133	40	3	3	NUM
ap-2970	133	41	depicts	depict	VERB
ap-2970	133	42	the	the	DET
ap-2970	133	43	situation	situation	NOUN
ap-2970	133	44	just	just	ADV
ap-2970	133	45	described	describe	VERB
ap-2970	133	46	.	.	PUNCT
ap-2970	134	1	at	at	ADP
ap-2970	134	2	the	the	DET
ap-2970	134	3	top	top	NOUN
ap-2970	134	4	,	,	PUNCT
ap-2970	134	5	the	the	DET
ap-2970	134	6	reduction	reduction	NOUN
ap-2970	134	7	process	process	NOUN
ap-2970	134	8	of	of	ADP
ap-2970	134	9	the	the	DET
ap-2970	134	10	stiffness	stiffness	ADJ
ap-2970	134	11	matrix	matrix	NOUN
ap-2970	134	12	is	be	AUX
ap-2970	134	13	shown	show	VERB
ap-2970	134	14	:	:	PUNCT
ap-2970	134	15	t	t	PROPN
ap-2970	134	16	is	be	AUX
ap-2970	134	17	an	an	DET
ap-2970	134	18	orthogonal	orthogonal	ADJ
ap-2970	134	19	matrix	matrix	NOUN
ap-2970	134	20	,	,	PUNCT
ap-2970	134	21	which	which	PRON
ap-2970	134	22	allows	allow	VERB
ap-2970	134	23	the	the	DET
ap-2970	134	24	state	state	NOUN
ap-2970	134	25	variables	variable	NOUN
ap-2970	134	26	to	to	PART
ap-2970	134	27	be	be	AUX
ap-2970	134	28	projected	project	VERB
ap-2970	134	29	onto	onto	ADP
ap-2970	134	30	the	the	DET
ap-2970	134	31	subspace	subspace	NOUN
ap-2970	134	32	spanned	span	VERB
ap-2970	134	33	by	by	ADP
ap-2970	134	34	its	its	PRON
ap-2970	134	35	columns	column	NOUN
ap-2970	134	36	.	.	PUNCT
ap-2970	135	1	matrix	matrix	NOUN
ap-2970	135	2	k	k	NOUN
ap-2970	135	3	accounts	account	VERB
ap-2970	135	4	for	for	ADP
ap-2970	135	5	the	the	DET
ap-2970	135	6	deformation	deformation	NOUN
ap-2970	135	7	due	due	ADP
ap-2970	135	8	to	to	ADP
ap-2970	135	9	the	the	DET
ap-2970	135	10	reciprocal	reciprocal	ADJ
ap-2970	135	11	displacement	displacement	NOUN
ap-2970	135	12	of	of	ADP
ap-2970	135	13	the	the	DET
ap-2970	135	14	nodes	node	NOUN
ap-2970	135	15	.	.	PUNCT
ap-2970	136	1	from	from	ADP
ap-2970	136	2	continuum	continuum	ADJ
ap-2970	136	3	mechanics	mechanic	NOUN
ap-2970	136	4	,	,	PUNCT
ap-2970	136	5	however	however	ADV
ap-2970	136	6	,	,	PUNCT
ap-2970	136	7	rigid	rigid	ADJ
ap-2970	136	8	rotation	rotation	NOUN
ap-2970	136	9	is	be	AUX
ap-2970	136	10	ruled	rule	VERB
ap-2970	136	11	out	out	ADP
ap-2970	136	12	by	by	ADP
ap-2970	136	13	applying	apply	VERB
ap-2970	136	14	a	a	DET
ap-2970	136	15	decomposition	decomposition	NOUN
ap-2970	136	16	to	to	PART
ap-2970	136	17	describe	describe	VERB
ap-2970	136	18	the	the	DET
ap-2970	136	19	deformation	deformation	NOUN
ap-2970	136	20	through	through	ADP
ap-2970	136	21	the	the	DET
ap-2970	136	22	action	action	NOUN
ap-2970	136	23	of	of	ADP
ap-2970	136	24	the	the	DET
ap-2970	136	25	stretch	stretch	NOUN
ap-2970	136	26	which	which	PRON
ap-2970	136	27	,	,	PUNCT
ap-2970	136	28	unlike	unlike	ADP
ap-2970	136	29	the	the	DET
ap-2970	136	30	rigid	rigid	ADJ
ap-2970	136	31	rotation	rotation	NOUN
ap-2970	136	32	,	,	PUNCT
ap-2970	136	33	is	be	AUX
ap-2970	136	34	responsible	responsible	ADJ
ap-2970	136	35	for	for	ADP
ap-2970	136	36	the	the	DET
ap-2970	136	37	stress	stress	NOUN
ap-2970	136	38	.	.	PUNCT
ap-2970	137	1	consequently	consequently	ADV
ap-2970	137	2	(	(	PUNCT
ap-2970	137	3	figure	figure	NOUN
ap-2970	137	4	3	3	NUM
ap-2970	137	5	bottom	bottom	NOUN
ap-2970	137	6	)	)	PUNCT
ap-2970	137	7	,	,	PUNCT
ap-2970	137	8	the	the	DET
ap-2970	137	9	rotation	rotation	NOUN
ap-2970	137	10	and	and	CCONJ
ap-2970	137	11	the	the	DET
ap-2970	137	12	stretch	stretch	NOUN
ap-2970	137	13	,	,	PUNCT
ap-2970	137	14	which	which	PRON
ap-2970	137	15	,	,	PUNCT
ap-2970	137	16	after	after	SCONJ
ap-2970	137	17	the	the	DET
ap-2970	137	18	process	process	NOUN
ap-2970	137	19	of	of	ADP
ap-2970	137	20	reduction	reduction	NOUN
ap-2970	137	21	are	be	AUX
ap-2970	137	22	originally	originally	ADV
ap-2970	137	23	blended	blend	VERB
ap-2970	137	24	,	,	PUNCT
ap-2970	137	25	can	can	AUX
ap-2970	137	26	each	each	PRON
ap-2970	137	27	be	be	AUX
ap-2970	137	28	made	make	VERB
ap-2970	137	29	visible	visible	ADJ
ap-2970	137	30	by	by	ADP
ap-2970	137	31	the	the	DET
ap-2970	137	32	factors	factor	NOUN
ap-2970	137	33	of	of	ADP
ap-2970	137	34	a	a	DET
ap-2970	137	35	singular	singular	ADJ
ap-2970	137	36	value	value	NOUN
ap-2970	137	37	decomposition	decomposition	NOUN
ap-2970	137	38	(	(	PUNCT
ap-2970	137	39	applied	apply	VERB
ap-2970	137	40	in	in	ADP
ap-2970	137	41	this	this	DET
ap-2970	137	42	example	example	NOUN
ap-2970	137	43	to	to	ADP
ap-2970	137	44	the	the	DET
ap-2970	137	45	stiffness	stiffness	ADJ
ap-2970	137	46	matrix	matrix	NOUN
ap-2970	137	47	):	):	PUNCT
ap-2970	137	48	an	an	DET
ap-2970	137	49	orthogonal	orthogonal	ADJ
ap-2970	137	50	matrix	matrix	NOUN
ap-2970	137	51	v	v	NOUN
ap-2970	137	52	and	and	CCONJ
ap-2970	137	53	the	the	DET
ap-2970	137	54	matrix	matrix	NOUN
ap-2970	137	55	of	of	ADP
ap-2970	137	56	singular	singular	ADJ
ap-2970	137	57	values	value	NOUN
ap-2970	137	58	that	that	PRON
ap-2970	137	59	define	define	VERB
ap-2970	137	60	the	the	DET
ap-2970	137	61	part	part	NOUN
ap-2970	137	62	responsible	responsible	ADJ
ap-2970	137	63	for	for	ADP
ap-2970	137	64	the	the	DET
ap-2970	137	65	deformation	deformation	NOUN
ap-2970	137	66	.	.	PUNCT
ap-2970	138	1	polar	polar	ADJ
ap-2970	138	2	decomposition	decomposition	NOUN
ap-2970	138	3	can	can	AUX
ap-2970	138	4	therefore	therefore	ADV
ap-2970	138	5	be	be	AUX
ap-2970	138	6	considered	consider	VERB
ap-2970	138	7	as	as	ADP
ap-2970	138	8	the	the	DET
ap-2970	138	9	conceptual	conceptual	ADJ
ap-2970	138	10	tool	tool	NOUN
ap-2970	138	11	that	that	PRON
ap-2970	138	12	,	,	PUNCT
ap-2970	138	13	by	by	ADP
ap-2970	138	14	analogy	analogy	NOUN
ap-2970	138	15	with	with	ADP
ap-2970	138	16	continuum	continuum	ADJ
ap-2970	138	17	mechanics	mechanic	NOUN
ap-2970	138	18	,	,	PUNCT
ap-2970	138	19	allows	allow	VERB
ap-2970	138	20	us	we	PRON
ap-2970	138	21	to	to	PART
ap-2970	138	22	identify	identify	VERB
ap-2970	138	23	which	which	DET
ap-2970	138	24	component	component	NOUN
ap-2970	138	25	of	of	ADP
ap-2970	138	26	the	the	DET
ap-2970	138	27	rigid	rigid	ADJ
ap-2970	138	28	rotation	rotation	NOUN
ap-2970	138	29	to	to	PART
ap-2970	138	30	rule	rule	VERB
ap-2970	138	31	out	out	ADP
ap-2970	138	32	;	;	PUNCT
ap-2970	138	33	svd	svd	NOUN
ap-2970	138	34	practically	practically	ADV
ap-2970	138	35	allows	allow	VERB
ap-2970	138	36	us	we	PRON
ap-2970	138	37	to	to	PART
ap-2970	138	38	compute	compute	VERB
ap-2970	138	39	the	the	DET
ap-2970	138	40	components	component	NOUN
ap-2970	138	41	of	of	ADP
ap-2970	138	42	the	the	DET
ap-2970	138	43	reduced	reduce	VERB
ap-2970	138	44	matrix	matrix	NOUN
ap-2970	138	45	pertaining	pertain	VERB
ap-2970	138	46	to	to	ADP
ap-2970	138	47	the	the	DET
ap-2970	138	48	change	change	NOUN
ap-2970	138	49	of	of	ADP
ap-2970	138	50	coordinates	coordinate	NOUN
ap-2970	138	51	and	and	CCONJ
ap-2970	138	52	stretch	stretch	VERB
ap-2970	138	53	.	.	PUNCT
ap-2970	139	1	to	to	PART
ap-2970	139	2	compute	compute	VERB
ap-2970	139	3	the	the	DET
ap-2970	139	4	s	s	NOUN
ap-2970	139	5	-	-	NOUN
ap-2970	139	6	component	component	NOUN
ap-2970	139	7	,	,	PUNCT
ap-2970	139	8	it	it	PRON
ap-2970	139	9	will	will	AUX
ap-2970	139	10	therefore	therefore	ADV
ap-2970	139	11	be	be	AUX
ap-2970	139	12	necessary	necessary	ADJ
ap-2970	139	13	to	to	PART
ap-2970	139	14	apply	apply	VERB
ap-2970	139	15	an	an	DET
ap-2970	139	16	svd	svd	PROPN
ap-2970	139	17	method	method	NOUN
ap-2970	139	18	to	to	ADP
ap-2970	139	19	the	the	DET
ap-2970	139	20	matrices	matrix	NOUN
ap-2970	139	21	of	of	ADP
ap-2970	139	22	interest	interest	NOUN
ap-2970	139	23	.	.	PUNCT
ap-2970	140	1	the	the	DET
ap-2970	140	2	following	follow	VERB
ap-2970	140	3	section	section	NOUN
ap-2970	140	4	shows	show	VERB
ap-2970	140	5	this	this	DET
ap-2970	140	6	step	step	NOUN
ap-2970	140	7	.	.	PUNCT
ap-2970	141	1	3.3	3.3	NUM
ap-2970	141	2	.	.	PUNCT
ap-2970	141	3	application	application	NOUN
ap-2970	141	4	of	of	ADP
ap-2970	141	5	the	the	DET
ap-2970	141	6	proposed	propose	VERB
ap-2970	141	7	interpolation	interpolation	NOUN
ap-2970	141	8	method	method	NOUN
ap-2970	141	9	in	in	ADP
ap-2970	141	10	order	order	NOUN
ap-2970	141	11	to	to	PART
ap-2970	141	12	obtain	obtain	VERB
ap-2970	141	13	the	the	DET
ap-2970	141	14	s	s	NOUN
ap-2970	141	15	matrix	matrix	NOUN
ap-2970	141	16	,	,	PUNCT
ap-2970	141	17	it	it	PRON
ap-2970	141	18	is	be	AUX
ap-2970	141	19	therefore	therefore	ADV
ap-2970	141	20	necessary	necessary	ADJ
ap-2970	141	21	to	to	PART
ap-2970	141	22	carry	carry	VERB
ap-2970	141	23	out	out	ADP
ap-2970	141	24	a	a	DET
ap-2970	141	25	singular	singular	ADJ
ap-2970	141	26	value	value	NOUN
ap-2970	141	27	decomposition	decomposition	NOUN
ap-2970	141	28	,	,	PUNCT
ap-2970	141	29	and	and	CCONJ
ap-2970	141	30	to	to	PART
ap-2970	141	31	exploit	exploit	VERB
ap-2970	141	32	only	only	ADV
ap-2970	141	33	two	two	NUM
ap-2970	141	34	of	of	ADP
ap-2970	141	35	its	its	PRON
ap-2970	141	36	factors	factor	NOUN
ap-2970	141	37	.	.	PUNCT
ap-2970	142	1	it	it	PRON
ap-2970	142	2	is	be	AUX
ap-2970	142	3	important	important	ADJ
ap-2970	142	4	to	to	PART
ap-2970	142	5	highlight	highlight	VERB
ap-2970	142	6	this	this	PRON
ap-2970	142	7	,	,	PUNCT
ap-2970	142	8	because	because	SCONJ
ap-2970	142	9	it	it	PRON
ap-2970	142	10	might	might	AUX
ap-2970	142	11	lead	lead	VERB
ap-2970	142	12	to	to	ADP
ap-2970	142	13	the	the	DET
ap-2970	142	14	idea	idea	NOUN
ap-2970	142	15	that	that	SCONJ
ap-2970	142	16	svd	svd	PROPN
ap-2970	142	17	is	be	AUX
ap-2970	142	18	applied	apply	VERB
ap-2970	142	19	to	to	ADP
ap-2970	142	20	the	the	DET
ap-2970	142	21	matrices	matrix	NOUN
ap-2970	142	22	in	in	ADP
ap-2970	142	23	its	its	PRON
ap-2970	142	24	entirety	entirety	NOUN
ap-2970	142	25	,	,	PUNCT
ap-2970	142	26	whereas	whereas	SCONJ
ap-2970	142	27	only	only	ADV
ap-2970	142	28	a	a	DET
ap-2970	142	29	part	part	NOUN
ap-2970	142	30	of	of	ADP
ap-2970	142	31	its	its	PRON
ap-2970	142	32	generated	generate	VERB
ap-2970	142	33	factors	factor	NOUN
ap-2970	142	34	is	be	AUX
ap-2970	142	35	in	in	ADP
ap-2970	142	36	fact	fact	NOUN
ap-2970	142	37	used	use	VERB
ap-2970	142	38	.	.	PUNCT
ap-2970	143	1	since	since	SCONJ
ap-2970	143	2	the	the	DET
ap-2970	143	3	svd	svd	PROPN
ap-2970	143	4	method	method	NOUN
ap-2970	143	5	is	be	AUX
ap-2970	143	6	numerically	numerically	ADV
ap-2970	143	7	stable	stable	ADJ
ap-2970	143	8	and	and	CCONJ
ap-2970	143	9	is	be	AUX
ap-2970	143	10	implemented	implement	VERB
ap-2970	143	11	in	in	ADP
ap-2970	143	12	different	different	ADJ
ap-2970	143	13	computational	computational	ADJ
ap-2970	143	14	software	software	NOUN
ap-2970	143	15	programs	program	NOUN
ap-2970	143	16	,	,	PUNCT
ap-2970	143	17	its	its	PRON
ap-2970	143	18	use	use	NOUN
ap-2970	143	19	for	for	ADP
ap-2970	143	20	calculating	calculate	VERB
ap-2970	143	21	s	s	NOUN
ap-2970	143	22	is	be	AUX
ap-2970	143	23	simple	simple	ADJ
ap-2970	143	24	and	and	CCONJ
ap-2970	143	25	fast	fast	ADJ
ap-2970	143	26	.	.	PUNCT
ap-2970	144	1	suppose	suppose	VERB
ap-2970	144	2	that	that	SCONJ
ap-2970	144	3	two	two	NUM
ap-2970	144	4	finite	finite	ADJ
ap-2970	144	5	element	element	NOUN
ap-2970	144	6	analyses	analysis	NOUN
ap-2970	144	7	have	have	AUX
ap-2970	144	8	been	be	AUX
ap-2970	144	9	run	run	VERB
ap-2970	144	10	,	,	PUNCT
ap-2970	144	11	and	and	CCONJ
ap-2970	144	12	that	that	SCONJ
ap-2970	144	13	the	the	DET
ap-2970	144	14	matrices	matrix	NOUN
ap-2970	144	15	of	of	ADP
ap-2970	144	16	mass	mass	NOUN
ap-2970	144	17	m	m	PROPN
ap-2970	144	18	and	and	CCONJ
ap-2970	144	19	stiffness	stiffness	NOUN
ap-2970	144	20	k	k	PROPN
ap-2970	144	21	have	have	AUX
ap-2970	144	22	been	be	AUX
ap-2970	144	23	derived	derive	VERB
ap-2970	144	24	.	.	PUNCT
ap-2970	145	1	two	two	NUM
ap-2970	145	2	couples	couple	NOUN
ap-2970	145	3	of	of	ADP
ap-2970	145	4	matrices	matrix	NOUN
ap-2970	145	5	are	be	AUX
ap-2970	145	6	now	now	ADV
ap-2970	145	7	available	available	ADJ
ap-2970	145	8	:	:	PUNCT
ap-2970	145	9	(	(	PUNCT
ap-2970	145	10	k1,k2	k1,k2	PROPN
ap-2970	145	11	)	)	PUNCT
ap-2970	145	12	and	and	CCONJ
ap-2970	145	13	(	(	PUNCT
ap-2970	145	14	m1,m2	m1,m2	PROPN
ap-2970	145	15	)	)	PUNCT
ap-2970	145	16	.	.	PUNCT
ap-2970	146	1	the	the	DET
ap-2970	146	2	first	first	ADJ
ap-2970	146	3	step	step	NOUN
ap-2970	146	4	consists	consist	VERB
ap-2970	146	5	of	of	ADP
ap-2970	146	6	performing	perform	VERB
ap-2970	146	7	an	an	DET
ap-2970	146	8	svd	svd	NOUN
ap-2970	146	9	and	and	CCONJ
ap-2970	146	10	extracting	extract	VERB
ap-2970	146	11	the	the	DET
ap-2970	146	12	matrices	matrix	NOUN
ap-2970	146	13	v	v	NOUN
ap-2970	146	14	and	and	CCONJ
ap-2970	146	15	d	d	NOUN
ap-2970	146	16	for	for	ADP
ap-2970	146	17	each	each	PRON
ap-2970	146	18	of	of	ADP
ap-2970	146	19	these	these	DET
ap-2970	146	20	4	4	NUM
ap-2970	146	21	matrices	matrix	NOUN
ap-2970	146	22	.	.	PUNCT
ap-2970	147	1	let	let	VERB
ap-2970	147	2	us	we	PRON
ap-2970	147	3	use	use	VERB
ap-2970	147	4	(	(	PUNCT
ap-2970	147	5	vk1,vk2,dk1,dk2	vk1,vk2,dk1,dk2	NOUN
ap-2970	147	6	)	)	PUNCT
ap-2970	147	7	and	and	CCONJ
ap-2970	147	8	(	(	PUNCT
ap-2970	147	9	vm1,vm2,dm1,dm2	vm1,vm2,dm1,dm2	PROPN
ap-2970	147	10	)	)	PUNCT
ap-2970	147	11	to	to	PART
ap-2970	147	12	refer	refer	VERB
ap-2970	147	13	to	to	ADP
ap-2970	147	14	the	the	DET
ap-2970	147	15	8	8	NUM
ap-2970	147	16	matrices	matrix	NOUN
ap-2970	147	17	pertaining	pertain	VERB
ap-2970	147	18	to	to	ADP
ap-2970	147	19	the	the	DET
ap-2970	147	20	svd	svd	PROPN
ap-2970	147	21	applied	apply	VERB
ap-2970	147	22	to	to	ADP
ap-2970	147	23	each	each	PRON
ap-2970	147	24	of	of	ADP
ap-2970	147	25	the	the	DET
ap-2970	147	26	4	4	NUM
ap-2970	147	27	matrices	matrix	NOUN
ap-2970	147	28	(	(	PUNCT
ap-2970	147	29	k1,k2	k1,k2	PROPN
ap-2970	147	30	)	)	PUNCT
ap-2970	147	31	and	and	CCONJ
ap-2970	147	32	(	(	PUNCT
ap-2970	147	33	m1,m2	m1,m2	PROPN
ap-2970	147	34	)	)	PUNCT
ap-2970	147	35	.	.	PUNCT
ap-2970	148	1	the	the	DET
ap-2970	148	2	parametric	parametric	ADJ
ap-2970	148	3	stiffness	stiffness	NOUN
ap-2970	148	4	and	and	CCONJ
ap-2970	148	5	the	the	DET
ap-2970	148	6	mass	mass	ADJ
ap-2970	148	7	matrices	matrix	NOUN
ap-2970	148	8	can	can	AUX
ap-2970	148	9	now	now	ADV
ap-2970	148	10	be	be	AUX
ap-2970	148	11	ascertained	ascertain	VERB
ap-2970	148	12	:	:	PUNCT
ap-2970	148	13	k(p	k(p	PROPN
ap-2970	148	14	)	)	PUNCT
ap-2970	149	1	=	=	SYM
ap-2970	149	2	α1(p)vk1α2(p)dk1α3(p)v	α1(p)vk1α2(p)dk1α3(p)v	PROPN
ap-2970	149	3	t	t	NOUN
ap-2970	149	4	k1	k1	NOUN
ap-2970	149	5	+	+	CCONJ
ap-2970	149	6	(	(	PUNCT
ap-2970	149	7	1−	1−	NUM
ap-2970	149	8	α1)(p)vk2(1−	α1)(p)vk2(1−	NOUN
ap-2970	149	9	α2)(p)dk2(1−	α2)(p)dk2(1−	NOUN
ap-2970	149	10	α3)(p)v	α3)(p)v	NUM
ap-2970	149	11	t	t	PROPN
ap-2970	149	12	k2	k2	PROPN
ap-2970	149	13	,	,	PUNCT
ap-2970	149	14	m(p	m(p	PROPN
ap-2970	149	15	)	)	PUNCT
ap-2970	149	16	=	=	SYM
ap-2970	149	17	β1(p)vm1β2(p)dm1β3(p)v	β1(p)vm1β2(p)dm1β3(p)v	PUNCT
ap-2970	149	18	t	t	NOUN
ap-2970	149	19	m1	m1	NOUN
ap-2970	149	20	(	(	PUNCT
ap-2970	149	21	9	9	NUM
ap-2970	149	22	)	)	PUNCT
ap-2970	149	23	+	+	CCONJ
ap-2970	149	24	(	(	PUNCT
ap-2970	149	25	1−	1−	NUM
ap-2970	149	26	β1)(p)vm2(1−	β1)(p)vm2(1−	PROPN
ap-2970	149	27	β2)(p)dm2(1−	β2)(p)dm2(1−	PROPN
ap-2970	149	28	β3)(p)v	β3)(p)v	X
ap-2970	149	29	t	t	PROPN
ap-2970	149	30	m2	m2	PROPN
ap-2970	149	31	,	,	PUNCT
ap-2970	149	32	where	where	SCONJ
ap-2970	149	33	we	we	PRON
ap-2970	149	34	shorten	shorten	VERB
ap-2970	149	35	(	(	PUNCT
ap-2970	149	36	p	p	NOUN
ap-2970	149	37	)	)	PUNCT
ap-2970	149	38	=	=	SYM
ap-2970	149	39	(	(	PUNCT
ap-2970	149	40	p1	p1	PROPN
ap-2970	149	41	,	,	PUNCT
ap-2970	149	42	p2	p2	NOUN
ap-2970	149	43	,	,	PUNCT
ap-2970	149	44	.	.	PUNCT
ap-2970	149	45	.	.	PUNCT
ap-2970	149	46	.	.	PUNCT
ap-2970	149	47	)	)	PUNCT
ap-2970	149	48	.	.	PUNCT
ap-2970	150	1	the	the	DET
ap-2970	150	2	coefficients	coefficient	NOUN
ap-2970	150	3	are	be	AUX
ap-2970	150	4	an	an	DET
ap-2970	150	5	essential	essential	ADJ
ap-2970	150	6	part	part	NOUN
ap-2970	150	7	of	of	ADP
ap-2970	150	8	this	this	DET
ap-2970	150	9	model	model	NOUN
ap-2970	150	10	.	.	PUNCT
ap-2970	151	1	more	more	ADV
ap-2970	151	2	specifically	specifically	ADV
ap-2970	151	3	,	,	PUNCT
ap-2970	151	4	for	for	ADP
ap-2970	151	5	those	those	DET
ap-2970	151	6	values	value	NOUN
ap-2970	151	7	of	of	ADP
ap-2970	151	8	the	the	DET
ap-2970	151	9	parameter(s	parameter(s	NOUN
ap-2970	151	10	)	)	PUNCT
ap-2970	151	11	411	411	NUM
ap-2970	151	12	s.	s.	PROPN
ap-2970	151	13	nasisi	nasisi	VERB
ap-2970	151	14	,	,	PUNCT
ap-2970	151	15	m.	m.	NOUN
ap-2970	151	16	valášek	valášek	PROPN
ap-2970	151	17	,	,	PUNCT
ap-2970	151	18	t.	t.	PROPN
ap-2970	151	19	vampola	vampola	PROPN
ap-2970	151	20	acta	acta	PROPN
ap-2970	151	21	polytechnica	polytechnica	PROPN
ap-2970	151	22	figure	figure	NOUN
ap-2970	151	23	5	5	NUM
ap-2970	151	24	.	.	PUNCT
ap-2970	151	25	error	error	NOUN
ap-2970	151	26	committed	commit	VERB
ap-2970	151	27	with	with	ADP
ap-2970	151	28	the	the	DET
ap-2970	151	29	use	use	NOUN
ap-2970	151	30	of	of	ADP
ap-2970	151	31	serep	serep	NOUN
ap-2970	151	32	-	-	PUNCT
ap-2970	151	33	cms	cms	PROPN
ap-2970	151	34	for	for	ADP
ap-2970	151	35	calculating	calculate	VERB
ap-2970	151	36	the	the	DET
ap-2970	151	37	first	first	ADJ
ap-2970	151	38	20	20	NUM
ap-2970	151	39	frequencies	frequency	NOUN
ap-2970	151	40	of	of	ADP
ap-2970	151	41	interest	interest	NOUN
ap-2970	151	42	of	of	ADP
ap-2970	151	43	a	a	DET
ap-2970	151	44	hexapod	hexapod	NOUN
ap-2970	151	45	.	.	PUNCT
ap-2970	152	1	figure	figure	NOUN
ap-2970	152	2	4	4	NUM
ap-2970	152	3	.	.	PUNCT
ap-2970	152	4	3d	3d	NUM
ap-2970	152	5	model	model	NOUN
ap-2970	152	6	of	of	ADP
ap-2970	152	7	a	a	DET
ap-2970	152	8	hexapod	hexapod	NOUN
ap-2970	152	9	.	.	PUNCT
ap-2970	153	1	at	at	ADP
ap-2970	153	2	which	which	PRON
ap-2970	153	3	(	(	PUNCT
ap-2970	153	4	k1,m1	k1,m1	PROPN
ap-2970	153	5	)	)	PUNCT
ap-2970	153	6	are	be	AUX
ap-2970	153	7	obtained	obtain	VERB
ap-2970	153	8	,	,	PUNCT
ap-2970	153	9	αi	αi	VERB
ap-2970	153	10	=	=	PUNCT
ap-2970	153	11	βi	βi	PROPN
ap-2970	153	12	=	=	SYM
ap-2970	153	13	1	1	NUM
ap-2970	153	14	while	while	SCONJ
ap-2970	153	15	in	in	ADP
ap-2970	153	16	the	the	DET
ap-2970	153	17	correspondence	correspondence	NOUN
ap-2970	153	18	of	of	ADP
ap-2970	153	19	those	those	DET
ap-2970	153	20	values	value	NOUN
ap-2970	153	21	at	at	ADP
ap-2970	153	22	which	which	PRON
ap-2970	153	23	(	(	PUNCT
ap-2970	153	24	k2,m2	k2,m2	PROPN
ap-2970	153	25	)	)	PUNCT
ap-2970	153	26	are	be	AUX
ap-2970	153	27	computed	compute	VERB
ap-2970	153	28	,	,	PUNCT
ap-2970	153	29	αi	αi	VERB
ap-2970	153	30	=	=	PUNCT
ap-2970	153	31	βi	βi	PROPN
ap-2970	153	32	=	=	SYM
ap-2970	153	33	0	0	NUM
ap-2970	153	34	,	,	PUNCT
ap-2970	153	35	i	i	PRON
ap-2970	153	36	=	=	NOUN
ap-2970	153	37	1	1	NUM
ap-2970	153	38	,	,	PUNCT
ap-2970	153	39	2	2	NUM
ap-2970	153	40	,	,	PUNCT
ap-2970	153	41	3	3	NUM
ap-2970	153	42	.	.	PUNCT
ap-2970	154	1	the	the	DET
ap-2970	154	2	advantages	advantage	NOUN
ap-2970	154	3	of	of	ADP
ap-2970	154	4	this	this	DET
ap-2970	154	5	method	method	NOUN
ap-2970	154	6	rely	rely	VERB
ap-2970	154	7	on	on	ADP
ap-2970	154	8	three	three	NUM
ap-2970	154	9	factors	factor	NOUN
ap-2970	154	10	:	:	PUNCT
ap-2970	154	11	(	(	PUNCT
ap-2970	154	12	1	1	X
ap-2970	154	13	.	.	PUNCT
ap-2970	154	14	)	)	PUNCT
ap-2970	155	1	unlike	unlike	ADP
ap-2970	155	2	the	the	DET
ap-2970	155	3	direct	direct	ADJ
ap-2970	155	4	matrix	matrix	NOUN
ap-2970	155	5	method	method	NOUN
ap-2970	155	6	,	,	PUNCT
ap-2970	155	7	this	this	DET
ap-2970	155	8	method	method	NOUN
ap-2970	155	9	accounts	account	VERB
ap-2970	155	10	for	for	ADP
ap-2970	155	11	6	6	NUM
ap-2970	155	12	coefficients	coefficient	NOUN
ap-2970	155	13	,	,	PUNCT
ap-2970	155	14	thus	thus	ADV
ap-2970	155	15	allowing	allow	VERB
ap-2970	155	16	the	the	DET
ap-2970	155	17	model	model	NOUN
ap-2970	155	18	to	to	PART
ap-2970	155	19	be	be	AUX
ap-2970	155	20	tuned	tune	VERB
ap-2970	155	21	up	up	ADP
ap-2970	155	22	efficiently	efficiently	ADV
ap-2970	155	23	.	.	PUNCT
ap-2970	156	1	(	(	PUNCT
ap-2970	156	2	2	2	NUM
ap-2970	156	3	.	.	PUNCT
ap-2970	156	4	)	)	PUNCT
ap-2970	157	1	the	the	DET
ap-2970	157	2	decomposition	decomposition	NOUN
ap-2970	157	3	discussed	discuss	VERB
ap-2970	157	4	above	above	ADV
ap-2970	157	5	is	be	AUX
ap-2970	157	6	guaranteed	guarantee	VERB
ap-2970	157	7	to	to	PART
ap-2970	157	8	act	act	VERB
ap-2970	157	9	on	on	ADP
ap-2970	157	10	more	more	ADJ
ap-2970	157	11	components	component	NOUN
ap-2970	157	12	that	that	SCONJ
ap-2970	157	13	,	,	PUNCT
ap-2970	157	14	without	without	ADP
ap-2970	157	15	decomposition	decomposition	NOUN
ap-2970	157	16	,	,	PUNCT
ap-2970	157	17	would	would	AUX
ap-2970	157	18	remain	remain	AUX
ap-2970	157	19	encapsulated	encapsulate	VERB
ap-2970	157	20	into	into	ADP
ap-2970	157	21	the	the	DET
ap-2970	157	22	reduced	reduce	VERB
ap-2970	157	23	stiffness	stiffness	NOUN
ap-2970	157	24	and	and	CCONJ
ap-2970	157	25	mass	mass	ADJ
ap-2970	157	26	matrices	matrix	NOUN
ap-2970	157	27	;	;	PUNCT
ap-2970	157	28	namely	namely	ADV
ap-2970	157	29	the	the	DET
ap-2970	157	30	component	component	NOUN
ap-2970	157	31	pertaining	pertain	VERB
ap-2970	157	32	to	to	ADP
ap-2970	157	33	the	the	DET
ap-2970	157	34	transformation	transformation	NOUN
ap-2970	157	35	matrix	matrix	NOUN
ap-2970	157	36	and	and	CCONJ
ap-2970	157	37	the	the	DET
ap-2970	157	38	component	component	NOUN
ap-2970	157	39	associated	associate	VERB
ap-2970	157	40	to	to	ADP
ap-2970	157	41	the	the	DET
ap-2970	157	42	shape	shape	NOUN
ap-2970	157	43	functions	function	NOUN
ap-2970	157	44	of	of	ADP
ap-2970	157	45	the	the	DET
ap-2970	157	46	matrices	matrix	NOUN
ap-2970	157	47	of	of	ADP
ap-2970	157	48	the	the	DET
ap-2970	157	49	fe	fe	PROPN
ap-2970	157	50	assemblage	assemblage	NOUN
ap-2970	157	51	.	.	PUNCT
ap-2970	158	1	(	(	PUNCT
ap-2970	158	2	3	3	NUM
ap-2970	158	3	.	.	PUNCT
ap-2970	158	4	)	)	PUNCT
ap-2970	159	1	the	the	DET
ap-2970	159	2	useless	useless	ADJ
ap-2970	159	3	component	component	NOUN
ap-2970	159	4	related	relate	VERB
ap-2970	159	5	to	to	ADP
ap-2970	159	6	the	the	DET
ap-2970	159	7	rigid	rigid	ADJ
ap-2970	159	8	rotation	rotation	NOUN
ap-2970	159	9	has	have	AUX
ap-2970	159	10	been	be	AUX
ap-2970	159	11	ruled	rule	VERB
ap-2970	159	12	out	out	ADP
ap-2970	159	13	,	,	PUNCT
ap-2970	159	14	so	so	SCONJ
ap-2970	159	15	it	it	PRON
ap-2970	159	16	does	do	AUX
ap-2970	159	17	not	not	PART
ap-2970	159	18	participate	participate	VERB
ap-2970	159	19	actively	actively	ADV
ap-2970	159	20	and	and	CCONJ
ap-2970	159	21	harmfully	harmfully	ADV
ap-2970	159	22	in	in	ADP
ap-2970	159	23	the	the	DET
ap-2970	159	24	process	process	NOUN
ap-2970	159	25	of	of	ADP
ap-2970	159	26	interpolation	interpolation	NOUN
ap-2970	159	27	.	.	PUNCT
ap-2970	160	1	4	4	X
ap-2970	160	2	.	.	X
ap-2970	160	3	results	result	NOUN
ap-2970	160	4	we	we	PRON
ap-2970	160	5	now	now	ADV
ap-2970	160	6	present	present	ADJ
ap-2970	160	7	as	as	ADP
ap-2970	160	8	a	a	DET
ap-2970	160	9	numerical	numerical	ADJ
ap-2970	160	10	example	example	NOUN
ap-2970	160	11	a	a	DET
ap-2970	160	12	study	study	NOUN
ap-2970	160	13	of	of	ADP
ap-2970	160	14	a	a	DET
ap-2970	160	15	hexapod	hexapod	ADJ
ap-2970	160	16	structure	structure	NOUN
ap-2970	160	17	with	with	ADP
ap-2970	160	18	piezoactuators	piezoactuator	NOUN
ap-2970	160	19	that	that	PRON
ap-2970	160	20	was	be	AUX
ap-2970	160	21	created	create	VERB
ap-2970	160	22	at	at	ADP
ap-2970	160	23	the	the	DET
ap-2970	160	24	faculty	faculty	NOUN
ap-2970	160	25	of	of	ADP
ap-2970	160	26	mechanical	mechanical	ADJ
ap-2970	160	27	engineering	engineering	NOUN
ap-2970	160	28	of	of	ADP
ap-2970	160	29	the	the	DET
ap-2970	160	30	czech	czech	PROPN
ap-2970	160	31	technical	technical	PROPN
ap-2970	160	32	university	university	PROPN
ap-2970	160	33	in	in	ADP
ap-2970	160	34	prague	prague	PROPN
ap-2970	160	35	.	.	PUNCT
ap-2970	161	1	the	the	DET
ap-2970	161	2	aim	aim	NOUN
ap-2970	161	3	is	be	AUX
ap-2970	161	4	to	to	PART
ap-2970	161	5	investigate	investigate	VERB
ap-2970	161	6	the	the	DET
ap-2970	161	7	suppression	suppression	NOUN
ap-2970	161	8	of	of	ADP
ap-2970	161	9	vibrations	vibration	NOUN
ap-2970	161	10	of	of	ADP
ap-2970	161	11	compliant	compliant	ADJ
ap-2970	161	12	mechanical	mechanical	ADJ
ap-2970	161	13	structures	structure	NOUN
ap-2970	161	14	.	.	PUNCT
ap-2970	162	1	this	this	DET
ap-2970	162	2	structure	structure	NOUN
ap-2970	162	3	will	will	AUX
ap-2970	162	4	show	show	VERB
ap-2970	162	5	how	how	SCONJ
ap-2970	162	6	the	the	DET
ap-2970	162	7	implementation	implementation	NOUN
ap-2970	162	8	of	of	ADP
ap-2970	162	9	rsdm	rsdm	NOUN
ap-2970	162	10	copes	cope	VERB
ap-2970	162	11	with	with	ADP
ap-2970	162	12	the	the	DET
ap-2970	162	13	use	use	NOUN
ap-2970	162	14	of	of	ADP
ap-2970	162	15	a	a	DET
ap-2970	162	16	large	large	ADJ
ap-2970	162	17	-	-	PUNCT
ap-2970	162	18	scale	scale	NOUN
ap-2970	162	19	system	system	NOUN
ap-2970	162	20	.	.	PUNCT
ap-2970	163	1	the	the	DET
ap-2970	163	2	matrices	matrix	NOUN
ap-2970	163	3	of	of	ADP
ap-2970	163	4	the	the	DET
ap-2970	163	5	original	original	ADJ
ap-2970	163	6	finite	finite	PROPN
ap-2970	163	7	element	element	NOUN
ap-2970	163	8	model	model	NOUN
ap-2970	163	9	have	have	VERB
ap-2970	163	10	dimensions	dimension	NOUN
ap-2970	163	11	198015×	198015×	NUM
ap-2970	163	12	198015	198015	NUM
ap-2970	163	13	and	and	CCONJ
ap-2970	163	14	they	they	PRON
ap-2970	163	15	are	be	AUX
ap-2970	163	16	reduced	reduce	VERB
ap-2970	163	17	to	to	ADP
ap-2970	163	18	70×70	70×70	NUM
ap-2970	163	19	(	(	PUNCT
ap-2970	163	20	0.035	0.035	NUM
ap-2970	163	21	%	%	NOUN
ap-2970	163	22	)	)	PUNCT
ap-2970	163	23	.	.	PUNCT
ap-2970	164	1	it	it	PRON
ap-2970	164	2	is	be	AUX
ap-2970	164	3	interesting	interesting	ADJ
ap-2970	164	4	to	to	PART
ap-2970	164	5	assess	assess	VERB
ap-2970	164	6	the	the	DET
ap-2970	164	7	degree	degree	NOUN
ap-2970	164	8	of	of	ADP
ap-2970	164	9	fidelity	fidelity	NOUN
ap-2970	164	10	with	with	ADP
ap-2970	164	11	which	which	DET
ap-2970	164	12	rsdm	rsdm	NOUN
ap-2970	164	13	is	be	AUX
ap-2970	164	14	able	able	ADJ
ap-2970	164	15	to	to	PART
ap-2970	164	16	generate	generate	VERB
ap-2970	164	17	the	the	DET
ap-2970	164	18	rom	rom	NOUN
ap-2970	164	19	at	at	ADP
ap-2970	164	20	a	a	DET
ap-2970	164	21	desired	desire	VERB
ap-2970	164	22	test	test	NOUN
ap-2970	164	23	point	point	NOUN
ap-2970	164	24	.	.	PUNCT
ap-2970	165	1	only	only	ADV
ap-2970	165	2	one	one	NUM
ap-2970	165	3	parameter	parameter	NOUN
ap-2970	165	4	was	be	AUX
ap-2970	165	5	considered	consider	VERB
ap-2970	165	6	for	for	ADP
ap-2970	165	7	this	this	DET
ap-2970	165	8	structure	structure	NOUN
ap-2970	165	9	,	,	PUNCT
ap-2970	165	10	namely	namely	ADV
ap-2970	165	11	the	the	DET
ap-2970	165	12	radius	radius	NOUN
ap-2970	165	13	of	of	ADP
ap-2970	165	14	the	the	DET
ap-2970	165	15	legs	leg	NOUN
ap-2970	165	16	.	.	PUNCT
ap-2970	166	1	the	the	DET
ap-2970	166	2	initial	initial	ADJ
ap-2970	166	3	value	value	NOUN
ap-2970	166	4	of	of	ADP
ap-2970	166	5	the	the	DET
ap-2970	166	6	parameter	parameter	NOUN
ap-2970	166	7	was	be	AUX
ap-2970	166	8	increased	increase	VERB
ap-2970	166	9	by	by	ADP
ap-2970	166	10	100	100	NUM
ap-2970	166	11	%	%	NOUN
ap-2970	166	12	and	and	CCONJ
ap-2970	166	13	only	only	ADV
ap-2970	166	14	two	two	NUM
ap-2970	166	15	finite	finite	ADJ
ap-2970	166	16	element	element	NOUN
ap-2970	166	17	analyses	analysis	NOUN
ap-2970	166	18	were	be	AUX
ap-2970	166	19	run	run	VERB
ap-2970	166	20	.	.	PUNCT
ap-2970	167	1	to	to	PART
ap-2970	167	2	assess	assess	VERB
ap-2970	167	3	the	the	DET
ap-2970	167	4	accuracy	accuracy	NOUN
ap-2970	167	5	with	with	ADP
ap-2970	167	6	which	which	PRON
ap-2970	167	7	the	the	DET
ap-2970	167	8	rom	rom	NOUN
ap-2970	167	9	interpolated	interpolate	VERB
ap-2970	167	10	by	by	ADP
ap-2970	167	11	rsdm	rsdm	NOUN
ap-2970	167	12	was	be	AUX
ap-2970	167	13	computed	compute	VERB
ap-2970	167	14	,	,	PUNCT
ap-2970	167	15	a	a	DET
ap-2970	167	16	full	full	ADJ
ap-2970	167	17	model	model	NOUN
ap-2970	167	18	was	be	AUX
ap-2970	167	19	compared	compare	VERB
ap-2970	167	20	with	with	ADP
ap-2970	167	21	the	the	DET
ap-2970	167	22	computed	computed	ADJ
ap-2970	167	23	rom	rom	NOUN
ap-2970	167	24	at	at	ADP
ap-2970	167	25	a	a	DET
ap-2970	167	26	chosen	choose	VERB
ap-2970	167	27	test	test	NOUN
ap-2970	167	28	point	point	NOUN
ap-2970	167	29	lying	lie	VERB
ap-2970	167	30	within	within	ADP
ap-2970	167	31	the	the	DET
ap-2970	167	32	design	design	NOUN
ap-2970	167	33	space	space	NOUN
ap-2970	167	34	identified	identify	VERB
ap-2970	167	35	by	by	ADP
ap-2970	167	36	the	the	DET
ap-2970	167	37	radius	radius	NOUN
ap-2970	167	38	of	of	ADP
ap-2970	167	39	the	the	DET
ap-2970	167	40	legs	leg	NOUN
ap-2970	167	41	.	.	PUNCT
ap-2970	168	1	the	the	DET
ap-2970	168	2	reduction	reduction	NOUN
ap-2970	168	3	process	process	NOUN
ap-2970	168	4	of	of	ADP
ap-2970	168	5	reduction	reduction	NOUN
ap-2970	168	6	for	for	ADP
ap-2970	168	7	obtaining	obtain	VERB
ap-2970	168	8	the	the	DET
ap-2970	168	9	two	two	NUM
ap-2970	168	10	initial	initial	ADJ
ap-2970	168	11	roms	rom	NOUN
ap-2970	168	12	employed	employ	VERB
ap-2970	168	13	compund	compund	PROPN
ap-2970	168	14	serep	serep	PROPN
ap-2970	168	15	-	-	PROPN
ap-2970	168	16	cms	cms	PROPN
ap-2970	168	17	mor	mor	NOUN
ap-2970	168	18	,	,	PUNCT
ap-2970	168	19	i.e.	i.e.	X
ap-2970	168	20	first	first	ADV
ap-2970	168	21	the	the	DET
ap-2970	168	22	serep	serep	PROPN
ap-2970	168	23	method	method	NOUN
ap-2970	168	24	was	be	AUX
ap-2970	168	25	used	use	VERB
ap-2970	168	26	to	to	PART
ap-2970	168	27	preserve	preserve	VERB
ap-2970	168	28	the	the	DET
ap-2970	168	29	lowest	low	ADJ
ap-2970	168	30	20	20	NUM
ap-2970	168	31	frequencies	frequency	NOUN
ap-2970	168	32	and	and	CCONJ
ap-2970	168	33	subsequently	subsequently	ADV
ap-2970	168	34	a	a	DET
ap-2970	168	35	component	component	NOUN
ap-2970	168	36	-	-	PUNCT
ap-2970	168	37	mode	mode	NOUN
ap-2970	168	38	synthesis	synthesis	NOUN
ap-2970	168	39	method	method	NOUN
ap-2970	168	40	(	(	PUNCT
ap-2970	168	41	craig	craig	PROPN
ap-2970	168	42	-	-	PUNCT
ap-2970	168	43	bampton	bampton	NOUN
ap-2970	168	44	)	)	PUNCT
ap-2970	168	45	was	be	AUX
ap-2970	168	46	applied	apply	VERB
ap-2970	168	47	to	to	ADP
ap-2970	168	48	the	the	DET
ap-2970	168	49	reduced	reduce	VERB
ap-2970	168	50	matrices	matrix	NOUN
ap-2970	168	51	obtained	obtain	VERB
ap-2970	168	52	by	by	ADP
ap-2970	168	53	serep	serep	PROPN
ap-2970	168	54	.	.	PUNCT
ap-2970	169	1	the	the	DET
ap-2970	169	2	accuracy	accuracy	NOUN
ap-2970	169	3	of	of	ADP
ap-2970	169	4	the	the	DET
ap-2970	169	5	rom	rom	NOUN
ap-2970	169	6	was	be	AUX
ap-2970	169	7	assessed	assess	VERB
ap-2970	169	8	by	by	ADP
ap-2970	169	9	applying	apply	VERB
ap-2970	169	10	two	two	NUM
ap-2970	169	11	criteria	criterion	NOUN
ap-2970	169	12	:	:	PUNCT
ap-2970	169	13	computation	computation	NOUN
ap-2970	169	14	of	of	ADP
ap-2970	169	15	the	the	DET
ap-2970	169	16	normalized	normalize	VERB
ap-2970	169	17	relative	relative	ADJ
ap-2970	169	18	frequency	frequency	NOUN
ap-2970	169	19	difference	difference	NOUN
ap-2970	169	20	or	or	CCONJ
ap-2970	169	21	nrfd	nrfd	NOUN
ap-2970	169	22	,	,	PUNCT
ap-2970	169	23	and	and	CCONJ
ap-2970	169	24	the	the	DET
ap-2970	169	25	mac	mac	PROPN
ap-2970	169	26	number	number	NOUN
ap-2970	169	27	.	.	PUNCT
ap-2970	170	1	412	412	NUM
ap-2970	170	2	vol	vol	NOUN
ap-2970	170	3	.	.	PUNCT
ap-2970	171	1	55	55	NUM
ap-2970	171	2	no	no	NOUN
ap-2970	171	3	.	.	PUNCT
ap-2970	172	1	6/2015	6/2015	NUM
ap-2970	172	2	an	an	DET
ap-2970	172	3	interpolation	interpolation	NOUN
ap-2970	172	4	method	method	NOUN
ap-2970	172	5	for	for	ADP
ap-2970	172	6	determining	determine	VERB
ap-2970	172	7	the	the	DET
ap-2970	172	8	frequencies	frequency	NOUN
ap-2970	172	9	figure	figure	VERB
ap-2970	172	10	6	6	NUM
ap-2970	172	11	.	.	PUNCT
ap-2970	173	1	computation	computation	NOUN
ap-2970	173	2	of	of	ADP
ap-2970	173	3	the	the	DET
ap-2970	173	4	first	first	ADJ
ap-2970	173	5	6	6	NUM
ap-2970	173	6	frequencies	frequency	NOUN
ap-2970	173	7	by	by	ADP
ap-2970	173	8	the	the	DET
ap-2970	173	9	parametric	parametric	PROPN
ap-2970	173	10	rom	rom	NOUN
ap-2970	173	11	at	at	ADP
ap-2970	173	12	the	the	DET
ap-2970	173	13	test	test	NOUN
ap-2970	173	14	point	point	NOUN
ap-2970	173	15	(	(	PUNCT
ap-2970	173	16	a	a	X
ap-2970	173	17	)	)	PUNCT
ap-2970	173	18	;	;	PUNCT
ap-2970	173	19	modal	modal	NOUN
ap-2970	173	20	assurance	assurance	NOUN
ap-2970	173	21	criterion	criterion	NOUN
ap-2970	173	22	(	(	PUNCT
ap-2970	173	23	mac	mac	NOUN
ap-2970	173	24	)	)	PUNCT
ap-2970	174	1	[	[	X
ap-2970	174	2	1	1	NUM
ap-2970	174	3	]	]	PUNCT
ap-2970	174	4	.	.	PUNCT
ap-2970	175	1	the	the	DET
ap-2970	175	2	computed	computed	ADJ
ap-2970	175	3	rom	rom	NOUN
ap-2970	175	4	at	at	ADP
ap-2970	175	5	the	the	DET
ap-2970	175	6	test	test	NOUN
ap-2970	175	7	point	point	NOUN
ap-2970	175	8	exhibits	exhibit	VERB
ap-2970	175	9	a	a	DET
ap-2970	175	10	good	good	ADJ
ap-2970	175	11	correlation	correlation	NOUN
ap-2970	175	12	,	,	PUNCT
ap-2970	175	13	despite	despite	SCONJ
ap-2970	175	14	the	the	DET
ap-2970	175	15	relevant	relevant	ADJ
ap-2970	175	16	reduction	reduction	NOUN
ap-2970	175	17	of	of	ADP
ap-2970	175	18	the	the	DET
ap-2970	175	19	full	full	ADJ
ap-2970	175	20	system	system	NOUN
ap-2970	175	21	(	(	PUNCT
ap-2970	175	22	b	b	X
ap-2970	175	23	)	)	PUNCT
ap-2970	175	24	the	the	DET
ap-2970	175	25	error	error	NOUN
ap-2970	175	26	estimate	estimate	NOUN
ap-2970	175	27	therefore	therefore	ADV
ap-2970	175	28	relies	rely	VERB
ap-2970	175	29	on	on	ADP
ap-2970	175	30	the	the	DET
ap-2970	175	31	following	following	NOUN
ap-2970	175	32	:	:	PUNCT
ap-2970	175	33	nrfd	nrfd	PROPN
ap-2970	175	34	=	=	SYM
ap-2970	175	35	∣∣∣1−	∣∣∣1−	NUM
ap-2970	175	36	exact	exact	ADJ
ap-2970	175	37	frequency(i	frequency(i	NOUN
ap-2970	175	38	)	)	PUNCT
ap-2970	175	39	approximatingfrequency(i	approximatingfrequency(i	NOUN
ap-2970	175	40	)	)	PUNCT
ap-2970	175	41	∣∣∣	∣∣∣	NOUN
ap-2970	175	42	·	·	PUNCT
ap-2970	175	43	100	100	NUM
ap-2970	175	44	%	%	NOUN
ap-2970	175	45	,	,	PUNCT
ap-2970	175	46	(	(	PUNCT
ap-2970	175	47	10	10	NUM
ap-2970	175	48	)	)	PUNCT
ap-2970	175	49	i	i	NOUN
ap-2970	175	50	=	=	NOUN
ap-2970	175	51	1	1	NUM
ap-2970	175	52	,	,	PUNCT
ap-2970	175	53	2	2	NUM
ap-2970	175	54	,	,	PUNCT
ap-2970	175	55	.	.	PUNCT
ap-2970	175	56	.	.	PUNCT
ap-2970	175	57	.	.	PUNCT
ap-2970	176	1	,	,	PUNCT
ap-2970	176	2	nfoi3	nfoi3	PROPN
ap-2970	176	3	,	,	PUNCT
ap-2970	176	4	while	while	SCONJ
ap-2970	176	5	computing	compute	VERB
ap-2970	176	6	the	the	DET
ap-2970	176	7	mac	mac	PROPN
ap-2970	176	8	number	number	NOUN
ap-2970	176	9	we	we	PRON
ap-2970	176	10	used	use	VERB
ap-2970	176	11	mac(i	mac(i	PROPN
ap-2970	176	12	,	,	PUNCT
ap-2970	176	13	j	j	NOUN
ap-2970	176	14	)	)	PUNCT
ap-2970	176	15	=	=	PUNCT
ap-2970	177	1	(	(	PUNCT
ap-2970	177	2	dr	dr	PROPN
ap-2970	177	3	tpφt	tpφt	PROPN
ap-2970	177	4	i	i	PRON
ap-2970	177	5	pr	pr	VERB
ap-2970	177	6	tpψi	tpψi	NOUN
ap-2970	177	7	)	)	PUNCT
ap-2970	177	8	(	(	PUNCT
ap-2970	177	9	dr	dr	PROPN
ap-2970	177	10	tpφt	tpφt	PROPN
ap-2970	178	1	i	i	PRON
ap-2970	178	2	dr	dr	PROPN
ap-2970	178	3	tpφi	tpφi	PROPN
ap-2970	178	4	)	)	PUNCT
ap-2970	178	5	·	·	PUNCT
ap-2970	178	6	(	(	PUNCT
ap-2970	178	7	pr	pr	PART
ap-2970	178	8	tpψt	tpψt	NOUN
ap-2970	178	9	i	i	PRON
ap-2970	178	10	pr	pr	VERB
ap-2970	178	11	tpψi	tpψi	NOUN
ap-2970	178	12	)	)	PUNCT
ap-2970	178	13	(	(	PUNCT
ap-2970	178	14	11	11	NUM
ap-2970	178	15	)	)	PUNCT
ap-2970	178	16	where	where	SCONJ
ap-2970	178	17	φ	φ	PROPN
ap-2970	178	18	and	and	CCONJ
ap-2970	178	19	ψ	ψ	PROPN
ap-2970	178	20	are	be	AUX
ap-2970	178	21	the	the	DET
ap-2970	178	22	modal	modal	ADJ
ap-2970	178	23	matrix	matrix	NOUN
ap-2970	178	24	pertaining	pertain	VERB
ap-2970	178	25	to	to	ADP
ap-2970	178	26	the	the	DET
ap-2970	178	27	direct	direct	ADJ
ap-2970	178	28	rom	rom	NOUN
ap-2970	178	29	(	(	PUNCT
ap-2970	178	30	dr	dr	PROPN
ap-2970	178	31	)	)	PUNCT
ap-2970	178	32	and	and	CCONJ
ap-2970	178	33	the	the	DET
ap-2970	178	34	interpolated	interpolate	VERB
ap-2970	178	35	rom	rom	NOUN
ap-2970	178	36	(	(	PUNCT
ap-2970	178	37	pr	pr	NOUN
ap-2970	178	38	)	)	PUNCT
ap-2970	178	39	obtained	obtain	VERB
ap-2970	178	40	at	at	ADP
ap-2970	178	41	the	the	DET
ap-2970	178	42	test	test	NOUN
ap-2970	178	43	point	point	NOUN
ap-2970	178	44	(	(	PUNCT
ap-2970	178	45	tp	tp	NOUN
ap-2970	178	46	)	)	PUNCT
ap-2970	178	47	,	,	PUNCT
ap-2970	178	48	respectively	respectively	ADV
ap-2970	178	49	.	.	PUNCT
ap-2970	179	1	figure	figure	NOUN
ap-2970	179	2	5	5	NUM
ap-2970	179	3	shows	show	VERB
ap-2970	179	4	the	the	DET
ap-2970	179	5	nrfd	nrfd	NOUN
ap-2970	179	6	using	use	VERB
ap-2970	179	7	a	a	DET
ap-2970	179	8	serep	serep	ADJ
ap-2970	179	9	-	-	PUNCT
ap-2970	179	10	cms	cms	PROPN
ap-2970	179	11	mor	mor	NOUN
ap-2970	179	12	,	,	PUNCT
ap-2970	179	13	and	and	CCONJ
ap-2970	179	14	how	how	SCONJ
ap-2970	179	15	successful	successful	ADJ
ap-2970	179	16	the	the	DET
ap-2970	179	17	reduction	reduction	NOUN
ap-2970	179	18	process	process	NOUN
ap-2970	179	19	was	be	AUX
ap-2970	179	20	successful	successful	ADJ
ap-2970	179	21	in	in	ADP
ap-2970	179	22	capturing	capture	VERB
ap-2970	179	23	the	the	DET
ap-2970	179	24	dynamics	dynamic	NOUN
ap-2970	179	25	of	of	ADP
ap-2970	179	26	the	the	DET
ap-2970	179	27	original	original	ADJ
ap-2970	179	28	system	system	NOUN
ap-2970	179	29	despite	despite	SCONJ
ap-2970	179	30	the	the	DET
ap-2970	179	31	considerable	considerable	ADJ
ap-2970	179	32	reduction	reduction	NOUN
ap-2970	179	33	.	.	PUNCT
ap-2970	180	1	4.1	4.1	NUM
ap-2970	180	2	.	.	PUNCT
ap-2970	180	3	performance	performance	NOUN
ap-2970	180	4	of	of	ADP
ap-2970	180	5	rsdm	rsdm	NOUN
ap-2970	180	6	for	for	ADP
ap-2970	180	7	frequency	frequency	NOUN
ap-2970	180	8	prediction	prediction	NOUN
ap-2970	180	9	of	of	ADP
ap-2970	180	10	a	a	DET
ap-2970	180	11	hexapod	hexapod	NOUN
ap-2970	180	12	despite	despite	SCONJ
ap-2970	180	13	the	the	DET
ap-2970	180	14	high	high	ADJ
ap-2970	180	15	accuracy	accuracy	NOUN
ap-2970	180	16	of	of	ADP
ap-2970	180	17	the	the	DET
ap-2970	180	18	mor	mor	NOUN
ap-2970	180	19	throughout	throughout	ADP
ap-2970	180	20	the	the	DET
ap-2970	180	21	range	range	NOUN
ap-2970	180	22	of	of	ADP
ap-2970	180	23	the	the	DET
ap-2970	180	24	20	20	NUM
ap-2970	180	25	frequencies	frequency	NOUN
ap-2970	180	26	,	,	PUNCT
ap-2970	180	27	figure	figure	VERB
ap-2970	180	28	6	6	NUM
ap-2970	180	29	shows	show	VERB
ap-2970	180	30	how	how	SCONJ
ap-2970	180	31	the	the	DET
ap-2970	180	32	dramatic	dramatic	ADJ
ap-2970	180	33	reduction	reduction	NOUN
ap-2970	180	34	along	along	ADP
ap-2970	180	35	with	with	ADP
ap-2970	180	36	a	a	DET
ap-2970	180	37	100	100	NUM
ap-2970	180	38	%	%	NOUN
ap-2970	180	39	change	change	NOUN
ap-2970	180	40	of	of	ADP
ap-2970	180	41	the	the	DET
ap-2970	180	42	parameter	parameter	NOUN
ap-2970	180	43	has	have	AUX
ap-2970	180	44	influenced	influence	VERB
ap-2970	180	45	the	the	DET
ap-2970	180	46	preservation	preservation	NOUN
ap-2970	180	47	of	of	ADP
ap-2970	180	48	the	the	DET
ap-2970	180	49	whole	whole	ADJ
ap-2970	180	50	range	range	NOUN
ap-2970	180	51	of	of	ADP
ap-2970	180	52	frequencies	frequency	NOUN
ap-2970	180	53	at	at	ADP
ap-2970	180	54	which	which	PRON
ap-2970	180	55	the	the	DET
ap-2970	180	56	initial	initial	ADJ
ap-2970	180	57	serep	serep	NOUN
ap-2970	180	58	method	method	NOUN
ap-2970	180	59	was	be	AUX
ap-2970	180	60	calibrated	calibrate	VERB
ap-2970	180	61	.	.	PUNCT
ap-2970	181	1	the	the	DET
ap-2970	181	2	picture	picture	NOUN
ap-2970	181	3	highlights	highlight	VERB
ap-2970	181	4	the	the	DET
ap-2970	181	5	following	follow	VERB
ap-2970	181	6	features	feature	NOUN
ap-2970	181	7	.	.	PUNCT
ap-2970	182	1	first	first	ADV
ap-2970	182	2	,	,	PUNCT
ap-2970	182	3	the	the	DET
ap-2970	182	4	error	error	NOUN
ap-2970	182	5	committed	commit	VERB
ap-2970	182	6	by	by	ADP
ap-2970	182	7	the	the	DET
ap-2970	182	8	rom	rom	NOUN
ap-2970	182	9	for	for	ADP
ap-2970	182	10	calculating	calculate	VERB
ap-2970	182	11	the	the	DET
ap-2970	182	12	fundamental	fundamental	ADJ
ap-2970	182	13	frequency	frequency	NOUN
ap-2970	182	14	is	be	AUX
ap-2970	182	15	about	about	ADV
ap-2970	182	16	0.0006	0.0006	NUM
ap-2970	182	17	%	%	NOUN
ap-2970	182	18	,	,	PUNCT
ap-2970	182	19	and	and	CCONJ
ap-2970	182	20	it	it	PRON
ap-2970	182	21	is	be	AUX
ap-2970	182	22	less	less	ADJ
ap-2970	182	23	than	than	ADP
ap-2970	182	24	0.7	0.7	NUM
ap-2970	182	25	%	%	NOUN
ap-2970	182	26	for	for	ADP
ap-2970	182	27	the	the	DET
ap-2970	182	28	first	first	ADJ
ap-2970	182	29	three	three	NUM
ap-2970	182	30	frequencies	frequency	NOUN
ap-2970	182	31	.	.	PUNCT
ap-2970	183	1	second	second	ADJ
ap-2970	183	2	,	,	PUNCT
ap-2970	183	3	the	the	DET
ap-2970	183	4	maximum	maximum	ADJ
ap-2970	183	5	error	error	NOUN
ap-2970	183	6	committed	commit	VERB
ap-2970	183	7	for	for	ADP
ap-2970	183	8	the	the	DET
ap-2970	183	9	first	first	ADJ
ap-2970	183	10	5	5	NUM
ap-2970	183	11	frequencies	frequency	NOUN
ap-2970	183	12	is	be	AUX
ap-2970	183	13	below	below	ADP
ap-2970	183	14	1.5	1.5	NUM
ap-2970	183	15	%	%	NOUN
ap-2970	183	16	.	.	PUNCT
ap-2970	184	1	third	third	ADJ
ap-2970	184	2	,	,	PUNCT
ap-2970	184	3	the	the	DET
ap-2970	184	4	maximum	maximum	ADJ
ap-2970	184	5	error	error	NOUN
ap-2970	184	6	is	be	AUX
ap-2970	184	7	observed	observe	VERB
ap-2970	184	8	for	for	ADP
ap-2970	184	9	the	the	DET
ap-2970	184	10	mode	mode	NOUN
ap-2970	184	11	number	number	NOUN
ap-2970	184	12	6	6	NUM
ap-2970	184	13	,	,	PUNCT
ap-2970	184	14	at	at	ADP
ap-2970	184	15	which	which	PRON
ap-2970	184	16	the	the	DET
ap-2970	184	17	error	error	NOUN
ap-2970	184	18	is	be	AUX
ap-2970	184	19	slightly	slightly	ADV
ap-2970	184	20	smaller	small	ADJ
ap-2970	184	21	than	than	ADP
ap-2970	184	22	3.9	3.9	NUM
ap-2970	184	23	%	%	NOUN
ap-2970	184	24	.	.	PUNCT
ap-2970	185	1	the	the	DET
ap-2970	185	2	initial	initial	ADJ
ap-2970	185	3	5	5	NUM
ap-2970	185	4	frequencies	frequency	NOUN
ap-2970	185	5	are	be	AUX
ap-2970	185	6	the	the	DET
ap-2970	185	7	3number	3number	NUM
ap-2970	185	8	of	of	ADP
ap-2970	185	9	frequencies	frequency	NOUN
ap-2970	185	10	of	of	ADP
ap-2970	185	11	interest	interest	NOUN
ap-2970	185	12	frequencies	frequency	NOUN
ap-2970	185	13	of	of	ADP
ap-2970	185	14	main	main	ADJ
ap-2970	185	15	interest	interest	NOUN
ap-2970	185	16	for	for	ADP
ap-2970	185	17	an	an	DET
ap-2970	185	18	engineer	engineer	NOUN
ap-2970	185	19	.	.	PUNCT
ap-2970	186	1	consequently	consequently	ADV
ap-2970	186	2	,	,	PUNCT
ap-2970	186	3	rsdm	rsdm	NOUN
ap-2970	186	4	is	be	AUX
ap-2970	186	5	able	able	ADJ
ap-2970	186	6	to	to	PART
ap-2970	186	7	preserve	preserve	VERB
ap-2970	186	8	the	the	DET
ap-2970	186	9	most	most	ADV
ap-2970	186	10	important	important	ADJ
ap-2970	186	11	range	range	NOUN
ap-2970	186	12	.	.	PUNCT
ap-2970	187	1	for	for	ADP
ap-2970	187	2	the	the	DET
ap-2970	187	3	present	present	ADJ
ap-2970	187	4	study	study	NOUN
ap-2970	187	5	-	-	PUNCT
ap-2970	187	6	case	case	NOUN
ap-2970	187	7	,	,	PUNCT
ap-2970	187	8	nrfd	nrfd	NOUN
ap-2970	187	9	is	be	AUX
ap-2970	187	10	also	also	ADV
ap-2970	187	11	supported	support	VERB
ap-2970	187	12	also	also	ADV
ap-2970	187	13	by	by	ADP
ap-2970	187	14	the	the	DET
ap-2970	187	15	calculation	calculation	NOUN
ap-2970	187	16	of	of	ADP
ap-2970	187	17	the	the	DET
ap-2970	187	18	modal	modal	ADJ
ap-2970	187	19	assurance	assurance	NOUN
ap-2970	187	20	criterion	criterion	NOUN
ap-2970	187	21	(	(	PUNCT
ap-2970	187	22	mac	mac	PROPN
ap-2970	187	23	)	)	PUNCT
ap-2970	187	24	,	,	PUNCT
ap-2970	187	25	the	the	DET
ap-2970	187	26	results	result	NOUN
ap-2970	187	27	for	for	ADP
ap-2970	187	28	which	which	PRON
ap-2970	187	29	are	be	AUX
ap-2970	187	30	plotted	plot	VERB
ap-2970	187	31	in	in	ADP
ap-2970	187	32	figure	figure	NOUN
ap-2970	187	33	6(b	6(b	NUM
ap-2970	187	34	)	)	PUNCT
ap-2970	187	35	.	.	PUNCT
ap-2970	188	1	for	for	ADP
ap-2970	188	2	the	the	DET
ap-2970	188	3	first	first	ADJ
ap-2970	188	4	6	6	NUM
ap-2970	188	5	frequencies	frequency	NOUN
ap-2970	188	6	,	,	PUNCT
ap-2970	188	7	the	the	DET
ap-2970	188	8	values	value	NOUN
ap-2970	188	9	of	of	ADP
ap-2970	188	10	mac	mac	PROPN
ap-2970	188	11	along	along	ADP
ap-2970	188	12	the	the	DET
ap-2970	188	13	main	main	ADJ
ap-2970	188	14	diagonal	diagonal	ADJ
ap-2970	188	15	range	range	NOUN
ap-2970	188	16	between	between	ADP
ap-2970	188	17	a	a	DET
ap-2970	188	18	minimum	minimum	NOUN
ap-2970	188	19	of	of	ADP
ap-2970	188	20	98.7	98.7	NUM
ap-2970	188	21	%	%	NOUN
ap-2970	188	22	and	and	CCONJ
ap-2970	188	23	a	a	DET
ap-2970	188	24	maximum	maximum	NOUN
ap-2970	188	25	of	of	ADP
ap-2970	188	26	99.9	99.9	NUM
ap-2970	188	27	%	%	NOUN
ap-2970	188	28	.	.	PUNCT
ap-2970	189	1	these	these	DET
ap-2970	189	2	results	result	NOUN
ap-2970	189	3	provide	provide	VERB
ap-2970	189	4	evidence	evidence	NOUN
ap-2970	189	5	that	that	SCONJ
ap-2970	189	6	the	the	DET
ap-2970	189	7	rom	rom	NOUN
ap-2970	189	8	generated	generate	VERB
ap-2970	189	9	at	at	ADP
ap-2970	189	10	the	the	DET
ap-2970	189	11	test	test	NOUN
ap-2970	189	12	point	point	NOUN
ap-2970	189	13	by	by	ADP
ap-2970	189	14	rsdm	rsdm	NOUN
ap-2970	189	15	is	be	AUX
ap-2970	189	16	accurate	accurate	ADJ
ap-2970	189	17	for	for	ADP
ap-2970	189	18	the	the	DET
ap-2970	189	19	first	first	ADJ
ap-2970	189	20	6	6	NUM
ap-2970	189	21	frequencies	frequency	NOUN
ap-2970	189	22	,	,	PUNCT
ap-2970	189	23	even	even	ADV
ap-2970	189	24	though	though	SCONJ
ap-2970	189	25	a	a	DET
ap-2970	189	26	consistent	consistent	ADJ
ap-2970	189	27	reduction	reduction	NOUN
ap-2970	189	28	was	be	AUX
ap-2970	189	29	performed	perform	VERB
ap-2970	189	30	by	by	ADP
ap-2970	189	31	serep	serep	PROPN
ap-2970	189	32	-	-	PROPN
ap-2970	189	33	cms	cms	PROPN
ap-2970	189	34	(	(	PUNCT
ap-2970	189	35	0.035	0.035	NUM
ap-2970	189	36	%	%	NOUN
ap-2970	189	37	of	of	ADP
ap-2970	189	38	the	the	DET
ap-2970	189	39	full	full	ADJ
ap-2970	189	40	model	model	NOUN
ap-2970	189	41	)	)	PUNCT
ap-2970	189	42	.	.	PUNCT
ap-2970	190	1	5	5	X
ap-2970	190	2	.	.	X
ap-2970	190	3	conclusions	conclusion	NOUN
ap-2970	190	4	the	the	DET
ap-2970	190	5	main	main	ADJ
ap-2970	190	6	challenge	challenge	NOUN
ap-2970	190	7	that	that	PRON
ap-2970	190	8	had	have	VERB
ap-2970	190	9	to	to	PART
ap-2970	190	10	be	be	AUX
ap-2970	190	11	faced	face	VERB
ap-2970	190	12	in	in	ADP
ap-2970	190	13	improving	improve	VERB
ap-2970	190	14	the	the	DET
ap-2970	190	15	accuracy	accuracy	NOUN
ap-2970	190	16	of	of	ADP
ap-2970	190	17	parameterized	parameterized	ADJ
ap-2970	190	18	large	large	ADJ
ap-2970	190	19	-	-	PUNCT
ap-2970	190	20	scale	scale	NOUN
ap-2970	190	21	systems	system	NOUN
ap-2970	190	22	was	be	AUX
ap-2970	190	23	to	to	PART
ap-2970	190	24	optimize	optimize	VERB
ap-2970	190	25	the	the	DET
ap-2970	190	26	direct	direct	ADJ
ap-2970	190	27	matrix	matrix	NOUN
ap-2970	190	28	interpolation	interpolation	NOUN
ap-2970	190	29	method	method	NOUN
ap-2970	190	30	,	,	PUNCT
ap-2970	190	31	i.e.	i.e.	X
ap-2970	190	32	to	to	PART
ap-2970	190	33	minimize	minimize	VERB
ap-2970	190	34	the	the	DET
ap-2970	190	35	number	number	NOUN
ap-2970	190	36	of	of	ADP
ap-2970	190	37	detailed	detailed	ADJ
ap-2970	190	38	finite	finite	ADJ
ap-2970	190	39	element	element	NOUN
ap-2970	190	40	analyses	analysis	NOUN
ap-2970	190	41	and	and	CCONJ
ap-2970	190	42	to	to	PART
ap-2970	190	43	guarantee	guarantee	VERB
ap-2970	190	44	high	high	ADJ
ap-2970	190	45	accuracy	accuracy	NOUN
ap-2970	190	46	,	,	PUNCT
ap-2970	190	47	while	while	SCONJ
ap-2970	190	48	introducing	introduce	VERB
ap-2970	190	49	as	as	ADV
ap-2970	190	50	few	few	ADJ
ap-2970	190	51	as	as	ADP
ap-2970	190	52	possible	possible	ADJ
ap-2970	190	53	mathematical	mathematical	ADJ
ap-2970	190	54	concepts	concept	NOUN
ap-2970	190	55	.	.	PUNCT
ap-2970	191	1	in	in	ADP
ap-2970	191	2	an	an	DET
ap-2970	191	3	attempt	attempt	NOUN
ap-2970	191	4	to	to	PART
ap-2970	191	5	achieve	achieve	VERB
ap-2970	191	6	this	this	DET
ap-2970	191	7	outcome	outcome	NOUN
ap-2970	191	8	,	,	PUNCT
ap-2970	191	9	rsdm	rsdm	NOUN
ap-2970	191	10	has	have	AUX
ap-2970	191	11	been	be	AUX
ap-2970	191	12	proposed	propose	VERB
ap-2970	191	13	as	as	ADP
ap-2970	191	14	promising	promise	VERB
ap-2970	191	15	interpolation	interpolation	NOUN
ap-2970	191	16	method	method	NOUN
ap-2970	191	17	for	for	ADP
ap-2970	191	18	obtaining	obtain	VERB
ap-2970	191	19	accurate	accurate	ADJ
ap-2970	191	20	parametric	parametric	ADJ
ap-2970	191	21	roms	rom	NOUN
ap-2970	191	22	.	.	PUNCT
ap-2970	192	1	the	the	DET
ap-2970	192	2	application	application	NOUN
ap-2970	192	3	of	of	ADP
ap-2970	192	4	this	this	DET
ap-2970	192	5	method	method	NOUN
ap-2970	192	6	relies	rely	VERB
ap-2970	192	7	on	on	ADP
ap-2970	192	8	a	a	DET
ap-2970	192	9	carefully	carefully	ADV
ap-2970	192	10	manipulated	manipulate	VERB
ap-2970	192	11	svd	svd	PROPN
ap-2970	192	12	of	of	ADP
ap-2970	192	13	the	the	DET
ap-2970	192	14	reduced	reduce	VERB
ap-2970	192	15	stiffness	stiffness	NOUN
ap-2970	192	16	and	and	CCONJ
ap-2970	192	17	mass	mass	NOUN
ap-2970	192	18	matrices	matrix	NOUN
ap-2970	192	19	,	,	PUNCT
ap-2970	192	20	and	and	CCONJ
ap-2970	192	21	on	on	ADP
ap-2970	192	22	the	the	DET
ap-2970	192	23	use	use	NOUN
ap-2970	192	24	of	of	ADP
ap-2970	192	25	only	only	ADV
ap-2970	192	26	two	two	NUM
ap-2970	192	27	finite	finite	ADJ
ap-2970	192	28	element	element	NOUN
ap-2970	192	29	analyses	analysis	NOUN
ap-2970	192	30	.	.	PUNCT
ap-2970	193	1	however	however	ADV
ap-2970	193	2	,	,	PUNCT
ap-2970	193	3	there	there	PRON
ap-2970	193	4	are	be	VERB
ap-2970	193	5	several	several	ADJ
ap-2970	193	6	reasons	reason	NOUN
ap-2970	193	7	why	why	SCONJ
ap-2970	193	8	this	this	DET
ap-2970	193	9	optimization	optimization	NOUN
ap-2970	193	10	may	may	AUX
ap-2970	193	11	be	be	AUX
ap-2970	193	12	compromised	compromise	VERB
ap-2970	193	13	.	.	PUNCT
ap-2970	194	1	first	first	ADV
ap-2970	194	2	,	,	PUNCT
ap-2970	194	3	if	if	SCONJ
ap-2970	194	4	the	the	DET
ap-2970	194	5	number	number	NOUN
ap-2970	194	6	of	of	ADP
ap-2970	194	7	the	the	DET
ap-2970	194	8	parameters	parameter	NOUN
ap-2970	194	9	and	and	CCONJ
ap-2970	194	10	the	the	DET
ap-2970	194	11	design	design	NOUN
ap-2970	194	12	space	space	NOUN
ap-2970	194	13	are	be	AUX
ap-2970	194	14	large	large	ADJ
ap-2970	194	15	,	,	PUNCT
ap-2970	194	16	only	only	ADV
ap-2970	194	17	two	two	NUM
ap-2970	194	18	finite	finite	ADJ
ap-2970	194	19	element	element	NOUN
ap-2970	194	20	analyses	analysis	NOUN
ap-2970	194	21	might	might	AUX
ap-2970	194	22	not	not	PART
ap-2970	194	23	be	be	AUX
ap-2970	194	24	sufficient	sufficient	ADJ
ap-2970	194	25	.	.	PUNCT
ap-2970	195	1	second	second	ADJ
ap-2970	195	2	,	,	PUNCT
ap-2970	195	3	if	if	SCONJ
ap-2970	195	4	the	the	DET
ap-2970	195	5	size	size	NOUN
ap-2970	195	6	of	of	ADP
ap-2970	195	7	the	the	DET
ap-2970	195	8	rom	rom	NOUN
ap-2970	195	9	is	be	AUX
ap-2970	195	10	reduced	reduce	VERB
ap-2970	195	11	to	to	ADP
ap-2970	195	12	less	less	ADJ
ap-2970	195	13	than	than	ADP
ap-2970	195	14	0.1	0.1	NUM
ap-2970	195	15	%	%	NOUN
ap-2970	195	16	of	of	ADP
ap-2970	195	17	the	the	DET
ap-2970	195	18	size	size	NOUN
ap-2970	195	19	of	of	ADP
ap-2970	195	20	the	the	DET
ap-2970	195	21	original	original	ADJ
ap-2970	195	22	discretized	discretized	ADJ
ap-2970	195	23	structure	structure	NOUN
ap-2970	195	24	,	,	PUNCT
ap-2970	195	25	then	then	ADV
ap-2970	195	26	the	the	DET
ap-2970	195	27	model	model	NOUN
ap-2970	195	28	might	might	AUX
ap-2970	195	29	not	not	PART
ap-2970	195	30	be	be	AUX
ap-2970	195	31	able	able	ADJ
ap-2970	195	32	to	to	PART
ap-2970	195	33	capture	capture	VERB
ap-2970	195	34	consistently	consistently	ADV
ap-2970	195	35	capture	capture	VERB
ap-2970	195	36	the	the	DET
ap-2970	195	37	eigenbehavior	eigenbehavior	NOUN
ap-2970	195	38	of	of	ADP
ap-2970	195	39	the	the	DET
ap-2970	195	40	system	system	NOUN
ap-2970	195	41	for	for	ADP
ap-2970	195	42	the	the	DET
ap-2970	195	43	whole	whole	ADJ
ap-2970	195	44	range	range	NOUN
ap-2970	195	45	of	of	ADP
ap-2970	195	46	frequencies	frequency	NOUN
ap-2970	195	47	of	of	ADP
ap-2970	195	48	interest	interest	NOUN
ap-2970	195	49	.	.	PUNCT
ap-2970	196	1	nevertheless	nevertheless	ADV
ap-2970	196	2	,	,	PUNCT
ap-2970	196	3	this	this	PRON
ap-2970	196	4	413	413	NUM
ap-2970	196	5	s.	s.	PROPN
ap-2970	196	6	nasisi	nasisi	VERB
ap-2970	196	7	,	,	PUNCT
ap-2970	196	8	m.	m.	NOUN
ap-2970	196	9	valášek	valášek	PROPN
ap-2970	196	10	,	,	PUNCT
ap-2970	196	11	t.	t.	PROPN
ap-2970	196	12	vampola	vampola	PROPN
ap-2970	196	13	acta	acta	PROPN
ap-2970	196	14	polytechnica	polytechnica	PROPN
ap-2970	196	15	increase	increase	NOUN
ap-2970	196	16	in	in	ADP
ap-2970	196	17	ideality	ideality	NOUN
ap-2970	196	18	is	be	AUX
ap-2970	196	19	manageable	manageable	ADJ
ap-2970	196	20	,	,	PUNCT
ap-2970	196	21	and	and	CCONJ
ap-2970	196	22	our	our	PRON
ap-2970	196	23	paper	paper	NOUN
ap-2970	196	24	has	have	AUX
ap-2970	196	25	shown	show	VERB
ap-2970	196	26	how	how	SCONJ
ap-2970	196	27	to	to	PART
ap-2970	196	28	address	address	VERB
ap-2970	196	29	the	the	DET
ap-2970	196	30	related	related	ADJ
ap-2970	196	31	difficulties	difficulty	NOUN
ap-2970	196	32	by	by	ADP
ap-2970	196	33	introducing	introduce	VERB
ap-2970	196	34	of	of	ADP
ap-2970	196	35	a	a	DET
ap-2970	196	36	new	new	ADJ
ap-2970	196	37	method	method	NOUN
ap-2970	196	38	of	of	ADP
ap-2970	196	39	interpolation	interpolation	NOUN
ap-2970	196	40	,	,	PUNCT
ap-2970	196	41	named	name	VERB
ap-2970	196	42	rsdm	rsdm	NOUN
ap-2970	196	43	,	,	PUNCT
ap-2970	196	44	with	with	ADP
ap-2970	196	45	the	the	DET
ap-2970	196	46	aim	aim	NOUN
ap-2970	196	47	of	of	ADP
ap-2970	196	48	restoring	restore	VERB
ap-2970	196	49	and	and	CCONJ
ap-2970	196	50	making	make	VERB
ap-2970	196	51	available	available	ADJ
ap-2970	196	52	to	to	ADP
ap-2970	196	53	the	the	DET
ap-2970	196	54	interpolation	interpolation	NOUN
ap-2970	196	55	tool	tool	NOUN
ap-2970	196	56	certain	certain	ADJ
ap-2970	196	57	natural	natural	ADJ
ap-2970	196	58	components	component	NOUN
ap-2970	196	59	belonging	belong	VERB
ap-2970	196	60	to	to	ADP
ap-2970	196	61	the	the	DET
ap-2970	196	62	matrices	matrix	NOUN
ap-2970	196	63	of	of	ADP
ap-2970	196	64	the	the	DET
ap-2970	196	65	full	full	ADJ
ap-2970	196	66	model	model	NOUN
ap-2970	196	67	that	that	PRON
ap-2970	196	68	are	be	AUX
ap-2970	196	69	related	relate	VERB
ap-2970	196	70	,	,	PUNCT
ap-2970	196	71	on	on	ADP
ap-2970	196	72	the	the	DET
ap-2970	196	73	one	one	NUM
ap-2970	196	74	hand	hand	NOUN
ap-2970	196	75	,	,	PUNCT
ap-2970	196	76	to	to	ADP
ap-2970	196	77	the	the	DET
ap-2970	196	78	process	process	NOUN
ap-2970	196	79	of	of	ADP
ap-2970	196	80	reduction	reduction	NOUN
ap-2970	196	81	and	and	CCONJ
ap-2970	196	82	,	,	PUNCT
ap-2970	196	83	on	on	ADP
ap-2970	196	84	the	the	DET
ap-2970	196	85	other	other	ADJ
ap-2970	196	86	hand	hand	NOUN
ap-2970	196	87	,	,	PUNCT
ap-2970	196	88	to	to	ADP
ap-2970	196	89	the	the	DET
ap-2970	196	90	characteristics	characteristic	NOUN
ap-2970	196	91	of	of	ADP
ap-2970	196	92	a	a	DET
ap-2970	196	93	solid	solid	NOUN
ap-2970	196	94	in	in	ADP
ap-2970	196	95	the	the	DET
ap-2970	196	96	fe	fe	PROPN
ap-2970	196	97	theory	theory	NOUN
ap-2970	196	98	.	.	PUNCT
ap-2970	197	1	this	this	PRON
ap-2970	197	2	is	be	AUX
ap-2970	197	3	a	a	DET
ap-2970	197	4	point	point	NOUN
ap-2970	197	5	that	that	PRON
ap-2970	197	6	has	have	AUX
ap-2970	197	7	been	be	AUX
ap-2970	197	8	neglected	neglect	VERB
ap-2970	197	9	in	in	ADP
ap-2970	197	10	previously	previously	ADV
ap-2970	197	11	published	publish	VERB
ap-2970	197	12	works	work	NOUN
ap-2970	197	13	,	,	PUNCT
ap-2970	197	14	yet	yet	CCONJ
ap-2970	197	15	it	it	PRON
ap-2970	197	16	seems	seem	VERB
ap-2970	197	17	to	to	PART
ap-2970	197	18	be	be	AUX
ap-2970	197	19	an	an	DET
ap-2970	197	20	indispensable	indispensable	ADJ
ap-2970	197	21	step	step	NOUN
ap-2970	197	22	to	to	PART
ap-2970	197	23	adopt	adopt	VERB
ap-2970	197	24	.	.	PUNCT
ap-2970	198	1	cautious	cautious	ADJ
ap-2970	198	2	use	use	NOUN
ap-2970	198	3	of	of	ADP
ap-2970	198	4	the	the	DET
ap-2970	198	5	svd	svd	PROPN
ap-2970	198	6	method	method	NOUN
ap-2970	198	7	for	for	ADP
ap-2970	198	8	achieving	achieve	VERB
ap-2970	198	9	this	this	DET
ap-2970	198	10	purpose	purpose	NOUN
ap-2970	198	11	is	be	AUX
ap-2970	198	12	effective	effective	ADJ
ap-2970	198	13	for	for	ADP
ap-2970	198	14	2	2	NUM
ap-2970	198	15	reasons	reason	NOUN
ap-2970	198	16	:	:	PUNCT
ap-2970	198	17	first	first	ADV
ap-2970	198	18	,	,	PUNCT
ap-2970	198	19	it	it	PRON
ap-2970	198	20	is	be	AUX
ap-2970	198	21	numerically	numerically	ADV
ap-2970	198	22	stable	stable	ADJ
ap-2970	198	23	[	[	X
ap-2970	198	24	12	12	NUM
ap-2970	198	25	]	]	PUNCT
ap-2970	198	26	and	and	CCONJ
ap-2970	198	27	its	its	PRON
ap-2970	198	28	algorithm	algorithm	NOUN
ap-2970	198	29	is	be	AUX
ap-2970	198	30	embedded	embed	VERB
ap-2970	198	31	in	in	ADP
ap-2970	198	32	different	different	ADJ
ap-2970	198	33	computational	computational	ADJ
ap-2970	198	34	software	software	NOUN
ap-2970	198	35	programs	program	NOUN
ap-2970	198	36	;	;	PUNCT
ap-2970	198	37	second	second	X
ap-2970	198	38	,	,	PUNCT
ap-2970	198	39	the	the	DET
ap-2970	198	40	use	use	NOUN
ap-2970	198	41	of	of	ADP
ap-2970	198	42	reduced	reduce	VERB
ap-2970	198	43	matrices	matrix	NOUN
ap-2970	198	44	limits	limit	VERB
ap-2970	198	45	the	the	DET
ap-2970	198	46	computation	computation	NOUN
ap-2970	198	47	time	time	NOUN
ap-2970	198	48	that	that	PRON
ap-2970	198	49	it	it	PRON
ap-2970	198	50	needs	need	VERB
ap-2970	198	51	.	.	PUNCT
ap-2970	199	1	when	when	SCONJ
ap-2970	199	2	the	the	DET
ap-2970	199	3	proposed	propose	VERB
ap-2970	199	4	method	method	NOUN
ap-2970	199	5	is	be	AUX
ap-2970	199	6	applied	apply	VERB
ap-2970	199	7	according	accord	VERB
ap-2970	199	8	to	to	ADP
ap-2970	199	9	algorithm	algorithm	PROPN
ap-2970	199	10	2	2	NUM
ap-2970	199	11	the	the	DET
ap-2970	199	12	following	follow	VERB
ap-2970	199	13	performances	performance	NOUN
ap-2970	199	14	have	have	AUX
ap-2970	199	15	been	be	AUX
ap-2970	199	16	observed	observe	VERB
ap-2970	199	17	:	:	PUNCT
ap-2970	199	18	(	(	PUNCT
ap-2970	199	19	1	1	NUM
ap-2970	199	20	.	.	PUNCT
ap-2970	199	21	)	)	PUNCT
ap-2970	200	1	for	for	ADP
ap-2970	200	2	the	the	DET
ap-2970	200	3	large	large	ADJ
ap-2970	200	4	-	-	PUNCT
ap-2970	200	5	scale	scale	NOUN
ap-2970	200	6	hexapod	hexapod	NOUN
ap-2970	200	7	structure	structure	NOUN
ap-2970	200	8	the	the	DET
ap-2970	200	9	error	error	NOUN
ap-2970	200	10	committed	commit	VERB
ap-2970	200	11	lies	lie	NOUN
ap-2970	200	12	between	between	ADP
ap-2970	200	13	0.0006	0.0006	NUM
ap-2970	200	14	%	%	NOUN
ap-2970	200	15	and	and	CCONJ
ap-2970	200	16	less	less	ADJ
ap-2970	200	17	than	than	ADP
ap-2970	200	18	1.5	1.5	NUM
ap-2970	200	19	%	%	NOUN
ap-2970	200	20	for	for	ADP
ap-2970	200	21	the	the	DET
ap-2970	200	22	first	first	ADJ
ap-2970	200	23	5	5	NUM
ap-2970	200	24	frequencies	frequency	NOUN
ap-2970	200	25	despite	despite	SCONJ
ap-2970	200	26	the	the	DET
ap-2970	200	27	consistent	consistent	ADJ
ap-2970	200	28	,	,	PUNCT
ap-2970	200	29	initial	initial	ADJ
ap-2970	200	30	reduction	reduction	NOUN
ap-2970	200	31	.	.	PUNCT
ap-2970	201	1	(	(	PUNCT
ap-2970	201	2	2	2	NUM
ap-2970	201	3	.	.	PUNCT
ap-2970	201	4	)	)	PUNCT
ap-2970	202	1	there	there	PRON
ap-2970	202	2	is	be	VERB
ap-2970	202	3	very	very	ADV
ap-2970	202	4	accurate	accurate	ADJ
ap-2970	202	5	correlation	correlation	NOUN
ap-2970	202	6	,	,	PUNCT
ap-2970	202	7	as	as	SCONJ
ap-2970	202	8	shown	show	VERB
ap-2970	202	9	by	by	ADP
ap-2970	202	10	the	the	DET
ap-2970	202	11	mac	mac	PROPN
ap-2970	202	12	number	number	NOUN
ap-2970	202	13	.	.	PUNCT
ap-2970	203	1	engineering	engineering	NOUN
ap-2970	203	2	systems	system	NOUN
ap-2970	203	3	can	can	AUX
ap-2970	203	4	be	be	AUX
ap-2970	203	5	modeled	model	VERB
ap-2970	203	6	by	by	ADP
ap-2970	203	7	effective	effective	ADJ
ap-2970	203	8	roms	rom	NOUN
ap-2970	203	9	displaying	display	VERB
ap-2970	203	10	various	various	ADJ
ap-2970	203	11	degrees	degree	NOUN
ap-2970	203	12	of	of	ADP
ap-2970	203	13	accuracy	accuracy	NOUN
ap-2970	203	14	.	.	PUNCT
ap-2970	204	1	on	on	ADP
ap-2970	204	2	the	the	DET
ap-2970	204	3	basis	basis	NOUN
ap-2970	204	4	of	of	ADP
ap-2970	204	5	the	the	DET
ap-2970	204	6	results	result	NOUN
ap-2970	204	7	obtained	obtain	VERB
ap-2970	204	8	here	here	ADV
ap-2970	204	9	,	,	PUNCT
ap-2970	204	10	it	it	PRON
ap-2970	204	11	is	be	AUX
ap-2970	204	12	evident	evident	ADJ
ap-2970	204	13	that	that	SCONJ
ap-2970	204	14	despite	despite	SCONJ
ap-2970	204	15	the	the	DET
ap-2970	204	16	increase	increase	NOUN
ap-2970	204	17	in	in	ADP
ap-2970	204	18	ideality	ideality	NOUN
ap-2970	204	19	attained	attain	VERB
ap-2970	204	20	by	by	ADP
ap-2970	204	21	the	the	DET
ap-2970	204	22	rsdm	rsdm	NOUN
ap-2970	204	23	,	,	PUNCT
ap-2970	204	24	this	this	DET
ap-2970	204	25	degree	degree	NOUN
ap-2970	204	26	of	of	ADP
ap-2970	204	27	fidelity	fidelity	NOUN
ap-2970	204	28	of	of	ADP
ap-2970	204	29	rom	rom	NOUN
ap-2970	204	30	is	be	AUX
ap-2970	204	31	in	in	ADP
ap-2970	204	32	some	some	DET
ap-2970	204	33	way	way	NOUN
ap-2970	204	34	undermined	undermine	VERB
ap-2970	204	35	by	by	ADP
ap-2970	204	36	a	a	DET
ap-2970	204	37	combination	combination	NOUN
ap-2970	204	38	of	of	ADP
ap-2970	204	39	the	the	DET
ap-2970	204	40	dramatic	dramatic	ADJ
ap-2970	204	41	reduction	reduction	NOUN
ap-2970	204	42	of	of	ADP
ap-2970	204	43	the	the	DET
ap-2970	204	44	original	original	ADJ
ap-2970	204	45	system	system	NOUN
ap-2970	204	46	and	and	CCONJ
ap-2970	204	47	the	the	DET
ap-2970	204	48	large	large	ADJ
ap-2970	204	49	number	number	NOUN
ap-2970	204	50	of	of	ADP
ap-2970	204	51	parameters	parameter	NOUN
ap-2970	204	52	.	.	PUNCT
ap-2970	205	1	one	one	NUM
ap-2970	205	2	challenge	challenge	NOUN
ap-2970	205	3	that	that	PRON
ap-2970	205	4	must	must	AUX
ap-2970	205	5	be	be	AUX
ap-2970	205	6	pointed	point	VERB
ap-2970	205	7	out	out	ADP
ap-2970	205	8	here	here	ADV
ap-2970	205	9	is	be	AUX
ap-2970	205	10	the	the	DET
ap-2970	205	11	need	need	NOUN
ap-2970	205	12	to	to	PART
ap-2970	205	13	further	far	ADV
ap-2970	205	14	optimize	optimize	VERB
ap-2970	205	15	the	the	DET
ap-2970	205	16	interpolation	interpolation	NOUN
ap-2970	205	17	tool	tool	NOUN
ap-2970	205	18	,	,	PUNCT
ap-2970	205	19	in	in	ADP
ap-2970	205	20	order	order	NOUN
ap-2970	205	21	to	to	PART
ap-2970	205	22	deal	deal	VERB
ap-2970	205	23	ideally	ideally	ADV
ap-2970	205	24	with	with	ADP
ap-2970	205	25	opposing	oppose	VERB
ap-2970	205	26	requirements	requirement	NOUN
ap-2970	205	27	of	of	ADP
ap-2970	205	28	computation	computation	NOUN
ap-2970	205	29	time	time	NOUN
ap-2970	205	30	and	and	CCONJ
ap-2970	205	31	accuracy	accuracy	NOUN
ap-2970	205	32	.	.	PUNCT
ap-2970	206	1	this	this	PRON
ap-2970	206	2	of	of	ADP
ap-2970	206	3	course	course	NOUN
ap-2970	206	4	entails	entail	VERB
ap-2970	206	5	first	first	ADV
ap-2970	206	6	investigating	investigate	VERB
ap-2970	206	7	how	how	SCONJ
ap-2970	206	8	the	the	DET
ap-2970	206	9	error	error	NOUN
ap-2970	206	10	depends	depend	VERB
ap-2970	206	11	on	on	ADP
ap-2970	206	12	the	the	DET
ap-2970	206	13	number	number	NOUN
ap-2970	206	14	of	of	ADP
ap-2970	206	15	finite	finite	ADJ
ap-2970	206	16	element	element	NOUN
ap-2970	206	17	analyses	analysis	NOUN
ap-2970	206	18	,	,	PUNCT
ap-2970	206	19	on	on	ADP
ap-2970	206	20	the	the	DET
ap-2970	206	21	interpolation	interpolation	NOUN
ap-2970	206	22	method	method	NOUN
ap-2970	206	23	,	,	PUNCT
ap-2970	206	24	and	and	CCONJ
ap-2970	206	25	on	on	ADP
ap-2970	206	26	the	the	DET
ap-2970	206	27	size	size	NOUN
ap-2970	206	28	of	of	ADP
ap-2970	206	29	the	the	DET
ap-2970	206	30	final	final	ADJ
ap-2970	206	31	rom	rom	NOUN
ap-2970	206	32	.	.	PUNCT
ap-2970	207	1	acknowledgements	acknowledgement	NOUN
ap-2970	207	2	this	this	DET
ap-2970	207	3	work	work	NOUN
ap-2970	207	4	was	be	AUX
ap-2970	207	5	supported	support	VERB
ap-2970	207	6	by	by	ADP
ap-2970	207	7	research	research	NOUN
ap-2970	207	8	grant	grant	NOUN
ap-2970	207	9	p101/1339100s	p101/1339100s	PROPN
ap-2970	207	10	,	,	PUNCT
ap-2970	207	11	mechatronic	mechatronic	ADJ
ap-2970	207	12	flexible	flexible	ADJ
ap-2970	207	13	joint	joint	NOUN
ap-2970	207	14	.	.	PUNCT
ap-2970	208	1	references	reference	NOUN
ap-2970	208	2	[	[	X
ap-2970	208	3	1	1	NUM
ap-2970	208	4	]	]	X
ap-2970	208	5	j.a	j.a	PROPN
ap-2970	208	6	.	.	PROPN
ap-2970	208	7	randall	randall	PROPN
ap-2970	208	8	,	,	PUNCT
ap-2970	208	9	the	the	DET
ap-2970	208	10	modal	modal	NOUN
ap-2970	208	11	assurance	assurance	NOUN
ap-2970	208	12	criterion	criterion	NOUN
ap-2970	208	13	twenty	twenty	NUM
ap-2970	208	14	years	year	NOUN
ap-2970	208	15	of	of	ADP
ap-2970	208	16	use	use	NOUN
ap-2970	208	17	and	and	CCONJ
ap-2970	208	18	abuse	abuse	NOUN
ap-2970	208	19	,	,	PUNCT
ap-2970	208	20	journal	journal	NOUN
ap-2970	208	21	of	of	ADP
ap-2970	208	22	sound	sound	NOUN
ap-2970	208	23	and	and	CCONJ
ap-2970	208	24	vibration	vibration	NOUN
ap-2970	208	25	,	,	PUNCT
ap-2970	208	26	(	(	PUNCT
ap-2970	208	27	august	august	PROPN
ap-2970	208	28	2003	2003	NUM
ap-2970	208	29	)	)	PUNCT
ap-2970	208	30	14	14	NUM
ap-2970	208	31	-	-	SYM
ap-2970	208	32	21	21	NUM
ap-2970	208	33	.	.	PUNCT
ap-2970	209	1	[	[	X
ap-2970	209	2	2	2	X
ap-2970	209	3	]	]	X
ap-2970	209	4	r.w	r.w	PROPN
ap-2970	209	5	.	.	PROPN
ap-2970	209	6	freund	freund	PROPN
ap-2970	209	7	,	,	PUNCT
ap-2970	209	8	model	model	NOUN
ap-2970	209	9	reduction	reduction	NOUN
ap-2970	209	10	methods	method	NOUN
ap-2970	209	11	based	base	VERB
ap-2970	209	12	on	on	ADP
ap-2970	209	13	krylov	krylov	NOUN
ap-2970	209	14	subspaces	subspace	NOUN
ap-2970	209	15	,	,	PUNCT
ap-2970	209	16	acta	acta	PROPN
ap-2970	209	17	numerica	numerica	PROPN
ap-2970	209	18	,	,	PUNCT
ap-2970	209	19	12	12	NUM
ap-2970	209	20	(	(	PUNCT
ap-2970	209	21	may	may	PROPN
ap-2970	209	22	2003	2003	NUM
ap-2970	209	23	)	)	PUNCT
ap-2970	209	24	267	267	NUM
ap-2970	209	25	-	-	SYM
ap-2970	209	26	319	319	NUM
ap-2970	209	27	.	.	PUNCT
ap-2970	209	28	doi:10.1017	doi:10.1017	PROPN
ap-2970	209	29	/	/	SYM
ap-2970	209	30	cbo9780511550157.004	cbo9780511550157.004	PROPN
ap-2970	209	31	.	.	PUNCT
ap-2970	210	1	[	[	X
ap-2970	210	2	3	3	X
ap-2970	210	3	]	]	X
ap-2970	210	4	b.	b.	PROPN
ap-2970	210	5	moore	moore	PROPN
ap-2970	210	6	,	,	PUNCT
ap-2970	210	7	principal	principal	ADJ
ap-2970	210	8	component	component	NOUN
ap-2970	210	9	analysis	analysis	NOUN
ap-2970	210	10	in	in	ADP
ap-2970	210	11	linear	linear	PROPN
ap-2970	210	12	systems	system	NOUN
ap-2970	210	13	:	:	PUNCT
ap-2970	210	14	controllability	controllability	NOUN
ap-2970	210	15	,	,	PUNCT
ap-2970	210	16	observability	observability	NOUN
ap-2970	210	17	,	,	PUNCT
ap-2970	210	18	and	and	CCONJ
ap-2970	210	19	model	model	NOUN
ap-2970	210	20	reduction	reduction	NOUN
ap-2970	210	21	,	,	PUNCT
ap-2970	210	22	ieee	ieee	NOUN
ap-2970	210	23	transactions	transaction	NOUN
ap-2970	210	24	on	on	ADP
ap-2970	210	25	automatic	automatic	ADJ
ap-2970	210	26	control	control	NOUN
ap-2970	210	27	,	,	PUNCT
ap-2970	210	28	26	26	NUM
ap-2970	210	29	(	(	PUNCT
ap-2970	210	30	february	february	PROPN
ap-2970	210	31	1981	1981	NUM
ap-2970	210	32	)	)	PUNCT
ap-2970	210	33	17	17	NUM
ap-2970	210	34	-	-	SYM
ap-2970	210	35	32	32	NUM
ap-2970	210	36	.	.	PUNCT
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ap-2970	212	20	fluid	fluid	NOUN
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ap-2970	212	27	)	)	PUNCT
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ap-2970	212	35	-	-	PUNCT
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ap-2970	213	33	)	)	PUNCT
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ap-2970	213	35	-	-	SYM
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ap-2970	214	2	6	6	NUM
ap-2970	214	3	]	]	PUNCT
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ap-2970	214	23	-	-	PUNCT
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ap-2970	214	33	science	science	NOUN
ap-2970	214	34	,	,	PUNCT
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ap-2970	214	39	(	(	PUNCT
ap-2970	214	40	2001	2001	NUM
ap-2970	214	41	)	)	PUNCT
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ap-2970	216	1	[	[	X
ap-2970	216	2	7	7	NUM
ap-2970	216	3	]	]	PUNCT
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ap-2970	216	14	-	-	PUNCT
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ap-2970	216	16	systems	system	NOUN
ap-2970	216	17	with	with	ADP
ap-2970	216	18	proportional	proportional	ADJ
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ap-2970	216	20	,	,	PUNCT
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ap-2970	216	25	ieee	ieee	NOUN
ap-2970	216	26	conference	conference	NOUN
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ap-2970	216	28	decision	decision	NOUN
ap-2970	216	29	and	and	CCONJ
ap-2970	216	30	control	control	NOUN
ap-2970	216	31	,	,	PUNCT
ap-2970	216	32	and	and	CCONJ
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ap-2970	216	34	european	european	PROPN
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ap-2970	216	36	conference	conference	PROPN
ap-2970	216	37	,	,	PUNCT
ap-2970	216	38	(	(	PUNCT
ap-2970	216	39	12	12	NUM
ap-2970	216	40	-	-	SYM
ap-2970	216	41	15	15	NUM
ap-2970	216	42	december	december	PROPN
ap-2970	216	43	2005	2005	NUM
ap-2970	216	44	)	)	PUNCT
ap-2970	216	45	.	.	PUNCT
ap-2970	217	1	doi:10.1109	doi:10.1109	VERB
ap-2970	217	2	/	/	SYM
ap-2970	218	1	cdc.2005.1582501	cdc.2005.1582501	PRON
ap-2970	218	2	[	[	PUNCT
ap-2970	218	3	8	8	NUM
ap-2970	218	4	]	]	PUNCT
ap-2970	218	5	l.	l.	PROPN
ap-2970	218	6	feng	feng	PROPN
ap-2970	218	7	,	,	PUNCT
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ap-2970	218	9	b.	b.	PROPN
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ap-2970	218	11	,	,	PUNCT
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ap-2970	218	13	g.	g.	PROPN
ap-2970	218	14	korvink	korvink	PROPN
ap-2970	218	15	,	,	PUNCT
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ap-2970	218	18	reduction	reduction	NOUN
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ap-2970	218	21	simulation	simulation	NOUN
ap-2970	218	22	of	of	ADP
ap-2970	218	23	cyclic	cyclic	ADJ
ap-2970	218	24	voltammograms	voltammogram	NOUN
ap-2970	218	25	,	,	PUNCT
ap-2970	218	26	american	american	ADJ
ap-2970	218	27	scientific	scientific	ADJ
ap-2970	218	28	publishers	publisher	NOUN
ap-2970	218	29	,	,	PUNCT
ap-2970	218	30	4	4	NUM
ap-2970	218	31	(	(	PUNCT
ap-2970	218	32	2006	2006	NUM
ap-2970	218	33	)	)	PUNCT
ap-2970	218	34	1	1	NUM
ap-2970	218	35	-	-	SYM
ap-2970	218	36	10	10	NUM
ap-2970	218	37	.	.	PUNCT
ap-2970	219	1	doi:10.1166	doi:10.1166	ADJ
ap-2970	219	2	/	/	SYM
ap-2970	219	3	sl.2006.021	sl.2006.021	PROPN
ap-2970	220	1	[	[	X
ap-2970	220	2	9	9	NUM
ap-2970	220	3	]	]	X
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ap-2970	220	5	.	.	PROPN
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ap-2970	220	7	-	-	PUNCT
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ap-2970	220	10	,	,	PUNCT
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ap-2970	220	12	model	model	NOUN
ap-2970	220	13	order	order	NOUN
ap-2970	220	14	reduction	reduction	NOUN
ap-2970	220	15	technique	technique	NOUN
ap-2970	220	16	for	for	ADP
ap-2970	220	17	design	design	NOUN
ap-2970	220	18	optimization	optimization	NOUN
ap-2970	220	19	,	,	PUNCT
ap-2970	220	20	ieee	ieee	NOUN
ap-2970	220	21	international	international	ADJ
ap-2970	220	22	symposium	symposium	NOUN
ap-2970	220	23	on	on	ADP
ap-2970	220	24	circuits	circuit	NOUN
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ap-2970	220	27	,	,	PUNCT
ap-2970	220	28	2	2	NUM
ap-2970	220	29	(	(	PUNCT
ap-2970	220	30	2326	2326	NUM
ap-2970	220	31	may	may	PROPN
ap-2970	220	32	2005	2005	NUM
ap-2970	220	33	)	)	PUNCT
ap-2970	220	34	1290	1290	NUM
ap-2970	220	35	-	-	SYM
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ap-2970	220	37	.	.	PUNCT
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ap-2970	221	2	/	/	SYM
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ap-2970	222	2	10	10	NUM
ap-2970	222	3	]	]	PUNCT
ap-2970	222	4	b.	b.	PROPN
ap-2970	222	5	lohmann	lohmann	PROPN
ap-2970	222	6	,	,	PUNCT
ap-2970	222	7	b.	b.	PROPN
ap-2970	222	8	salimbahrami	salimbahrami	PROPN
ap-2970	222	9	,	,	PUNCT
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ap-2970	222	15	second	second	ADJ
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ap-2970	222	17	models	model	NOUN
ap-2970	222	18	by	by	ADP
ap-2970	222	19	moment	moment	NOUN
ap-2970	222	20	matching	matching	NOUN
ap-2970	222	21	,	,	PUNCT
ap-2970	222	22	proc	proc	NOUN
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ap-2970	224	3	,	,	PUNCT
ap-2970	224	4	4(1	4(1	X
ap-2970	224	5	)	)	PUNCT
ap-2970	224	6	(	(	PUNCT
ap-2970	224	7	2004	2004	NUM
ap-2970	224	8	)	)	PUNCT
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ap-2970	225	2	.	.	PUNCT
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ap-2970	227	2	11	11	NUM
ap-2970	227	3	]	]	PUNCT
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ap-2970	227	5	f.	f.	PROPN
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ap-2970	227	7	,	,	PUNCT
ap-2970	227	8	applied	apply	VERB
ap-2970	227	9	mechanics	mechanic	NOUN
ap-2970	227	10	of	of	ADP
ap-2970	227	11	solids	solid	NOUN
ap-2970	227	12	,	,	PUNCT
ap-2970	227	13	crc	crc	NOUN
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ap-2970	228	1	[	[	X
ap-2970	228	2	12	12	NUM
ap-2970	228	3	]	]	X
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ap-2970	228	5	.	.	PROPN
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ap-2970	228	7	,	,	PUNCT
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ap-2970	228	15	,	,	PUNCT
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ap-2970	228	18	of	of	ADP
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ap-2970	228	20	computation	computation	NOUN
ap-2970	228	21	,	,	PUNCT
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ap-2970	228	23	(	(	PUNCT
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ap-2970	228	26	)	)	PUNCT
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ap-2970	228	29	1174	1174	NUM
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ap-2970	230	2	13	13	NUM
ap-2970	230	3	]	]	PUNCT
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ap-2970	230	5	,	,	PUNCT
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ap-2970	230	7	solid	solid	ADJ
ap-2970	230	8	mechanics	mechanic	NOUN
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ap-2970	231	8	wiley	wiley	PROPN
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ap-2970	232	2	14	14	NUM
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ap-2970	232	19	.	.	PUNCT
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ap-2970	233	2	15	15	NUM
ap-2970	233	3	]	]	PUNCT
ap-2970	233	4	d.amsallem	d.amsallem	NOUN
ap-2970	233	5	,	,	PUNCT
ap-2970	233	6	c.farhat	c.farhat	ADP
ap-2970	233	7	,	,	PUNCT
ap-2970	233	8	an	an	DET
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ap-2970	233	18	models	model	NOUN
ap-2970	233	19	,	,	PUNCT
ap-2970	233	20	siam	siam	PROPN
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ap-2970	235	1	,	,	PUNCT
ap-2970	235	2	33	33	NUM
ap-2970	235	3	(	(	PUNCT
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ap-2970	235	7	-	-	SYM
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ap-2970	236	3	16	16	NUM
ap-2970	236	4	]	]	PUNCT
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ap-2970	236	13	reduction	reduction	NOUN
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ap-2970	236	19	by	by	ADP
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ap-2970	236	28	anwendungen	anwendungen	NOUN
ap-2970	236	29	der	der	NOUN
ap-2970	236	30	regelungstechnik	regelungstechnik	VERB
ap-2970	236	31	,	,	PUNCT
ap-2970	236	32	(	(	PUNCT
ap-2970	236	33	2009	2009	NUM
ap-2970	236	34	)	)	PUNCT
ap-2970	236	35	,	,	PUNCT
ap-2970	236	36	erlangen	erlangen	PROPN
ap-2970	236	37	-	-	PUNCT
ap-2970	236	38	münchener	münchener	NOUN
ap-2970	236	39	workshops	workshop	NOUN
ap-2970	236	40	.	.	PUNCT
ap-2970	237	1	[	[	X
ap-2970	237	2	17	17	NUM
ap-2970	237	3	]	]	X
ap-2970	237	4	d.	d.	PROPN
ap-2970	237	5	amsallem	amsallem	PROPN
ap-2970	237	6	,	,	PUNCT
ap-2970	237	7	j.	j.	PROPN
ap-2970	237	8	cortial	cortial	PROPN
ap-2970	237	9	,	,	PUNCT
ap-2970	237	10	k.	k.	PROPN
ap-2970	237	11	carlberg	carlberg	PROPN
ap-2970	237	12	,	,	PUNCT
ap-2970	237	13	c.	c.	PROPN
ap-2970	237	14	farhat	farhat	PROPN
ap-2970	237	15	,	,	PUNCT
ap-2970	237	16	an	an	DET
ap-2970	237	17	online	online	ADJ
ap-2970	237	18	method	method	NOUN
ap-2970	237	19	for	for	ADP
ap-2970	237	20	interpolating	interpolate	VERB
ap-2970	237	21	linear	linear	ADJ
ap-2970	237	22	reduced	reduce	VERB
ap-2970	237	23	-	-	PUNCT
ap-2970	237	24	order	order	NOUN
ap-2970	237	25	structural	structural	ADJ
ap-2970	237	26	dynamics	dynamic	NOUN
ap-2970	237	27	models	model	NOUN
ap-2970	237	28	,	,	PUNCT
ap-2970	237	29	proceedings	proceeding	NOUN
ap-2970	237	30	of	of	ADP
ap-2970	237	31	50th	50th	ADJ
ap-2970	237	32	aiaa	aiaa	PROPN
ap-2970	237	33	/	/	SYM
ap-2970	237	34	asme	asme	PROPN
ap-2970	237	35	/	/	SYM
ap-2970	237	36	asce	asce	PROPN
ap-2970	237	37	/	/	SYM
ap-2970	237	38	ahs	ahs	PROPN
ap-2970	237	39	/	/	SYM
ap-2970	237	40	asc	asc	PROPN
ap-2970	237	41	structures	structures	PROPN
ap-2970	237	42	,	,	PUNCT
ap-2970	237	43	structural	structural	ADJ
ap-2970	237	44	dynamics	dynamic	NOUN
ap-2970	237	45	,	,	PUNCT
ap-2970	237	46	and	and	CCONJ
ap-2970	237	47	materials	material	NOUN
ap-2970	237	48	conference	conference	NOUN
ap-2970	237	49	(	(	PUNCT
ap-2970	237	50	2009	2009	NUM
ap-2970	237	51	)	)	PUNCT
ap-2970	237	52	.	.	PUNCT
ap-2970	238	1	doi:10.2514/6.2009	doi:10.2514/6.2009	PROPN
ap-2970	238	2	-	-	PUNCT
ap-2970	238	3	2432	2432	NUM
ap-2970	238	4	[	[	X
ap-2970	238	5	18	18	NUM
ap-2970	238	6	]	]	X
ap-2970	238	7	h.	h.	PROPN
ap-2970	238	8	panzer	panzer	PROPN
ap-2970	238	9	,	,	PUNCT
ap-2970	238	10	r.	r.	PROPN
ap-2970	238	11	eid	eid	PROPN
ap-2970	238	12	,	,	PUNCT
ap-2970	238	13	b.	b.	PROPN
ap-2970	238	14	lohmann	lohmann	PROPN
ap-2970	238	15	,	,	PUNCT
ap-2970	238	16	parametric	parametric	ADJ
ap-2970	238	17	model	model	NOUN
ap-2970	238	18	order	order	NOUN
ap-2970	238	19	reduction	reduction	NOUN
ap-2970	238	20	by	by	ADP
ap-2970	238	21	matrix	matrix	NOUN
ap-2970	238	22	interpolation	interpolation	NOUN
ap-2970	238	23	,	,	PUNCT
ap-2970	238	24	automatisierungstechnik	automatisierungstechnik	NOUN
ap-2970	238	25	,	,	PUNCT
ap-2970	238	26	58	58	NUM
ap-2970	238	27	(	(	PUNCT
ap-2970	238	28	2010	2010	NUM
ap-2970	238	29	)	)	PUNCT
ap-2970	238	30	475	475	NUM
ap-2970	238	31	-	-	SYM
ap-2970	238	32	484	484	NUM
ap-2970	238	33	.	.	PUNCT
ap-2970	239	1	doi:10.1524	doi:10.1524	PROPN
ap-2970	239	2	/	/	SYM
ap-2970	239	3	auto.2010.0863	auto.2010.0863	PROPN
ap-2970	240	1	[	[	X
ap-2970	240	2	19	19	NUM
ap-2970	240	3	]	]	PUNCT
ap-2970	240	4	z.	z.	PROPN
ap-2970	240	5	bai	bai	PROPN
ap-2970	240	6	,	,	PUNCT
ap-2970	240	7	j.	j.	PROPN
ap-2970	240	8	clark	clark	PROPN
ap-2970	240	9	,	,	PUNCT
ap-2970	240	10	j.	j.	PROPN
ap-2970	240	11	demmel	demmel	PROPN
ap-2970	240	12	,	,	PUNCT
ap-2970	240	13	k.	k.	PROPN
ap-2970	240	14	pister	pister	PROPN
ap-2970	240	15	,	,	PUNCT
ap-2970	240	16	n.	n.	PROPN
ap-2970	240	17	zhou	zhou	PROPN
ap-2970	240	18	,	,	PUNCT
ap-2970	240	19	new	new	ADJ
ap-2970	240	20	numerical	numerical	ADJ
ap-2970	240	21	techniques	technique	NOUN
ap-2970	240	22	and	and	CCONJ
ap-2970	240	23	tools	tool	NOUN
ap-2970	240	24	in	in	ADP
ap-2970	240	25	sugar	sugar	NOUN
ap-2970	240	26	for	for	ADP
ap-2970	240	27	3d	3d	PROPN
ap-2970	240	28	mems	mems	PROPN
ap-2970	240	29	simulation	simulation	NOUN
ap-2970	240	30	,	,	PUNCT
ap-2970	240	31	technical	technical	ADJ
ap-2970	240	32	proceedings	proceeding	NOUN
ap-2970	240	33	of	of	ADP
ap-2970	240	34	the	the	DET
ap-2970	240	35	2001	2001	NUM
ap-2970	240	36	international	international	ADJ
ap-2970	240	37	conference	conference	NOUN
ap-2970	240	38	on	on	ADP
ap-2970	240	39	modeling	modeling	NOUN
ap-2970	240	40	and	and	CCONJ
ap-2970	240	41	simulation	simulation	NOUN
ap-2970	240	42	of	of	ADP
ap-2970	240	43	microsystems	microsystem	NOUN
ap-2970	240	44	,	,	PUNCT
ap-2970	240	45	1	1	NUM
ap-2970	240	46	(	(	PUNCT
ap-2970	240	47	2001	2001	NUM
ap-2970	240	48	)	)	PUNCT
ap-2970	240	49	31	31	NUM
ap-2970	240	50	-	-	SYM
ap-2970	240	51	34	34	NUM
ap-2970	240	52	.	.	PUNCT
ap-2970	240	53	414	414	NUM
ap-2970	240	54	http://dx.doi.org/10.1017/cbo9780511550157.004	http://dx.doi.org/10.1017/cbo9780511550157.004	PROPN
ap-2970	240	55	.	.	PUNCT
ap-2970	240	56	http://dx.doi.org/10.1109/tac.1981.1102568	http://dx.doi.org/10.1109/tac.1981.1102568	PROPN
ap-2970	241	1	http://dx.doi.org/10.1016/b978-008043944-0/50977-x	http://dx.doi.org/10.1016/b978-008043944-0/50977-x	PROPN
ap-2970	241	2	.	.	PROPN
ap-2970	241	3	http://dx.doi.org/10.1109/9.544000	http://dx.doi.org/10.1109/9.544000	X
ap-2970	241	4	http://dx.doi.org/10.1090/conm/280/04630c	http://dx.doi.org/10.1090/conm/280/04630c	NUM
ap-2970	241	5	http://dx.doi.org/10.1109/cdc.2005.1582501	http://dx.doi.org/10.1109/cdc.2005.1582501	VERB
ap-2970	241	6	http://dx.doi.org/10.1166/sl.2006.021	http://dx.doi.org/10.1166/sl.2006.021	NOUN
ap-2970	241	7	http://dx.doi.org/10.1109/iscas.2005.1464831	http://dx.doi.org/10.1109/iscas.2005.1464831	PROPN
ap-2970	241	8	http://dx.doi.org/10.1002/pamm.200410317	http://dx.doi.org/10.1002/pamm.200410317	PUNCT
ap-2970	241	9	http://dx.doi.org/10.1137/0907079	http://dx.doi.org/10.1137/0907079	PROPN
ap-2970	241	10	http://dx.doi.org/10.1137/100813051	http://dx.doi.org/10.1137/100813051	PROPN
ap-2970	241	11	http://dx.doi.org/10.2514/6.2009-2432	http://dx.doi.org/10.2514/6.2009-2432	PROPN
ap-2970	241	12	http://dx.doi.org/10.1524/auto.2010.0863	http://dx.doi.org/10.1524/auto.2010.0863	PROPN
ap-2970	241	13	acta	acta	PROPN
ap-2970	241	14	polytechnica	polytechnica	PROPN
ap-2970	241	15	55(6):407–414	55(6):407–414	PROPN
ap-2970	241	16	,	,	PUNCT
ap-2970	241	17	2015	2015	NUM
ap-2970	241	18	1	1	NUM
ap-2970	241	19	introduction	introduction	NOUN
ap-2970	241	20	1.1	1.1	NUM
ap-2970	241	21	parametric	parametric	ADJ
ap-2970	241	22	model	model	NOUN
ap-2970	241	23	order	order	NOUN
ap-2970	241	24	reduction	reduction	NOUN
ap-2970	241	25	and	and	CCONJ
ap-2970	241	26	its	its	PRON
ap-2970	241	27	interpolation	interpolation	NOUN
ap-2970	241	28	1.2	1.2	NUM
ap-2970	241	29	problems	problem	NOUN
ap-2970	241	30	related	relate	VERB
ap-2970	241	31	to	to	ADP
ap-2970	241	32	the	the	DET
ap-2970	241	33	interpolation	interpolation	NOUN
ap-2970	241	34	method	method	NOUN
ap-2970	241	35	2	2	NUM
ap-2970	241	36	aims	aim	VERB
ap-2970	241	37	3	3	NUM
ap-2970	241	38	description	description	NOUN
ap-2970	241	39	of	of	ADP
ap-2970	241	40	the	the	DET
ap-2970	241	41	interpolation	interpolation	NOUN
ap-2970	241	42	method	method	NOUN
ap-2970	241	43	3.1	3.1	NUM
ap-2970	241	44	foundations	foundation	NOUN
ap-2970	241	45	and	and	CCONJ
ap-2970	241	46	derivation	derivation	NOUN
ap-2970	241	47	of	of	ADP
ap-2970	241	48	the	the	DET
ap-2970	241	49	proposed	propose	VERB
ap-2970	241	50	interpolation	interpolation	NOUN
ap-2970	241	51	method	method	NOUN
ap-2970	241	52	.	.	PUNCT
ap-2970	242	1	an	an	DET
ap-2970	242	2	analogy	analogy	NOUN
ap-2970	242	3	with	with	ADP
ap-2970	242	4	continuum	continuum	ADJ
ap-2970	242	5	mechanics	mechanic	NOUN
ap-2970	242	6	3.2	3.2	NUM
ap-2970	242	7	polar	polar	ADJ
ap-2970	242	8	decomposition	decomposition	NOUN
ap-2970	242	9	3.3	3.3	NUM
ap-2970	242	10	application	application	NOUN
ap-2970	242	11	of	of	ADP
ap-2970	242	12	the	the	DET
ap-2970	242	13	proposed	propose	VERB
ap-2970	242	14	interpolation	interpolation	NOUN
ap-2970	242	15	method	method	NOUN
ap-2970	242	16	4	4	NUM
ap-2970	242	17	results	result	VERB
ap-2970	242	18	4.1	4.1	NUM
ap-2970	242	19	performance	performance	NOUN
ap-2970	242	20	of	of	ADP
ap-2970	242	21	rsdm	rsdm	NOUN
ap-2970	242	22	for	for	ADP
ap-2970	242	23	frequency	frequency	NOUN
ap-2970	242	24	prediction	prediction	NOUN
ap-2970	242	25	of	of	ADP
ap-2970	242	26	a	a	DET
ap-2970	242	27	hexapod	hexapod	NOUN
ap-2970	242	28	5	5	NUM
ap-2970	242	29	conclusions	conclusion	NOUN
ap-2970	242	30	acknowledgements	acknowledgement	NOUN
ap-2970	242	31	references	reference	NOUN