id	sid	tid	token	lemma	pos
ap-1400	1	1	acta	acta	PROPN
ap-1400	1	2	polytechnica	polytechnica	PROPN
ap-1400	1	3	vol	vol	NOUN
ap-1400	1	4	.	.	PUNCT
ap-1400	2	1	51	51	NUM
ap-1400	2	2	no	no	INTJ
ap-1400	2	3	.	.	PUNCT
ap-1400	3	1	4/2011	4/2011	NUM
ap-1400	3	2	singularities	singularity	NOUN
ap-1400	3	3	in	in	ADP
ap-1400	3	4	structural	structural	ADJ
ap-1400	3	5	optimization	optimization	NOUN
ap-1400	3	6	of	of	ADP
ap-1400	3	7	the	the	DET
ap-1400	3	8	ziegler	ziegler	PROPN
ap-1400	3	9	pendulum	pendulum	PROPN
ap-1400	3	10	o.	o.	PROPN
ap-1400	3	11	n.	n.	PROPN
ap-1400	3	12	kirillov	kirillov	PROPN
ap-1400	3	13	abstract	abstract	ADJ
ap-1400	3	14	structural	structural	ADJ
ap-1400	3	15	optimization	optimization	NOUN
ap-1400	3	16	of	of	ADP
ap-1400	3	17	non	non	ADJ
ap-1400	3	18	-	-	ADJ
ap-1400	3	19	conservative	conservative	ADJ
ap-1400	3	20	systems	system	NOUN
ap-1400	3	21	with	with	ADP
ap-1400	3	22	respect	respect	NOUN
ap-1400	3	23	to	to	ADP
ap-1400	3	24	stability	stability	NOUN
ap-1400	3	25	criteria	criterion	NOUN
ap-1400	3	26	is	be	AUX
ap-1400	3	27	a	a	DET
ap-1400	3	28	research	research	NOUN
ap-1400	3	29	area	area	NOUN
ap-1400	3	30	with	with	ADP
ap-1400	3	31	important	important	ADJ
ap-1400	3	32	applications	application	NOUN
ap-1400	3	33	in	in	ADP
ap-1400	3	34	fluid	fluid	ADJ
ap-1400	3	35	-	-	PUNCT
ap-1400	3	36	structure	structure	NOUN
ap-1400	3	37	interactions	interaction	NOUN
ap-1400	3	38	,	,	PUNCT
ap-1400	3	39	friction	friction	NOUN
ap-1400	3	40	-	-	PUNCT
ap-1400	3	41	induced	induce	VERB
ap-1400	3	42	instabilities	instability	NOUN
ap-1400	3	43	,	,	PUNCT
ap-1400	3	44	and	and	CCONJ
ap-1400	3	45	civil	civil	ADJ
ap-1400	3	46	engineering	engineering	NOUN
ap-1400	3	47	.	.	PUNCT
ap-1400	4	1	in	in	ADP
ap-1400	4	2	contrast	contrast	NOUN
ap-1400	4	3	to	to	ADP
ap-1400	4	4	optimization	optimization	NOUN
ap-1400	4	5	of	of	ADP
ap-1400	4	6	conservative	conservative	ADJ
ap-1400	4	7	systems	system	NOUN
ap-1400	4	8	where	where	SCONJ
ap-1400	4	9	rigorously	rigorously	ADV
ap-1400	4	10	proven	prove	VERB
ap-1400	4	11	optimal	optimal	ADJ
ap-1400	4	12	solutions	solution	NOUN
ap-1400	4	13	in	in	ADP
ap-1400	4	14	buckling	buckle	VERB
ap-1400	4	15	problems	problem	NOUN
ap-1400	4	16	have	have	AUX
ap-1400	4	17	been	be	AUX
ap-1400	4	18	found	find	VERB
ap-1400	4	19	,	,	PUNCT
ap-1400	4	20	for	for	ADP
ap-1400	4	21	nonconservative	nonconservative	ADJ
ap-1400	4	22	optimization	optimization	NOUN
ap-1400	4	23	problems	problem	NOUN
ap-1400	4	24	only	only	ADV
ap-1400	4	25	numerically	numerically	ADV
ap-1400	4	26	optimized	optimize	VERB
ap-1400	4	27	designs	design	NOUN
ap-1400	4	28	have	have	AUX
ap-1400	4	29	been	be	AUX
ap-1400	4	30	reported	report	VERB
ap-1400	4	31	.	.	PUNCT
ap-1400	5	1	the	the	DET
ap-1400	5	2	proof	proof	NOUN
ap-1400	5	3	of	of	ADP
ap-1400	5	4	optimality	optimality	NOUN
ap-1400	5	5	in	in	ADP
ap-1400	5	6	non	non	ADJ
ap-1400	5	7	-	-	ADJ
ap-1400	5	8	conservative	conservative	ADJ
ap-1400	5	9	optimization	optimization	NOUN
ap-1400	5	10	problems	problem	NOUN
ap-1400	5	11	is	be	AUX
ap-1400	5	12	a	a	DET
ap-1400	5	13	mathematical	mathematical	ADJ
ap-1400	5	14	challenge	challenge	NOUN
ap-1400	5	15	related	relate	VERB
ap-1400	5	16	to	to	ADP
ap-1400	5	17	multiple	multiple	ADJ
ap-1400	5	18	eigenvalues	eigenvalue	NOUN
ap-1400	5	19	,	,	PUNCT
ap-1400	5	20	singularities	singularity	NOUN
ap-1400	5	21	in	in	ADP
ap-1400	5	22	the	the	DET
ap-1400	5	23	stability	stability	NOUN
ap-1400	5	24	domain	domain	NOUN
ap-1400	5	25	,	,	PUNCT
ap-1400	5	26	and	and	CCONJ
ap-1400	5	27	non	non	ADJ
ap-1400	5	28	-	-	NOUN
ap-1400	5	29	convexity	convexity	NOUN
ap-1400	5	30	of	of	ADP
ap-1400	5	31	the	the	DET
ap-1400	5	32	merit	merit	NOUN
ap-1400	5	33	functional	functional	ADJ
ap-1400	5	34	.	.	PUNCT
ap-1400	6	1	we	we	PRON
ap-1400	6	2	present	present	VERB
ap-1400	6	3	here	here	ADV
ap-1400	6	4	a	a	DET
ap-1400	6	5	study	study	NOUN
ap-1400	6	6	of	of	ADP
ap-1400	6	7	optimal	optimal	ADJ
ap-1400	6	8	mass	mass	ADJ
ap-1400	6	9	distribution	distribution	NOUN
ap-1400	6	10	in	in	ADP
ap-1400	6	11	a	a	DET
ap-1400	6	12	classical	classical	ADJ
ap-1400	6	13	ziegler	ziegler	NOUN
ap-1400	6	14	pendulum	pendulum	NOUN
ap-1400	6	15	where	where	SCONJ
ap-1400	6	16	local	local	ADJ
ap-1400	6	17	and	and	CCONJ
ap-1400	6	18	global	global	ADJ
ap-1400	6	19	extrema	extrema	NOUN
ap-1400	6	20	can	can	AUX
ap-1400	6	21	be	be	AUX
ap-1400	6	22	found	find	VERB
ap-1400	6	23	explicitly	explicitly	ADV
ap-1400	6	24	.	.	PUNCT
ap-1400	7	1	in	in	ADP
ap-1400	7	2	particular	particular	ADJ
ap-1400	7	3	,	,	PUNCT
ap-1400	7	4	for	for	ADP
ap-1400	7	5	the	the	DET
ap-1400	7	6	undamped	undampe	VERB
ap-1400	7	7	case	case	NOUN
ap-1400	7	8	,	,	PUNCT
ap-1400	7	9	the	the	DET
ap-1400	7	10	two	two	NUM
ap-1400	7	11	maxima	maxima	NOUN
ap-1400	7	12	of	of	ADP
ap-1400	7	13	the	the	DET
ap-1400	7	14	critical	critical	ADJ
ap-1400	7	15	flutter	flutter	NOUN
ap-1400	7	16	load	load	NOUN
ap-1400	7	17	correspond	correspond	ADV
ap-1400	7	18	to	to	ADP
ap-1400	7	19	a	a	DET
ap-1400	7	20	vanishing	vanish	VERB
ap-1400	7	21	mass	mass	NOUN
ap-1400	7	22	either	either	CCONJ
ap-1400	7	23	in	in	ADP
ap-1400	7	24	a	a	DET
ap-1400	7	25	joint	joint	NOUN
ap-1400	7	26	or	or	CCONJ
ap-1400	7	27	at	at	ADP
ap-1400	7	28	the	the	DET
ap-1400	7	29	free	free	ADJ
ap-1400	7	30	end	end	NOUN
ap-1400	7	31	of	of	ADP
ap-1400	7	32	the	the	DET
ap-1400	7	33	pendulum	pendulum	NOUN
ap-1400	7	34	;	;	PUNCT
ap-1400	7	35	in	in	ADP
ap-1400	7	36	the	the	DET
ap-1400	7	37	minimum	minimum	NOUN
ap-1400	7	38	,	,	PUNCT
ap-1400	7	39	the	the	DET
ap-1400	7	40	ratio	ratio	NOUN
ap-1400	7	41	of	of	ADP
ap-1400	7	42	the	the	DET
ap-1400	7	43	masses	masse	NOUN
ap-1400	7	44	is	be	AUX
ap-1400	7	45	equal	equal	ADJ
ap-1400	7	46	to	to	ADP
ap-1400	7	47	the	the	DET
ap-1400	7	48	ratio	ratio	NOUN
ap-1400	7	49	of	of	ADP
ap-1400	7	50	the	the	DET
ap-1400	7	51	stiffness	stiffness	ADJ
ap-1400	7	52	coefficients	coefficient	NOUN
ap-1400	7	53	.	.	PUNCT
ap-1400	8	1	the	the	DET
ap-1400	8	2	role	role	NOUN
ap-1400	8	3	of	of	ADP
ap-1400	8	4	the	the	DET
ap-1400	8	5	singularities	singularity	NOUN
ap-1400	8	6	on	on	ADP
ap-1400	8	7	the	the	DET
ap-1400	8	8	stability	stability	NOUN
ap-1400	8	9	boundary	boundary	ADJ
ap-1400	8	10	in	in	ADP
ap-1400	8	11	the	the	DET
ap-1400	8	12	optimization	optimization	NOUN
ap-1400	8	13	is	be	AUX
ap-1400	8	14	highlighted	highlight	VERB
ap-1400	8	15	,	,	PUNCT
ap-1400	8	16	and	and	CCONJ
ap-1400	8	17	an	an	DET
ap-1400	8	18	extension	extension	NOUN
ap-1400	8	19	to	to	ADP
ap-1400	8	20	the	the	DET
ap-1400	8	21	damped	damped	NOUN
ap-1400	8	22	case	case	NOUN
ap-1400	8	23	as	as	ADV
ap-1400	8	24	well	well	ADV
ap-1400	8	25	as	as	ADP
ap-1400	8	26	to	to	ADP
ap-1400	8	27	the	the	DET
ap-1400	8	28	case	case	NOUN
ap-1400	8	29	of	of	ADP
ap-1400	8	30	higher	high	ADJ
ap-1400	8	31	degrees	degree	NOUN
ap-1400	8	32	of	of	ADP
ap-1400	8	33	freedom	freedom	NOUN
ap-1400	8	34	is	be	AUX
ap-1400	8	35	discussed	discuss	VERB
ap-1400	8	36	.	.	PUNCT
ap-1400	9	1	keywords	keyword	NOUN
ap-1400	9	2	:	:	PUNCT
ap-1400	9	3	circulatory	circulatory	ADJ
ap-1400	9	4	system	system	NOUN
ap-1400	9	5	,	,	PUNCT
ap-1400	9	6	structural	structural	ADJ
ap-1400	9	7	optimization	optimization	NOUN
ap-1400	9	8	,	,	PUNCT
ap-1400	9	9	ziegler	ziegler	PROPN
ap-1400	9	10	pendulum	pendulum	PROPN
ap-1400	9	11	,	,	PUNCT
ap-1400	9	12	beck	beck	PROPN
ap-1400	9	13	column	column	PROPN
ap-1400	9	14	,	,	PUNCT
ap-1400	9	15	flutter	flutter	NOUN
ap-1400	9	16	,	,	PUNCT
ap-1400	9	17	divergence	divergence	NOUN
ap-1400	9	18	,	,	PUNCT
ap-1400	9	19	damping	damp	VERB
ap-1400	9	20	,	,	PUNCT
ap-1400	9	21	whitney	whitney	NOUN
ap-1400	9	22	umbrella	umbrella	NOUN
ap-1400	9	23	.	.	PUNCT
ap-1400	10	1	1	1	NUM
ap-1400	10	2	introduction	introduction	NOUN
ap-1400	10	3	structural	structural	ADJ
ap-1400	10	4	optimization	optimization	NOUN
ap-1400	10	5	of	of	ADP
ap-1400	10	6	conservative	conservative	ADJ
ap-1400	10	7	and	and	CCONJ
ap-1400	10	8	non	non	ADJ
ap-1400	10	9	-	-	ADJ
ap-1400	10	10	conservative	conservative	ADJ
ap-1400	10	11	systems	system	NOUN
ap-1400	10	12	with	with	ADP
ap-1400	10	13	respect	respect	NOUN
ap-1400	10	14	to	to	ADP
ap-1400	10	15	stability	stability	NOUN
ap-1400	10	16	criteria	criterion	NOUN
ap-1400	10	17	is	be	AUX
ap-1400	10	18	a	a	DET
ap-1400	10	19	rapidly	rapidly	ADV
ap-1400	10	20	growing	grow	VERB
ap-1400	10	21	research	research	NOUN
ap-1400	10	22	area	area	NOUN
ap-1400	10	23	with	with	ADP
ap-1400	10	24	important	important	ADJ
ap-1400	10	25	applications	application	NOUN
ap-1400	10	26	in	in	ADP
ap-1400	10	27	industry	industry	NOUN
ap-1400	10	28	[	[	X
ap-1400	10	29	1–3	1–3	NOUN
ap-1400	10	30	]	]	X
ap-1400	10	31	.	.	PUNCT
ap-1400	11	1	optimization	optimization	NOUN
ap-1400	11	2	of	of	ADP
ap-1400	11	3	conservative	conservative	ADJ
ap-1400	11	4	elastic	elastic	ADJ
ap-1400	11	5	systems	system	NOUN
ap-1400	11	6	such	such	ADJ
ap-1400	11	7	as	as	ADP
ap-1400	11	8	the	the	DET
ap-1400	11	9	problem	problem	NOUN
ap-1400	11	10	of	of	ADP
ap-1400	11	11	the	the	DET
ap-1400	11	12	optimal	optimal	ADJ
ap-1400	11	13	shape	shape	NOUN
ap-1400	11	14	of	of	ADP
ap-1400	11	15	a	a	DET
ap-1400	11	16	column	column	NOUN
ap-1400	11	17	against	against	ADP
ap-1400	11	18	buckling	buckling	NOUN
ap-1400	11	19	is	be	AUX
ap-1400	11	20	already	already	ADV
ap-1400	11	21	non	non	ADJ
ap-1400	11	22	-	-	ADJ
ap-1400	11	23	trivial	trivial	ADJ
ap-1400	11	24	,	,	PUNCT
ap-1400	11	25	because	because	SCONJ
ap-1400	11	26	some	some	DET
ap-1400	11	27	optimal	optimal	ADJ
ap-1400	11	28	solutions	solution	NOUN
ap-1400	11	29	could	could	AUX
ap-1400	11	30	be	be	AUX
ap-1400	11	31	multi	multi	ADJ
ap-1400	11	32	-	-	ADJ
ap-1400	11	33	modal	modal	ADJ
ap-1400	11	34	and	and	CCONJ
ap-1400	11	35	thus	thus	ADV
ap-1400	11	36	correspond	correspond	VERB
ap-1400	11	37	to	to	ADP
ap-1400	11	38	a	a	DET
ap-1400	11	39	multiple	multiple	ADJ
ap-1400	11	40	semi	semi	ADJ
ap-1400	11	41	-	-	ADJ
ap-1400	11	42	simple	simple	ADJ
ap-1400	11	43	eigenvalue	eigenvalue	NOUN
ap-1400	11	44	which	which	PRON
ap-1400	11	45	creates	create	VERB
ap-1400	11	46	a	a	DET
ap-1400	11	47	conical	conical	ADJ
ap-1400	11	48	singularity	singularity	NOUN
ap-1400	11	49	of	of	ADP
ap-1400	11	50	the	the	DET
ap-1400	11	51	merit	merit	NOUN
ap-1400	11	52	functional	functional	ADJ
ap-1400	11	53	[	[	X
ap-1400	11	54	3	3	NUM
ap-1400	11	55	]	]	PUNCT
ap-1400	11	56	.	.	PUNCT
ap-1400	12	1	despite	despite	SCONJ
ap-1400	12	2	these	these	DET
ap-1400	12	3	complications	complication	NOUN
ap-1400	12	4	,	,	PUNCT
ap-1400	12	5	a	a	DET
ap-1400	12	6	number	number	NOUN
ap-1400	12	7	of	of	ADP
ap-1400	12	8	rigorous	rigorous	ADJ
ap-1400	12	9	optimal	optimal	ADJ
ap-1400	12	10	solutions	solution	NOUN
ap-1400	12	11	are	be	AUX
ap-1400	12	12	known	know	VERB
ap-1400	12	13	in	in	ADP
ap-1400	12	14	conservative	conservative	ADJ
ap-1400	12	15	structural	structural	ADJ
ap-1400	12	16	optimization	optimization	NOUN
ap-1400	12	17	.	.	PUNCT
ap-1400	13	1	nevertheless	nevertheless	ADV
ap-1400	13	2	,	,	PUNCT
ap-1400	13	3	the	the	DET
ap-1400	13	4	increase	increase	NOUN
ap-1400	13	5	in	in	ADP
ap-1400	13	6	the	the	DET
ap-1400	13	7	critical	critical	ADJ
ap-1400	13	8	divergence	divergence	NOUN
ap-1400	13	9	load	load	NOUN
ap-1400	13	10	given	give	VERB
ap-1400	13	11	by	by	ADP
ap-1400	13	12	the	the	DET
ap-1400	13	13	optimal	optimal	ADJ
ap-1400	13	14	design	design	NOUN
ap-1400	13	15	in	in	ADP
ap-1400	13	16	such	such	ADJ
ap-1400	13	17	problems	problem	NOUN
ap-1400	13	18	is	be	AUX
ap-1400	13	19	usually	usually	ADV
ap-1400	13	20	not	not	PART
ap-1400	13	21	very	very	ADV
ap-1400	13	22	large	large	ADJ
ap-1400	13	23	in	in	ADP
ap-1400	13	24	comparison	comparison	NOUN
ap-1400	13	25	with	with	ADP
ap-1400	13	26	the	the	DET
ap-1400	13	27	initial	initial	ADJ
ap-1400	13	28	design	design	NOUN
ap-1400	13	29	[	[	X
ap-1400	13	30	2	2	NUM
ap-1400	13	31	,	,	PUNCT
ap-1400	13	32	3	3	NUM
ap-1400	13	33	]	]	PUNCT
ap-1400	13	34	.	.	PUNCT
ap-1400	14	1	in	in	ADP
ap-1400	14	2	contrast	contrast	NOUN
ap-1400	14	3	to	to	ADP
ap-1400	14	4	conservative	conservative	ADJ
ap-1400	14	5	systems	system	NOUN
ap-1400	14	6	,	,	PUNCT
ap-1400	14	7	non	non	ADJ
ap-1400	14	8	-	-	ADJ
ap-1400	14	9	conservative	conservative	ADJ
ap-1400	14	10	systems	system	NOUN
ap-1400	14	11	can	can	AUX
ap-1400	14	12	loose	loose	VERB
ap-1400	14	13	stability	stability	NOUN
ap-1400	14	14	both	both	CCONJ
ap-1400	14	15	by	by	ADP
ap-1400	14	16	divergence	divergence	NOUN
ap-1400	14	17	and	and	CCONJ
ap-1400	14	18	by	by	ADP
ap-1400	14	19	flutter	flutter	NOUN
ap-1400	14	20	.	.	PUNCT
ap-1400	15	1	it	it	PRON
ap-1400	15	2	is	be	AUX
ap-1400	15	3	known	know	VERB
ap-1400	15	4	that	that	SCONJ
ap-1400	15	5	mass	mass	NOUN
ap-1400	15	6	and	and	CCONJ
ap-1400	15	7	stiffness	stiffness	ADJ
ap-1400	15	8	modification	modification	NOUN
ap-1400	15	9	can	can	AUX
ap-1400	15	10	increase	increase	VERB
ap-1400	15	11	the	the	DET
ap-1400	15	12	critical	critical	ADJ
ap-1400	15	13	flutter	flutter	NOUN
ap-1400	15	14	load	load	NOUN
ap-1400	15	15	by	by	ADP
ap-1400	15	16	hundreds	hundred	NOUN
ap-1400	15	17	percent	percent	NOUN
ap-1400	15	18	,	,	PUNCT
ap-1400	15	19	which	which	PRON
ap-1400	15	20	is	be	AUX
ap-1400	15	21	an	an	DET
ap-1400	15	22	order	order	NOUN
ap-1400	15	23	of	of	ADP
ap-1400	15	24	magnitude	magnitude	NOUN
ap-1400	15	25	higher	high	ADJ
ap-1400	15	26	than	than	ADP
ap-1400	15	27	typical	typical	ADJ
ap-1400	15	28	gains	gain	NOUN
ap-1400	15	29	achieved	achieve	VERB
ap-1400	15	30	in	in	ADP
ap-1400	15	31	optimization	optimization	NOUN
ap-1400	15	32	of	of	ADP
ap-1400	15	33	conservative	conservative	ADJ
ap-1400	15	34	systems	system	NOUN
ap-1400	16	1	[	[	X
ap-1400	16	2	4–18	4–18	PROPN
ap-1400	16	3	]	]	X
ap-1400	16	4	.	.	PUNCT
ap-1400	17	1	for	for	ADP
ap-1400	17	2	example	example	NOUN
ap-1400	17	3	,	,	PUNCT
ap-1400	17	4	ringertz	ringertz	NOUN
ap-1400	17	5	[	[	X
ap-1400	17	6	9	9	NUM
ap-1400	17	7	]	]	PUNCT
ap-1400	17	8	reported	report	VERB
ap-1400	17	9	an	an	DET
ap-1400	17	10	838	838	NUM
ap-1400	17	11	%	%	NOUN
ap-1400	17	12	increase	increase	NOUN
ap-1400	17	13	of	of	ADP
ap-1400	17	14	the	the	DET
ap-1400	17	15	critical	critical	ADJ
ap-1400	17	16	flutter	flutter	NOUN
ap-1400	17	17	load	load	NOUN
ap-1400	17	18	for	for	ADP
ap-1400	17	19	the	the	DET
ap-1400	17	20	beck	beck	NOUN
ap-1400	17	21	column	column	NOUN
ap-1400	17	22	[	[	X
ap-1400	17	23	19	19	NUM
ap-1400	17	24	]	]	PUNCT
ap-1400	17	25	,	,	PUNCT
ap-1400	17	26	from	from	ADP
ap-1400	17	27	20.05	20.05	NUM
ap-1400	17	28	for	for	ADP
ap-1400	17	29	a	a	DET
ap-1400	17	30	uniform	uniform	ADJ
ap-1400	17	31	design	design	NOUN
ap-1400	17	32	to	to	ADP
ap-1400	17	33	188.1	188.1	NUM
ap-1400	17	34	for	for	ADP
ap-1400	17	35	an	an	DET
ap-1400	17	36	optimized	optimize	VERB
ap-1400	17	37	shape	shape	NOUN
ap-1400	17	38	.	.	PUNCT
ap-1400	18	1	recently	recently	ADV
ap-1400	18	2	,	,	PUNCT
ap-1400	18	3	temis	temis	PROPN
ap-1400	18	4	and	and	CCONJ
ap-1400	18	5	fedorov	fedorov	PROPN
ap-1400	19	1	[	[	X
ap-1400	19	2	17	17	NUM
ap-1400	19	3	]	]	PUNCT
ap-1400	19	4	found	find	VERB
ap-1400	19	5	for	for	ADP
ap-1400	19	6	a	a	DET
ap-1400	19	7	free	free	ADJ
ap-1400	19	8	-	-	PUNCT
ap-1400	19	9	free	free	ADJ
ap-1400	19	10	beam	beam	NOUN
ap-1400	19	11	moving	move	VERB
ap-1400	19	12	under	under	ADP
ap-1400	19	13	the	the	DET
ap-1400	19	14	follower	follower	NOUN
ap-1400	19	15	thrust	thrust	VERB
ap-1400	19	16	an	an	DET
ap-1400	19	17	optimal	optimal	ADJ
ap-1400	19	18	design	design	NOUN
ap-1400	19	19	with	with	ADP
ap-1400	19	20	a	a	DET
ap-1400	19	21	critical	critical	ADJ
ap-1400	19	22	flutter	flutter	NOUN
ap-1400	19	23	load	load	NOUN
ap-1400	19	24	that	that	PRON
ap-1400	19	25	exceeds	exceed	VERB
ap-1400	19	26	the	the	DET
ap-1400	19	27	load	load	NOUN
ap-1400	19	28	for	for	ADP
ap-1400	19	29	a	a	DET
ap-1400	19	30	uniform	uniform	ADJ
ap-1400	19	31	beam	beam	NOUN
ap-1400	19	32	by	by	ADP
ap-1400	19	33	823	823	NUM
ap-1400	19	34	%	%	NOUN
ap-1400	19	35	.	.	PUNCT
ap-1400	20	1	we	we	PRON
ap-1400	20	2	note	note	VERB
ap-1400	20	3	that	that	SCONJ
ap-1400	20	4	although	although	SCONJ
ap-1400	20	5	the	the	DET
ap-1400	20	6	very	very	ADJ
ap-1400	20	7	notion	notion	NOUN
ap-1400	20	8	of	of	ADP
ap-1400	20	9	the	the	DET
ap-1400	20	10	follower	follower	NOUN
ap-1400	20	11	forces	force	NOUN
ap-1400	20	12	was	be	AUX
ap-1400	20	13	debated	debate	VERB
ap-1400	20	14	in	in	ADP
ap-1400	20	15	[	[	X
ap-1400	20	16	20–22	20–22	NUM
ap-1400	20	17	]	]	X
ap-1400	20	18	,	,	PUNCT
ap-1400	20	19	the	the	DET
ap-1400	20	20	beck	beck	NOUN
ap-1400	20	21	column	column	NOUN
ap-1400	20	22	[	[	X
ap-1400	20	23	19	19	NUM
ap-1400	20	24	]	]	PUNCT
ap-1400	20	25	as	as	ADV
ap-1400	20	26	well	well	ADV
ap-1400	20	27	as	as	ADP
ap-1400	20	28	its	its	PRON
ap-1400	20	29	discrete	discrete	ADJ
ap-1400	20	30	analogues	analogue	NOUN
ap-1400	20	31	[	[	X
ap-1400	20	32	23–25	23–25	NOUN
ap-1400	20	33	]	]	PUNCT
ap-1400	20	34	including	include	VERB
ap-1400	20	35	the	the	DET
ap-1400	20	36	ziegler	ziegler	PROPN
ap-1400	20	37	pendulum	pendulum	NOUN
ap-1400	21	1	[	[	X
ap-1400	21	2	26	26	NUM
ap-1400	21	3	]	]	PUNCT
ap-1400	21	4	,	,	PUNCT
ap-1400	21	5	remain	remain	VERB
ap-1400	21	6	popular	popular	ADJ
ap-1400	21	7	models	model	NOUN
ap-1400	21	8	for	for	ADP
ap-1400	21	9	investigating	investigate	VERB
ap-1400	21	10	mode	mode	NOUN
ap-1400	21	11	-	-	PUNCT
ap-1400	21	12	coupling	couple	VERB
ap-1400	21	13	instabilities	instability	NOUN
ap-1400	21	14	in	in	ADP
ap-1400	21	15	non	non	ADJ
ap-1400	21	16	-	-	ADJ
ap-1400	21	17	conservative	conservative	ADJ
ap-1400	21	18	systems	system	NOUN
ap-1400	21	19	and	and	CCONJ
ap-1400	21	20	related	relate	VERB
ap-1400	21	21	optimization	optimization	NOUN
ap-1400	21	22	problems	problem	NOUN
ap-1400	21	23	.	.	PUNCT
ap-1400	22	1	in	in	ADP
ap-1400	22	2	both	both	CCONJ
ap-1400	22	3	conservative	conservative	ADJ
ap-1400	22	4	and	and	CCONJ
ap-1400	22	5	non	non	ADJ
ap-1400	22	6	-	-	ADJ
ap-1400	22	7	conservative	conservative	ADJ
ap-1400	22	8	problems	problem	NOUN
ap-1400	22	9	of	of	ADP
ap-1400	22	10	structural	structural	ADJ
ap-1400	22	11	optimization	optimization	NOUN
ap-1400	22	12	of	of	ADP
ap-1400	22	13	slender	slender	ADJ
ap-1400	22	14	structures	structure	NOUN
ap-1400	22	15	,	,	PUNCT
ap-1400	22	16	their	their	PRON
ap-1400	22	17	optimal	optimal	ADJ
ap-1400	22	18	or	or	CCONJ
ap-1400	22	19	optimized	optimize	VERB
ap-1400	22	20	shapes	shape	NOUN
ap-1400	22	21	often	often	ADV
ap-1400	22	22	possess	possess	VERB
ap-1400	22	23	places	place	NOUN
ap-1400	22	24	with	with	ADP
ap-1400	22	25	small	small	ADJ
ap-1400	22	26	or	or	CCONJ
ap-1400	22	27	even	even	ADV
ap-1400	22	28	vanishing	vanish	VERB
ap-1400	22	29	cross	cross	NOUN
ap-1400	22	30	-	-	NOUN
ap-1400	22	31	sections	section	NOUN
ap-1400	22	32	.	.	PUNCT
ap-1400	23	1	the	the	DET
ap-1400	23	2	known	know	VERB
ap-1400	23	3	optimized	optimize	VERB
ap-1400	23	4	shapes	shape	NOUN
ap-1400	23	5	of	of	ADP
ap-1400	23	6	the	the	DET
ap-1400	23	7	beck	beck	NOUN
ap-1400	23	8	column	column	NOUN
ap-1400	23	9	or	or	CCONJ
ap-1400	23	10	of	of	ADP
ap-1400	23	11	a	a	DET
ap-1400	23	12	free	free	ADJ
ap-1400	23	13	-	-	PUNCT
ap-1400	23	14	free	free	ADJ
ap-1400	23	15	rod	rod	NOUN
ap-1400	23	16	moving	move	VERB
ap-1400	23	17	under	under	ADP
ap-1400	23	18	follower	follower	NOUN
ap-1400	23	19	thrust	thrust	NOUN
ap-1400	23	20	have	have	VERB
ap-1400	23	21	an	an	DET
ap-1400	23	22	almost	almost	ADV
ap-1400	23	23	vanishing	vanish	VERB
ap-1400	23	24	cross	cross	NOUN
ap-1400	23	25	-	-	NOUN
ap-1400	23	26	section	section	NOUN
ap-1400	23	27	,	,	PUNCT
ap-1400	23	28	e.g.	e.g.	ADV
ap-1400	23	29	,	,	PUNCT
ap-1400	23	30	at	at	ADP
ap-1400	23	31	the	the	DET
ap-1400	23	32	free	free	ADJ
ap-1400	23	33	end	end	NOUN
ap-1400	23	34	,	,	PUNCT
ap-1400	23	35	which	which	PRON
ap-1400	23	36	means	mean	VERB
ap-1400	23	37	vanishing	vanish	VERB
ap-1400	23	38	mass	mass	NOUN
ap-1400	23	39	of	of	ADP
ap-1400	23	40	a	a	DET
ap-1400	23	41	finite	finite	ADJ
ap-1400	23	42	element	element	NOUN
ap-1400	23	43	in	in	ADP
ap-1400	23	44	the	the	DET
ap-1400	23	45	corresponding	correspond	VERB
ap-1400	23	46	discretization	discretization	NOUN
ap-1400	23	47	[	[	X
ap-1400	23	48	9–12,17	9–12,17	NOUN
ap-1400	23	49	,	,	PUNCT
ap-1400	23	50	18	18	NUM
ap-1400	23	51	]	]	PUNCT
ap-1400	23	52	.	.	PUNCT
ap-1400	24	1	another	another	DET
ap-1400	24	2	intriguing	intriguing	ADJ
ap-1400	24	3	feature	feature	NOUN
ap-1400	24	4	of	of	ADP
ap-1400	24	5	optimizing	optimize	VERB
ap-1400	24	6	non	non	ADJ
ap-1400	24	7	-	-	ADJ
ap-1400	24	8	conservative	conservative	ADJ
ap-1400	24	9	systems	system	NOUN
ap-1400	24	10	is	be	AUX
ap-1400	24	11	the	the	DET
ap-1400	24	12	‘	'	PUNCT
ap-1400	24	13	wandering	wandering	ADJ
ap-1400	24	14	’	'	PUNCT
ap-1400	24	15	critical	critical	ADJ
ap-1400	24	16	frequency	frequency	NOUN
ap-1400	24	17	at	at	ADP
ap-1400	24	18	the	the	DET
ap-1400	24	19	optimal	optimal	ADJ
ap-1400	24	20	critical	critical	ADJ
ap-1400	24	21	load	load	NOUN
ap-1400	24	22	.	.	PUNCT
ap-1400	25	1	during	during	ADP
ap-1400	25	2	optimization	optimization	NOUN
ap-1400	25	3	the	the	DET
ap-1400	25	4	eigenvalue	eigenvalue	PROPN
ap-1400	25	5	branches	branch	NOUN
ap-1400	25	6	experience	experience	VERB
ap-1400	25	7	numerous	numerous	ADJ
ap-1400	25	8	mutual	mutual	ADJ
ap-1400	25	9	overlappings	overlapping	NOUN
ap-1400	25	10	and	and	CCONJ
ap-1400	25	11	veerings	veering	NOUN
ap-1400	25	12	[	[	X
ap-1400	25	13	4	4	NUM
ap-1400	25	14	,	,	PUNCT
ap-1400	25	15	6	6	NUM
ap-1400	25	16	,	,	PUNCT
ap-1400	25	17	7	7	NUM
ap-1400	25	18	,	,	PUNCT
ap-1400	25	19	27–29	27–29	NUM
ap-1400	25	20	]	]	PUNCT
ap-1400	25	21	with	with	ADP
ap-1400	25	22	a	a	DET
ap-1400	25	23	tendency	tendency	NOUN
ap-1400	25	24	for	for	SCONJ
ap-1400	25	25	the	the	DET
ap-1400	25	26	critical	critical	ADJ
ap-1400	25	27	frequency	frequency	NOUN
ap-1400	25	28	to	to	PART
ap-1400	25	29	increase	increase	VERB
ap-1400	25	30	and	and	CCONJ
ap-1400	25	31	to	to	PART
ap-1400	25	32	correspond	correspond	VERB
ap-1400	25	33	to	to	ADP
ap-1400	25	34	higher	high	ADJ
ap-1400	25	35	modes	mode	NOUN
ap-1400	25	36	[	[	X
ap-1400	25	37	9	9	NUM
ap-1400	25	38	,	,	PUNCT
ap-1400	25	39	14–17,30	14–17,30	NUM
ap-1400	25	40	]	]	PUNCT
ap-1400	25	41	.	.	PUNCT
ap-1400	26	1	this	this	DET
ap-1400	26	2	puzzling	puzzle	VERB
ap-1400	26	3	behavior	behavior	NOUN
ap-1400	26	4	of	of	ADP
ap-1400	26	5	the	the	DET
ap-1400	26	6	critical	critical	ADJ
ap-1400	26	7	frequency	frequency	NOUN
ap-1400	26	8	still	still	ADV
ap-1400	26	9	awaits	await	VERB
ap-1400	26	10	an	an	DET
ap-1400	26	11	explanation	explanation	NOUN
ap-1400	26	12	.	.	PUNCT
ap-1400	27	1	in	in	ADP
ap-1400	27	2	some	some	DET
ap-1400	27	3	problems	problem	NOUN
ap-1400	27	4	,	,	PUNCT
ap-1400	27	5	such	such	ADJ
ap-1400	27	6	as	as	ADP
ap-1400	27	7	the	the	DET
ap-1400	27	8	optimal	optimal	ADJ
ap-1400	27	9	placement	placement	NOUN
ap-1400	27	10	of	of	ADP
ap-1400	27	11	the	the	DET
ap-1400	27	12	point	point	NOUN
ap-1400	27	13	mass	mass	NOUN
ap-1400	27	14	along	along	ADP
ap-1400	27	15	a	a	DET
ap-1400	27	16	uniform	uniform	ADJ
ap-1400	27	17	free	free	ADV
ap-1400	27	18	-	-	PUNCT
ap-1400	27	19	free	free	ADJ
ap-1400	27	20	rod	rod	NOUN
ap-1400	27	21	moving	move	VERB
ap-1400	27	22	under	under	ADP
ap-1400	27	23	the	the	DET
ap-1400	27	24	follower	follower	NOUN
ap-1400	27	25	thrust	thrust	VERB
ap-1400	27	26	[	[	X
ap-1400	27	27	5,8	5,8	NUM
ap-1400	27	28	]	]	PUNCT
ap-1400	27	29	,	,	PUNCT
ap-1400	27	30	the	the	DET
ap-1400	27	31	local	local	ADJ
ap-1400	27	32	maxima	maxima	NOUN
ap-1400	27	33	were	be	AUX
ap-1400	27	34	found	find	VERB
ap-1400	27	35	to	to	PART
ap-1400	27	36	correspond	correspond	VERB
ap-1400	27	37	to	to	ADP
ap-1400	27	38	singularities	singularity	NOUN
ap-1400	27	39	of	of	ADP
ap-1400	27	40	the	the	DET
ap-1400	27	41	flutter	flutter	NOUN
ap-1400	27	42	boundary	boundary	ADJ
ap-1400	27	43	such	such	ADJ
ap-1400	27	44	as	as	ADP
ap-1400	27	45	cuspidal	cuspidal	NOUN
ap-1400	27	46	points	point	NOUN
ap-1400	27	47	where	where	SCONJ
ap-1400	27	48	multiple	multiple	ADJ
ap-1400	27	49	eigenvalues	eigenvalue	VERB
ap-1400	27	50	with	with	ADP
ap-1400	27	51	the	the	DET
ap-1400	27	52	jordan	jordan	PROPN
ap-1400	27	53	block	block	PROPN
ap-1400	27	54	exist	exist	VERB
ap-1400	27	55	[	[	X
ap-1400	27	56	11	11	NUM
ap-1400	27	57	,	,	PUNCT
ap-1400	27	58	12	12	NUM
ap-1400	27	59	]	]	PUNCT
ap-1400	27	60	.	.	PUNCT
ap-1400	28	1	in	in	ADP
ap-1400	28	2	order	order	NOUN
ap-1400	28	3	for	for	SCONJ
ap-1400	28	4	the	the	DET
ap-1400	28	5	last	last	ADJ
ap-1400	28	6	phenomenon	phenomenon	NOUN
ap-1400	28	7	to	to	PART
ap-1400	28	8	happen	happen	VERB
ap-1400	28	9	,	,	PUNCT
ap-1400	28	10	we	we	PRON
ap-1400	28	11	need	need	VERB
ap-1400	28	12	at	at	ADV
ap-1400	28	13	least	least	ADV
ap-1400	28	14	three	three	NUM
ap-1400	28	15	modes	mode	NOUN
ap-1400	28	16	[	[	X
ap-1400	28	17	11	11	NUM
ap-1400	28	18	,	,	PUNCT
ap-1400	28	19	12	12	NUM
ap-1400	28	20	]	]	PUNCT
ap-1400	28	21	,	,	PUNCT
ap-1400	28	22	meaning	mean	VERB
ap-1400	28	23	that	that	SCONJ
ap-1400	28	24	two	two	NUM
ap-1400	28	25	-	-	PUNCT
ap-1400	28	26	mode	mode	NOUN
ap-1400	28	27	approximations	approximation	NOUN
ap-1400	28	28	[	[	X
ap-1400	28	29	5	5	NUM
ap-1400	28	30	,	,	PUNCT
ap-1400	28	31	8	8	NUM
ap-1400	28	32	]	]	SYM
ap-1400	28	33	32	32	NUM
ap-1400	28	34	acta	acta	PROPN
ap-1400	28	35	polytechnica	polytechnica	PROPN
ap-1400	28	36	vol	vol	NOUN
ap-1400	28	37	.	.	PUNCT
ap-1400	29	1	51	51	NUM
ap-1400	29	2	no	no	NOUN
ap-1400	29	3	.	.	PUNCT
ap-1400	30	1	4/2011	4/2011	NUM
ap-1400	30	2	are	be	AUX
ap-1400	30	3	unable	unable	ADJ
ap-1400	30	4	to	to	PART
ap-1400	30	5	detect	detect	VERB
ap-1400	30	6	such	such	ADJ
ap-1400	30	7	optima	optima	NOUN
ap-1400	30	8	.	.	PUNCT
ap-1400	31	1	this	this	PRON
ap-1400	31	2	reflects	reflect	VERB
ap-1400	31	3	a	a	DET
ap-1400	31	4	general	general	ADJ
ap-1400	31	5	question	question	NOUN
ap-1400	31	6	on	on	ADP
ap-1400	31	7	model	model	NOUN
ap-1400	31	8	reduction	reduction	NOUN
ap-1400	31	9	and	and	CCONJ
ap-1400	31	10	the	the	DET
ap-1400	31	11	validity	validity	NOUN
ap-1400	31	12	of	of	ADP
ap-1400	31	13	lowdimensional	lowdimensional	ADJ
ap-1400	31	14	approximations	approximation	NOUN
ap-1400	31	15	in	in	ADP
ap-1400	31	16	non	non	ADJ
ap-1400	31	17	-	-	ADJ
ap-1400	31	18	conservative	conservative	ADJ
ap-1400	31	19	problems	problem	NOUN
ap-1400	31	20	,	,	PUNCT
ap-1400	31	21	already	already	ADV
ap-1400	31	22	discussed	discuss	VERB
ap-1400	31	23	by	by	ADP
ap-1400	31	24	bolotin	bolotin	NOUN
ap-1400	31	25	[	[	X
ap-1400	31	26	30	30	NUM
ap-1400	31	27	]	]	PUNCT
ap-1400	31	28	and	and	CCONJ
ap-1400	31	29	gasparini	gasparini	NOUN
ap-1400	31	30	et	et	PROPN
ap-1400	31	31	al	al	PROPN
ap-1400	31	32	.	.	PUNCT
ap-1400	32	1	[	[	X
ap-1400	32	2	23	23	NUM
ap-1400	32	3	]	]	PUNCT
ap-1400	32	4	and	and	CCONJ
ap-1400	32	5	recently	recently	ADV
ap-1400	32	6	raised	raise	VERB
ap-1400	32	7	again	again	ADV
ap-1400	32	8	in	in	ADP
ap-1400	32	9	the	the	DET
ap-1400	32	10	context	context	NOUN
ap-1400	32	11	of	of	ADP
ap-1400	32	12	friction	friction	NOUN
ap-1400	32	13	-	-	PUNCT
ap-1400	32	14	induced	induce	VERB
ap-1400	32	15	vibrations	vibration	NOUN
ap-1400	32	16	by	by	ADP
ap-1400	32	17	butlin	butlin	PROPN
ap-1400	32	18	and	and	CCONJ
ap-1400	32	19	woodhouse	woodhouse	NOUN
ap-1400	33	1	[	[	X
ap-1400	33	2	31	31	NUM
ap-1400	33	3	]	]	PUNCT
ap-1400	33	4	.	.	PUNCT
ap-1400	34	1	the	the	DET
ap-1400	34	2	above	above	ADV
ap-1400	34	3	-	-	PUNCT
ap-1400	34	4	mentioned	mention	VERB
ap-1400	34	5	phenomena	phenomenon	NOUN
ap-1400	34	6	make	make	VERB
ap-1400	34	7	rigorous	rigorous	ADJ
ap-1400	34	8	proofs	proof	NOUN
ap-1400	34	9	of	of	ADP
ap-1400	34	10	optimality	optimality	NOUN
ap-1400	34	11	in	in	ADP
ap-1400	34	12	non	non	ADJ
ap-1400	34	13	-	-	ADJ
ap-1400	34	14	conservative	conservative	ADJ
ap-1400	34	15	optimization	optimization	NOUN
ap-1400	34	16	problems	problem	NOUN
ap-1400	34	17	substantially	substantially	ADV
ap-1400	34	18	more	more	ADV
ap-1400	34	19	difficult	difficult	ADJ
ap-1400	34	20	than	than	ADP
ap-1400	34	21	in	in	ADP
ap-1400	34	22	conservative	conservative	ADJ
ap-1400	34	23	ones	one	NOUN
ap-1400	34	24	.	.	PUNCT
ap-1400	35	1	to	to	ADP
ap-1400	35	2	the	the	DET
ap-1400	35	3	best	good	ADJ
ap-1400	35	4	of	of	ADP
ap-1400	35	5	our	our	PRON
ap-1400	35	6	knowledge	knowledge	NOUN
ap-1400	35	7	,	,	PUNCT
ap-1400	35	8	no	no	DET
ap-1400	35	9	rigorously	rigorously	ADV
ap-1400	35	10	proven	prove	VERB
ap-1400	35	11	optimal	optimal	ADJ
ap-1400	35	12	solutions	solution	NOUN
ap-1400	35	13	in	in	ADP
ap-1400	35	14	optimization	optimization	NOUN
ap-1400	35	15	problems	problem	NOUN
ap-1400	35	16	for	for	ADP
ap-1400	35	17	distributed	distribute	VERB
ap-1400	35	18	circulatory	circulatory	ADJ
ap-1400	35	19	systems	system	NOUN
ap-1400	35	20	have	have	AUX
ap-1400	35	21	been	be	AUX
ap-1400	35	22	found	find	VERB
ap-1400	35	23	.	.	PUNCT
ap-1400	36	1	although	although	SCONJ
ap-1400	36	2	the	the	DET
ap-1400	36	3	situation	situation	NOUN
ap-1400	36	4	is	be	AUX
ap-1400	36	5	not	not	PART
ap-1400	36	6	much	much	ADV
ap-1400	36	7	better	well	ADJ
ap-1400	36	8	in	in	ADP
ap-1400	36	9	the	the	DET
ap-1400	36	10	finite	finite	ADJ
ap-1400	36	11	-	-	ADJ
ap-1400	36	12	dimensional	dimensional	ADJ
ap-1400	36	13	case	case	NOUN
ap-1400	36	14	,	,	PUNCT
ap-1400	36	15	it	it	PRON
ap-1400	36	16	seems	seem	VERB
ap-1400	36	17	reasonable	reasonable	ADJ
ap-1400	36	18	to	to	PART
ap-1400	36	19	try	try	VERB
ap-1400	36	20	to	to	PART
ap-1400	36	21	understand	understand	VERB
ap-1400	36	22	the	the	DET
ap-1400	36	23	nature	nature	NOUN
ap-1400	36	24	of	of	ADP
ap-1400	36	25	the	the	DET
ap-1400	36	26	observed	observe	VERB
ap-1400	36	27	difficulties	difficulty	NOUN
ap-1400	36	28	of	of	ADP
ap-1400	36	29	optimization	optimization	NOUN
ap-1400	36	30	on	on	ADP
ap-1400	36	31	final	final	ADJ
ap-1400	36	32	dimensional	dimensional	ADJ
ap-1400	36	33	non	non	ADJ
ap-1400	36	34	-	-	ADJ
ap-1400	36	35	conservative	conservative	ADJ
ap-1400	36	36	systems	system	NOUN
ap-1400	36	37	that	that	PRON
ap-1400	36	38	depend	depend	VERB
ap-1400	36	39	on	on	ADP
ap-1400	36	40	a	a	DET
ap-1400	36	41	finite	finite	ADJ
ap-1400	36	42	number	number	NOUN
ap-1400	36	43	of	of	ADP
ap-1400	36	44	control	control	NOUN
ap-1400	36	45	parameters	parameter	NOUN
ap-1400	36	46	.	.	PUNCT
ap-1400	37	1	let	let	VERB
ap-1400	37	2	us	we	PRON
ap-1400	37	3	consider	consider	VERB
ap-1400	37	4	a	a	DET
ap-1400	37	5	circulatory	circulatory	ADJ
ap-1400	37	6	system	system	NOUN
ap-1400	37	7	mẍ+kx	mẍ+kx	PROPN
ap-1400	38	1	=	=	SYM
ap-1400	38	2	0	0	PROPN
ap-1400	38	3	,	,	PUNCT
ap-1400	38	4	(	(	PUNCT
ap-1400	38	5	1	1	X
ap-1400	38	6	)	)	PUNCT
ap-1400	38	7	where	where	SCONJ
ap-1400	38	8	dot	dot	NOUN
ap-1400	38	9	indicates	indicate	VERB
ap-1400	38	10	time	time	NOUN
ap-1400	38	11	differentiation	differentiation	NOUN
ap-1400	38	12	,	,	PUNCT
ap-1400	38	13	m	m	VERB
ap-1400	38	14	is	be	AUX
ap-1400	38	15	a	a	DET
ap-1400	38	16	real	real	ADJ
ap-1400	38	17	symmetric	symmetric	ADJ
ap-1400	38	18	m×m	m×m	ADJ
ap-1400	38	19	mass	mass	NOUN
ap-1400	38	20	matrix	matrix	NOUN
ap-1400	38	21	andk	andk	NOUN
ap-1400	38	22	is	be	AUX
ap-1400	38	23	a	a	DET
ap-1400	38	24	real	real	ADJ
ap-1400	38	25	non	non	ADJ
ap-1400	38	26	-	-	ADJ
ap-1400	38	27	symmetric	symmetric	ADJ
ap-1400	38	28	m	m	PROPN
ap-1400	38	29	×	×	NOUN
ap-1400	38	30	m	m	NOUN
ap-1400	38	31	matrix	matrix	NOUN
ap-1400	38	32	of	of	ADP
ap-1400	38	33	positional	positional	ADJ
ap-1400	38	34	forces	force	NOUN
ap-1400	38	35	that	that	PRON
ap-1400	38	36	include	include	VERB
ap-1400	38	37	both	both	CCONJ
ap-1400	38	38	potential	potential	ADJ
ap-1400	38	39	and	and	CCONJ
ap-1400	38	40	non	non	ADJ
ap-1400	38	41	-	-	ADJ
ap-1400	38	42	potential	potential	ADJ
ap-1400	38	43	(	(	PUNCT
ap-1400	38	44	circulatory	circulatory	ADJ
ap-1400	38	45	)	)	PUNCT
ap-1400	38	46	forces	force	NOUN
ap-1400	38	47	.	.	PUNCT
ap-1400	39	1	equation	equation	NOUN
ap-1400	39	2	(	(	PUNCT
ap-1400	39	3	1	1	X
ap-1400	39	4	)	)	PUNCT
ap-1400	39	5	typically	typically	ADV
ap-1400	39	6	originates	originate	VERB
ap-1400	39	7	after	after	ADP
ap-1400	39	8	linearization	linearization	NOUN
ap-1400	39	9	and	and	CCONJ
ap-1400	39	10	discretization	discretization	NOUN
ap-1400	39	11	of	of	ADP
ap-1400	39	12	stability	stability	NOUN
ap-1400	39	13	problems	problem	NOUN
ap-1400	39	14	for	for	ADP
ap-1400	39	15	structures	structure	NOUN
ap-1400	39	16	under	under	ADP
ap-1400	39	17	follower	follower	NOUN
ap-1400	39	18	loads	load	NOUN
ap-1400	39	19	,	,	PUNCT
ap-1400	39	20	in	in	ADP
ap-1400	39	21	problems	problem	NOUN
ap-1400	39	22	of	of	ADP
ap-1400	39	23	friction	friction	NOUN
ap-1400	39	24	-	-	PUNCT
ap-1400	39	25	induced	induce	VERB
ap-1400	39	26	vibrations	vibration	NOUN
ap-1400	39	27	,	,	PUNCT
ap-1400	39	28	and	and	CCONJ
ap-1400	39	29	even	even	ADV
ap-1400	39	30	in	in	ADP
ap-1400	39	31	rotor	rotor	NOUN
ap-1400	39	32	dynamics	dynamic	NOUN
ap-1400	39	33	when	when	SCONJ
ap-1400	39	34	the	the	DET
ap-1400	39	35	damping	damp	VERB
ap-1400	39	36	is	be	AUX
ap-1400	39	37	not	not	PART
ap-1400	39	38	taken	take	VERB
ap-1400	39	39	into	into	ADP
ap-1400	39	40	account	account	NOUN
ap-1400	39	41	[	[	X
ap-1400	39	42	30	30	NUM
ap-1400	39	43	,	,	PUNCT
ap-1400	39	44	28	28	NUM
ap-1400	39	45	,	,	PUNCT
ap-1400	39	46	32	32	NUM
ap-1400	39	47	]	]	PUNCT
ap-1400	39	48	.	.	PUNCT
ap-1400	40	1	the	the	DET
ap-1400	40	2	characteristic	characteristic	ADJ
ap-1400	40	3	equation	equation	NOUN
ap-1400	40	4	for	for	ADP
ap-1400	40	5	the	the	DET
ap-1400	40	6	circulatory	circulatory	ADJ
ap-1400	40	7	system	system	NOUN
ap-1400	40	8	(	(	PUNCT
ap-1400	40	9	1	1	X
ap-1400	40	10	)	)	PUNCT
ap-1400	40	11	is	be	AUX
ap-1400	40	12	given	give	VERB
ap-1400	40	13	by	by	ADP
ap-1400	40	14	the	the	DET
ap-1400	40	15	modified	modify	VERB
ap-1400	40	16	leverrier	leverri	ADJ
ap-1400	40	17	algorithm	algorithm	NOUN
ap-1400	40	18	[	[	X
ap-1400	40	19	33	33	NUM
ap-1400	40	20	]	]	PUNCT
ap-1400	40	21	.	.	PUNCT
ap-1400	41	1	in	in	ADP
ap-1400	41	2	the	the	DET
ap-1400	41	3	case	case	NOUN
ap-1400	41	4	when	when	SCONJ
ap-1400	41	5	m	m	VERB
ap-1400	41	6	=	=	SYM
ap-1400	41	7	2	2	NUM
ap-1400	41	8	,	,	PUNCT
ap-1400	41	9	it	it	PRON
ap-1400	41	10	reads	read	VERB
ap-1400	41	11	detmλ4	detmλ4	NOUN
ap-1400	42	1	+	+	CCONJ
ap-1400	42	2	(	(	PUNCT
ap-1400	42	3	trmtrk−	trmtrk−	NOUN
ap-1400	42	4	tr(mk))λ2	tr(mk))λ2	PROPN
ap-1400	42	5	+	+	CCONJ
ap-1400	42	6	detk	detk	ADJ
ap-1400	42	7	=	=	SYM
ap-1400	42	8	0	0	NUM
ap-1400	42	9	,	,	PUNCT
ap-1400	42	10	(	(	PUNCT
ap-1400	42	11	2	2	X
ap-1400	42	12	)	)	PUNCT
ap-1400	42	13	where	where	SCONJ
ap-1400	42	14	λ	λ	PROPN
ap-1400	42	15	is	be	AUX
ap-1400	42	16	an	an	DET
ap-1400	42	17	eigenvalue	eigenvalue	NOUN
ap-1400	42	18	that	that	PRON
ap-1400	42	19	determines	determine	VERB
ap-1400	42	20	the	the	DET
ap-1400	42	21	stability	stability	NOUN
ap-1400	42	22	of	of	ADP
ap-1400	42	23	the	the	DET
ap-1400	42	24	trivial	trivial	ADJ
ap-1400	42	25	solution	solution	NOUN
ap-1400	42	26	.	.	PUNCT
ap-1400	43	1	the	the	DET
ap-1400	43	2	coefficients	coefficient	NOUN
ap-1400	43	3	of	of	ADP
ap-1400	43	4	matrixk	matrixk	PROPN
ap-1400	43	5	usually	usually	ADV
ap-1400	43	6	contain	contain	VERB
ap-1400	43	7	the	the	DET
ap-1400	43	8	loading	loading	NOUN
ap-1400	43	9	parameter	parameter	NOUN
ap-1400	43	10	,	,	PUNCT
ap-1400	43	11	say	say	VERB
ap-1400	43	12	p	p	X
ap-1400	43	13	,	,	PUNCT
ap-1400	43	14	that	that	SCONJ
ap-1400	43	15	we	we	PRON
ap-1400	43	16	need	need	VERB
ap-1400	43	17	to	to	PART
ap-1400	43	18	increase	increase	VERB
ap-1400	43	19	by	by	ADP
ap-1400	43	20	varying	vary	VERB
ap-1400	43	21	the	the	DET
ap-1400	43	22	coefficients	coefficient	NOUN
ap-1400	43	23	of	of	ADP
ap-1400	43	24	,	,	PUNCT
ap-1400	43	25	e.g.	e.g.	ADV
ap-1400	43	26	,	,	PUNCT
ap-1400	43	27	the	the	DET
ap-1400	43	28	mass	mass	ADJ
ap-1400	43	29	matrix	matrix	NOUN
ap-1400	43	30	.	.	PUNCT
ap-1400	44	1	during	during	ADP
ap-1400	44	2	this	this	DET
ap-1400	44	3	optimization	optimization	NOUN
ap-1400	44	4	process	process	NOUN
ap-1400	44	5	some	some	DET
ap-1400	44	6	masses	masse	NOUN
ap-1400	44	7	can	can	AUX
ap-1400	44	8	come	come	VERB
ap-1400	44	9	close	close	ADV
ap-1400	44	10	to	to	ADP
ap-1400	44	11	zero	zero	NUM
ap-1400	44	12	,	,	PUNCT
ap-1400	44	13	so	so	SCONJ
ap-1400	44	14	that	that	SCONJ
ap-1400	44	15	the	the	DET
ap-1400	44	16	mass	mass	ADJ
ap-1400	44	17	matrix	matrix	NOUN
ap-1400	44	18	can	can	AUX
ap-1400	44	19	degenerate	degenerate	VERB
ap-1400	44	20	yielding	yield	VERB
ap-1400	44	21	detm	detm	NOUN
ap-1400	44	22	=	=	NOUN
ap-1400	45	1	0	0	X
ap-1400	45	2	.	.	PUNCT
ap-1400	46	1	as	as	ADP
ap-1400	46	2	a	a	DET
ap-1400	46	3	consequence	consequence	NOUN
ap-1400	46	4	,	,	PUNCT
ap-1400	46	5	some	some	PRON
ap-1400	46	6	eigenvalues	eigenvalue	VERB
ap-1400	46	7	λ	λ	NOUN
ap-1400	46	8	can	can	AUX
ap-1400	46	9	increase	increase	VERB
ap-1400	46	10	substantially	substantially	ADV
ap-1400	46	11	.	.	PUNCT
ap-1400	47	1	however	however	ADV
ap-1400	47	2	,	,	PUNCT
ap-1400	47	3	such	such	DET
ap-1400	47	4	a	a	DET
ap-1400	47	5	singular	singular	ADJ
ap-1400	47	6	perturbation	perturbation	NOUN
ap-1400	47	7	of	of	ADP
ap-1400	47	8	the	the	DET
ap-1400	47	9	characteristic	characteristic	ADJ
ap-1400	47	10	polynomial	polynomial	NOUN
ap-1400	47	11	may	may	AUX
ap-1400	47	12	cause	cause	VERB
ap-1400	47	13	large	large	ADJ
ap-1400	47	14	values	value	NOUN
ap-1400	47	15	of	of	ADP
ap-1400	47	16	the	the	DET
ap-1400	47	17	gradient	gradient	NOUN
ap-1400	47	18	of	of	ADP
ap-1400	47	19	the	the	DET
ap-1400	47	20	critical	critical	ADJ
ap-1400	47	21	load	load	NOUN
ap-1400	47	22	with	with	ADP
ap-1400	47	23	respect	respect	NOUN
ap-1400	47	24	to	to	ADP
ap-1400	47	25	the	the	DET
ap-1400	47	26	mass	mass	ADJ
ap-1400	47	27	distribution	distribution	NOUN
ap-1400	47	28	.	.	PUNCT
ap-1400	48	1	we	we	PRON
ap-1400	48	2	see	see	VERB
ap-1400	48	3	that	that	SCONJ
ap-1400	48	4	a	a	DET
ap-1400	48	5	problem	problem	NOUN
ap-1400	48	6	of	of	ADP
ap-1400	48	7	optimal	optimal	ADJ
ap-1400	48	8	mass	mass	ADJ
ap-1400	48	9	distribution	distribution	NOUN
ap-1400	48	10	in	in	ADP
ap-1400	48	11	a	a	DET
ap-1400	48	12	finite	finite	ADJ
ap-1400	48	13	-	-	ADJ
ap-1400	48	14	dimensional	dimensional	ADJ
ap-1400	48	15	circulatory	circulatory	ADJ
ap-1400	48	16	system	system	NOUN
ap-1400	48	17	(	(	PUNCT
ap-1400	48	18	1	1	NUM
ap-1400	48	19	)	)	PUNCT
ap-1400	48	20	in	in	ADP
ap-1400	48	21	order	order	NOUN
ap-1400	48	22	to	to	PART
ap-1400	48	23	increase	increase	VERB
ap-1400	48	24	the	the	DET
ap-1400	48	25	critical	critical	ADJ
ap-1400	48	26	flutter	flutter	NOUN
ap-1400	48	27	load	load	NOUN
ap-1400	48	28	,	,	PUNCT
ap-1400	48	29	looks	looks	AUX
ap-1400	48	30	promising	promise	VERB
ap-1400	48	31	for	for	ADP
ap-1400	48	32	explaining	explain	VERB
ap-1400	48	33	the	the	DET
ap-1400	48	34	peculiarities	peculiarity	NOUN
ap-1400	48	35	of	of	ADP
ap-1400	48	36	optimizing	optimize	VERB
ap-1400	48	37	distributed	distribute	VERB
ap-1400	48	38	non	non	ADJ
ap-1400	48	39	-	-	ADJ
ap-1400	48	40	conservative	conservative	ADJ
ap-1400	48	41	structures	structure	NOUN
ap-1400	48	42	.	.	PUNCT
ap-1400	49	1	however	however	ADV
ap-1400	49	2	,	,	PUNCT
ap-1400	49	3	it	it	PRON
ap-1400	49	4	makes	make	VERB
ap-1400	49	5	sense	sense	NOUN
ap-1400	49	6	to	to	PART
ap-1400	49	7	tackle	tackle	VERB
ap-1400	49	8	first	first	ADV
ap-1400	49	9	not	not	PART
ap-1400	49	10	the	the	DET
ap-1400	49	11	most	most	ADV
ap-1400	49	12	general	general	ADJ
ap-1400	49	13	system	system	NOUN
ap-1400	49	14	(	(	PUNCT
ap-1400	49	15	1	1	NUM
ap-1400	49	16	)	)	PUNCT
ap-1400	49	17	but	but	CCONJ
ap-1400	49	18	rather	rather	ADV
ap-1400	49	19	a	a	DET
ap-1400	49	20	particular	particular	ADJ
ap-1400	49	21	finite	finite	ADJ
ap-1400	49	22	-	-	ADJ
ap-1400	49	23	dimensional	dimensional	ADJ
ap-1400	49	24	nonconservative	nonconservative	ADJ
ap-1400	49	25	system	system	NOUN
ap-1400	49	26	with	with	ADP
ap-1400	49	27	m	m	PROPN
ap-1400	49	28	degrees	degree	NOUN
ap-1400	49	29	of	of	ADP
ap-1400	49	30	freedom	freedom	NOUN
ap-1400	49	31	.	.	PUNCT
ap-1400	50	1	in	in	ADP
ap-1400	50	2	this	this	DET
ap-1400	50	3	paper	paper	NOUN
ap-1400	50	4	,	,	PUNCT
ap-1400	50	5	we	we	PRON
ap-1400	50	6	propose	propose	VERB
ap-1400	50	7	to	to	PART
ap-1400	50	8	take	take	VERB
ap-1400	50	9	an	an	DET
ap-1400	50	10	m	m	NOUN
ap-1400	50	11	-	-	PUNCT
ap-1400	50	12	link	link	ADJ
ap-1400	50	13	ziegler	ziegler	NOUN
ap-1400	50	14	pendulum	pendulum	NOUN
ap-1400	51	1	[	[	X
ap-1400	51	2	23–26	23–26	X
ap-1400	51	3	]	]	PUNCT
ap-1400	51	4	as	as	ADP
ap-1400	51	5	a	a	DET
ap-1400	51	6	toy	toy	NOUN
ap-1400	51	7	model	model	NOUN
ap-1400	51	8	for	for	ADP
ap-1400	51	9	an	an	DET
ap-1400	51	10	investigation	investigation	NOUN
ap-1400	51	11	of	of	ADP
ap-1400	51	12	the	the	DET
ap-1400	51	13	optimal	optimal	ADJ
ap-1400	51	14	mass	mass	NOUN
ap-1400	51	15	and	and	CCONJ
ap-1400	51	16	stiffness	stiffness	ADJ
ap-1400	51	17	distributions	distribution	NOUN
ap-1400	51	18	that	that	PRON
ap-1400	51	19	give	give	VERB
ap-1400	51	20	an	an	DET
ap-1400	51	21	extremum	extremum	NOUN
ap-1400	51	22	to	to	ADP
ap-1400	51	23	the	the	DET
ap-1400	51	24	critical	critical	ADJ
ap-1400	51	25	flutter	flutter	NOUN
ap-1400	51	26	load	load	NOUN
ap-1400	51	27	.	.	PUNCT
ap-1400	52	1	it	it	PRON
ap-1400	52	2	appears	appear	VERB
ap-1400	52	3	that	that	SCONJ
ap-1400	52	4	even	even	ADV
ap-1400	52	5	the	the	DET
ap-1400	52	6	classical	classical	ADJ
ap-1400	52	7	two	two	NUM
ap-1400	52	8	-	-	PUNCT
ap-1400	52	9	link	link	NOUN
ap-1400	52	10	ziegler	ziegler	NOUN
ap-1400	52	11	pendulum	pendulum	NOUN
ap-1400	52	12	has	have	AUX
ap-1400	52	13	rarely	rarely	ADV
ap-1400	52	14	been	be	AUX
ap-1400	52	15	studied	study	VERB
ap-1400	52	16	from	from	ADP
ap-1400	52	17	this	this	DET
ap-1400	52	18	point	point	NOUN
ap-1400	52	19	of	of	ADP
ap-1400	52	20	view	view	NOUN
ap-1400	52	21	,	,	PUNCT
ap-1400	52	22	in	in	ADP
ap-1400	52	23	contrast	contrast	NOUN
ap-1400	52	24	to	to	ADP
ap-1400	52	25	its	its	PRON
ap-1400	52	26	continuous	continuous	ADJ
ap-1400	52	27	analogue	analogue	NOUN
ap-1400	52	28	—	—	PUNCT
ap-1400	52	29	the	the	DET
ap-1400	52	30	beck	beck	NOUN
ap-1400	52	31	column	column	PROPN
ap-1400	52	32	.	.	PUNCT
ap-1400	53	1	the	the	DET
ap-1400	53	2	only	only	ADJ
ap-1400	53	3	example	example	NOUN
ap-1400	53	4	of	of	ADP
ap-1400	53	5	such	such	DET
ap-1400	53	6	a	a	DET
ap-1400	53	7	study	study	NOUN
ap-1400	53	8	known	know	VERB
ap-1400	53	9	to	to	ADP
ap-1400	53	10	the	the	DET
ap-1400	53	11	author	author	NOUN
ap-1400	53	12	is	be	AUX
ap-1400	53	13	contained	contain	VERB
ap-1400	53	14	in	in	ADP
ap-1400	53	15	the	the	DET
ap-1400	53	16	book	book	NOUN
ap-1400	53	17	by	by	ADP
ap-1400	53	18	gajewski	gajewski	NOUN
ap-1400	53	19	and	and	CCONJ
ap-1400	53	20	zyczkowski	zyczkowski	PROPN
ap-1400	54	1	[	[	X
ap-1400	54	2	1	1	NUM
ap-1400	54	3	]	]	PUNCT
ap-1400	54	4	.	.	PUNCT
ap-1400	55	1	this	this	DET
ap-1400	55	2	paper	paper	NOUN
ap-1400	55	3	is	be	AUX
ap-1400	55	4	organized	organize	VERB
ap-1400	55	5	as	as	SCONJ
ap-1400	55	6	follows	follow	VERB
ap-1400	55	7	.	.	PUNCT
ap-1400	56	1	in	in	ADP
ap-1400	56	2	the	the	DET
ap-1400	56	3	next	next	ADJ
ap-1400	56	4	section	section	NOUN
ap-1400	56	5	,	,	PUNCT
ap-1400	56	6	we	we	PRON
ap-1400	56	7	first	first	ADV
ap-1400	56	8	consider	consider	VERB
ap-1400	56	9	optimization	optimization	NOUN
ap-1400	56	10	of	of	ADP
ap-1400	56	11	an	an	DET
ap-1400	56	12	undamped	undampe	VERB
ap-1400	56	13	two	two	NUM
ap-1400	56	14	-	-	PUNCT
ap-1400	56	15	link	link	NOUN
ap-1400	56	16	ziegler	ziegler	NOUN
ap-1400	56	17	pendulum	pendulum	NOUN
ap-1400	56	18	.	.	PUNCT
ap-1400	57	1	we	we	PRON
ap-1400	57	2	find	find	VERB
ap-1400	57	3	an	an	DET
ap-1400	57	4	explicit	explicit	ADJ
ap-1400	57	5	expression	expression	NOUN
ap-1400	57	6	for	for	ADP
ap-1400	57	7	the	the	DET
ap-1400	57	8	critical	critical	ADJ
ap-1400	57	9	flutter	flutter	NOUN
ap-1400	57	10	load	load	NOUN
ap-1400	57	11	as	as	ADP
ap-1400	57	12	a	a	DET
ap-1400	57	13	function	function	NOUN
ap-1400	57	14	of	of	ADP
ap-1400	57	15	the	the	DET
ap-1400	57	16	mass	mass	ADJ
ap-1400	57	17	or	or	CCONJ
ap-1400	57	18	stiffness	stiffness	ADJ
ap-1400	57	19	distribution	distribution	NOUN
ap-1400	57	20	,	,	PUNCT
ap-1400	57	21	and	and	CCONJ
ap-1400	57	22	demonstrate	demonstrate	VERB
ap-1400	57	23	that	that	SCONJ
ap-1400	57	24	in	in	ADP
ap-1400	57	25	the	the	DET
ap-1400	57	26	space	space	NOUN
ap-1400	57	27	of	of	ADP
ap-1400	57	28	the	the	DET
ap-1400	57	29	two	two	NUM
ap-1400	57	30	mass	mass	ADJ
ap-1400	57	31	coefficients	coefficient	NOUN
ap-1400	57	32	and	and	CCONJ
ap-1400	57	33	the	the	DET
ap-1400	57	34	flutter	flutter	NOUN
ap-1400	57	35	load	load	NOUN
ap-1400	57	36	as	as	ADV
ap-1400	57	37	well	well	ADV
ap-1400	57	38	as	as	ADP
ap-1400	57	39	in	in	ADP
ap-1400	57	40	the	the	DET
ap-1400	57	41	space	space	NOUN
ap-1400	57	42	of	of	ADP
ap-1400	57	43	the	the	DET
ap-1400	57	44	two	two	NUM
ap-1400	57	45	stiffness	stiffness	ADJ
ap-1400	57	46	coefficients	coefficient	NOUN
ap-1400	57	47	and	and	CCONJ
ap-1400	57	48	the	the	DET
ap-1400	57	49	flutter	flutter	NOUN
ap-1400	57	50	load	load	NOUN
ap-1400	57	51	,	,	PUNCT
ap-1400	57	52	the	the	DET
ap-1400	57	53	critical	critical	ADJ
ap-1400	57	54	flutter	flutter	NOUN
ap-1400	57	55	load	load	NOUN
ap-1400	57	56	forms	form	VERB
ap-1400	57	57	a	a	DET
ap-1400	57	58	surface	surface	NOUN
ap-1400	57	59	with	with	ADP
ap-1400	57	60	a	a	DET
ap-1400	57	61	self	self	NOUN
ap-1400	57	62	-	-	PUNCT
ap-1400	57	63	intersection	intersection	NOUN
ap-1400	57	64	and	and	CCONJ
ap-1400	57	65	with	with	ADP
ap-1400	57	66	the	the	DET
ap-1400	57	67	whitney	whitney	PROPN
ap-1400	57	68	umbrella	umbrella	NOUN
ap-1400	57	69	singular	singular	ADJ
ap-1400	57	70	point	point	NOUN
ap-1400	57	71	.	.	PUNCT
ap-1400	58	1	we	we	PRON
ap-1400	58	2	consider	consider	VERB
ap-1400	58	3	the	the	DET
ap-1400	58	4	problem	problem	NOUN
ap-1400	58	5	of	of	ADP
ap-1400	58	6	optimal	optimal	ADJ
ap-1400	58	7	mass	mass	NOUN
ap-1400	58	8	redistribution	redistribution	NOUN
ap-1400	58	9	and	and	CCONJ
ap-1400	58	10	find	find	VERB
ap-1400	58	11	that	that	SCONJ
ap-1400	58	12	the	the	DET
ap-1400	58	13	only	only	ADJ
ap-1400	58	14	two	two	NUM
ap-1400	58	15	maxima	maxima	NOUN
ap-1400	58	16	of	of	ADP
ap-1400	58	17	the	the	DET
ap-1400	58	18	critical	critical	ADJ
ap-1400	58	19	flutter	flutter	NOUN
ap-1400	58	20	load	load	NOUN
ap-1400	58	21	correspond	correspond	ADV
ap-1400	58	22	to	to	ADP
ap-1400	58	23	a	a	DET
ap-1400	58	24	vanishing	vanish	VERB
ap-1400	58	25	mass	mass	NOUN
ap-1400	58	26	either	either	CCONJ
ap-1400	58	27	in	in	ADP
ap-1400	58	28	a	a	DET
ap-1400	58	29	joint	joint	NOUN
ap-1400	58	30	or	or	CCONJ
ap-1400	58	31	at	at	ADP
ap-1400	58	32	the	the	DET
ap-1400	58	33	free	free	ADJ
ap-1400	58	34	end	end	NOUN
ap-1400	58	35	of	of	ADP
ap-1400	58	36	the	the	DET
ap-1400	58	37	pendulum	pendulum	NOUN
ap-1400	58	38	;	;	PUNCT
ap-1400	58	39	in	in	ADP
ap-1400	58	40	the	the	DET
ap-1400	58	41	only	only	ADJ
ap-1400	58	42	minimum	minimum	NOUN
ap-1400	58	43	,	,	PUNCT
ap-1400	58	44	the	the	DET
ap-1400	58	45	ratio	ratio	NOUN
ap-1400	58	46	of	of	ADP
ap-1400	58	47	the	the	DET
ap-1400	58	48	masses	masse	NOUN
ap-1400	58	49	is	be	AUX
ap-1400	58	50	equal	equal	ADJ
ap-1400	58	51	to	to	ADP
ap-1400	58	52	the	the	DET
ap-1400	58	53	ratio	ratio	NOUN
ap-1400	58	54	of	of	ADP
ap-1400	58	55	the	the	DET
ap-1400	58	56	stiffness	stiffness	ADJ
ap-1400	58	57	coefficients	coefficient	NOUN
ap-1400	58	58	.	.	PUNCT
ap-1400	59	1	the	the	DET
ap-1400	59	2	maxima	maxima	NOUN
ap-1400	59	3	are	be	AUX
ap-1400	59	4	attained	attain	VERB
ap-1400	59	5	at	at	ADP
ap-1400	59	6	the	the	DET
ap-1400	59	7	singular	singular	ADJ
ap-1400	59	8	cuspidal	cuspidal	NOUN
ap-1400	59	9	points	point	NOUN
ap-1400	59	10	of	of	ADP
ap-1400	59	11	the	the	DET
ap-1400	59	12	stability	stability	NOUN
ap-1400	59	13	domain	domain	NOUN
ap-1400	59	14	and	and	CCONJ
ap-1400	59	15	are	be	AUX
ap-1400	59	16	characterized	characterize	VERB
ap-1400	59	17	by	by	ADP
ap-1400	59	18	a	a	DET
ap-1400	59	19	dramatic	dramatic	ADJ
ap-1400	59	20	increase	increase	NOUN
ap-1400	59	21	in	in	ADP
ap-1400	59	22	the	the	DET
ap-1400	59	23	critical	critical	ADJ
ap-1400	59	24	frequency	frequency	NOUN
ap-1400	59	25	of	of	ADP
ap-1400	59	26	the	the	DET
ap-1400	59	27	vibrations	vibration	NOUN
ap-1400	59	28	.	.	PUNCT
ap-1400	60	1	then	then	ADV
ap-1400	60	2	,	,	PUNCT
ap-1400	60	3	we	we	PRON
ap-1400	60	4	write	write	VERB
ap-1400	60	5	down	down	ADP
ap-1400	60	6	the	the	DET
ap-1400	60	7	equations	equation	NOUN
ap-1400	60	8	of	of	ADP
ap-1400	60	9	motion	motion	NOUN
ap-1400	60	10	of	of	ADP
ap-1400	60	11	an	an	DET
ap-1400	60	12	m	m	NOUN
ap-1400	60	13	-	-	PUNCT
ap-1400	60	14	link	link	NOUN
ap-1400	60	15	undamped	undampe	VERB
ap-1400	60	16	ziegler	ziegler	NOUN
ap-1400	60	17	pendulum	pendulum	NOUN
ap-1400	60	18	and	and	CCONJ
ap-1400	60	19	consider	consider	VERB
ap-1400	60	20	the	the	DET
ap-1400	60	21	case	case	NOUN
ap-1400	60	22	m	m	NOUN
ap-1400	60	23	=	=	SYM
ap-1400	60	24	3	3	NUM
ap-1400	60	25	,	,	PUNCT
ap-1400	60	26	in	in	ADP
ap-1400	60	27	which	which	PRON
ap-1400	60	28	we	we	PRON
ap-1400	60	29	again	again	ADV
ap-1400	60	30	find	find	VERB
ap-1400	60	31	that	that	SCONJ
ap-1400	60	32	the	the	DET
ap-1400	60	33	optimal	optimal	ADJ
ap-1400	60	34	mass	mass	NOUN
ap-1400	60	35	distributions	distribution	NOUN
ap-1400	60	36	maximizing	maximize	VERB
ap-1400	60	37	the	the	DET
ap-1400	60	38	critical	critical	ADJ
ap-1400	60	39	flutter	flutter	NOUN
ap-1400	60	40	load	load	NOUN
ap-1400	60	41	correspond	correspond	ADV
ap-1400	60	42	to	to	ADP
ap-1400	60	43	vanishing	vanish	VERB
ap-1400	60	44	of	of	ADP
ap-1400	60	45	some	some	PRON
ap-1400	60	46	of	of	ADP
ap-1400	60	47	the	the	DET
ap-1400	60	48	three	three	NUM
ap-1400	60	49	point	point	NOUN
ap-1400	60	50	masses	masse	NOUN
ap-1400	60	51	.	.	PUNCT
ap-1400	61	1	other	other	ADJ
ap-1400	61	2	types	type	NOUN
ap-1400	61	3	of	of	ADP
ap-1400	61	4	local	local	ADJ
ap-1400	61	5	extrema	extrema	NOUN
ap-1400	61	6	are	be	AUX
ap-1400	61	7	also	also	ADV
ap-1400	61	8	found	find	VERB
ap-1400	61	9	that	that	PRON
ap-1400	61	10	correspond	correspond	VERB
ap-1400	61	11	to	to	ADP
ap-1400	61	12	points	point	NOUN
ap-1400	61	13	where	where	SCONJ
ap-1400	61	14	the	the	DET
ap-1400	61	15	flutter	flutter	NOUN
ap-1400	61	16	boundary	boundary	NOUN
ap-1400	61	17	has	have	VERB
ap-1400	61	18	a	a	DET
ap-1400	61	19	vertical	vertical	ADJ
ap-1400	61	20	tangent	tangent	NOUN
ap-1400	61	21	,	,	PUNCT
ap-1400	61	22	such	such	ADJ
ap-1400	61	23	as	as	ADP
ap-1400	61	24	cuspidal	cuspidal	NOUN
ap-1400	61	25	points	point	NOUN
ap-1400	61	26	with	with	ADP
ap-1400	61	27	triple	triple	ADJ
ap-1400	61	28	eigenvalues	eigenvalue	NOUN
ap-1400	61	29	,	,	PUNCT
ap-1400	61	30	cf	cf	NOUN
ap-1400	61	31	.	.	PUNCT
ap-1400	62	1	[	[	X
ap-1400	62	2	11,12	11,12	NUM
ap-1400	62	3	]	]	PUNCT
ap-1400	62	4	,	,	PUNCT
ap-1400	62	5	or	or	CCONJ
ap-1400	62	6	points	point	VERB
ap-1400	62	7	where	where	SCONJ
ap-1400	62	8	the	the	DET
ap-1400	62	9	flutter	flutter	NOUN
ap-1400	62	10	boundary	boundary	ADJ
ap-1400	62	11	experiences	experience	VERB
ap-1400	62	12	a	a	DET
ap-1400	62	13	sharp	sharp	ADJ
ap-1400	62	14	turn	turn	NOUN
ap-1400	62	15	,	,	PUNCT
ap-1400	62	16	cf	cf	INTJ
ap-1400	62	17	.	.	PUNCT
ap-1400	63	1	[	[	X
ap-1400	63	2	27–29	27–29	NUM
ap-1400	63	3	]	]	PUNCT
ap-1400	63	4	.	.	PUNCT
ap-1400	64	1	finally	finally	ADV
ap-1400	64	2	we	we	PRON
ap-1400	64	3	consider	consider	VERB
ap-1400	64	4	the	the	DET
ap-1400	64	5	problem	problem	NOUN
ap-1400	64	6	of	of	ADP
ap-1400	64	7	optimal	optimal	ADJ
ap-1400	64	8	mass	mass	ADJ
ap-1400	64	9	distribution	distribution	NOUN
ap-1400	64	10	for	for	ADP
ap-1400	64	11	a	a	DET
ap-1400	64	12	two	two	NUM
ap-1400	64	13	-	-	PUNCT
ap-1400	64	14	link	link	NOUN
ap-1400	64	15	ziegler	ziegler	NOUN
ap-1400	64	16	pendulum	pendulum	NOUN
ap-1400	64	17	with	with	ADP
ap-1400	64	18	dissipation	dissipation	NOUN
ap-1400	64	19	.	.	PUNCT
ap-1400	65	1	in	in	ADP
ap-1400	65	2	conclusion	conclusion	NOUN
ap-1400	65	3	,	,	PUNCT
ap-1400	65	4	we	we	PRON
ap-1400	65	5	formulate	formulate	VERB
ap-1400	65	6	an	an	DET
ap-1400	65	7	optimization	optimization	NOUN
ap-1400	65	8	problem	problem	NOUN
ap-1400	65	9	for	for	ADP
ap-1400	65	10	an	an	DET
ap-1400	65	11	m	m	NOUN
ap-1400	65	12	-	-	PUNCT
ap-1400	65	13	link	link	ADJ
ap-1400	65	14	ziegler	ziegler	NOUN
ap-1400	65	15	pendulum	pendulum	PROPN
ap-1400	65	16	and	and	CCONJ
ap-1400	65	17	discuss	discuss	VERB
ap-1400	65	18	some	some	DET
ap-1400	65	19	hypotheses	hypothesis	NOUN
ap-1400	65	20	on	on	ADP
ap-1400	65	21	plausible	plausible	ADJ
ap-1400	65	22	optimal	optimal	ADJ
ap-1400	65	23	solutions	solution	NOUN
ap-1400	65	24	and	and	CCONJ
ap-1400	65	25	their	their	PRON
ap-1400	65	26	expected	expect	VERB
ap-1400	65	27	properties	property	NOUN
ap-1400	65	28	.	.	PUNCT
ap-1400	66	1	2	2	NUM
ap-1400	66	2	structural	structural	ADJ
ap-1400	66	3	optimization	optimization	NOUN
ap-1400	66	4	of	of	ADP
ap-1400	66	5	the	the	DET
ap-1400	66	6	ziegler	ziegler	PROPN
ap-1400	66	7	pendulum	pendulum	NOUN
ap-1400	66	8	let	let	VERB
ap-1400	66	9	us	we	PRON
ap-1400	66	10	consider	consider	VERB
ap-1400	66	11	the	the	DET
ap-1400	66	12	classical	classical	ADJ
ap-1400	66	13	ziegler	ziegler	NOUN
ap-1400	66	14	pendulum	pendulum	NOUN
ap-1400	66	15	consisting	consist	VERB
ap-1400	66	16	of	of	ADP
ap-1400	66	17	two	two	NUM
ap-1400	66	18	light	light	ADJ
ap-1400	66	19	and	and	CCONJ
ap-1400	66	20	rigid	rigid	ADJ
ap-1400	66	21	rods	rod	NOUN
ap-1400	66	22	of	of	ADP
ap-1400	66	23	equal	equal	ADJ
ap-1400	66	24	length	length	NOUN
ap-1400	66	25	l.	l.	PROPN
ap-1400	66	26	the	the	DET
ap-1400	66	27	pendulum	pendulum	NOUN
ap-1400	66	28	is	be	AUX
ap-1400	66	29	attached	attach	VERB
ap-1400	66	30	to	to	ADP
ap-1400	66	31	a	a	DET
ap-1400	66	32	firm	firm	ADJ
ap-1400	66	33	basement	basement	NOUN
ap-1400	66	34	by	by	ADP
ap-1400	66	35	a	a	DET
ap-1400	66	36	viscoelastic	viscoelastic	ADJ
ap-1400	66	37	revolute	revolute	NOUN
ap-1400	66	38	joint	joint	NOUN
ap-1400	66	39	with	with	ADP
ap-1400	66	40	stiffness	stiffness	ADJ
ap-1400	66	41	coefficient	coefficient	NOUN
ap-1400	66	42	c1	c1	NOUN
ap-1400	66	43	and	and	CCONJ
ap-1400	66	44	damping	damp	VERB
ap-1400	66	45	33	33	NUM
ap-1400	66	46	acta	acta	PROPN
ap-1400	66	47	polytechnica	polytechnica	PROPN
ap-1400	66	48	vol	vol	NOUN
ap-1400	66	49	.	.	PUNCT
ap-1400	67	1	51	51	NUM
ap-1400	67	2	no	no	NOUN
ap-1400	67	3	.	.	PUNCT
ap-1400	68	1	4/2011	4/2011	NUM
ap-1400	68	2	fig	fig	NOUN
ap-1400	68	3	.	.	PUNCT
ap-1400	69	1	1	1	NUM
ap-1400	69	2	:	:	PUNCT
ap-1400	69	3	undamped	undampe	VERB
ap-1400	69	4	2	2	NUM
ap-1400	69	5	-	-	PUNCT
ap-1400	69	6	link	link	NOUN
ap-1400	69	7	ziegler	ziegler	NOUN
ap-1400	69	8	pendulum	pendulum	PROPN
ap-1400	69	9	.	.	PUNCT
ap-1400	70	1	(	(	PUNCT
ap-1400	70	2	a	a	X
ap-1400	70	3	)	)	PUNCT
ap-1400	70	4	the	the	DET
ap-1400	70	5	critical	critical	ADJ
ap-1400	70	6	load	load	NOUN
ap-1400	70	7	p	p	NOUN
ap-1400	70	8	(	(	PUNCT
ap-1400	70	9	c1	c1	PROPN
ap-1400	70	10	,	,	PUNCT
ap-1400	70	11	c2	c2	PROPN
ap-1400	70	12	)	)	PUNCT
ap-1400	70	13	as	as	ADP
ap-1400	70	14	a	a	DET
ap-1400	70	15	function	function	NOUN
ap-1400	70	16	of	of	ADP
ap-1400	70	17	the	the	DET
ap-1400	70	18	stiffness	stiffness	ADJ
ap-1400	70	19	coefficients	coefficient	NOUN
ap-1400	70	20	forms	form	VERB
ap-1400	70	21	a	a	DET
ap-1400	70	22	conical	conical	ADJ
ap-1400	70	23	surface	surface	NOUN
ap-1400	70	24	in	in	ADP
ap-1400	70	25	the	the	DET
ap-1400	70	26	(	(	PUNCT
ap-1400	70	27	c1	c1	PROPN
ap-1400	70	28	,	,	PUNCT
ap-1400	70	29	c2	c2	PROPN
ap-1400	70	30	,	,	PUNCT
ap-1400	70	31	p	p	NOUN
ap-1400	70	32	)	)	PUNCT
ap-1400	70	33	-space	-space	NOUN
ap-1400	70	34	(	(	PUNCT
ap-1400	70	35	the	the	DET
ap-1400	70	36	case	case	NOUN
ap-1400	70	37	when	when	SCONJ
ap-1400	70	38	m1	m1	PROPN
ap-1400	70	39	=	=	PROPN
ap-1400	70	40	m2	m2	PROPN
ap-1400	70	41	=	=	SYM
ap-1400	70	42	1	1	NUM
ap-1400	70	43	and	and	CCONJ
ap-1400	70	44	l	l	NOUN
ap-1400	70	45	=	=	SYM
ap-1400	70	46	1	1	NUM
ap-1400	70	47	is	be	AUX
ap-1400	70	48	shown	show	VERB
ap-1400	70	49	)	)	PUNCT
ap-1400	70	50	;	;	PUNCT
ap-1400	70	51	(	(	PUNCT
ap-1400	70	52	b	b	X
ap-1400	70	53	)	)	PUNCT
ap-1400	70	54	the	the	DET
ap-1400	70	55	critical	critical	ADJ
ap-1400	70	56	load	load	NOUN
ap-1400	70	57	p(m1	p(m1	NOUN
ap-1400	70	58	,	,	PUNCT
ap-1400	70	59	m2	m2	PROPN
ap-1400	70	60	)	)	PUNCT
ap-1400	70	61	as	as	ADP
ap-1400	70	62	a	a	DET
ap-1400	70	63	function	function	NOUN
ap-1400	70	64	of	of	ADP
ap-1400	70	65	the	the	DET
ap-1400	70	66	masses	masse	NOUN
ap-1400	70	67	,	,	PUNCT
ap-1400	70	68	forms	form	VERB
ap-1400	70	69	a	a	DET
ap-1400	70	70	self	self	NOUN
ap-1400	70	71	-	-	PUNCT
ap-1400	70	72	intersecting	intersect	VERB
ap-1400	70	73	surface	surface	NOUN
ap-1400	70	74	with	with	ADP
ap-1400	70	75	the	the	DET
ap-1400	70	76	whitney	whitney	NOUN
ap-1400	70	77	umbrella	umbrella	NOUN
ap-1400	70	78	singularity	singularity	NOUN
ap-1400	70	79	at	at	ADP
ap-1400	70	80	point	point	NOUN
ap-1400	70	81	(	(	PUNCT
ap-1400	70	82	0	0	NUM
ap-1400	70	83	,	,	PUNCT
ap-1400	70	84	0	0	NUM
ap-1400	70	85	,	,	PUNCT
ap-1400	70	86	2	2	NUM
ap-1400	70	87	)	)	PUNCT
ap-1400	70	88	of	of	ADP
ap-1400	70	89	the	the	DET
ap-1400	70	90	(	(	PUNCT
ap-1400	70	91	m1	m1	PROPN
ap-1400	70	92	,	,	PUNCT
ap-1400	70	93	m2	m2	PROPN
ap-1400	70	94	,	,	PUNCT
ap-1400	70	95	p)-space	p)-space	PUNCT
ap-1400	70	96	(	(	PUNCT
ap-1400	70	97	the	the	DET
ap-1400	70	98	case	case	NOUN
ap-1400	70	99	when	when	SCONJ
ap-1400	70	100	c1	c1	PROPN
ap-1400	70	101	=	=	PROPN
ap-1400	70	102	c2	c2	PROPN
ap-1400	70	103	=	=	SYM
ap-1400	70	104	1	1	NUM
ap-1400	70	105	is	be	AUX
ap-1400	70	106	shown	show	VERB
ap-1400	70	107	)	)	PUNCT
ap-1400	70	108	coefficient	coefficient	NOUN
ap-1400	70	109	d1	d1	PROPN
ap-1400	70	110	.	.	PUNCT
ap-1400	71	1	another	another	DET
ap-1400	71	2	viscoelastic	viscoelastic	ADJ
ap-1400	71	3	revolute	revolute	NOUN
ap-1400	71	4	joint	joint	NOUN
ap-1400	71	5	with	with	ADP
ap-1400	71	6	stiffness	stiffness	ADJ
ap-1400	71	7	coefficient	coefficient	NOUN
ap-1400	71	8	c2	c2	PROPN
ap-1400	71	9	and	and	CCONJ
ap-1400	71	10	damping	damp	VERB
ap-1400	71	11	coefficient	coefficient	NOUN
ap-1400	71	12	d2	d2	PROPN
ap-1400	71	13	connects	connect	VERB
ap-1400	71	14	the	the	DET
ap-1400	71	15	two	two	NUM
ap-1400	71	16	rods	rod	NOUN
ap-1400	71	17	[	[	X
ap-1400	71	18	26,32	26,32	NUM
ap-1400	71	19	]	]	PUNCT
ap-1400	71	20	.	.	PUNCT
ap-1400	72	1	the	the	DET
ap-1400	72	2	point	point	NOUN
ap-1400	72	3	masses	mass	VERB
ap-1400	72	4	m1	m1	PROPN
ap-1400	72	5	and	and	CCONJ
ap-1400	72	6	m2	m2	PROPN
ap-1400	72	7	are	be	AUX
ap-1400	72	8	located	locate	VERB
ap-1400	72	9	at	at	ADP
ap-1400	72	10	the	the	DET
ap-1400	72	11	second	second	ADJ
ap-1400	72	12	revolute	revolute	NOUN
ap-1400	72	13	joint	joint	NOUN
ap-1400	72	14	and	and	CCONJ
ap-1400	72	15	at	at	ADP
ap-1400	72	16	the	the	DET
ap-1400	72	17	free	free	ADJ
ap-1400	72	18	end	end	NOUN
ap-1400	72	19	of	of	ADP
ap-1400	72	20	the	the	DET
ap-1400	72	21	second	second	ADJ
ap-1400	72	22	rod	rod	NOUN
ap-1400	72	23	,	,	PUNCT
ap-1400	72	24	respectively	respectively	ADV
ap-1400	72	25	.	.	PUNCT
ap-1400	73	1	the	the	DET
ap-1400	73	2	second	second	ADJ
ap-1400	73	3	rod	rod	NOUN
ap-1400	73	4	is	be	AUX
ap-1400	73	5	subjected	subject	VERB
ap-1400	73	6	to	to	ADP
ap-1400	73	7	a	a	DET
ap-1400	73	8	tangential	tangential	ADJ
ap-1400	73	9	follower	follower	NOUN
ap-1400	73	10	load	load	NOUN
ap-1400	73	11	p	p	NOUN
ap-1400	74	1	[	[	X
ap-1400	74	2	26	26	NUM
ap-1400	74	3	,	,	PUNCT
ap-1400	74	4	32	32	NUM
ap-1400	74	5	]	]	PUNCT
ap-1400	74	6	.	.	PUNCT
ap-1400	75	1	2.1	2.1	NUM
ap-1400	75	2	undamped	undampe	VERB
ap-1400	75	3	case	case	NOUN
ap-1400	75	4	small	small	ADJ
ap-1400	75	5	deviations	deviation	NOUN
ap-1400	75	6	from	from	ADP
ap-1400	75	7	the	the	DET
ap-1400	75	8	vertical	vertical	ADJ
ap-1400	75	9	equilibrium	equilibrium	NOUN
ap-1400	75	10	for	for	ADP
ap-1400	75	11	an	an	DET
ap-1400	75	12	undamped	undamped	ADJ
ap-1400	75	13	ziegler	ziegler	NOUN
ap-1400	75	14	pendulum	pendulum	NOUN
ap-1400	75	15	are	be	AUX
ap-1400	75	16	described	describe	VERB
ap-1400	75	17	by	by	ADP
ap-1400	75	18	equation	equation	NOUN
ap-1400	75	19	(	(	PUNCT
ap-1400	75	20	1	1	NUM
ap-1400	75	21	)	)	PUNCT
ap-1400	75	22	with	with	ADP
ap-1400	75	23	mass	mass	NOUN
ap-1400	75	24	and	and	CCONJ
ap-1400	75	25	stiffness	stiffness	ADJ
ap-1400	75	26	matrices	matrix	NOUN
ap-1400	75	27	that	that	PRON
ap-1400	75	28	have	have	VERB
ap-1400	75	29	the	the	DET
ap-1400	75	30	following	follow	VERB
ap-1400	75	31	form	form	NOUN
ap-1400	75	32	[	[	X
ap-1400	75	33	26,32	26,32	X
ap-1400	75	34	]	]	X
ap-1400	75	35	m	m	NOUN
ap-1400	75	36	=	=	NOUN
ap-1400	75	37	l2	l2	NOUN
ap-1400	75	38	(	(	PUNCT
ap-1400	75	39	m1	m1	PROPN
ap-1400	75	40	+	+	CCONJ
ap-1400	75	41	m2	m2	PROPN
ap-1400	75	42	m2	m2	PROPN
ap-1400	75	43	m2	m2	PROPN
ap-1400	75	44	m2	m2	PROPN
ap-1400	75	45	)	)	PUNCT
ap-1400	75	46	,	,	PUNCT
ap-1400	75	47	k	k	PROPN
ap-1400	76	1	=	=	PRON
ap-1400	76	2	(	(	PUNCT
ap-1400	76	3	c1	c1	PROPN
ap-1400	76	4	+	+	CCONJ
ap-1400	76	5	c2	c2	PROPN
ap-1400	76	6	−	−	PROPN
ap-1400	76	7	pl	pl	PROPN
ap-1400	76	8	p	p	PROPN
ap-1400	76	9	l	l	NOUN
ap-1400	76	10	−	−	PROPN
ap-1400	77	1	c2	c2	PROPN
ap-1400	77	2	−c2	−c2	PROPN
ap-1400	77	3	c2	c2	PROPN
ap-1400	77	4	)	)	PUNCT
ap-1400	77	5	,	,	PUNCT
ap-1400	77	6	(	(	PUNCT
ap-1400	77	7	3	3	X
ap-1400	77	8	)	)	PUNCT
ap-1400	77	9	where	where	SCONJ
ap-1400	77	10	x	x	SYM
ap-1400	77	11	=	=	PRON
ap-1400	77	12	(	(	PUNCT
ap-1400	77	13	θ1	θ1	PROPN
ap-1400	77	14	,	,	PUNCT
ap-1400	77	15	θ2)t	θ2)t	PROPN
ap-1400	77	16	is	be	AUX
ap-1400	77	17	the	the	DET
ap-1400	77	18	vector	vector	NOUN
ap-1400	77	19	consisting	consist	VERB
ap-1400	77	20	of	of	ADP
ap-1400	77	21	small	small	ADJ
ap-1400	77	22	angle	angle	NOUN
ap-1400	77	23	deviations	deviation	NOUN
ap-1400	77	24	from	from	ADP
ap-1400	77	25	the	the	DET
ap-1400	77	26	vertical	vertical	ADJ
ap-1400	77	27	equilibrium	equilibrium	NOUN
ap-1400	77	28	position	position	NOUN
ap-1400	77	29	.	.	PUNCT
ap-1400	78	1	calculating	calculate	VERB
ap-1400	78	2	the	the	DET
ap-1400	78	3	characteristic	characteristic	ADJ
ap-1400	78	4	equation	equation	NOUN
ap-1400	78	5	det(mλ2+k	det(mλ2+k	NOUN
ap-1400	78	6	)	)	PUNCT
ap-1400	78	7	=	=	SYM
ap-1400	78	8	0	0	NUM
ap-1400	78	9	for	for	ADP
ap-1400	78	10	the	the	DET
ap-1400	78	11	ziegler	ziegler	PROPN
ap-1400	78	12	pendulum	pendulum	NOUN
ap-1400	78	13	without	without	ADP
ap-1400	78	14	dissipation	dissipation	NOUN
ap-1400	78	15	,	,	PUNCT
ap-1400	78	16	we	we	PRON
ap-1400	78	17	find	find	VERB
ap-1400	78	18	m1m2l	m1m2l	NUM
ap-1400	78	19	4λ4	4λ4	NUM
ap-1400	79	1	+	+	CCONJ
ap-1400	79	2	(	(	PUNCT
ap-1400	79	3	m1c2	m1c2	NUM
ap-1400	79	4	+	+	SYM
ap-1400	79	5	4m2c2	4m2c2	NUM
ap-1400	80	1	+	+	CCONJ
ap-1400	80	2	c1m2	c1m2	X
ap-1400	80	3	−	−	PROPN
ap-1400	80	4	2plm2)l2λ2	2plm2)l2λ2	NUM
ap-1400	80	5	+	+	CCONJ
ap-1400	80	6	c1c2	c1c2	NOUN
ap-1400	80	7	=	=	NOUN
ap-1400	80	8	0	0	NUM
ap-1400	80	9	.	.	PUNCT
ap-1400	81	1	(	(	PUNCT
ap-1400	81	2	4	4	NUM
ap-1400	81	3	)	)	PUNCT
ap-1400	81	4	by	by	ADP
ap-1400	81	5	direct	direct	ADJ
ap-1400	81	6	calculation	calculation	NOUN
ap-1400	81	7	of	of	ADP
ap-1400	81	8	the	the	DET
ap-1400	81	9	roots	root	NOUN
ap-1400	81	10	of	of	ADP
ap-1400	81	11	the	the	DET
ap-1400	81	12	characteristic	characteristic	ADJ
ap-1400	81	13	equation	equation	NOUN
ap-1400	81	14	(	(	PUNCT
ap-1400	81	15	4	4	NUM
ap-1400	81	16	)	)	PUNCT
ap-1400	81	17	or	or	CCONJ
ap-1400	81	18	by	by	ADP
ap-1400	81	19	using	use	VERB
ap-1400	81	20	the	the	DET
ap-1400	81	21	gallina	gallina	ADJ
ap-1400	81	22	criterion	criterion	NOUN
ap-1400	81	23	[	[	X
ap-1400	81	24	24	24	NUM
ap-1400	81	25	]	]	PUNCT
ap-1400	81	26	,	,	PUNCT
ap-1400	81	27	we	we	PRON
ap-1400	81	28	find	find	VERB
ap-1400	81	29	a	a	DET
ap-1400	81	30	critical	critical	ADJ
ap-1400	81	31	surface	surface	NOUN
ap-1400	81	32	that	that	PRON
ap-1400	81	33	separates	separate	VERB
ap-1400	81	34	the	the	DET
ap-1400	81	35	flutter	flutter	NOUN
ap-1400	81	36	instability	instability	NOUN
ap-1400	81	37	and	and	CCONJ
ap-1400	81	38	the	the	DET
ap-1400	81	39	marginal	marginal	ADJ
ap-1400	81	40	stability	stability	NOUN
ap-1400	81	41	domains	domain	NOUN
ap-1400	81	42	(	(	PUNCT
ap-1400	81	43	2lm2p	2lm2p	NUM
ap-1400	81	44	−	−	NOUN
ap-1400	81	45	4m2c2	4m2c2	NUM
ap-1400	82	1	−	−	NOUN
ap-1400	83	1	m1c1	m1c1	X
ap-1400	83	2	−	−	X
ap-1400	83	3	m2c1	m2c1	NOUN
ap-1400	83	4	)	)	PUNCT
ap-1400	83	5	2	2	NUM
ap-1400	84	1	+	+	CCONJ
ap-1400	84	2	(	(	PUNCT
ap-1400	84	3	m1c1	m1c1	AUX
ap-1400	84	4	−	−	X
ap-1400	84	5	m2c2	m2c2	NOUN
ap-1400	84	6	)	)	PUNCT
ap-1400	84	7	2	2	NUM
ap-1400	84	8	=	=	SYM
ap-1400	84	9	(	(	PUNCT
ap-1400	84	10	m1c1	m1c1	X
ap-1400	84	11	+	+	X
ap-1400	84	12	m2c2	m2c2	X
ap-1400	84	13	)	)	PUNCT
ap-1400	84	14	2	2	NUM
ap-1400	84	15	.	.	PUNCT
ap-1400	84	16	(	(	PUNCT
ap-1400	84	17	5	5	NUM
ap-1400	84	18	)	)	PUNCT
ap-1400	84	19	equation	equation	NOUN
ap-1400	84	20	(	(	PUNCT
ap-1400	84	21	5	5	X
ap-1400	84	22	)	)	PUNCT
ap-1400	84	23	defines	define	VERB
ap-1400	84	24	a	a	DET
ap-1400	84	25	conical	conical	ADJ
ap-1400	84	26	surface	surface	NOUN
ap-1400	84	27	in	in	ADP
ap-1400	84	28	the	the	DET
ap-1400	84	29	(	(	PUNCT
ap-1400	84	30	c1	c1	PROPN
ap-1400	84	31	,	,	PUNCT
ap-1400	84	32	c2	c2	PROPN
ap-1400	84	33	,	,	PUNCT
ap-1400	84	34	p	p	NOUN
ap-1400	84	35	)	)	PUNCT
ap-1400	84	36	-space	-space	NOUN
ap-1400	84	37	when	when	SCONJ
ap-1400	84	38	m1,2	m1,2	ADJ
ap-1400	84	39	and	and	CCONJ
ap-1400	84	40	l	l	NOUN
ap-1400	84	41	are	be	AUX
ap-1400	84	42	fixed	fix	VERB
ap-1400	84	43	:	:	PUNCT
ap-1400	84	44	flutter	flutter	NOUN
ap-1400	84	45	inside	inside	ADP
ap-1400	84	46	the	the	DET
ap-1400	84	47	cone	cone	NOUN
ap-1400	84	48	,	,	PUNCT
ap-1400	84	49	figure	figure	NOUN
ap-1400	84	50	1(a	1(a	NUM
ap-1400	84	51	)	)	PUNCT
ap-1400	84	52	.	.	PUNCT
ap-1400	85	1	however	however	ADV
ap-1400	85	2	,	,	PUNCT
ap-1400	85	3	in	in	ADP
ap-1400	85	4	the	the	DET
ap-1400	85	5	(	(	PUNCT
ap-1400	85	6	m1	m1	PROPN
ap-1400	85	7	,	,	PUNCT
ap-1400	85	8	m2	m2	PROPN
ap-1400	85	9	,	,	PUNCT
ap-1400	85	10	p	p	NOUN
ap-1400	85	11	)	)	PUNCT
ap-1400	85	12	-space	-space	NOUN
ap-1400	85	13	the	the	DET
ap-1400	85	14	critical	critical	ADJ
ap-1400	85	15	surface	surface	NOUN
ap-1400	85	16	(	(	PUNCT
ap-1400	85	17	5	5	X
ap-1400	85	18	)	)	PUNCT
ap-1400	85	19	looks	look	VERB
ap-1400	85	20	different	different	ADJ
ap-1400	85	21	and	and	CCONJ
ap-1400	85	22	has	have	VERB
ap-1400	85	23	the	the	DET
ap-1400	85	24	form	form	NOUN
ap-1400	85	25	of	of	ADP
ap-1400	85	26	a	a	DET
ap-1400	85	27	self	self	NOUN
ap-1400	85	28	-	-	PUNCT
ap-1400	85	29	intersecting	intersect	VERB
ap-1400	85	30	surface	surface	NOUN
ap-1400	85	31	with	with	ADP
ap-1400	85	32	the	the	DET
ap-1400	85	33	whitney	whitney	NOUN
ap-1400	85	34	umbrella	umbrella	NOUN
ap-1400	85	35	singularity	singularity	NOUN
ap-1400	85	36	at	at	ADP
ap-1400	85	37	the	the	DET
ap-1400	85	38	(	(	PUNCT
ap-1400	85	39	0	0	NUM
ap-1400	85	40	,	,	PUNCT
ap-1400	85	41	0	0	NUM
ap-1400	85	42	,	,	PUNCT
ap-1400	85	43	2c2	2c2	NUM
ap-1400	85	44	/	/	SYM
ap-1400	85	45	l)-point	l)-point	NOUN
ap-1400	85	46	.	.	PUNCT
ap-1400	86	1	indeed	indeed	ADV
ap-1400	86	2	,	,	PUNCT
ap-1400	86	3	expressing	express	VERB
ap-1400	86	4	the	the	DET
ap-1400	86	5	critical	critical	ADJ
ap-1400	86	6	load	load	NOUN
ap-1400	86	7	p	p	NOUN
ap-1400	86	8	from	from	ADP
ap-1400	86	9	(	(	PUNCT
ap-1400	86	10	5	5	NUM
ap-1400	86	11	)	)	PUNCT
ap-1400	86	12	we	we	PRON
ap-1400	86	13	get	get	VERB
ap-1400	86	14	p	p	NOUN
ap-1400	86	15	=	=	PUNCT
ap-1400	86	16	4m2c2	4m2c2	NUM
ap-1400	87	1	+	+	CCONJ
ap-1400	87	2	(	(	PUNCT
ap-1400	87	3	√	√	NUM
ap-1400	87	4	m1c2	m1c2	NUM
ap-1400	87	5	±	±	NOUN
ap-1400	87	6	√	√	PROPN
ap-1400	87	7	m2c1	m2c1	NOUN
ap-1400	87	8	)	)	PUNCT
ap-1400	87	9	2	2	NUM
ap-1400	87	10	2lm2	2lm2	NUM
ap-1400	87	11	≥	≥	NUM
ap-1400	87	12	2c2	2c2	NUM
ap-1400	87	13	l	l	NOUN
ap-1400	87	14	.	.	PUNCT
ap-1400	88	1	(	(	PUNCT
ap-1400	88	2	6	6	X
ap-1400	88	3	)	)	PUNCT
ap-1400	88	4	defining	define	VERB
ap-1400	88	5	the	the	DET
ap-1400	88	6	new	new	ADJ
ap-1400	88	7	critical	critical	ADJ
ap-1400	88	8	flutter	flutter	NOUN
ap-1400	88	9	load	load	NOUN
ap-1400	88	10	as	as	ADP
ap-1400	88	11	p	p	X
ap-1400	88	12	:	:	PUNCT
ap-1400	88	13	=	=	SYM
ap-1400	88	14	pl	pl	PROPN
ap-1400	88	15	/	/	SYM
ap-1400	88	16	c2	c2	PROPN
ap-1400	88	17	we	we	PRON
ap-1400	88	18	come	come	VERB
ap-1400	88	19	to	to	ADP
ap-1400	88	20	the	the	DET
ap-1400	88	21	more	more	ADV
ap-1400	88	22	symmetric	symmetric	ADJ
ap-1400	88	23	expression	expression	NOUN
ap-1400	88	24	p	p	NOUN
ap-1400	88	25	=	=	SYM
ap-1400	88	26	2	2	NUM
ap-1400	88	27	+	+	CCONJ
ap-1400	88	28	1	1	NUM
ap-1400	88	29	2	2	NUM
ap-1400	88	30	(	(	PUNCT
ap-1400	88	31	√	√	NUM
ap-1400	88	32	m1	m1	PROPN
ap-1400	88	33	m2	m2	PROPN
ap-1400	88	34	±	±	PROPN
ap-1400	88	35	√	√	PROPN
ap-1400	88	36	c1	c1	PROPN
ap-1400	88	37	c2	c2	PROPN
ap-1400	88	38	)	)	PUNCT
ap-1400	88	39	2	2	NUM
ap-1400	88	40	≥	≥	NOUN
ap-1400	88	41	2	2	NUM
ap-1400	88	42	.	.	PUNCT
ap-1400	89	1	(	(	PUNCT
ap-1400	89	2	7	7	NUM
ap-1400	89	3	)	)	PUNCT
ap-1400	89	4	34	34	NUM
ap-1400	89	5	acta	acta	PROPN
ap-1400	89	6	polytechnica	polytechnica	PROPN
ap-1400	89	7	vol	vol	NOUN
ap-1400	89	8	.	.	PUNCT
ap-1400	90	1	51	51	NUM
ap-1400	90	2	no	no	NOUN
ap-1400	90	3	.	.	PUNCT
ap-1400	91	1	4/2011	4/2011	NUM
ap-1400	91	2	fig	fig	NOUN
ap-1400	91	3	.	.	PUNCT
ap-1400	92	1	2	2	NUM
ap-1400	92	2	:	:	PUNCT
ap-1400	92	3	undamped	undampe	VERB
ap-1400	92	4	2	2	NUM
ap-1400	92	5	-	-	PUNCT
ap-1400	92	6	link	link	NOUN
ap-1400	92	7	ziegler	ziegler	NOUN
ap-1400	92	8	pendulum	pendulum	NOUN
ap-1400	92	9	with	with	ADP
ap-1400	92	10	c1	c1	PROPN
ap-1400	92	11	=	=	SYM
ap-1400	92	12	1	1	NUM
ap-1400	92	13	,	,	PUNCT
ap-1400	92	14	c2	c2	PROPN
ap-1400	92	15	=	=	SYM
ap-1400	92	16	1	1	NUM
ap-1400	92	17	:	:	PUNCT
ap-1400	92	18	the	the	DET
ap-1400	92	19	critical	critical	ADJ
ap-1400	92	20	flutter	flutter	NOUN
ap-1400	92	21	load	load	NOUN
ap-1400	92	22	p(α	p(α	PROPN
ap-1400	92	23	)	)	PUNCT
ap-1400	92	24	as	as	ADP
ap-1400	92	25	a	a	DET
ap-1400	92	26	function	function	NOUN
ap-1400	92	27	of	of	ADP
ap-1400	92	28	the	the	DET
ap-1400	92	29	azimuth	azimuth	PROPN
ap-1400	92	30	angle	angle	NOUN
ap-1400	92	31	α	α	PROPN
ap-1400	92	32	indicating	indicate	VERB
ap-1400	92	33	the	the	DET
ap-1400	92	34	direction	direction	NOUN
ap-1400	92	35	in	in	ADP
ap-1400	92	36	the	the	DET
ap-1400	92	37	(	(	PUNCT
ap-1400	92	38	m1	m1	NOUN
ap-1400	92	39	,	,	PUNCT
ap-1400	92	40	m2)-plane	m2)-plane	PROPN
ap-1400	92	41	.	.	PUNCT
ap-1400	92	42	point	point	NOUN
ap-1400	92	43	a	a	PRON
ap-1400	92	44	is	be	AUX
ap-1400	92	45	an	an	DET
ap-1400	92	46	absolute	absolute	ADJ
ap-1400	92	47	minimum	minimum	NOUN
ap-1400	92	48	of	of	ADP
ap-1400	92	49	the	the	DET
ap-1400	92	50	flutter	flutter	NOUN
ap-1400	92	51	load	load	NOUN
ap-1400	92	52	:	:	PUNCT
ap-1400	93	1	pa	pa	PROPN
ap-1400	93	2	=	=	SYM
ap-1400	93	3	2	2	NUM
ap-1400	93	4	,	,	PUNCT
ap-1400	93	5	point	point	NOUN
ap-1400	93	6	b	b	NUM
ap-1400	93	7	corresponds	correspond	VERB
ap-1400	93	8	to	to	ADP
ap-1400	93	9	the	the	DET
ap-1400	93	10	local	local	ADJ
ap-1400	93	11	maximum	maximum	NOUN
ap-1400	93	12	:	:	PUNCT
ap-1400	93	13	pb	pb	ADP
ap-1400	93	14	=	=	SYM
ap-1400	93	15	2	2	NUM
ap-1400	93	16	+	+	NUM
ap-1400	93	17	c1/(2c2	c1/(2c2	NOUN
ap-1400	93	18	)	)	PUNCT
ap-1400	93	19	with	with	ADP
ap-1400	93	20	m1	m1	PROPN
ap-1400	93	21	=	=	SYM
ap-1400	93	22	0	0	NUM
ap-1400	93	23	,	,	PUNCT
ap-1400	93	24	and	and	CCONJ
ap-1400	93	25	the	the	DET
ap-1400	93	26	absolute	absolute	ADJ
ap-1400	93	27	maximum	maximum	ADJ
ap-1400	93	28	corresponds	correspond	NOUN
ap-1400	93	29	to	to	PART
ap-1400	93	30	point	point	VERB
ap-1400	93	31	c	c	PROPN
ap-1400	93	32	(	(	PUNCT
ap-1400	93	33	not	not	PART
ap-1400	93	34	shown	show	VERB
ap-1400	93	35	)	)	PUNCT
ap-1400	93	36	with	with	ADP
ap-1400	93	37	pc	pc	NOUN
ap-1400	93	38	=	=	PUNCT
ap-1400	94	1	+	+	NOUN
ap-1400	94	2	∞	∞	NUM
ap-1400	94	3	and	and	CCONJ
ap-1400	94	4	m2	m2	PROPN
ap-1400	94	5	=	=	PROPN
ap-1400	94	6	0	0	PROPN
ap-1400	94	7	.	.	PUNCT
ap-1400	95	1	point	point	NOUN
ap-1400	95	2	z	z	NOUN
ap-1400	95	3	corresponds	correspond	NOUN
ap-1400	95	4	to	to	ADP
ap-1400	95	5	ziegler	ziegler	PROPN
ap-1400	95	6	’s	’s	PART
ap-1400	95	7	original	original	ADJ
ap-1400	95	8	design	design	NOUN
ap-1400	95	9	:	:	PUNCT
ap-1400	95	10	m1	m1	NOUN
ap-1400	95	11	/	/	SYM
ap-1400	95	12	m2	m2	PROPN
ap-1400	95	13	=	=	PROPN
ap-1400	95	14	2	2	NUM
ap-1400	95	15	the	the	DET
ap-1400	95	16	case	case	NOUN
ap-1400	95	17	when	when	SCONJ
ap-1400	95	18	c1	c1	PROPN
ap-1400	95	19	=	=	PROPN
ap-1400	95	20	c2	c2	PROPN
ap-1400	95	21	=	=	SYM
ap-1400	95	22	1	1	NUM
ap-1400	95	23	,	,	PUNCT
ap-1400	95	24	m1	m1	PROPN
ap-1400	95	25	=	=	SYM
ap-1400	95	26	2	2	NUM
ap-1400	95	27	and	and	CCONJ
ap-1400	95	28	m2	m2	PROPN
ap-1400	95	29	=	=	SYM
ap-1400	95	30	1	1	NUM
ap-1400	95	31	corresponds	correspond	VERB
ap-1400	95	32	to	to	ADP
ap-1400	95	33	the	the	DET
ap-1400	95	34	classical	classical	ADJ
ap-1400	95	35	result	result	NOUN
ap-1400	95	36	of	of	ADP
ap-1400	95	37	ziegler	ziegler	PROPN
ap-1400	96	1	[	[	X
ap-1400	96	2	26	26	NUM
ap-1400	96	3	]	]	X
ap-1400	96	4	p	p	X
ap-1400	96	5	=	=	NOUN
ap-1400	96	6	7	7	NUM
ap-1400	96	7	2	2	NUM
ap-1400	96	8	±	±	NUM
ap-1400	96	9	√	√	ADV
ap-1400	96	10	2	2	NUM
ap-1400	96	11	.	.	PUNCT
ap-1400	97	1	(	(	PUNCT
ap-1400	97	2	8)	8)	NUM
ap-1400	97	3	the	the	DET
ap-1400	97	4	lower	low	ADJ
ap-1400	97	5	value	value	NOUN
ap-1400	97	6	of	of	ADP
ap-1400	97	7	the	the	DET
ap-1400	97	8	critical	critical	ADJ
ap-1400	97	9	load	load	NOUN
ap-1400	97	10	corresponds	correspond	VERB
ap-1400	97	11	to	to	ADP
ap-1400	97	12	the	the	DET
ap-1400	97	13	boundary	boundary	NOUN
ap-1400	97	14	between	between	ADP
ap-1400	97	15	marginal	marginal	ADJ
ap-1400	97	16	stability	stability	NOUN
ap-1400	97	17	and	and	CCONJ
ap-1400	97	18	flutter	flutter	NOUN
ap-1400	97	19	,	,	PUNCT
ap-1400	97	20	while	while	SCONJ
ap-1400	97	21	the	the	DET
ap-1400	97	22	higher	high	ADJ
ap-1400	97	23	critical	critical	ADJ
ap-1400	97	24	load	load	NOUN
ap-1400	97	25	corresponds	correspond	VERB
ap-1400	97	26	to	to	ADP
ap-1400	97	27	the	the	DET
ap-1400	97	28	conventional	conventional	ADJ
ap-1400	97	29	transition	transition	NOUN
ap-1400	97	30	from	from	ADP
ap-1400	97	31	flutter	flutter	NOUN
ap-1400	97	32	to	to	PART
ap-1400	97	33	divergence	divergence	VERB
ap-1400	97	34	through	through	ADP
ap-1400	97	35	the	the	DET
ap-1400	97	36	double	double	ADJ
ap-1400	97	37	zero	zero	NUM
ap-1400	97	38	eigenvalue	eigenvalue	NOUN
ap-1400	97	39	with	with	ADP
ap-1400	97	40	the	the	DET
ap-1400	97	41	jordan	jordan	PROPN
ap-1400	97	42	block	block	PROPN
ap-1400	97	43	.	.	PUNCT
ap-1400	98	1	the	the	DET
ap-1400	98	2	critical	critical	ADJ
ap-1400	98	3	load	load	NOUN
ap-1400	98	4	(	(	PUNCT
ap-1400	98	5	7	7	NUM
ap-1400	98	6	)	)	PUNCT
ap-1400	98	7	as	as	ADP
ap-1400	98	8	a	a	DET
ap-1400	98	9	function	function	NOUN
ap-1400	98	10	of	of	ADP
ap-1400	98	11	the	the	DET
ap-1400	98	12	masses	masse	NOUN
ap-1400	98	13	p	p	NOUN
ap-1400	98	14	=	=	NOUN
ap-1400	98	15	p(m1	p(m1	NOUN
ap-1400	98	16	,	,	PUNCT
ap-1400	98	17	m2	m2	PROPN
ap-1400	98	18	)	)	PUNCT
ap-1400	98	19	is	be	AUX
ap-1400	98	20	plotted	plot	VERB
ap-1400	98	21	in	in	ADP
ap-1400	98	22	figure	figure	NOUN
ap-1400	98	23	1(b	1(b	NUM
ap-1400	98	24	)	)	PUNCT
ap-1400	98	25	.	.	PUNCT
ap-1400	99	1	it	it	PRON
ap-1400	99	2	is	be	AUX
ap-1400	99	3	seen	see	VERB
ap-1400	99	4	that	that	SCONJ
ap-1400	99	5	the	the	DET
ap-1400	99	6	stability	stability	NOUN
ap-1400	99	7	boundary	boundary	NOUN
ap-1400	99	8	has	have	VERB
ap-1400	99	9	a	a	DET
ap-1400	99	10	self	self	NOUN
ap-1400	99	11	-	-	PUNCT
ap-1400	99	12	intersection	intersection	NOUN
ap-1400	99	13	along	along	ADP
ap-1400	99	14	a	a	DET
ap-1400	99	15	ray	ray	NOUN
ap-1400	99	16	of	of	ADP
ap-1400	99	17	the	the	DET
ap-1400	99	18	p	p	NOUN
ap-1400	99	19	-	-	PUNCT
ap-1400	99	20	axis	axis	NOUN
ap-1400	99	21	that	that	PRON
ap-1400	99	22	starts	start	VERB
ap-1400	99	23	at	at	ADP
ap-1400	99	24	the	the	DET
ap-1400	99	25	whitney	whitney	NOUN
ap-1400	99	26	umbrella	umbrella	NOUN
ap-1400	99	27	singularity	singularity	NOUN
ap-1400	99	28	with	with	ADP
ap-1400	99	29	the	the	DET
ap-1400	99	30	coordinates	coordinate	NOUN
ap-1400	99	31	(	(	PUNCT
ap-1400	99	32	0	0	NUM
ap-1400	99	33	,	,	PUNCT
ap-1400	99	34	0	0	NUM
ap-1400	99	35	,	,	PUNCT
ap-1400	99	36	2	2	NUM
ap-1400	99	37	)	)	PUNCT
ap-1400	99	38	in	in	ADP
ap-1400	99	39	the	the	DET
ap-1400	99	40	(	(	PUNCT
ap-1400	99	41	m1	m1	PROPN
ap-1400	99	42	,	,	PUNCT
ap-1400	99	43	m2	m2	PROPN
ap-1400	99	44	,	,	PUNCT
ap-1400	99	45	p)-space	p)-space	NOUN
ap-1400	99	46	.	.	PUNCT
ap-1400	100	1	indeed	indeed	ADV
ap-1400	100	2	,	,	PUNCT
ap-1400	100	3	for	for	ADP
ap-1400	100	4	small	small	ADJ
ap-1400	100	5	absolute	absolute	ADJ
ap-1400	100	6	values	value	NOUN
ap-1400	100	7	of	of	ADP
ap-1400	100	8	m1c2	m1c2	NOUN
ap-1400	100	9	−m2c1	−m2c1	ADJ
ap-1400	100	10	we	we	PRON
ap-1400	100	11	can	can	AUX
ap-1400	100	12	expand	expand	VERB
ap-1400	100	13	the	the	DET
ap-1400	100	14	critical	critical	ADJ
ap-1400	100	15	load	load	NOUN
ap-1400	100	16	in	in	ADP
ap-1400	100	17	a	a	DET
ap-1400	100	18	series	series	NOUN
ap-1400	100	19	p	p	NOUN
ap-1400	100	20	=	=	PROPN
ap-1400	100	21	2	2	NUM
ap-1400	100	22	+	+	CCONJ
ap-1400	100	23	(	(	PUNCT
ap-1400	100	24	m1c2	m1c2	NOUN
ap-1400	100	25	−	−	NOUN
ap-1400	100	26	m2c1	m2c1	NOUN
ap-1400	100	27	)	)	PUNCT
ap-1400	100	28	2	2	NUM
ap-1400	100	29	8c1c2m22	8c1c2m22	NOUN
ap-1400	100	30	+	+	CCONJ
ap-1400	101	1	o((m1c2	o((m1c2	NOUN
ap-1400	101	2	−	−	NOUN
ap-1400	101	3	m2c1	m2c1	NOUN
ap-1400	101	4	)	)	PUNCT
ap-1400	101	5	3	3	NUM
ap-1400	101	6	)	)	PUNCT
ap-1400	101	7	,	,	PUNCT
ap-1400	101	8	(	(	PUNCT
ap-1400	101	9	9	9	X
ap-1400	101	10	)	)	PUNCT
ap-1400	101	11	which	which	PRON
ap-1400	101	12	gives	give	VERB
ap-1400	101	13	an	an	DET
ap-1400	101	14	approximation	approximation	NOUN
ap-1400	101	15	to	to	ADP
ap-1400	101	16	the	the	DET
ap-1400	101	17	flutter	flutter	NOUN
ap-1400	101	18	boundary	boundary	ADJ
ap-1400	101	19	having	have	VERB
ap-1400	101	20	a	a	DET
ap-1400	101	21	canonical	canonical	ADJ
ap-1400	101	22	form	form	NOUN
ap-1400	101	23	for	for	ADP
ap-1400	101	24	the	the	DET
ap-1400	101	25	whitney	whitney	NOUN
ap-1400	101	26	umbrella	umbrella	NOUN
ap-1400	101	27	z	z	NOUN
ap-1400	101	28	=	=	SYM
ap-1400	101	29	x2	x2	PROPN
ap-1400	101	30	/	/	SYM
ap-1400	101	31	y	y	PROPN
ap-1400	101	32	2	2	NUM
ap-1400	101	33	.	.	PUNCT
ap-1400	101	34	due	due	ADP
ap-1400	101	35	to	to	ADP
ap-1400	101	36	the	the	DET
ap-1400	101	37	symmetry	symmetry	NOUN
ap-1400	101	38	of	of	ADP
ap-1400	101	39	the	the	DET
ap-1400	101	40	expression	expression	NOUN
ap-1400	101	41	(	(	PUNCT
ap-1400	101	42	7	7	NUM
ap-1400	101	43	)	)	PUNCT
ap-1400	101	44	,	,	PUNCT
ap-1400	101	45	the	the	DET
ap-1400	101	46	critical	critical	ADJ
ap-1400	101	47	load	load	NOUN
ap-1400	101	48	as	as	ADP
ap-1400	101	49	a	a	DET
ap-1400	101	50	function	function	NOUN
ap-1400	101	51	of	of	ADP
ap-1400	101	52	the	the	DET
ap-1400	101	53	stiffness	stiffness	ADJ
ap-1400	101	54	coefficients	coefficient	NOUN
ap-1400	101	55	,	,	PUNCT
ap-1400	101	56	p	p	NOUN
ap-1400	101	57	=	=	NOUN
ap-1400	101	58	p(c1	p(c1	PROPN
ap-1400	101	59	,	,	PUNCT
ap-1400	101	60	c2	c2	PROPN
ap-1400	101	61	)	)	PUNCT
ap-1400	101	62	,	,	PUNCT
ap-1400	101	63	forms	form	VERB
ap-1400	101	64	the	the	DET
ap-1400	101	65	identical	identical	ADJ
ap-1400	101	66	surface	surface	NOUN
ap-1400	101	67	in	in	ADP
ap-1400	101	68	the	the	DET
ap-1400	101	69	(	(	PUNCT
ap-1400	101	70	c1	c1	PROPN
ap-1400	101	71	,	,	PUNCT
ap-1400	101	72	c2	c2	PROPN
ap-1400	101	73	,	,	PUNCT
ap-1400	101	74	p)-space	p)-space	NOUN
ap-1400	101	75	.	.	PUNCT
ap-1400	102	1	in	in	ADP
ap-1400	102	2	the	the	DET
ap-1400	102	3	following	following	NOUN
ap-1400	102	4	we	we	PRON
ap-1400	102	5	will	will	AUX
ap-1400	102	6	study	study	VERB
ap-1400	102	7	the	the	DET
ap-1400	102	8	function	function	NOUN
ap-1400	102	9	p	p	NOUN
ap-1400	102	10	=	=	NOUN
ap-1400	102	11	p(m1	p(m1	NOUN
ap-1400	102	12	,	,	PUNCT
ap-1400	102	13	m2	m2	PROPN
ap-1400	102	14	)	)	PUNCT
ap-1400	102	15	.	.	PUNCT
ap-1400	103	1	according	accord	VERB
ap-1400	103	2	to	to	ADP
ap-1400	103	3	inequality	inequality	NOUN
ap-1400	103	4	(	(	PUNCT
ap-1400	103	5	7	7	NUM
ap-1400	103	6	)	)	PUNCT
ap-1400	103	7	,	,	PUNCT
ap-1400	103	8	the	the	DET
ap-1400	103	9	critical	critical	ADJ
ap-1400	103	10	load	load	NOUN
ap-1400	103	11	is	be	AUX
ap-1400	103	12	always	always	ADV
ap-1400	103	13	not	not	PART
ap-1400	103	14	less	less	ADJ
ap-1400	103	15	than	than	ADP
ap-1400	103	16	p0	p0	NOUN
ap-1400	103	17	=	=	SYM
ap-1400	103	18	2	2	X
ap-1400	103	19	.	.	PUNCT
ap-1400	104	1	the	the	DET
ap-1400	104	2	minimum	minimum	NOUN
ap-1400	104	3	is	be	AUX
ap-1400	104	4	reached	reach	VERB
ap-1400	104	5	when	when	SCONJ
ap-1400	104	6	the	the	DET
ap-1400	104	7	masses	masse	NOUN
ap-1400	104	8	satisfy	satisfy	VERB
ap-1400	104	9	the	the	DET
ap-1400	104	10	constraint	constraint	NOUN
ap-1400	104	11	m1c2	m1c2	NOUN
ap-1400	105	1	=	=	SYM
ap-1400	105	2	m2c1	m2c1	X
ap-1400	105	3	.	.	PUNCT
ap-1400	106	1	(	(	PUNCT
ap-1400	106	2	10	10	NUM
ap-1400	106	3	)	)	PUNCT
ap-1400	106	4	note	note	NOUN
ap-1400	106	5	that	that	SCONJ
ap-1400	106	6	the	the	DET
ap-1400	106	7	equal	equal	ADJ
ap-1400	106	8	stiffness	stiffness	NOUN
ap-1400	106	9	coefficients	coefficient	NOUN
ap-1400	106	10	c1	c1	NOUN
ap-1400	106	11	=	=	PROPN
ap-1400	107	1	c2	c2	PROPN
ap-1400	107	2	imply	imply	VERB
ap-1400	107	3	equal	equal	ADJ
ap-1400	107	4	masses	masse	NOUN
ap-1400	107	5	m1	m1	PROPN
ap-1400	107	6	=	=	SYM
ap-1400	107	7	m2	m2	PROPN
ap-1400	107	8	.	.	PUNCT
ap-1400	108	1	this	this	DET
ap-1400	108	2	situation	situation	NOUN
ap-1400	108	3	corresponds	correspond	VERB
ap-1400	108	4	to	to	PART
ap-1400	108	5	uniformly	uniformly	ADV
ap-1400	108	6	distributed	distribute	VERB
ap-1400	108	7	mass	mass	NOUN
ap-1400	108	8	and	and	CCONJ
ap-1400	108	9	stiffness	stiffness	NOUN
ap-1400	108	10	in	in	ADP
ap-1400	108	11	continuous	continuous	ADJ
ap-1400	108	12	systems	system	NOUN
ap-1400	108	13	such	such	ADJ
ap-1400	108	14	as	as	ADP
ap-1400	108	15	the	the	DET
ap-1400	108	16	beck	beck	NOUN
ap-1400	108	17	column	column	NOUN
ap-1400	108	18	[	[	X
ap-1400	108	19	19	19	NUM
ap-1400	108	20	]	]	PUNCT
ap-1400	108	21	.	.	PUNCT
ap-1400	109	1	in	in	ADP
ap-1400	109	2	structural	structural	ADJ
ap-1400	109	3	optimization	optimization	NOUN
ap-1400	109	4	problems	problem	NOUN
ap-1400	109	5	the	the	DET
ap-1400	109	6	uniformly	uniformly	ADV
ap-1400	109	7	distributed	distribute	VERB
ap-1400	109	8	stiffness	stiffness	NOUN
ap-1400	109	9	and	and	CCONJ
ap-1400	109	10	mass	mass	NOUN
ap-1400	109	11	are	be	AUX
ap-1400	109	12	usually	usually	ADV
ap-1400	109	13	considered	consider	VERB
ap-1400	109	14	as	as	ADP
ap-1400	109	15	the	the	DET
ap-1400	109	16	initial	initial	ADJ
ap-1400	109	17	design	design	NOUN
ap-1400	109	18	that	that	PRON
ap-1400	109	19	is	be	AUX
ap-1400	109	20	the	the	DET
ap-1400	109	21	starting	starting	NOUN
ap-1400	109	22	point	point	NOUN
ap-1400	109	23	in	in	ADP
ap-1400	109	24	optimization	optimization	NOUN
ap-1400	109	25	procedures	procedure	NOUN
ap-1400	109	26	.	.	PUNCT
ap-1400	110	1	the	the	DET
ap-1400	110	2	critical	critical	ADJ
ap-1400	110	3	load	load	NOUN
ap-1400	110	4	of	of	ADP
ap-1400	110	5	the	the	DET
ap-1400	110	6	optimized	optimize	VERB
ap-1400	110	7	structure	structure	NOUN
ap-1400	110	8	is	be	AUX
ap-1400	110	9	conventionally	conventionally	ADV
ap-1400	110	10	compared	compare	VERB
ap-1400	110	11	to	to	ADP
ap-1400	110	12	that	that	PRON
ap-1400	110	13	of	of	ADP
ap-1400	110	14	the	the	DET
ap-1400	110	15	same	same	ADJ
ap-1400	110	16	structure	structure	NOUN
ap-1400	110	17	with	with	ADP
ap-1400	110	18	uniform	uniform	ADJ
ap-1400	110	19	mass	mass	NOUN
ap-1400	110	20	and	and	CCONJ
ap-1400	110	21	stiffness	stiffness	ADJ
ap-1400	110	22	distributions	distribution	NOUN
ap-1400	110	23	[	[	X
ap-1400	110	24	4–10,13–18	4–10,13–18	NUM
ap-1400	110	25	]	]	PUNCT
ap-1400	110	26	.	.	PUNCT
ap-1400	111	1	since	since	SCONJ
ap-1400	111	2	p(m1	p(m1	NOUN
ap-1400	111	3	,	,	PUNCT
ap-1400	111	4	m2	m2	PROPN
ap-1400	111	5	)	)	PUNCT
ap-1400	111	6	is	be	AUX
ap-1400	111	7	a	a	DET
ap-1400	111	8	ruled	rule	VERB
ap-1400	111	9	surface	surface	NOUN
ap-1400	111	10	and	and	CCONJ
ap-1400	111	11	thus	thus	ADV
ap-1400	111	12	p	p	NOUN
ap-1400	111	13	effectively	effectively	ADV
ap-1400	111	14	depends	depend	VERB
ap-1400	111	15	on	on	ADP
ap-1400	111	16	the	the	DET
ap-1400	111	17	mass	mass	NOUN
ap-1400	111	18	ratio	ratio	NOUN
ap-1400	111	19	only	only	ADV
ap-1400	111	20	,	,	PUNCT
ap-1400	111	21	it	it	PRON
ap-1400	111	22	is	be	AUX
ap-1400	111	23	convenient	convenient	ADJ
ap-1400	111	24	to	to	PART
ap-1400	111	25	introduce	introduce	VERB
ap-1400	111	26	the	the	DET
ap-1400	111	27	azimuth	azimuth	NOUN
ap-1400	111	28	angle	angle	NOUN
ap-1400	111	29	α	α	INTJ
ap-1400	111	30	by	by	ADP
ap-1400	111	31	assuming	assume	VERB
ap-1400	111	32	m1	m1	PROPN
ap-1400	111	33	=	=	SYM
ap-1400	111	34	cos	cos	ADP
ap-1400	111	35	α	α	PROPN
ap-1400	111	36	and	and	CCONJ
ap-1400	111	37	m2	m2	PROPN
ap-1400	111	38	=	=	PROPN
ap-1400	111	39	sin	sin	NOUN
ap-1400	111	40	α	α	NOUN
ap-1400	111	41	and	and	CCONJ
ap-1400	111	42	to	to	PART
ap-1400	111	43	plot	plot	VERB
ap-1400	111	44	the	the	DET
ap-1400	111	45	critical	critical	ADJ
ap-1400	111	46	load	load	NOUN
ap-1400	111	47	as	as	ADP
ap-1400	111	48	a	a	DET
ap-1400	111	49	function	function	NOUN
ap-1400	111	50	of	of	ADP
ap-1400	111	51	α	α	NOUN
ap-1400	111	52	.	.	PUNCT
ap-1400	112	1	in	in	ADP
ap-1400	112	2	figure	figure	NOUN
ap-1400	112	3	2	2	NUM
ap-1400	112	4	,	,	PUNCT
ap-1400	112	5	the	the	DET
ap-1400	112	6	curves	curve	NOUN
ap-1400	112	7	p	p	X
ap-1400	112	8	=	=	SYM
ap-1400	112	9	p(α	p(α	PROPN
ap-1400	112	10	)	)	PUNCT
ap-1400	112	11	bound	bind	VERB
ap-1400	112	12	the	the	DET
ap-1400	112	13	flutter	flutter	NOUN
ap-1400	112	14	domain	domain	NOUN
ap-1400	112	15	shown	show	VERB
ap-1400	112	16	in	in	ADP
ap-1400	112	17	light	light	ADJ
ap-1400	112	18	gray	gray	ADJ
ap-1400	112	19	.	.	PUNCT
ap-1400	113	1	when	when	SCONJ
ap-1400	113	2	α	α	PROPN
ap-1400	113	3	tends	tend	VERB
ap-1400	113	4	to	to	ADP
ap-1400	113	5	zero	zero	NUM
ap-1400	113	6	,	,	PUNCT
ap-1400	113	7	which	which	PRON
ap-1400	113	8	corresponds	correspond	VERB
ap-1400	113	9	to	to	ADP
ap-1400	113	10	the	the	DET
ap-1400	113	11	vanishing	vanish	VERB
ap-1400	113	12	mass	mass	NOUN
ap-1400	113	13	m2	m2	PROPN
ap-1400	113	14	,	,	PUNCT
ap-1400	113	15	the	the	DET
ap-1400	113	16	critical	critical	ADJ
ap-1400	113	17	load	load	NOUN
ap-1400	113	18	increases	increase	NOUN
ap-1400	113	19	to	to	ADP
ap-1400	113	20	infinity	infinity	NOUN
ap-1400	113	21	.	.	PUNCT
ap-1400	114	1	when	when	SCONJ
ap-1400	114	2	α	α	PROPN
ap-1400	114	3	tends	tend	VERB
ap-1400	114	4	to	to	ADP
ap-1400	114	5	π	π	PROPN
ap-1400	114	6	2	2	NUM
ap-1400	114	7	35	35	NUM
ap-1400	114	8	acta	acta	PROPN
ap-1400	114	9	polytechnica	polytechnica	PROPN
ap-1400	114	10	vol	vol	NOUN
ap-1400	114	11	.	.	PUNCT
ap-1400	115	1	51	51	NUM
ap-1400	115	2	no	no	INTJ
ap-1400	115	3	.	.	PUNCT
ap-1400	116	1	4/2011	4/2011	NUM
ap-1400	116	2	and	and	CCONJ
ap-1400	116	3	,	,	PUNCT
ap-1400	116	4	correspondingly	correspondingly	ADV
ap-1400	116	5	,	,	PUNCT
ap-1400	116	6	mass	mass	ADJ
ap-1400	116	7	m1	m1	PROPN
ap-1400	116	8	is	be	AUX
ap-1400	116	9	vanishing	vanish	VERB
ap-1400	116	10	,	,	PUNCT
ap-1400	116	11	then	then	ADV
ap-1400	116	12	the	the	DET
ap-1400	116	13	critical	critical	ADJ
ap-1400	116	14	flutter	flutter	NOUN
ap-1400	116	15	load	load	NOUN
ap-1400	116	16	increases	increase	NOUN
ap-1400	116	17	to	to	ADP
ap-1400	116	18	the	the	DET
ap-1400	116	19	value	value	NOUN
ap-1400	116	20	pb	pb	ADP
ap-1400	116	21	=	=	SYM
ap-1400	116	22	2	2	NUM
ap-1400	116	23	+	+	CCONJ
ap-1400	116	24	1	1	NUM
ap-1400	116	25	2	2	NUM
ap-1400	116	26	c1	c1	NOUN
ap-1400	116	27	c2	c2	PROPN
ap-1400	116	28	.	.	PUNCT
ap-1400	117	1	(	(	PUNCT
ap-1400	117	2	11	11	NUM
ap-1400	117	3	)	)	PUNCT
ap-1400	117	4	at	at	ADP
ap-1400	117	5	point	point	NOUN
ap-1400	117	6	b	b	PROPN
ap-1400	117	7	in	in	ADP
ap-1400	117	8	the	the	DET
ap-1400	117	9	stability	stability	NOUN
ap-1400	117	10	diagram	diagram	NOUN
ap-1400	117	11	of	of	ADP
ap-1400	117	12	figure	figure	NOUN
ap-1400	117	13	2	2	NUM
ap-1400	117	14	the	the	DET
ap-1400	117	15	flutter	flutter	NOUN
ap-1400	117	16	boundary	boundary	NOUN
ap-1400	117	17	has	have	VERB
ap-1400	117	18	a	a	DET
ap-1400	117	19	vertical	vertical	ADJ
ap-1400	117	20	tangent	tangent	NOUN
ap-1400	117	21	,	,	PUNCT
ap-1400	117	22	which	which	PRON
ap-1400	117	23	is	be	AUX
ap-1400	117	24	a	a	DET
ap-1400	117	25	typical	typical	ADJ
ap-1400	117	26	phenomenon	phenomenon	NOUN
ap-1400	117	27	in	in	ADP
ap-1400	117	28	non	non	ADJ
ap-1400	117	29	-	-	ADJ
ap-1400	117	30	conservative	conservative	ADJ
ap-1400	117	31	optimization	optimization	NOUN
ap-1400	117	32	[	[	X
ap-1400	117	33	27–29	27–29	NUM
ap-1400	117	34	]	]	PUNCT
ap-1400	117	35	.	.	PUNCT
ap-1400	118	1	the	the	DET
ap-1400	118	2	lower	low	ADJ
ap-1400	118	3	part	part	NOUN
ap-1400	118	4	of	of	ADP
ap-1400	118	5	the	the	DET
ap-1400	118	6	flutter	flutter	NOUN
ap-1400	118	7	boundary	boundary	ADJ
ap-1400	118	8	corresponds	correspond	VERB
ap-1400	118	9	to	to	ADP
ap-1400	118	10	designs	design	NOUN
ap-1400	118	11	with	with	ADP
ap-1400	118	12	a	a	DET
ap-1400	118	13	complex	complex	ADJ
ap-1400	118	14	conjugate	conjugate	ADJ
ap-1400	118	15	pair	pair	NOUN
ap-1400	118	16	of	of	ADP
ap-1400	118	17	pure	pure	ADJ
ap-1400	118	18	imaginary	imaginary	ADJ
ap-1400	118	19	double	double	ADJ
ap-1400	118	20	eigenvalues	eigenvalue	NOUN
ap-1400	118	21	with	with	ADP
ap-1400	118	22	the	the	DET
ap-1400	118	23	jordan	jordan	PROPN
ap-1400	118	24	block	block	NOUN
ap-1400	118	25	;	;	PUNCT
ap-1400	118	26	the	the	DET
ap-1400	118	27	upper	upper	ADJ
ap-1400	118	28	part	part	NOUN
ap-1400	118	29	is	be	AUX
ap-1400	118	30	the	the	DET
ap-1400	118	31	designs	design	NOUN
ap-1400	118	32	with	with	ADP
ap-1400	118	33	two	two	NUM
ap-1400	118	34	real	real	ADJ
ap-1400	118	35	double	double	ADJ
ap-1400	118	36	eigenvalues	eigenvalue	NOUN
ap-1400	118	37	of	of	ADP
ap-1400	118	38	the	the	DET
ap-1400	118	39	same	same	ADJ
ap-1400	118	40	magnitude	magnitude	NOUN
ap-1400	118	41	and	and	CCONJ
ap-1400	118	42	different	different	ADJ
ap-1400	118	43	sign	sign	NOUN
ap-1400	118	44	,	,	PUNCT
ap-1400	118	45	each	each	PRON
ap-1400	118	46	with	with	ADP
ap-1400	118	47	the	the	DET
ap-1400	118	48	jordan	jordan	PROPN
ap-1400	118	49	block	block	PROPN
ap-1400	118	50	.	.	PUNCT
ap-1400	119	1	above	above	ADP
ap-1400	119	2	the	the	DET
ap-1400	119	3	upper	upper	ADJ
ap-1400	119	4	flutter	flutter	NOUN
ap-1400	119	5	boundary	boundary	ADJ
ap-1400	119	6	lies	lie	VERB
ap-1400	119	7	the	the	DET
ap-1400	119	8	domain	domain	NOUN
ap-1400	119	9	of	of	ADP
ap-1400	119	10	statical	statical	ADJ
ap-1400	119	11	instability	instability	NOUN
ap-1400	119	12	or	or	CCONJ
ap-1400	119	13	divergence	divergence	NOUN
ap-1400	119	14	,	,	PUNCT
ap-1400	119	15	with	with	ADP
ap-1400	119	16	two	two	NUM
ap-1400	119	17	unstable	unstable	ADJ
ap-1400	119	18	modes	mode	NOUN
ap-1400	119	19	corresponding	correspond	VERB
ap-1400	119	20	to	to	ADP
ap-1400	119	21	two	two	NUM
ap-1400	119	22	different	different	ADJ
ap-1400	119	23	positive	positive	ADJ
ap-1400	119	24	real	real	ADJ
ap-1400	119	25	eigenvalues	eigenvalue	NOUN
ap-1400	119	26	.	.	PUNCT
ap-1400	120	1	at	at	ADP
ap-1400	120	2	point	point	NOUN
ap-1400	120	3	b	b	NOUN
ap-1400	120	4	,	,	PUNCT
ap-1400	120	5	the	the	DET
ap-1400	120	6	flutter	flutter	NOUN
ap-1400	120	7	boundary	boundary	NOUN
ap-1400	120	8	is	be	AUX
ap-1400	120	9	tangent	tangent	NOUN
ap-1400	120	10	to	to	ADP
ap-1400	120	11	the	the	DET
ap-1400	120	12	vertical	vertical	ADJ
ap-1400	120	13	part	part	NOUN
ap-1400	120	14	of	of	ADP
ap-1400	120	15	the	the	DET
ap-1400	120	16	divergence	divergence	NOUN
ap-1400	120	17	boundary	boundary	NOUN
ap-1400	120	18	.	.	PUNCT
ap-1400	121	1	to	to	ADP
ap-1400	121	2	the	the	DET
ap-1400	121	3	right	right	NOUN
ap-1400	121	4	of	of	ADP
ap-1400	121	5	this	this	DET
ap-1400	121	6	vertical	vertical	ADJ
ap-1400	121	7	line	line	NOUN
ap-1400	121	8	,	,	PUNCT
ap-1400	121	9	there	there	PRON
ap-1400	121	10	is	be	VERB
ap-1400	121	11	a	a	DET
ap-1400	121	12	pair	pair	NOUN
ap-1400	121	13	of	of	ADP
ap-1400	121	14	pure	pure	ADJ
ap-1400	121	15	imaginary	imaginary	ADJ
ap-1400	121	16	eigenvalues	eigenvalue	NOUN
ap-1400	121	17	and	and	CCONJ
ap-1400	121	18	a	a	DET
ap-1400	121	19	pair	pair	NOUN
ap-1400	121	20	of	of	ADP
ap-1400	121	21	real	real	ADJ
ap-1400	121	22	eigenvalues	eigenvalue	NOUN
ap-1400	121	23	with	with	ADP
ap-1400	121	24	the	the	DET
ap-1400	121	25	same	same	ADJ
ap-1400	121	26	magnitude	magnitude	NOUN
ap-1400	121	27	and	and	CCONJ
ap-1400	121	28	different	different	ADJ
ap-1400	121	29	signs	sign	NOUN
ap-1400	121	30	.	.	PUNCT
ap-1400	122	1	the	the	DET
ap-1400	122	2	transition	transition	NOUN
ap-1400	122	3	from	from	ADP
ap-1400	122	4	the	the	DET
ap-1400	122	5	stability	stability	NOUN
ap-1400	122	6	boundary	boundary	ADJ
ap-1400	122	7	to	to	ADP
ap-1400	122	8	the	the	DET
ap-1400	122	9	divergence	divergence	NOUN
ap-1400	122	10	boundary	boundary	NOUN
ap-1400	122	11	below	below	ADP
ap-1400	122	12	point	point	NOUN
ap-1400	122	13	b	b	PROPN
ap-1400	122	14	occurs	occur	VERB
ap-1400	122	15	when	when	SCONJ
ap-1400	122	16	a	a	DET
ap-1400	122	17	pair	pair	NOUN
ap-1400	122	18	of	of	ADP
ap-1400	122	19	pure	pure	ADJ
ap-1400	122	20	imaginary	imaginary	ADJ
ap-1400	122	21	eigenvalues	eigenvalue	NOUN
ap-1400	122	22	goes	go	VERB
ap-1400	122	23	out	out	ADP
ap-1400	122	24	of	of	ADP
ap-1400	122	25	the	the	DET
ap-1400	122	26	origin	origin	NOUN
ap-1400	122	27	in	in	ADP
ap-1400	122	28	the	the	DET
ap-1400	122	29	complex	complex	ADJ
ap-1400	122	30	plane	plane	NOUN
ap-1400	122	31	to	to	ADP
ap-1400	122	32	infinity	infinity	NOUN
ap-1400	122	33	,	,	PUNCT
ap-1400	122	34	merges	merge	VERB
ap-1400	122	35	there	there	ADV
ap-1400	122	36	and	and	CCONJ
ap-1400	122	37	returns	return	VERB
ap-1400	122	38	back	back	ADV
ap-1400	122	39	along	along	ADP
ap-1400	122	40	the	the	DET
ap-1400	122	41	real	real	ADJ
ap-1400	122	42	axis	axis	NOUN
ap-1400	122	43	.	.	PUNCT
ap-1400	123	1	this	this	PRON
ap-1400	123	2	happens	happen	VERB
ap-1400	123	3	because	because	SCONJ
ap-1400	123	4	at	at	ADP
ap-1400	123	5	the	the	DET
ap-1400	123	6	boundary	boundary	ADJ
ap-1400	123	7	m1	m1	PROPN
ap-1400	123	8	=	=	SYM
ap-1400	123	9	0	0	NUM
ap-1400	123	10	,	,	PUNCT
ap-1400	123	11	i.e.	i.e.	X
ap-1400	123	12	detm	detm	NOUN
ap-1400	123	13	=	=	SYM
ap-1400	123	14	0	0	X
ap-1400	123	15	.	.	PUNCT
ap-1400	124	1	a	a	DET
ap-1400	124	2	similar	similar	ADJ
ap-1400	124	3	divergence	divergence	NOUN
ap-1400	124	4	boundary	boundary	NOUN
ap-1400	124	5	exists	exist	VERB
ap-1400	124	6	at	at	ADP
ap-1400	124	7	α	α	NOUN
ap-1400	124	8	=	=	SYM
ap-1400	124	9	0	0	PROPN
ap-1400	124	10	,	,	PUNCT
ap-1400	124	11	which	which	PRON
ap-1400	124	12	corresponds	correspond	VERB
ap-1400	124	13	to	to	ADP
ap-1400	124	14	m2	m2	PROPN
ap-1400	124	15	=	=	SYM
ap-1400	124	16	0	0	PROPN
ap-1400	124	17	.	.	PUNCT
ap-1400	124	18	transition	transition	NOUN
ap-1400	124	19	through	through	ADP
ap-1400	124	20	the	the	DET
ap-1400	124	21	vertical	vertical	ADJ
ap-1400	124	22	line	line	NOUN
ap-1400	124	23	above	above	ADP
ap-1400	124	24	point	point	NOUN
ap-1400	124	25	b	b	PROPN
ap-1400	124	26	is	be	AUX
ap-1400	124	27	accompanied	accompany	VERB
ap-1400	124	28	by	by	ADP
ap-1400	124	29	another	another	DET
ap-1400	124	30	eigenvalue	eigenvalue	NOUN
ap-1400	124	31	bifurcation	bifurcation	NOUN
ap-1400	124	32	at	at	ADP
ap-1400	124	33	infinity	infinity	NOUN
ap-1400	124	34	:	:	PUNCT
ap-1400	124	35	two	two	NUM
ap-1400	124	36	real	real	ADJ
ap-1400	124	37	eigenvalues	eigenvalue	NOUN
ap-1400	124	38	of	of	ADP
ap-1400	124	39	the	the	DET
ap-1400	124	40	same	same	ADJ
ap-1400	124	41	magnitude	magnitude	NOUN
ap-1400	124	42	and	and	CCONJ
ap-1400	124	43	different	different	ADJ
ap-1400	124	44	signs	sign	NOUN
ap-1400	124	45	go	go	VERB
ap-1400	124	46	out	out	ADP
ap-1400	124	47	of	of	ADP
ap-1400	124	48	the	the	DET
ap-1400	124	49	origin	origin	NOUN
ap-1400	124	50	in	in	ADP
ap-1400	124	51	the	the	DET
ap-1400	124	52	complex	complex	ADJ
ap-1400	124	53	plane	plane	NOUN
ap-1400	124	54	in	in	ADP
ap-1400	124	55	order	order	NOUN
ap-1400	124	56	to	to	PART
ap-1400	124	57	merge	merge	VERB
ap-1400	124	58	at	at	ADP
ap-1400	124	59	infinity	infinity	NOUN
ap-1400	124	60	and	and	CCONJ
ap-1400	124	61	then	then	ADV
ap-1400	124	62	come	come	VERB
ap-1400	124	63	back	back	ADV
ap-1400	124	64	along	along	ADP
ap-1400	124	65	the	the	DET
ap-1400	124	66	imaginary	imaginary	ADJ
ap-1400	124	67	axis	axis	NOUN
ap-1400	124	68	.	.	PUNCT
ap-1400	125	1	the	the	DET
ap-1400	125	2	very	very	ADJ
ap-1400	125	3	point	point	NOUN
ap-1400	125	4	b	b	NOUN
ap-1400	125	5	corresponds	correspond	VERB
ap-1400	125	6	to	to	ADP
ap-1400	125	7	an	an	DET
ap-1400	125	8	antagonist	antagonist	NOUN
ap-1400	125	9	of	of	ADP
ap-1400	125	10	a	a	DET
ap-1400	125	11	quadruple	quadruple	NOUN
ap-1400	125	12	zero	zero	NUM
ap-1400	125	13	eigenvalue	eigenvalue	NOUN
ap-1400	125	14	with	with	ADP
ap-1400	125	15	the	the	DET
ap-1400	125	16	jordan	jordan	PROPN
ap-1400	125	17	block	block	PROPN
ap-1400	125	18	,	,	PUNCT
ap-1400	125	19	i.e.	i.e.	X
ap-1400	125	20	to	to	ADP
ap-1400	125	21	a	a	DET
ap-1400	125	22	quadruplet	quadruplet	NOUN
ap-1400	125	23	of	of	ADP
ap-1400	125	24	complex	complex	ADJ
ap-1400	125	25	eigenvalues	eigenvalue	NOUN
ap-1400	125	26	that	that	PRON
ap-1400	125	27	merge	merge	VERB
ap-1400	125	28	at	at	ADP
ap-1400	125	29	infinity	infinity	NOUN
ap-1400	125	30	in	in	ADP
ap-1400	125	31	the	the	DET
ap-1400	125	32	complex	complex	ADJ
ap-1400	125	33	plane	plane	NOUN
ap-1400	125	34	.	.	PUNCT
ap-1400	126	1	to	to	PART
ap-1400	126	2	summarize	summarize	VERB
ap-1400	126	3	,	,	PUNCT
ap-1400	126	4	the	the	DET
ap-1400	126	5	popular	popular	ADJ
ap-1400	126	6	initial	initial	ADJ
ap-1400	126	7	design	design	NOUN
ap-1400	126	8	corresponding	correspond	VERB
ap-1400	126	9	to	to	PART
ap-1400	126	10	uniformly	uniformly	ADV
ap-1400	126	11	distributed	distribute	VERB
ap-1400	126	12	mass	mass	NOUN
ap-1400	126	13	and	and	CCONJ
ap-1400	126	14	stiffness	stiffness	NOUN
ap-1400	126	15	turns	turn	VERB
ap-1400	126	16	out	out	ADP
ap-1400	126	17	to	to	PART
ap-1400	126	18	give	give	VERB
ap-1400	126	19	an	an	DET
ap-1400	126	20	absolute	absolute	ADJ
ap-1400	126	21	minimum	minimum	NOUN
ap-1400	126	22	to	to	ADP
ap-1400	126	23	the	the	DET
ap-1400	126	24	critical	critical	ADJ
ap-1400	126	25	flutter	flutter	NOUN
ap-1400	126	26	load	load	NOUN
ap-1400	126	27	of	of	ADP
ap-1400	126	28	the	the	DET
ap-1400	126	29	ziegler	ziegler	PROPN
ap-1400	126	30	pendulum	pendulum	NOUN
ap-1400	126	31	.	.	PUNCT
ap-1400	127	1	the	the	DET
ap-1400	127	2	critical	critical	ADJ
ap-1400	127	3	flutter	flutter	NOUN
ap-1400	127	4	load	load	NOUN
ap-1400	127	5	attains	attain	VERB
ap-1400	127	6	its	its	PRON
ap-1400	127	7	local	local	ADJ
ap-1400	127	8	maximum	maximum	NOUN
ap-1400	127	9	,	,	PUNCT
ap-1400	127	10	pb	pb	ADV
ap-1400	127	11	,	,	PUNCT
ap-1400	127	12	for	for	ADP
ap-1400	127	13	m1	m1	NOUN
ap-1400	127	14	=	=	SYM
ap-1400	127	15	0	0	NUM
ap-1400	128	1	at	at	ADP
ap-1400	128	2	the	the	DET
ap-1400	128	3	singular	singular	ADJ
ap-1400	128	4	cuspidal	cuspidal	NOUN
ap-1400	128	5	point	point	PROPN
ap-1400	128	6	b	b	PROPN
ap-1400	128	7	of	of	ADP
ap-1400	128	8	the	the	DET
ap-1400	128	9	stability	stability	NOUN
ap-1400	128	10	boundary	boundary	ADJ
ap-1400	128	11	where	where	SCONJ
ap-1400	128	12	the	the	DET
ap-1400	128	13	flutter	flutter	NOUN
ap-1400	128	14	domain	domain	NOUN
ap-1400	128	15	has	have	VERB
ap-1400	128	16	a	a	DET
ap-1400	128	17	vertical	vertical	ADJ
ap-1400	128	18	tangent	tangent	NOUN
ap-1400	128	19	and	and	CCONJ
ap-1400	128	20	touches	touch	VERB
ap-1400	128	21	the	the	DET
ap-1400	128	22	boundary	boundary	NOUN
ap-1400	128	23	of	of	ADP
ap-1400	128	24	the	the	DET
ap-1400	128	25	divergence	divergence	NOUN
ap-1400	128	26	domain	domain	NOUN
ap-1400	128	27	.	.	PUNCT
ap-1400	129	1	note	note	VERB
ap-1400	129	2	that	that	SCONJ
ap-1400	129	3	in	in	ADP
ap-1400	129	4	[	[	X
ap-1400	129	5	11	11	NUM
ap-1400	129	6	]	]	PUNCT
ap-1400	129	7	a	a	DET
ap-1400	129	8	local	local	ADJ
ap-1400	129	9	extremum	extremum	NOUN
ap-1400	129	10	of	of	ADP
ap-1400	129	11	the	the	DET
ap-1400	129	12	flutter	flutter	NOUN
ap-1400	129	13	load	load	NOUN
ap-1400	129	14	for	for	ADP
ap-1400	129	15	the	the	DET
ap-1400	129	16	free	free	ADJ
ap-1400	129	17	-	-	PUNCT
ap-1400	129	18	free	free	ADJ
ap-1400	129	19	beam	beam	NOUN
ap-1400	129	20	carrying	carry	VERB
ap-1400	129	21	a	a	DET
ap-1400	129	22	point	point	NOUN
ap-1400	129	23	mass	mass	NOUN
ap-1400	129	24	was	be	AUX
ap-1400	129	25	also	also	ADV
ap-1400	129	26	found	find	VERB
ap-1400	129	27	to	to	PART
ap-1400	129	28	be	be	AUX
ap-1400	129	29	at	at	ADP
ap-1400	129	30	the	the	DET
ap-1400	129	31	cuspidal	cuspidal	ADJ
ap-1400	129	32	point	point	NOUN
ap-1400	129	33	on	on	ADP
ap-1400	129	34	the	the	DET
ap-1400	129	35	flutter	flutter	NOUN
ap-1400	129	36	boundary	boundary	NOUN
ap-1400	129	37	.	.	PUNCT
ap-1400	130	1	the	the	DET
ap-1400	130	2	global	global	ADJ
ap-1400	130	3	maximum	maximum	NOUN
ap-1400	130	4	of	of	ADP
ap-1400	130	5	the	the	DET
ap-1400	130	6	critical	critical	ADJ
ap-1400	130	7	flutter	flutter	NOUN
ap-1400	130	8	load	load	NOUN
ap-1400	130	9	for	for	ADP
ap-1400	130	10	the	the	DET
ap-1400	130	11	undamped	undampe	VERB
ap-1400	130	12	ziegler	ziegler	PROPN
ap-1400	130	13	pendulum	pendulum	NOUN
ap-1400	130	14	is	be	AUX
ap-1400	130	15	at	at	ADP
ap-1400	130	16	infinity	infinity	NOUN
ap-1400	130	17	when	when	SCONJ
ap-1400	130	18	m2	m2	PROPN
ap-1400	130	19	=	=	PROPN
ap-1400	130	20	0	0	PROPN
ap-1400	130	21	.	.	PUNCT
ap-1400	131	1	the	the	DET
ap-1400	131	2	global	global	ADJ
ap-1400	131	3	maximum	maximum	ADJ
ap-1400	131	4	corresponds	correspond	NOUN
ap-1400	131	5	to	to	ADP
ap-1400	131	6	a	a	DET
ap-1400	131	7	vanishing	vanish	VERB
ap-1400	131	8	mass	mass	NOUN
ap-1400	131	9	at	at	ADP
ap-1400	131	10	the	the	DET
ap-1400	131	11	free	free	ADJ
ap-1400	131	12	end	end	NOUN
ap-1400	131	13	of	of	ADP
ap-1400	131	14	the	the	DET
ap-1400	131	15	column	column	NOUN
ap-1400	131	16	,	,	PUNCT
ap-1400	131	17	which	which	PRON
ap-1400	131	18	is	be	AUX
ap-1400	131	19	qualitatively	qualitatively	ADV
ap-1400	131	20	in	in	ADP
ap-1400	131	21	agreement	agreement	NOUN
ap-1400	131	22	with	with	ADP
ap-1400	131	23	the	the	DET
ap-1400	131	24	numerically	numerically	ADV
ap-1400	131	25	found	find	VERB
ap-1400	131	26	optimized	optimize	VERB
ap-1400	131	27	designs	design	NOUN
ap-1400	131	28	of	of	ADP
ap-1400	131	29	the	the	DET
ap-1400	131	30	beck	beck	NOUN
ap-1400	131	31	column	column	NOUN
ap-1400	131	32	available	available	ADJ
ap-1400	131	33	in	in	ADP
ap-1400	131	34	the	the	DET
ap-1400	131	35	literature	literature	NOUN
ap-1400	131	36	[	[	X
ap-1400	131	37	9,13–18	9,13–18	X
ap-1400	131	38	]	]	PUNCT
ap-1400	131	39	.	.	PUNCT
ap-1400	132	1	indeed	indeed	ADV
ap-1400	132	2	,	,	PUNCT
ap-1400	132	3	all	all	DET
ap-1400	132	4	known	know	VERB
ap-1400	132	5	optimized	optimize	VERB
ap-1400	132	6	designs	design	NOUN
ap-1400	132	7	of	of	ADP
ap-1400	132	8	the	the	DET
ap-1400	132	9	beck	beck	NOUN
ap-1400	132	10	column	column	NOUN
ap-1400	132	11	are	be	AUX
ap-1400	132	12	characterized	characterize	VERB
ap-1400	132	13	by	by	ADP
ap-1400	132	14	the	the	DET
ap-1400	132	15	vanishing	vanish	VERB
ap-1400	132	16	cross	cross	NOUN
ap-1400	132	17	-	-	NOUN
ap-1400	132	18	sections	section	NOUN
ap-1400	132	19	at	at	ADP
ap-1400	132	20	the	the	DET
ap-1400	132	21	free	free	ADJ
ap-1400	132	22	end	end	NOUN
ap-1400	132	23	.	.	PUNCT
ap-1400	133	1	moreover	moreover	ADV
ap-1400	133	2	,	,	PUNCT
ap-1400	133	3	the	the	DET
ap-1400	133	4	gradients	gradient	NOUN
ap-1400	133	5	of	of	ADP
ap-1400	133	6	the	the	DET
ap-1400	133	7	critical	critical	ADJ
ap-1400	133	8	flutter	flutter	NOUN
ap-1400	133	9	load	load	NOUN
ap-1400	133	10	with	with	ADP
ap-1400	133	11	respect	respect	NOUN
ap-1400	133	12	to	to	ADP
ap-1400	133	13	the	the	DET
ap-1400	133	14	mass	mass	ADJ
ap-1400	133	15	or	or	CCONJ
ap-1400	133	16	stiffness	stiffness	ADJ
ap-1400	133	17	distribution	distribution	NOUN
ap-1400	133	18	of	of	ADP
ap-1400	133	19	the	the	DET
ap-1400	133	20	beck	beck	NOUN
ap-1400	133	21	column	column	NOUN
ap-1400	133	22	are	be	AUX
ap-1400	133	23	large	large	ADJ
ap-1400	133	24	,	,	PUNCT
ap-1400	133	25	which	which	PRON
ap-1400	133	26	is	be	AUX
ap-1400	133	27	,	,	PUNCT
ap-1400	133	28	again	again	ADV
ap-1400	133	29	,	,	PUNCT
ap-1400	133	30	in	in	ADP
ap-1400	133	31	qualitative	qualitative	ADJ
ap-1400	133	32	agreement	agreement	NOUN
ap-1400	133	33	with	with	ADP
ap-1400	133	34	our	our	PRON
ap-1400	133	35	stability	stability	NOUN
ap-1400	133	36	diagram	diagram	NOUN
ap-1400	133	37	of	of	ADP
ap-1400	133	38	figure	figure	NOUN
ap-1400	133	39	2	2	NUM
ap-1400	133	40	.	.	PUNCT
ap-1400	133	41	most	most	ADV
ap-1400	133	42	interestingly	interestingly	ADV
ap-1400	133	43	,	,	PUNCT
ap-1400	133	44	with	with	SCONJ
ap-1400	133	45	the	the	DET
ap-1400	133	46	increase	increase	NOUN
ap-1400	133	47	in	in	ADP
ap-1400	133	48	the	the	DET
ap-1400	133	49	critical	critical	ADJ
ap-1400	133	50	flutter	flutter	NOUN
ap-1400	133	51	load	load	VERB
ap-1400	133	52	the	the	DET
ap-1400	133	53	higher	high	ADJ
ap-1400	133	54	and	and	CCONJ
ap-1400	133	55	higher	high	ADJ
ap-1400	133	56	modes	mode	NOUN
ap-1400	133	57	were	be	AUX
ap-1400	133	58	reported	report	VERB
ap-1400	133	59	to	to	PART
ap-1400	133	60	be	be	AUX
ap-1400	133	61	involved	involve	VERB
ap-1400	133	62	into	into	ADP
ap-1400	133	63	the	the	DET
ap-1400	133	64	coupling	coupling	NOUN
ap-1400	133	65	,	,	PUNCT
ap-1400	133	66	which	which	PRON
ap-1400	133	67	indicates	indicate	VERB
ap-1400	133	68	the	the	DET
ap-1400	133	69	onset	onset	NOUN
ap-1400	133	70	of	of	ADP
ap-1400	133	71	flutter	flutter	NOUN
ap-1400	133	72	[	[	X
ap-1400	133	73	9	9	NUM
ap-1400	133	74	,	,	PUNCT
ap-1400	133	75	13–18	13–18	NUM
ap-1400	133	76	]	]	PUNCT
ap-1400	133	77	.	.	PUNCT
ap-1400	134	1	our	our	PRON
ap-1400	134	2	simple	simple	ADJ
ap-1400	134	3	model	model	NOUN
ap-1400	134	4	shows	show	VERB
ap-1400	134	5	that	that	SCONJ
ap-1400	134	6	this	this	DET
ap-1400	134	7	phenomenon	phenomenon	NOUN
ap-1400	134	8	seems	seem	VERB
ap-1400	134	9	to	to	PART
ap-1400	134	10	be	be	AUX
ap-1400	134	11	natural	natural	ADJ
ap-1400	134	12	for	for	ADP
ap-1400	134	13	the	the	DET
ap-1400	134	14	optimal	optimal	ADJ
ap-1400	134	15	design	design	NOUN
ap-1400	134	16	that	that	PRON
ap-1400	134	17	causes	cause	VERB
ap-1400	134	18	the	the	DET
ap-1400	134	19	degeneracy	degeneracy	NOUN
ap-1400	134	20	in	in	ADP
ap-1400	134	21	the	the	DET
ap-1400	134	22	mass	mass	ADJ
ap-1400	134	23	matrix	matrix	NOUN
ap-1400	134	24	that	that	PRON
ap-1400	134	25	gives	give	VERB
ap-1400	134	26	rise	rise	NOUN
ap-1400	134	27	to	to	ADP
ap-1400	134	28	the	the	DET
ap-1400	134	29	critical	critical	ADJ
ap-1400	134	30	frequency	frequency	NOUN
ap-1400	134	31	that	that	PRON
ap-1400	134	32	increases	increase	VERB
ap-1400	134	33	without	without	ADP
ap-1400	134	34	bounds	bound	NOUN
ap-1400	134	35	.	.	PUNCT
ap-1400	135	1	2.2	2.2	NUM
ap-1400	135	2	the	the	DET
ap-1400	135	3	m	m	NOUN
ap-1400	135	4	-	-	PUNCT
ap-1400	135	5	link	link	ADJ
ap-1400	135	6	ziegler	ziegler	NOUN
ap-1400	135	7	pendulum	pendulum	NOUN
ap-1400	135	8	it	it	PRON
ap-1400	135	9	would	would	AUX
ap-1400	135	10	be	be	AUX
ap-1400	135	11	very	very	ADV
ap-1400	135	12	desirable	desirable	ADJ
ap-1400	135	13	to	to	PART
ap-1400	135	14	extend	extend	VERB
ap-1400	135	15	our	our	PRON
ap-1400	135	16	study	study	NOUN
ap-1400	135	17	to	to	ADP
ap-1400	135	18	the	the	DET
ap-1400	135	19	case	case	NOUN
ap-1400	135	20	of	of	ADP
ap-1400	135	21	the	the	DET
ap-1400	135	22	multiple	multiple	ADJ
ap-1400	135	23	-	-	PUNCT
ap-1400	135	24	degrees	degree	NOUN
ap-1400	135	25	-	-	PUNCT
ap-1400	135	26	of	of	ADP
ap-1400	135	27	-	-	PUNCT
ap-1400	135	28	freedom	freedom	NOUN
ap-1400	135	29	ziegler	ziegler	NOUN
ap-1400	135	30	pendulum	pendulum	PROPN
ap-1400	135	31	.	.	PUNCT
ap-1400	136	1	the	the	DET
ap-1400	136	2	corresponding	correspond	VERB
ap-1400	136	3	models	model	NOUN
ap-1400	136	4	and	and	CCONJ
ap-1400	136	5	recursive	recursive	ADJ
ap-1400	136	6	schemes	scheme	NOUN
ap-1400	136	7	for	for	ADP
ap-1400	136	8	deriving	derive	VERB
ap-1400	136	9	the	the	DET
ap-1400	136	10	equations	equation	NOUN
ap-1400	136	11	of	of	ADP
ap-1400	136	12	motion	motion	NOUN
ap-1400	136	13	were	be	AUX
ap-1400	136	14	proposed	propose	VERB
ap-1400	136	15	by	by	ADP
ap-1400	136	16	gasparini	gasparini	NOUN
ap-1400	136	17	et	et	PROPN
ap-1400	136	18	al	al	PROPN
ap-1400	136	19	.	.	PUNCT
ap-1400	137	1	[	[	X
ap-1400	137	2	23	23	NUM
ap-1400	137	3	]	]	PUNCT
ap-1400	137	4	and	and	CCONJ
ap-1400	137	5	by	by	ADP
ap-1400	137	6	lobas	lobas	PROPN
ap-1400	138	1	[	[	X
ap-1400	138	2	25	25	NUM
ap-1400	138	3	]	]	PUNCT
ap-1400	138	4	.	.	PUNCT
ap-1400	139	1	a	a	DET
ap-1400	139	2	three	three	NUM
ap-1400	139	3	-	-	PUNCT
ap-1400	139	4	link	link	NOUN
ap-1400	139	5	ziegler	ziegler	NOUN
ap-1400	139	6	pendulum	pendulum	NOUN
ap-1400	139	7	was	be	AUX
ap-1400	139	8	considered	consider	VERB
ap-1400	139	9	by	by	ADP
ap-1400	139	10	gallina	gallina	PROPN
ap-1400	139	11	[	[	X
ap-1400	139	12	24	24	NUM
ap-1400	139	13	]	]	PUNCT
ap-1400	139	14	.	.	PUNCT
ap-1400	140	1	we	we	PRON
ap-1400	140	2	take	take	VERB
ap-1400	140	3	the	the	DET
ap-1400	140	4	linearized	linearize	VERB
ap-1400	140	5	equations	equation	NOUN
ap-1400	140	6	of	of	ADP
ap-1400	140	7	lobas	lobas	PROPN
ap-1400	141	1	[	[	X
ap-1400	141	2	25	25	NUM
ap-1400	141	3	]	]	PUNCT
ap-1400	141	4	,	,	PUNCT
ap-1400	141	5	since	since	SCONJ
ap-1400	141	6	their	their	PRON
ap-1400	141	7	model	model	NOUN
ap-1400	141	8	deals	deal	VERB
ap-1400	141	9	with	with	ADP
ap-1400	141	10	the	the	DET
ap-1400	141	11	arbitrary	arbitrary	ADJ
ap-1400	141	12	masses	masse	NOUN
ap-1400	141	13	and	and	CCONJ
ap-1400	141	14	stiffnesses	stiffness	NOUN
ap-1400	141	15	in	in	ADP
ap-1400	141	16	the	the	DET
ap-1400	141	17	joints	joint	NOUN
ap-1400	141	18	of	of	ADP
ap-1400	141	19	an	an	DET
ap-1400	141	20	m	m	NOUN
ap-1400	141	21	-	-	PUNCT
ap-1400	141	22	link	link	ADJ
ap-1400	141	23	ziegler	ziegler	NOUN
ap-1400	141	24	pendulum	pendulum	NOUN
ap-1400	141	25	,	,	PUNCT
ap-1400	141	26	in	in	ADP
ap-1400	141	27	contrast	contrast	NOUN
ap-1400	141	28	to	to	ADP
ap-1400	141	29	the	the	DET
ap-1400	141	30	models	model	NOUN
ap-1400	141	31	of	of	ADP
ap-1400	141	32	gasparini	gasparini	NOUN
ap-1400	141	33	and	and	CCONJ
ap-1400	141	34	gallina	gallina	NOUN
ap-1400	142	1	[	[	X
ap-1400	142	2	23,24	23,24	ADP
ap-1400	142	3	]	]	PUNCT
ap-1400	142	4	.	.	PUNCT
ap-1400	143	1	the	the	DET
ap-1400	143	2	mass	mass	ADJ
ap-1400	143	3	and	and	CCONJ
ap-1400	143	4	stiffness	stiffness	ADJ
ap-1400	143	5	matrices	matrix	NOUN
ap-1400	143	6	of	of	ADP
ap-1400	143	7	the	the	DET
ap-1400	143	8	ziegler	ziegler	PROPN
ap-1400	143	9	-	-	PUNCT
ap-1400	143	10	lobas	lobas	PROPN
ap-1400	143	11	model	model	NOUN
ap-1400	143	12	look	look	VERB
ap-1400	143	13	like	like	ADP
ap-1400	143	14	m	m	NOUN
ap-1400	143	15	=	=	VERB
ap-1400	143	16	l2	l2	NOUN
ap-1400	143	17	⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝	⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝	NOUN
ap-1400	143	18	m∑	m∑	AUX
ap-1400	143	19	i=1	i=1	PROPN
ap-1400	143	20	mi	mi	PROPN
ap-1400	143	21	m∑	m∑	PROPN
ap-1400	143	22	i=2	i=2	PROPN
ap-1400	143	23	mi	mi	PROPN
ap-1400	143	24	·	·	PUNCT
ap-1400	143	25	·	·	PUNCT
ap-1400	143	26	·	·	PUNCT
ap-1400	144	1	m∑	m∑	INTJ
ap-1400	145	1	i	i	PRON
ap-1400	145	2	=	=	PROPN
ap-1400	145	3	m−1	m−1	PROPN
ap-1400	145	4	mi	mi	PROPN
ap-1400	145	5	m∑	m∑	PROPN
ap-1400	145	6	i	i	PROPN
ap-1400	145	7	=	=	PROPN
ap-1400	145	8	m	m	VERB
ap-1400	145	9	mi	mi	PROPN
ap-1400	145	10	m∑	m∑	PROPN
ap-1400	145	11	i=2	i=2	PROPN
ap-1400	145	12	mi	mi	PROPN
ap-1400	145	13	m∑	m∑	PROPN
ap-1400	145	14	i=2	i=2	PROPN
ap-1400	145	15	mi	mi	PROPN
ap-1400	145	16	·	·	PUNCT
ap-1400	145	17	·	·	PUNCT
ap-1400	145	18	·	·	PUNCT
ap-1400	145	19	m∑	m∑	INTJ
ap-1400	146	1	i	i	PRON
ap-1400	146	2	=	=	PROPN
ap-1400	146	3	m−1	m−1	PROPN
ap-1400	146	4	mi	mi	PROPN
ap-1400	146	5	m∑	m∑	PROPN
ap-1400	146	6	i	i	PROPN
ap-1400	146	7	=	=	PROPN
ap-1400	146	8	m	m	PROPN
ap-1400	146	9	mi	mi	X
ap-1400	146	10	·	·	PUNCT
ap-1400	146	11	·	·	PUNCT
ap-1400	146	12	·	·	PUNCT
ap-1400	146	13	·	·	PUNCT
ap-1400	146	14	·	·	PUNCT
ap-1400	146	15	·	·	PUNCT
ap-1400	146	16	·	·	PUNCT
ap-1400	146	17	·	·	PUNCT
ap-1400	146	18	·	·	PUNCT
ap-1400	146	19	·	·	PUNCT
ap-1400	146	20	·	·	PUNCT
ap-1400	146	21	·	·	PUNCT
ap-1400	146	22	·	·	PUNCT
ap-1400	146	23	·	·	PUNCT
ap-1400	146	24	·	·	PUNCT
ap-1400	146	25	m∑	m∑	INTJ
ap-1400	147	1	i	i	PRON
ap-1400	147	2	=	=	PROPN
ap-1400	147	3	m−1	m−1	PROPN
ap-1400	147	4	mi	mi	PROPN
ap-1400	147	5	m∑	m∑	PROPN
ap-1400	147	6	i	i	PROPN
ap-1400	147	7	=	=	PROPN
ap-1400	147	8	m−1	m−1	PROPN
ap-1400	147	9	mi	mi	PROPN
ap-1400	147	10	·	·	PUNCT
ap-1400	147	11	·	·	PUNCT
ap-1400	147	12	·	·	PUNCT
ap-1400	147	13	m∑	m∑	INTJ
ap-1400	148	1	i	i	PRON
ap-1400	148	2	=	=	PROPN
ap-1400	148	3	m−1	m−1	PROPN
ap-1400	148	4	mi	mi	PROPN
ap-1400	148	5	m∑	m∑	PROPN
ap-1400	148	6	i	i	PROPN
ap-1400	148	7	=	=	PROPN
ap-1400	148	8	m	m	VERB
ap-1400	148	9	mi	mi	PROPN
ap-1400	148	10	m∑	m∑	PROPN
ap-1400	148	11	i	i	PROPN
ap-1400	148	12	=	=	PROPN
ap-1400	148	13	m	m	VERB
ap-1400	148	14	mi	mi	PROPN
ap-1400	148	15	m∑	m∑	PROPN
ap-1400	148	16	i	i	PROPN
ap-1400	148	17	=	=	PROPN
ap-1400	148	18	m	m	PROPN
ap-1400	148	19	mi	mi	X
ap-1400	148	20	·	·	PUNCT
ap-1400	148	21	·	·	PUNCT
ap-1400	148	22	·	·	PUNCT
ap-1400	148	23	m∑	m∑	INTJ
ap-1400	148	24	i	i	PRON
ap-1400	148	25	=	=	PROPN
ap-1400	148	26	m	m	VERB
ap-1400	148	27	mi	mi	PROPN
ap-1400	148	28	m∑	m∑	PROPN
ap-1400	148	29	i	i	PROPN
ap-1400	148	30	=	=	PROPN
ap-1400	148	31	m	m	PROPN
ap-1400	148	32	mi	mi	PROPN
ap-1400	148	33	⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠	⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠	PROPN
ap-1400	148	34	,	,	PUNCT
ap-1400	148	35	(	(	PUNCT
ap-1400	148	36	12	12	NUM
ap-1400	148	37	)	)	PUNCT
ap-1400	148	38	36	36	NUM
ap-1400	148	39	acta	acta	PROPN
ap-1400	148	40	polytechnica	polytechnica	PROPN
ap-1400	148	41	vol	vol	NOUN
ap-1400	148	42	.	.	PUNCT
ap-1400	149	1	51	51	NUM
ap-1400	149	2	no	no	NOUN
ap-1400	149	3	.	.	PUNCT
ap-1400	150	1	4/2011	4/2011	NUM
ap-1400	150	2	fig	fig	NOUN
ap-1400	150	3	.	.	PUNCT
ap-1400	151	1	3	3	NUM
ap-1400	151	2	:	:	PUNCT
ap-1400	151	3	undamped	undampe	VERB
ap-1400	151	4	3	3	NUM
ap-1400	151	5	-	-	PUNCT
ap-1400	151	6	link	link	NOUN
ap-1400	151	7	ziegler	ziegler	NOUN
ap-1400	151	8	pendulum	pendulum	NOUN
ap-1400	151	9	with	with	ADP
ap-1400	151	10	l	l	NOUN
ap-1400	151	11	=	=	SYM
ap-1400	151	12	1	1	NUM
ap-1400	151	13	,	,	PUNCT
ap-1400	151	14	c1	c1	NOUN
ap-1400	151	15	=	=	PROPN
ap-1400	151	16	c2	c2	PROPN
ap-1400	151	17	=	=	PROPN
ap-1400	151	18	c3	c3	PROPN
ap-1400	151	19	=	=	PUNCT
ap-1400	151	20	1	1	NUM
ap-1400	151	21	:	:	PUNCT
ap-1400	151	22	the	the	DET
ap-1400	151	23	critical	critical	ADJ
ap-1400	151	24	flutter	flutter	NOUN
ap-1400	151	25	load	load	NOUN
ap-1400	151	26	p	p	PROPN
ap-1400	151	27	(	(	PUNCT
ap-1400	151	28	α	α	NOUN
ap-1400	151	29	)	)	PUNCT
ap-1400	151	30	as	as	ADP
ap-1400	151	31	a	a	DET
ap-1400	151	32	function	function	NOUN
ap-1400	151	33	of	of	ADP
ap-1400	151	34	the	the	DET
ap-1400	151	35	azimuth	azimuth	PROPN
ap-1400	151	36	angle	angle	NOUN
ap-1400	151	37	α	α	PROPN
ap-1400	151	38	indicating	indicate	VERB
ap-1400	151	39	the	the	DET
ap-1400	151	40	direction	direction	NOUN
ap-1400	151	41	in	in	ADP
ap-1400	151	42	the	the	DET
ap-1400	151	43	(	(	PUNCT
ap-1400	151	44	m2	m2	PROPN
ap-1400	151	45	,	,	PUNCT
ap-1400	151	46	m3)-plane	m3)-plane	NUM
ap-1400	151	47	at	at	ADP
ap-1400	151	48	the	the	DET
ap-1400	151	49	fixed	fix	VERB
ap-1400	151	50	radial	radial	ADJ
ap-1400	151	51	distance	distance	NOUN
ap-1400	151	52	r	r	NOUN
ap-1400	151	53	=	=	SYM
ap-1400	151	54	1	1	NUM
ap-1400	151	55	for	for	ADP
ap-1400	151	56	(	(	PUNCT
ap-1400	151	57	a	a	PRON
ap-1400	151	58	)	)	PUNCT
ap-1400	151	59	m1	m1	NOUN
ap-1400	151	60	=	=	SYM
ap-1400	151	61	0	0	NUM
ap-1400	151	62	,	,	PUNCT
ap-1400	151	63	(	(	PUNCT
ap-1400	151	64	b	b	X
ap-1400	151	65	)	)	PUNCT
ap-1400	151	66	m1	m1	NOUN
ap-1400	151	67	=	=	SYM
ap-1400	151	68	10	10	NUM
ap-1400	151	69	,	,	PUNCT
ap-1400	151	70	and	and	CCONJ
ap-1400	151	71	(	(	PUNCT
ap-1400	151	72	c	c	NOUN
ap-1400	151	73	)	)	PUNCT
ap-1400	151	74	m1	m1	NOUN
ap-1400	151	75	=	=	NUM
ap-1400	151	76	200	200	NUM
ap-1400	151	77	and	and	CCONJ
ap-1400	151	78	for	for	ADP
ap-1400	151	79	the	the	DET
ap-1400	151	80	fixed	fix	VERB
ap-1400	151	81	m1	m1	NOUN
ap-1400	151	82	=	=	SYM
ap-1400	151	83	5	5	NUM
ap-1400	151	84	and	and	CCONJ
ap-1400	151	85	(	(	PUNCT
ap-1400	151	86	d	d	NOUN
ap-1400	151	87	)	)	PUNCT
ap-1400	151	88	r	r	NOUN
ap-1400	151	89	=	=	SYM
ap-1400	151	90	1	1	NUM
ap-1400	151	91	,	,	PUNCT
ap-1400	151	92	(	(	PUNCT
ap-1400	151	93	e	e	NOUN
ap-1400	151	94	)	)	PUNCT
ap-1400	151	95	r	r	NOUN
ap-1400	151	96	=	=	SYM
ap-1400	151	97	0.65	0.65	NUM
ap-1400	151	98	and	and	CCONJ
ap-1400	151	99	(	(	PUNCT
ap-1400	151	100	f	f	X
ap-1400	151	101	)	)	PUNCT
ap-1400	151	102	r	r	NOUN
ap-1400	151	103	=	=	SYM
ap-1400	151	104	0.1	0.1	NUM
ap-1400	151	105	k	k	NOUN
ap-1400	151	106	=	=	PUNCT
ap-1400	151	107	⎛⎜⎜⎜⎜⎜⎜⎜⎝	⎛⎜⎜⎜⎜⎜⎜⎜⎝	NOUN
ap-1400	151	108	c1	c1	NOUN
ap-1400	151	109	+	+	CCONJ
ap-1400	151	110	c2	c2	PROPN
ap-1400	151	111	−	−	PROPN
ap-1400	151	112	pl	pl	PROPN
ap-1400	151	113	−c2	−c2	PROPN
ap-1400	151	114	·	·	PUNCT
ap-1400	151	115	·	·	PUNCT
ap-1400	151	116	·	·	PUNCT
ap-1400	151	117	0	0	PUNCT
ap-1400	152	1	pl	pl	PROPN
ap-1400	152	2	−c2	−c2	PROPN
ap-1400	152	3	c2	c2	PROPN
ap-1400	152	4	+	+	CCONJ
ap-1400	152	5	c3	c3	PROPN
ap-1400	152	6	−	−	PROPN
ap-1400	152	7	pl	pl	PROPN
ap-1400	152	8	·	·	PUNCT
ap-1400	152	9	·	·	PUNCT
ap-1400	152	10	·	·	PUNCT
ap-1400	152	11	0	0	PUNCT
ap-1400	152	12	pl	pl	X
ap-1400	152	13	·	·	PUNCT
ap-1400	152	14	·	·	PUNCT
ap-1400	152	15	·	·	PUNCT
ap-1400	152	16	·	·	PUNCT
ap-1400	152	17	·	·	PUNCT
ap-1400	152	18	·	·	PUNCT
ap-1400	152	19	·	·	PUNCT
ap-1400	152	20	·	·	PUNCT
ap-1400	152	21	·	·	PUNCT
ap-1400	152	22	·	·	PUNCT
ap-1400	152	23	·	·	PUNCT
ap-1400	152	24	·	·	PUNCT
ap-1400	152	25	·	·	PUNCT
ap-1400	152	26	·	·	PUNCT
ap-1400	152	27	·	·	PUNCT
ap-1400	152	28	0	0	NUM
ap-1400	152	29	0	0	NUM
ap-1400	152	30	·	·	PUNCT
ap-1400	152	31	·	·	PUNCT
ap-1400	152	32	·	·	PUNCT
ap-1400	152	33	cm−1	cm−1	NOUN
ap-1400	152	34	+	+	CCONJ
ap-1400	152	35	cm	cm	NOUN
ap-1400	152	36	−	−	NOUN
ap-1400	152	37	pl	pl	X
ap-1400	152	38	−cm−1	−cm−1	NOUN
ap-1400	152	39	+	+	CCONJ
ap-1400	152	40	pl	pl	PROPN
ap-1400	152	41	0	0	NUM
ap-1400	152	42	0	0	NUM
ap-1400	152	43	·	·	PUNCT
ap-1400	152	44	·	·	PUNCT
ap-1400	152	45	·	·	PUNCT
ap-1400	153	1	−cm−1	−cm−1	NUM
ap-1400	153	2	cm	cm	PROPN
ap-1400	153	3	⎞⎟⎟⎟⎟⎟⎟⎟⎠	⎞⎟⎟⎟⎟⎟⎟⎟⎠	PROPN
ap-1400	153	4	.	.	PUNCT
ap-1400	154	1	(	(	PUNCT
ap-1400	154	2	13	13	NUM
ap-1400	154	3	)	)	PUNCT
ap-1400	154	4	for	for	ADP
ap-1400	154	5	m	m	PROPN
ap-1400	154	6	=	=	SYM
ap-1400	154	7	2	2	NUM
ap-1400	154	8	,	,	PUNCT
ap-1400	154	9	matrices	matrix	NOUN
ap-1400	154	10	(	(	PUNCT
ap-1400	154	11	12	12	NUM
ap-1400	154	12	)	)	PUNCT
ap-1400	154	13	and	and	CCONJ
ap-1400	154	14	(	(	PUNCT
ap-1400	154	15	13	13	NUM
ap-1400	154	16	)	)	PUNCT
ap-1400	154	17	are	be	AUX
ap-1400	154	18	reduced	reduce	VERB
ap-1400	154	19	to	to	ADP
ap-1400	154	20	(	(	PUNCT
ap-1400	154	21	3	3	NUM
ap-1400	154	22	)	)	PUNCT
ap-1400	154	23	.	.	PUNCT
ap-1400	155	1	note	note	VERB
ap-1400	155	2	that	that	DET
ap-1400	155	3	detm	detm	NOUN
ap-1400	155	4	=	=	SYM
ap-1400	155	5	l2	l2	NOUN
ap-1400	155	6	m	m	PROPN
ap-1400	155	7	m∏	m∏	PROPN
ap-1400	155	8	i=1	i=1	PROPN
ap-1400	155	9	mi	mi	PROPN
ap-1400	155	10	.	.	PROPN
ap-1400	156	1	(	(	PUNCT
ap-1400	156	2	14	14	NUM
ap-1400	156	3	)	)	PUNCT
ap-1400	156	4	37	37	NUM
ap-1400	156	5	acta	acta	PROPN
ap-1400	156	6	polytechnica	polytechnica	PROPN
ap-1400	156	7	vol	vol	NOUN
ap-1400	156	8	.	.	PUNCT
ap-1400	157	1	51	51	NUM
ap-1400	157	2	no	no	INTJ
ap-1400	157	3	.	.	PUNCT
ap-1400	158	1	4/2011	4/2011	PROPN
ap-1400	158	2	let	let	VERB
ap-1400	158	3	us	we	PRON
ap-1400	158	4	consider	consider	VERB
ap-1400	158	5	the	the	DET
ap-1400	158	6	ziegler	ziegler	NOUN
ap-1400	158	7	-	-	PUNCT
ap-1400	158	8	lobas	lobas	PROPN
ap-1400	158	9	pendulum	pendulum	NOUN
ap-1400	158	10	with	with	ADP
ap-1400	158	11	m	m	PROPN
ap-1400	158	12	=	=	SYM
ap-1400	158	13	3	3	NUM
ap-1400	158	14	links	link	NOUN
ap-1400	158	15	.	.	PUNCT
ap-1400	159	1	now	now	ADV
ap-1400	159	2	the	the	DET
ap-1400	159	3	mass	mass	NOUN
ap-1400	159	4	at	at	ADP
ap-1400	159	5	the	the	DET
ap-1400	159	6	free	free	ADJ
ap-1400	159	7	end	end	NOUN
ap-1400	159	8	is	be	AUX
ap-1400	159	9	m3	m3	PROPN
ap-1400	159	10	,	,	PUNCT
ap-1400	159	11	while	while	SCONJ
ap-1400	159	12	the	the	DET
ap-1400	159	13	masses	masse	NOUN
ap-1400	159	14	m2	m2	PROPN
ap-1400	159	15	and	and	CCONJ
ap-1400	159	16	m1	m1	PROPN
ap-1400	159	17	are	be	AUX
ap-1400	159	18	located	locate	VERB
ap-1400	159	19	at	at	ADP
ap-1400	159	20	the	the	DET
ap-1400	159	21	third	third	ADJ
ap-1400	159	22	and	and	CCONJ
ap-1400	159	23	second	second	ADJ
ap-1400	159	24	joints	joint	NOUN
ap-1400	159	25	,	,	PUNCT
ap-1400	159	26	respectively	respectively	ADV
ap-1400	159	27	.	.	PUNCT
ap-1400	160	1	the	the	DET
ap-1400	160	2	first	first	ADJ
ap-1400	160	3	joint	joint	NOUN
ap-1400	160	4	connects	connect	VERB
ap-1400	160	5	the	the	DET
ap-1400	160	6	first	first	ADJ
ap-1400	160	7	rod	rod	NOUN
ap-1400	160	8	with	with	ADP
ap-1400	160	9	the	the	DET
ap-1400	160	10	basement	basement	NOUN
ap-1400	160	11	.	.	PUNCT
ap-1400	161	1	the	the	DET
ap-1400	161	2	length	length	NOUN
ap-1400	161	3	of	of	ADP
ap-1400	161	4	each	each	PRON
ap-1400	161	5	of	of	ADP
ap-1400	161	6	the	the	DET
ap-1400	161	7	three	three	NUM
ap-1400	161	8	rods	rod	NOUN
ap-1400	161	9	is	be	AUX
ap-1400	161	10	equal	equal	ADJ
ap-1400	161	11	to	to	AUX
ap-1400	161	12	l.	l.	VERB
ap-1400	161	13	the	the	DET
ap-1400	161	14	stiffness	stiffness	ADJ
ap-1400	161	15	coefficients	coefficient	NOUN
ap-1400	161	16	of	of	ADP
ap-1400	161	17	the	the	DET
ap-1400	161	18	joints	joint	NOUN
ap-1400	161	19	are	be	AUX
ap-1400	161	20	c3	c3	PROPN
ap-1400	161	21	,	,	PUNCT
ap-1400	161	22	c2	c2	PROPN
ap-1400	161	23	,	,	PUNCT
ap-1400	161	24	and	and	CCONJ
ap-1400	161	25	c1	c1	PROPN
ap-1400	161	26	,	,	PUNCT
ap-1400	161	27	respectively	respectively	ADV
ap-1400	161	28	.	.	PUNCT
ap-1400	162	1	for	for	ADP
ap-1400	162	2	simplicity	simplicity	NOUN
ap-1400	162	3	we	we	PRON
ap-1400	162	4	assume	assume	VERB
ap-1400	162	5	that	that	SCONJ
ap-1400	162	6	c1	c1	PROPN
ap-1400	162	7	=	=	PROPN
ap-1400	162	8	c2	c2	PROPN
ap-1400	162	9	=	=	SYM
ap-1400	162	10	c3	c3	PROPN
ap-1400	162	11	=	=	PROPN
ap-1400	162	12	c.	c.	PROPN
ap-1400	162	13	then	then	ADV
ap-1400	162	14	,	,	PUNCT
ap-1400	162	15	the	the	DET
ap-1400	162	16	characteristic	characteristic	ADJ
ap-1400	162	17	polynomial	polynomial	NOUN
ap-1400	162	18	has	have	VERB
ap-1400	162	19	the	the	DET
ap-1400	162	20	form	form	NOUN
ap-1400	162	21	a0λ	a0λ	NOUN
ap-1400	162	22	6	6	NUM
ap-1400	162	23	+	+	CCONJ
ap-1400	162	24	a1λ	a1λ	PROPN
ap-1400	162	25	4	4	NUM
ap-1400	162	26	+	+	NUM
ap-1400	162	27	a2λ	a2λ	NOUN
ap-1400	162	28	2	2	NUM
ap-1400	162	29	+	+	NUM
ap-1400	162	30	a3	a3	NOUN
ap-1400	162	31	=	=	SYM
ap-1400	162	32	0	0	NUM
ap-1400	162	33	,	,	PUNCT
ap-1400	162	34	(	(	PUNCT
ap-1400	162	35	15	15	NUM
ap-1400	162	36	)	)	PUNCT
ap-1400	162	37	with	with	ADP
ap-1400	162	38	the	the	DET
ap-1400	162	39	coefficients	coefficient	NOUN
ap-1400	162	40	a0	a0	PROPN
ap-1400	162	41	=	=	SYM
ap-1400	162	42	l6m1m2m3	l6m1m2m3	PROPN
ap-1400	162	43	,	,	PUNCT
ap-1400	163	1	a1	a1	NOUN
ap-1400	163	2	=	=	SYM
ap-1400	163	3	cl4(6m2m3	cl4(6m2m3	PROPN
ap-1400	163	4	+	+	CCONJ
ap-1400	163	5	5m1m3	5m1m3	NUM
ap-1400	163	6	+	+	CCONJ
ap-1400	163	7	m1m2	m1m2	X
ap-1400	163	8	)	)	PUNCT
ap-1400	163	9	−	−	PROPN
ap-1400	163	10	2l5pm3(m1	2l5pm3(m1	NOUN
ap-1400	163	11	+	+	CCONJ
ap-1400	163	12	m2	m2	NOUN
ap-1400	163	13	)	)	PUNCT
ap-1400	163	14	,	,	PUNCT
ap-1400	164	1	a2	a2	NOUN
ap-1400	164	2	=	=	SYM
ap-1400	164	3	3p	3p	NUM
ap-1400	164	4	2l4m3	2l4m3	NUM
ap-1400	164	5	−	−	NOUN
ap-1400	164	6	2(7m3	2(7m3	NUM
ap-1400	165	1	+	+	CCONJ
ap-1400	165	2	m2)pl3c	m2)pl3c	PROPN
ap-1400	165	3	+	+	CCONJ
ap-1400	165	4	(	(	PUNCT
ap-1400	165	5	m1	m1	PROPN
ap-1400	165	6	+	+	CCONJ
ap-1400	165	7	5m2	5m2	PROPN
ap-1400	165	8	+	+	CCONJ
ap-1400	165	9	14m3)l2c2	14m3)l2c2	NUM
ap-1400	165	10	,	,	PUNCT
ap-1400	165	11	a3	a3	NOUN
ap-1400	165	12	=	=	SYM
ap-1400	165	13	c3	c3	PROPN
ap-1400	165	14	.	.	PUNCT
ap-1400	166	1	(	(	PUNCT
ap-1400	166	2	16	16	NUM
ap-1400	166	3	)	)	PUNCT
ap-1400	166	4	composing	compose	VERB
ap-1400	166	5	the	the	DET
ap-1400	166	6	discriminant	discriminant	ADJ
ap-1400	166	7	matrix	matrix	NOUN
ap-1400	166	8	[	[	X
ap-1400	166	9	24	24	NUM
ap-1400	166	10	]	]	SYM
ap-1400	166	11	s	s	NOUN
ap-1400	166	12	=	=	SYM
ap-1400	166	13	⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝	⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝	NOUN
ap-1400	166	14	a0	a0	PROPN
ap-1400	166	15	a1	a1	PROPN
ap-1400	166	16	a2	a2	PROPN
ap-1400	166	17	a3	a3	VERB
ap-1400	166	18	0	0	NUM
ap-1400	166	19	0	0	SYM
ap-1400	166	20	0	0	NUM
ap-1400	166	21	3a0	3a0	NUM
ap-1400	166	22	2a1	2a1	NUM
ap-1400	166	23	a2	a2	PROPN
ap-1400	166	24	0	0	NUM
ap-1400	166	25	0	0	SYM
ap-1400	166	26	0	0	NUM
ap-1400	166	27	a0	a0	PROPN
ap-1400	166	28	a1	a1	PROPN
ap-1400	166	29	a2	a2	PROPN
ap-1400	166	30	a3	a3	VERB
ap-1400	166	31	0	0	NUM
ap-1400	166	32	0	0	SYM
ap-1400	166	33	0	0	NUM
ap-1400	166	34	3a0	3a0	NUM
ap-1400	166	35	2a1	2a1	NUM
ap-1400	166	36	a2	a2	PROPN
ap-1400	166	37	0	0	NUM
ap-1400	166	38	0	0	SYM
ap-1400	166	39	0	0	NUM
ap-1400	166	40	a0	a0	PROPN
ap-1400	166	41	a1	a1	PROPN
ap-1400	166	42	a2	a2	PROPN
ap-1400	166	43	a3	a3	VERB
ap-1400	166	44	0	0	NUM
ap-1400	166	45	0	0	SYM
ap-1400	166	46	0	0	NUM
ap-1400	166	47	3a0	3a0	NUM
ap-1400	166	48	2a1	2a1	NUM
ap-1400	166	49	a2	a2	PROPN
ap-1400	166	50	⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠	⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠	PROPN
ap-1400	166	51	(	(	PUNCT
ap-1400	166	52	17	17	NUM
ap-1400	166	53	)	)	PUNCT
ap-1400	166	54	and	and	CCONJ
ap-1400	166	55	calculating	calculate	VERB
ap-1400	166	56	the	the	DET
ap-1400	166	57	discriminant	discriminant	ADJ
ap-1400	166	58	sequence	sequence	NOUN
ap-1400	166	59	consisting	consist	VERB
ap-1400	166	60	of	of	ADP
ap-1400	166	61	the	the	DET
ap-1400	166	62	determinants	determinant	NOUN
ap-1400	166	63	of	of	ADP
ap-1400	166	64	the	the	DET
ap-1400	166	65	three	three	NUM
ap-1400	166	66	main	main	ADJ
ap-1400	166	67	minors	minor	NOUN
ap-1400	166	68	of	of	ADP
ap-1400	166	69	even	even	ADV
ap-1400	166	70	order	order	NOUN
ap-1400	166	71	,	,	PUNCT
ap-1400	166	72	we	we	PRON
ap-1400	166	73	find	find	VERB
ap-1400	166	74	that	that	DET
ap-1400	166	75	δ1	δ1	NOUN
ap-1400	166	76	=	=	SYM
ap-1400	166	77	3l12m21	3l12m21	NUM
ap-1400	166	78	m	m	NOUN
ap-1400	166	79	2	2	NUM
ap-1400	166	80	2	2	NUM
ap-1400	166	81	m	m	NUM
ap-1400	166	82	2	2	NUM
ap-1400	166	83	3	3	NUM
ap-1400	166	84	>	>	X
ap-1400	166	85	0	0	NUM
ap-1400	166	86	.	.	PUNCT
ap-1400	167	1	the	the	DET
ap-1400	167	2	expressions	expression	NOUN
ap-1400	167	3	for	for	ADP
ap-1400	167	4	determinants	determinant	NOUN
ap-1400	167	5	δ2	δ2	VERB
ap-1400	167	6	and	and	CCONJ
ap-1400	167	7	δ3	δ3	PROPN
ap-1400	167	8	=	=	PUNCT
ap-1400	167	9	dets	det	NOUN
ap-1400	167	10	are	be	AUX
ap-1400	167	11	rather	rather	ADV
ap-1400	167	12	involved	involve	VERB
ap-1400	167	13	,	,	PUNCT
ap-1400	167	14	and	and	CCONJ
ap-1400	167	15	for	for	ADP
ap-1400	167	16	this	this	DET
ap-1400	167	17	reason	reason	NOUN
ap-1400	167	18	we	we	PRON
ap-1400	167	19	omit	omit	VERB
ap-1400	167	20	them	they	PRON
ap-1400	167	21	here	here	ADV
ap-1400	167	22	.	.	PUNCT
ap-1400	168	1	however	however	ADV
ap-1400	168	2	,	,	PUNCT
ap-1400	168	3	numerical	numerical	ADJ
ap-1400	168	4	experiments	experiment	NOUN
ap-1400	168	5	evidence	evidence	VERB
ap-1400	168	6	that	that	SCONJ
ap-1400	168	7	the	the	DET
ap-1400	168	8	stability	stability	NOUN
ap-1400	168	9	boundary	boundary	NOUN
ap-1400	168	10	is	be	AUX
ap-1400	168	11	given	give	VERB
ap-1400	168	12	by	by	ADP
ap-1400	168	13	the	the	DET
ap-1400	168	14	equation	equation	NOUN
ap-1400	168	15	δ3	δ3	PROPN
ap-1400	168	16	=	=	SYM
ap-1400	168	17	0	0	NUM
ap-1400	168	18	for	for	ADP
ap-1400	168	19	the	the	DET
ap-1400	168	20	stability	stability	NOUN
ap-1400	168	21	condition	condition	NOUN
ap-1400	168	22	δ3	δ3	PROPN
ap-1400	168	23	>	>	X
ap-1400	168	24	0	0	NUM
ap-1400	168	25	implies	imply	VERB
ap-1400	168	26	δ2	δ2	VERB
ap-1400	168	27	>	>	X
ap-1400	168	28	0	0	X
ap-1400	168	29	.	.	PUNCT
ap-1400	169	1	in	in	ADP
ap-1400	169	2	figure	figure	NOUN
ap-1400	169	3	3	3	NUM
ap-1400	169	4	using	use	VERB
ap-1400	169	5	the	the	DET
ap-1400	169	6	inequality	inequality	NOUN
ap-1400	169	7	δ3	δ3	PROPN
ap-1400	169	8	>	>	X
ap-1400	169	9	0	0	PUNCT
ap-1400	169	10	we	we	PRON
ap-1400	169	11	present	present	VERB
ap-1400	169	12	the	the	DET
ap-1400	169	13	stability	stability	NOUN
ap-1400	169	14	diagrams	diagram	NOUN
ap-1400	169	15	in	in	ADP
ap-1400	169	16	the	the	DET
ap-1400	169	17	(	(	PUNCT
ap-1400	169	18	α	α	NOUN
ap-1400	169	19	,	,	PUNCT
ap-1400	169	20	p	p	NOUN
ap-1400	169	21	)	)	PUNCT
ap-1400	169	22	-plane	-plane	NOUN
ap-1400	169	23	,	,	PUNCT
ap-1400	169	24	where	where	SCONJ
ap-1400	169	25	the	the	DET
ap-1400	169	26	azimuth	azimuth	PROPN
ap-1400	169	27	angle	angle	NOUN
ap-1400	169	28	α	α	PROPN
ap-1400	169	29	in	in	ADP
ap-1400	169	30	the	the	DET
ap-1400	169	31	(	(	PUNCT
ap-1400	169	32	m2	m2	PROPN
ap-1400	169	33	,	,	PUNCT
ap-1400	169	34	m3)-plane	m3)-plane	PROPN
ap-1400	169	35	is	be	AUX
ap-1400	169	36	introduced	introduce	VERB
ap-1400	169	37	by	by	ADP
ap-1400	169	38	assuming	assume	VERB
ap-1400	169	39	m2	m2	PROPN
ap-1400	169	40	=	=	PROPN
ap-1400	169	41	r	r	PROPN
ap-1400	169	42	cos	cos	PROPN
ap-1400	169	43	α	α	PROPN
ap-1400	169	44	and	and	CCONJ
ap-1400	169	45	m3	m3	PROPN
ap-1400	169	46	=	=	PUNCT
ap-1400	169	47	r	r	NOUN
ap-1400	169	48	sin	sin	NOUN
ap-1400	169	49	α	α	NOUN
ap-1400	169	50	.	.	PUNCT
ap-1400	170	1	we	we	PRON
ap-1400	170	2	assume	assume	VERB
ap-1400	170	3	equal	equal	ADJ
ap-1400	170	4	lengths	length	NOUN
ap-1400	170	5	of	of	ADP
ap-1400	170	6	the	the	DET
ap-1400	170	7	links	link	NOUN
ap-1400	170	8	l	l	NOUN
ap-1400	170	9	=	=	SYM
ap-1400	170	10	1	1	NUM
ap-1400	170	11	and	and	CCONJ
ap-1400	170	12	equal	equal	ADJ
ap-1400	170	13	stiffness	stiffness	NOUN
ap-1400	170	14	coefficients	coefficient	NOUN
ap-1400	170	15	c1	c1	NOUN
ap-1400	170	16	=	=	PROPN
ap-1400	170	17	c2	c2	PROPN
ap-1400	170	18	=	=	SYM
ap-1400	170	19	c3	c3	PROPN
ap-1400	170	20	=	=	SYM
ap-1400	170	21	1	1	NUM
ap-1400	170	22	and	and	CCONJ
ap-1400	170	23	vary	vary	VERB
ap-1400	170	24	the	the	DET
ap-1400	170	25	radial	radial	ADJ
ap-1400	170	26	distance	distance	NOUN
ap-1400	170	27	r	r	NOUN
ap-1400	170	28	in	in	ADP
ap-1400	170	29	the	the	DET
ap-1400	170	30	(	(	PUNCT
ap-1400	170	31	m2	m2	PROPN
ap-1400	170	32	,	,	PUNCT
ap-1400	170	33	m3)-plane	m3)-plane	PROPN
ap-1400	170	34	and	and	CCONJ
ap-1400	170	35	the	the	DET
ap-1400	170	36	mass	mass	PROPN
ap-1400	170	37	m1	m1	PROPN
ap-1400	170	38	.	.	PUNCT
ap-1400	171	1	since	since	SCONJ
ap-1400	171	2	for	for	ADP
ap-1400	171	3	m	m	PROPN
ap-1400	171	4	=	=	NOUN
ap-1400	171	5	3	3	NUM
ap-1400	171	6	the	the	DET
ap-1400	171	7	critical	critical	ADJ
ap-1400	171	8	surface	surface	NOUN
ap-1400	171	9	p	p	NOUN
ap-1400	171	10	(	(	PUNCT
ap-1400	171	11	m2	m2	PROPN
ap-1400	171	12	,	,	PUNCT
ap-1400	171	13	m3	m3	PROPN
ap-1400	171	14	)	)	PUNCT
ap-1400	171	15	is	be	AUX
ap-1400	171	16	no	no	ADV
ap-1400	171	17	longer	long	ADV
ap-1400	171	18	a	a	DET
ap-1400	171	19	ruled	rule	VERB
ap-1400	171	20	surface	surface	NOUN
ap-1400	171	21	as	as	SCONJ
ap-1400	171	22	it	it	PRON
ap-1400	171	23	was	be	AUX
ap-1400	171	24	in	in	ADP
ap-1400	171	25	the	the	DET
ap-1400	171	26	case	case	NOUN
ap-1400	171	27	m	m	NOUN
ap-1400	171	28	=	=	SYM
ap-1400	171	29	2	2	NUM
ap-1400	171	30	,	,	PUNCT
ap-1400	171	31	the	the	DET
ap-1400	171	32	pictures	picture	NOUN
ap-1400	171	33	in	in	ADP
ap-1400	171	34	the	the	DET
ap-1400	171	35	(	(	PUNCT
ap-1400	171	36	α	α	NOUN
ap-1400	171	37	,	,	PUNCT
ap-1400	171	38	p	p	NOUN
ap-1400	171	39	)	)	PUNCT
ap-1400	171	40	-plane	-plane	ADJ
ap-1400	171	41	change	change	NOUN
ap-1400	171	42	with	with	ADP
ap-1400	171	43	the	the	DET
ap-1400	171	44	variation	variation	NOUN
ap-1400	171	45	of	of	ADP
ap-1400	171	46	the	the	DET
ap-1400	171	47	radial	radial	ADJ
ap-1400	171	48	distance	distance	NOUN
ap-1400	171	49	r	r	NOUN
ap-1400	171	50	,	,	PUNCT
ap-1400	171	51	which	which	PRON
ap-1400	171	52	complicates	complicate	VERB
ap-1400	171	53	the	the	DET
ap-1400	171	54	optimization	optimization	NOUN
ap-1400	171	55	problem	problem	NOUN
ap-1400	171	56	.	.	PUNCT
ap-1400	172	1	nevertheless	nevertheless	ADV
ap-1400	172	2	,	,	PUNCT
ap-1400	172	3	such	such	ADJ
ap-1400	172	4	diagrams	diagram	NOUN
ap-1400	172	5	are	be	AUX
ap-1400	172	6	convenient	convenient	ADJ
ap-1400	172	7	for	for	ADP
ap-1400	172	8	analyzing	analyze	VERB
ap-1400	172	9	the	the	DET
ap-1400	172	10	geometry	geometry	NOUN
ap-1400	172	11	of	of	ADP
ap-1400	172	12	the	the	DET
ap-1400	172	13	stability	stability	NOUN
ap-1400	172	14	boundary	boundary	ADJ
ap-1400	172	15	and	and	CCONJ
ap-1400	172	16	thus	thus	ADV
ap-1400	172	17	for	for	ADP
ap-1400	172	18	identifying	identify	VERB
ap-1400	172	19	the	the	DET
ap-1400	172	20	potential	potential	ADJ
ap-1400	172	21	extrema	extrema	NOUN
ap-1400	172	22	.	.	PUNCT
ap-1400	173	1	moreover	moreover	ADV
ap-1400	173	2	,	,	PUNCT
ap-1400	173	3	the	the	DET
ap-1400	173	4	critical	critical	ADJ
ap-1400	173	5	surface	surface	NOUN
ap-1400	173	6	p	p	NOUN
ap-1400	173	7	(	(	PUNCT
ap-1400	173	8	m2	m2	PROPN
ap-1400	173	9	,	,	PUNCT
ap-1400	173	10	m3	m3	PROPN
ap-1400	173	11	)	)	PUNCT
ap-1400	173	12	has	have	VERB
ap-1400	173	13	a	a	DET
ap-1400	173	14	self	self	NOUN
ap-1400	173	15	-	-	PUNCT
ap-1400	173	16	intersection	intersection	NOUN
ap-1400	173	17	along	along	ADP
ap-1400	173	18	a	a	DET
ap-1400	173	19	ray	ray	NOUN
ap-1400	173	20	of	of	ADP
ap-1400	173	21	the	the	DET
ap-1400	173	22	p	p	X
ap-1400	173	23	-axis	-axis	NOUN
ap-1400	173	24	that	that	PRON
ap-1400	173	25	starts	start	VERB
ap-1400	173	26	from	from	ADP
ap-1400	173	27	the	the	DET
ap-1400	173	28	singularity	singularity	NOUN
ap-1400	173	29	whitney	whitney	NOUN
ap-1400	173	30	umbrella	umbrella	NOUN
ap-1400	173	31	,	,	PUNCT
ap-1400	173	32	as	as	ADP
ap-1400	173	33	in	in	ADP
ap-1400	173	34	the	the	DET
ap-1400	173	35	case	case	NOUN
ap-1400	173	36	of	of	ADP
ap-1400	173	37	the	the	DET
ap-1400	173	38	2	2	NUM
ap-1400	173	39	-	-	PUNCT
ap-1400	173	40	link	link	NOUN
ap-1400	173	41	pendulum	pendulum	NOUN
ap-1400	173	42	.	.	PUNCT
ap-1400	174	1	therefore	therefore	ADV
ap-1400	174	2	,	,	PUNCT
ap-1400	174	3	at	at	ADP
ap-1400	174	4	small	small	ADJ
ap-1400	174	5	values	value	NOUN
ap-1400	174	6	of	of	ADP
ap-1400	174	7	m2	m2	PROPN
ap-1400	174	8	and	and	CCONJ
ap-1400	174	9	m3	m3	PROPN
ap-1400	174	10	the	the	DET
ap-1400	174	11	critical	critical	ADJ
ap-1400	174	12	load	load	NOUN
ap-1400	174	13	can	can	AUX
ap-1400	174	14	be	be	AUX
ap-1400	174	15	locally	locally	ADV
ap-1400	174	16	approximated	approximate	VERB
ap-1400	174	17	by	by	ADP
ap-1400	174	18	a	a	DET
ap-1400	174	19	ruled	rule	VERB
ap-1400	174	20	surface	surface	NOUN
ap-1400	174	21	.	.	PUNCT
ap-1400	175	1	in	in	ADP
ap-1400	175	2	the	the	DET
ap-1400	175	3	left	left	ADJ
ap-1400	175	4	column	column	NOUN
ap-1400	175	5	of	of	ADP
ap-1400	175	6	figure	figure	NOUN
ap-1400	175	7	3	3	NUM
ap-1400	175	8	the	the	DET
ap-1400	175	9	radial	radial	ADJ
ap-1400	175	10	distance	distance	NOUN
ap-1400	175	11	r	r	NOUN
ap-1400	175	12	in	in	ADP
ap-1400	175	13	the	the	DET
ap-1400	175	14	(	(	PUNCT
ap-1400	175	15	m2	m2	PROPN
ap-1400	175	16	,	,	PUNCT
ap-1400	175	17	m3)-plane	m3)-plane	PROPN
ap-1400	175	18	is	be	AUX
ap-1400	175	19	fixed	fix	VERB
ap-1400	175	20	to	to	ADP
ap-1400	175	21	r	r	NOUN
ap-1400	175	22	=	=	SYM
ap-1400	175	23	1	1	NUM
ap-1400	175	24	while	while	SCONJ
ap-1400	175	25	the	the	DET
ap-1400	175	26	mass	mass	PROPN
ap-1400	175	27	m1	m1	PROPN
ap-1400	175	28	is	be	AUX
ap-1400	175	29	increasing	increase	VERB
ap-1400	175	30	.	.	PUNCT
ap-1400	176	1	as	as	ADP
ap-1400	176	2	in	in	ADP
ap-1400	176	3	the	the	DET
ap-1400	176	4	case	case	NOUN
ap-1400	176	5	m	m	NOUN
ap-1400	176	6	=	=	SYM
ap-1400	176	7	2	2	NUM
ap-1400	176	8	,	,	PUNCT
ap-1400	176	9	(	(	PUNCT
ap-1400	176	10	marginal	marginal	ADJ
ap-1400	176	11	)	)	PUNCT
ap-1400	176	12	stability	stability	NOUN
ap-1400	176	13	is	be	AUX
ap-1400	176	14	possible	possible	ADJ
ap-1400	176	15	for	for	SCONJ
ap-1400	176	16	α	α	PRON
ap-1400	176	17	∈	∈	PROPN
ap-1400	177	1	[	[	X
ap-1400	177	2	0	0	NUM
ap-1400	177	3	,	,	PUNCT
ap-1400	177	4	π/2	π/2	NUM
ap-1400	177	5	]	]	PUNCT
ap-1400	177	6	.	.	PUNCT
ap-1400	178	1	for	for	ADP
ap-1400	178	2	m1	m1	PROPN
ap-1400	178	3	=	=	SYM
ap-1400	178	4	0	0	PROPN
ap-1400	178	5	,	,	PUNCT
ap-1400	178	6	two	two	NUM
ap-1400	178	7	finite	finite	ADJ
ap-1400	178	8	maximal	maximal	ADJ
ap-1400	178	9	values	value	NOUN
ap-1400	178	10	pa	pa	PROPN
ap-1400	178	11	and	and	CCONJ
ap-1400	178	12	pb	pb	PROPN
ap-1400	178	13	are	be	AUX
ap-1400	178	14	identified	identify	VERB
ap-1400	178	15	at	at	ADP
ap-1400	178	16	α	α	NOUN
ap-1400	178	17	=	=	SYM
ap-1400	178	18	0	0	PUNCT
ap-1400	179	1	(	(	PUNCT
ap-1400	179	2	m3	m3	PROPN
ap-1400	179	3	=	=	SYM
ap-1400	179	4	0	0	NUM
ap-1400	179	5	)	)	PUNCT
ap-1400	179	6	and	and	CCONJ
ap-1400	179	7	α	α	NOUN
ap-1400	179	8	=	=	SYM
ap-1400	179	9	π/2	π/2	PROPN
ap-1400	179	10	(	(	PUNCT
ap-1400	179	11	m2	m2	PROPN
ap-1400	179	12	=	=	PROPN
ap-1400	179	13	0	0	NUM
ap-1400	179	14	)	)	PUNCT
ap-1400	179	15	,	,	PUNCT
ap-1400	179	16	respectively	respectively	ADV
ap-1400	179	17	,	,	PUNCT
ap-1400	179	18	figure	figure	NOUN
ap-1400	179	19	3(a	3(a	NUM
ap-1400	179	20	)	)	PUNCT
ap-1400	179	21	.	.	PUNCT
ap-1400	180	1	both	both	DET
ap-1400	180	2	maxima	maxima	NOUN
ap-1400	180	3	are	be	AUX
ap-1400	180	4	attained	attain	VERB
ap-1400	180	5	at	at	ADP
ap-1400	180	6	the	the	DET
ap-1400	180	7	cuspidal	cuspidal	ADJ
ap-1400	180	8	points	point	NOUN
ap-1400	180	9	of	of	ADP
ap-1400	180	10	the	the	DET
ap-1400	180	11	stability	stability	NOUN
ap-1400	180	12	boundary	boundary	NOUN
ap-1400	180	13	,	,	PUNCT
ap-1400	180	14	where	where	SCONJ
ap-1400	180	15	it	it	PRON
ap-1400	180	16	has	have	VERB
ap-1400	180	17	vertical	vertical	ADJ
ap-1400	180	18	tangents	tangent	NOUN
ap-1400	180	19	.	.	PUNCT
ap-1400	181	1	however	however	ADV
ap-1400	181	2	,	,	PUNCT
ap-1400	181	3	the	the	DET
ap-1400	181	4	stability	stability	NOUN
ap-1400	181	5	diagram	diagram	NOUN
ap-1400	181	6	changes	change	NOUN
ap-1400	181	7	when	when	SCONJ
ap-1400	181	8	m1	m1	PROPN
ap-1400	181	9	=	=	PROPN
ap-1400	181	10	10	10	NUM
ap-1400	181	11	,	,	PUNCT
ap-1400	181	12	figure	figure	NOUN
ap-1400	181	13	3(b	3(b	NUM
ap-1400	181	14	)	)	PUNCT
ap-1400	181	15	.	.	PUNCT
ap-1400	182	1	again	again	ADV
ap-1400	182	2	,	,	PUNCT
ap-1400	182	3	local	local	ADJ
ap-1400	182	4	extrema	extrema	NOUN
ap-1400	182	5	exist	exist	VERB
ap-1400	182	6	at	at	ADP
ap-1400	182	7	the	the	DET
ap-1400	182	8	boundary	boundary	ADJ
ap-1400	182	9	points	point	NOUN
ap-1400	182	10	α	α	X
ap-1400	182	11	=	=	SYM
ap-1400	182	12	0	0	PUNCT
ap-1400	183	1	(	(	PUNCT
ap-1400	183	2	m3	m3	PROPN
ap-1400	183	3	=	=	SYM
ap-1400	183	4	0	0	NUM
ap-1400	183	5	)	)	PUNCT
ap-1400	183	6	and	and	CCONJ
ap-1400	183	7	α	α	NOUN
ap-1400	183	8	=	=	SYM
ap-1400	183	9	π/2	π/2	PROPN
ap-1400	183	10	(	(	PUNCT
ap-1400	183	11	m2	m2	PROPN
ap-1400	183	12	=	=	PROPN
ap-1400	183	13	0	0	NUM
ap-1400	183	14	)	)	PUNCT
ap-1400	183	15	,	,	PUNCT
ap-1400	183	16	while	while	SCONJ
ap-1400	183	17	the	the	DET
ap-1400	183	18	global	global	ADJ
ap-1400	183	19	maximum	maximum	NOUN
ap-1400	183	20	is	be	AUX
ap-1400	183	21	at	at	ADP
ap-1400	183	22	the	the	DET
ap-1400	183	23	point	point	NOUN
ap-1400	183	24	of	of	ADP
ap-1400	183	25	the	the	DET
ap-1400	183	26	sharp	sharp	ADJ
ap-1400	183	27	turn	turn	NOUN
ap-1400	183	28	of	of	ADP
ap-1400	183	29	the	the	DET
ap-1400	183	30	flutter	flutter	NOUN
ap-1400	183	31	boundary	boundary	ADJ
ap-1400	183	32	with	with	ADP
ap-1400	183	33	the	the	DET
ap-1400	183	34	vertical	vertical	ADJ
ap-1400	183	35	tangent	tangent	NOUN
ap-1400	183	36	near	near	ADP
ap-1400	183	37	the	the	DET
ap-1400	183	38	cuspidal	cuspidal	NOUN
ap-1400	183	39	point	point	PROPN
ap-1400	183	40	c1	c1	PROPN
ap-1400	183	41	�	�	PROPN
ap-1400	183	42	(	(	PUNCT
ap-1400	183	43	0.040	0.040	NUM
ap-1400	183	44	347	347	NUM
ap-1400	183	45	7	7	NUM
ap-1400	183	46	,	,	PUNCT
ap-1400	183	47	11.961	11.961	NUM
ap-1400	183	48	144	144	NUM
ap-1400	183	49	)	)	PUNCT
ap-1400	183	50	,	,	PUNCT
ap-1400	183	51	which	which	PRON
ap-1400	183	52	corresponds	correspond	VERB
ap-1400	183	53	to	to	ADP
ap-1400	183	54	triple	triple	ADJ
ap-1400	183	55	pure	pure	ADJ
ap-1400	183	56	imaginary	imaginary	ADJ
ap-1400	183	57	eigenvalues	eigenvalue	NOUN
ap-1400	183	58	λ	λ	PROPN
ap-1400	183	59	�	�	PROPN
ap-1400	183	60	±i1.163	±i1.163	PROPN
ap-1400	183	61	524	524	NUM
ap-1400	183	62	3	3	NUM
ap-1400	183	63	with	with	ADP
ap-1400	183	64	the	the	DET
ap-1400	183	65	jordan	jordan	PROPN
ap-1400	183	66	block	block	NOUN
ap-1400	183	67	of	of	ADP
ap-1400	183	68	the	the	DET
ap-1400	183	69	third	third	ADJ
ap-1400	183	70	order	order	NOUN
ap-1400	183	71	,	,	PUNCT
ap-1400	183	72	cf	cf	NOUN
ap-1400	183	73	.	.	PUNCT
ap-1400	184	1	[	[	X
ap-1400	184	2	11,12	11,12	X
ap-1400	184	3	]	]	PUNCT
ap-1400	184	4	where	where	SCONJ
ap-1400	184	5	at	at	ADP
ap-1400	184	6	such	such	DET
ap-1400	184	7	a	a	DET
ap-1400	184	8	singular	singular	ADJ
ap-1400	184	9	point	point	NOUN
ap-1400	184	10	a	a	DET
ap-1400	184	11	maximum	maximum	NOUN
ap-1400	184	12	of	of	ADP
ap-1400	184	13	the	the	DET
ap-1400	184	14	critical	critical	ADJ
ap-1400	184	15	flutter	flutter	NOUN
ap-1400	184	16	load	load	NOUN
ap-1400	184	17	was	be	AUX
ap-1400	184	18	found	find	VERB
ap-1400	184	19	for	for	ADP
ap-1400	184	20	a	a	DET
ap-1400	184	21	free	free	ADJ
ap-1400	184	22	-	-	PUNCT
ap-1400	184	23	free	free	ADJ
ap-1400	184	24	beam	beam	NOUN
ap-1400	184	25	under	under	ADP
ap-1400	184	26	the	the	DET
ap-1400	184	27	follower	follower	NOUN
ap-1400	184	28	thrust	thrust	NOUN
ap-1400	184	29	.	.	PUNCT
ap-1400	185	1	with	with	ADP
ap-1400	185	2	a	a	DET
ap-1400	185	3	further	further	ADJ
ap-1400	185	4	increase	increase	NOUN
ap-1400	185	5	in	in	ADP
ap-1400	185	6	the	the	DET
ap-1400	185	7	first	first	ADJ
ap-1400	185	8	mass	mass	NOUN
ap-1400	185	9	up	up	ADP
ap-1400	185	10	to	to	ADP
ap-1400	185	11	m1	m1	PROPN
ap-1400	185	12	=	=	NUM
ap-1400	185	13	200	200	NUM
ap-1400	185	14	,	,	PUNCT
ap-1400	185	15	the	the	DET
ap-1400	185	16	stability	stability	NOUN
ap-1400	185	17	diagram	diagram	NOUN
ap-1400	185	18	converges	converge	VERB
ap-1400	185	19	to	to	ADP
ap-1400	185	20	that	that	PRON
ap-1400	185	21	similar	similar	ADJ
ap-1400	185	22	to	to	ADP
ap-1400	185	23	the	the	DET
ap-1400	185	24	diagram	diagram	NOUN
ap-1400	185	25	of	of	ADP
ap-1400	185	26	the	the	DET
ap-1400	185	27	two	two	NUM
ap-1400	185	28	-	-	PUNCT
ap-1400	185	29	link	link	NOUN
ap-1400	185	30	pendulum	pendulum	NOUN
ap-1400	185	31	,	,	PUNCT
ap-1400	185	32	cf	cf	NOUN
ap-1400	185	33	.	.	PUNCT
ap-1400	185	34	figure	figure	NOUN
ap-1400	185	35	2	2	NUM
ap-1400	185	36	and	and	CCONJ
ap-1400	185	37	figure	figure	VERB
ap-1400	185	38	3(c	3(c	NUM
ap-1400	185	39	)	)	PUNCT
ap-1400	185	40	.	.	PUNCT
ap-1400	186	1	this	this	PRON
ap-1400	186	2	is	be	AUX
ap-1400	186	3	not	not	PART
ap-1400	186	4	surprising	surprising	ADJ
ap-1400	186	5	because	because	SCONJ
ap-1400	186	6	big	big	ADJ
ap-1400	186	7	inertia	inertia	NOUN
ap-1400	186	8	of	of	ADP
ap-1400	186	9	the	the	DET
ap-1400	186	10	first	first	ADJ
ap-1400	186	11	joint	joint	NOUN
ap-1400	186	12	makes	make	VERB
ap-1400	186	13	the	the	DET
ap-1400	186	14	three	three	NUM
ap-1400	186	15	-	-	PUNCT
ap-1400	186	16	link	link	NOUN
ap-1400	186	17	pendulum	pendulum	NOUN
ap-1400	186	18	effectively	effectively	ADV
ap-1400	186	19	a	a	DET
ap-1400	186	20	two	two	NUM
ap-1400	186	21	-	-	PUNCT
ap-1400	186	22	link	link	NOUN
ap-1400	186	23	pendulum	pendulum	NOUN
ap-1400	186	24	.	.	PUNCT
ap-1400	187	1	the	the	DET
ap-1400	187	2	right	right	ADJ
ap-1400	187	3	column	column	NOUN
ap-1400	187	4	in	in	ADP
ap-1400	187	5	figure	figure	NOUN
ap-1400	187	6	3	3	NUM
ap-1400	187	7	corresponds	correspond	NOUN
ap-1400	187	8	to	to	ADP
ap-1400	187	9	the	the	DET
ap-1400	187	10	fixed	fix	VERB
ap-1400	187	11	first	first	ADJ
ap-1400	187	12	mass	mass	NOUN
ap-1400	187	13	m1	m1	NOUN
ap-1400	187	14	=	=	SYM
ap-1400	187	15	5	5	NUM
ap-1400	187	16	and	and	CCONJ
ap-1400	187	17	varied	varied	ADJ
ap-1400	187	18	radial	radial	ADJ
ap-1400	187	19	distance	distance	NOUN
ap-1400	187	20	r	r	NOUN
ap-1400	187	21	in	in	ADP
ap-1400	187	22	the	the	DET
ap-1400	187	23	(	(	PUNCT
ap-1400	187	24	m2	m2	PROPN
ap-1400	187	25	,	,	PUNCT
ap-1400	187	26	m3)-plane	m3)-plane	PROPN
ap-1400	187	27	.	.	PUNCT
ap-1400	187	28	small	small	ADJ
ap-1400	187	29	values	value	NOUN
ap-1400	187	30	of	of	ADP
ap-1400	187	31	r	r	NOUN
ap-1400	187	32	correspond	correspond	VERB
ap-1400	187	33	effectively	effectively	ADV
ap-1400	187	34	to	to	ADP
ap-1400	187	35	a	a	DET
ap-1400	187	36	two	two	NUM
ap-1400	187	37	-	-	PUNCT
ap-1400	187	38	link	link	NOUN
ap-1400	187	39	pendulum	pendulum	NOUN
ap-1400	187	40	.	.	PUNCT
ap-1400	188	1	that	that	PRON
ap-1400	188	2	is	be	AUX
ap-1400	188	3	why	why	SCONJ
ap-1400	188	4	figure	figure	VERB
ap-1400	188	5	3(f	3(f	NUM
ap-1400	188	6	)	)	PUNCT
ap-1400	188	7	with	with	ADP
ap-1400	188	8	r	r	NOUN
ap-1400	188	9	=	=	SYM
ap-1400	188	10	0.1	0.1	NUM
ap-1400	188	11	looks	look	VERB
ap-1400	188	12	similar	similar	ADJ
ap-1400	188	13	to	to	PART
ap-1400	188	14	figure	figure	VERB
ap-1400	188	15	3(c	3(c	NUM
ap-1400	188	16	)	)	PUNCT
ap-1400	188	17	and	and	CCONJ
ap-1400	188	18	figure	figure	VERB
ap-1400	188	19	2	2	NUM
ap-1400	188	20	.	.	PUNCT
ap-1400	188	21	an	an	DET
ap-1400	188	22	increase	increase	NOUN
ap-1400	188	23	in	in	ADP
ap-1400	188	24	r	r	NOUN
ap-1400	188	25	is	be	AUX
ap-1400	188	26	accompanied	accompany	VERB
ap-1400	188	27	by	by	ADP
ap-1400	188	28	a	a	DET
ap-1400	188	29	complication	complication	NOUN
ap-1400	188	30	of	of	ADP
ap-1400	188	31	the	the	DET
ap-1400	188	32	stability	stability	NOUN
ap-1400	188	33	diagram	diagram	NOUN
ap-1400	188	34	.	.	PUNCT
ap-1400	189	1	in	in	ADP
ap-1400	189	2	particular	particular	ADJ
ap-1400	189	3	,	,	PUNCT
ap-1400	189	4	two	two	NUM
ap-1400	189	5	cusp	cusp	NOUN
ap-1400	189	6	point	point	NOUN
ap-1400	189	7	singularities	singularity	NOUN
ap-1400	189	8	originate	originate	VERB
ap-1400	189	9	corresponding	correspond	VERB
ap-1400	189	10	to	to	ADP
ap-1400	189	11	triple	triple	ADJ
ap-1400	189	12	pure	pure	ADJ
ap-1400	189	13	imaginary	imaginary	ADJ
ap-1400	189	14	eigenvalues	eigenvalue	NOUN
ap-1400	189	15	with	with	ADP
ap-1400	189	16	the	the	DET
ap-1400	189	17	jordan	jordan	PROPN
ap-1400	189	18	block	block	PROPN
ap-1400	189	19	,	,	PUNCT
ap-1400	189	20	figure	figure	VERB
ap-1400	189	21	3(d	3(d	NUM
ap-1400	189	22	,	,	PUNCT
ap-1400	189	23	e	e	NOUN
ap-1400	189	24	)	)	PUNCT
ap-1400	189	25	.	.	PUNCT
ap-1400	190	1	38	38	NUM
ap-1400	190	2	acta	acta	PROPN
ap-1400	190	3	polytechnica	polytechnica	PROPN
ap-1400	190	4	vol	vol	NOUN
ap-1400	190	5	.	.	PUNCT
ap-1400	191	1	51	51	NUM
ap-1400	191	2	no	no	INTJ
ap-1400	191	3	.	.	PUNCT
ap-1400	192	1	4/2011	4/2011	NUM
ap-1400	192	2	near	near	ADP
ap-1400	192	3	these	these	DET
ap-1400	192	4	singularities	singularity	NOUN
ap-1400	192	5	,	,	PUNCT
ap-1400	192	6	the	the	DET
ap-1400	192	7	stability	stability	NOUN
ap-1400	192	8	boundary	boundary	ADJ
ap-1400	192	9	experiences	experience	NOUN
ap-1400	192	10	a	a	DET
ap-1400	192	11	sharp	sharp	ADJ
ap-1400	192	12	turn	turn	NOUN
ap-1400	192	13	at	at	ADP
ap-1400	192	14	points	point	NOUN
ap-1400	192	15	b1	b1	NOUN
ap-1400	192	16	and	and	CCONJ
ap-1400	192	17	b2	b2	NOUN
ap-1400	192	18	,	,	PUNCT
ap-1400	192	19	where	where	SCONJ
ap-1400	192	20	the	the	DET
ap-1400	192	21	tangent	tangent	NOUN
ap-1400	192	22	to	to	ADP
ap-1400	192	23	the	the	DET
ap-1400	192	24	boundary	boundary	NOUN
ap-1400	192	25	is	be	AUX
ap-1400	192	26	vertical	vertical	ADJ
ap-1400	192	27	.	.	PUNCT
ap-1400	193	1	at	at	ADP
ap-1400	193	2	such	such	ADJ
ap-1400	193	3	points	point	NOUN
ap-1400	193	4	the	the	DET
ap-1400	193	5	eigencurves	eigencurve	NOUN
ap-1400	193	6	imλ(p	imλ(p	PART
ap-1400	193	7	)	)	PUNCT
ap-1400	193	8	form	form	VERB
ap-1400	193	9	a	a	DET
ap-1400	193	10	crossing	crossing	NOUN
ap-1400	193	11	that	that	PRON
ap-1400	193	12	can	can	AUX
ap-1400	193	13	change	change	VERB
ap-1400	193	14	either	either	ADV
ap-1400	193	15	to	to	PART
ap-1400	193	16	avoided	avoid	VERB
ap-1400	193	17	crossing	crossing	NOUN
ap-1400	193	18	or	or	CCONJ
ap-1400	193	19	to	to	ADP
ap-1400	193	20	overlapping	overlap	VERB
ap-1400	193	21	with	with	ADP
ap-1400	193	22	the	the	DET
ap-1400	193	23	origination	origination	NOUN
ap-1400	193	24	of	of	ADP
ap-1400	193	25	a	a	DET
ap-1400	193	26	bubble	bubble	NOUN
ap-1400	193	27	of	of	ADP
ap-1400	193	28	complex	complex	ADJ
ap-1400	193	29	eigenvalues	eigenvalue	NOUN
ap-1400	193	30	in	in	ADP
ap-1400	193	31	dependence	dependence	NOUN
ap-1400	193	32	on	on	ADP
ap-1400	193	33	the	the	DET
ap-1400	193	34	direction	direction	NOUN
ap-1400	193	35	of	of	ADP
ap-1400	193	36	variation	variation	NOUN
ap-1400	193	37	of	of	ADP
ap-1400	193	38	azimuth	azimuth	PROPN
ap-1400	193	39	angle	angle	PROPN
ap-1400	193	40	α	α	NOUN
ap-1400	193	41	.	.	PUNCT
ap-1400	194	1	this	this	DET
ap-1400	194	2	phenomenon	phenomenon	NOUN
ap-1400	194	3	has	have	AUX
ap-1400	194	4	been	be	AUX
ap-1400	194	5	observed	observe	VERB
ap-1400	194	6	in	in	ADP
ap-1400	194	7	many	many	ADJ
ap-1400	194	8	numerical	numerical	ADJ
ap-1400	194	9	studies	study	NOUN
ap-1400	194	10	of	of	ADP
ap-1400	194	11	non	non	ADJ
ap-1400	194	12	-	-	ADJ
ap-1400	194	13	conservative	conservative	ADJ
ap-1400	194	14	optimization	optimization	NOUN
ap-1400	194	15	problems	problem	NOUN
ap-1400	194	16	[	[	X
ap-1400	194	17	4	4	NUM
ap-1400	194	18	,	,	PUNCT
ap-1400	194	19	6	6	NUM
ap-1400	194	20	,	,	PUNCT
ap-1400	194	21	7	7	NUM
ap-1400	194	22	,	,	PUNCT
ap-1400	194	23	9	9	NUM
ap-1400	194	24	,	,	PUNCT
ap-1400	194	25	10	10	NUM
ap-1400	194	26	,	,	PUNCT
ap-1400	194	27	13	13	NUM
ap-1400	194	28	,	,	PUNCT
ap-1400	194	29	14,17	14,17	NUM
ap-1400	194	30	,	,	PUNCT
ap-1400	194	31	18	18	NUM
ap-1400	194	32	]	]	PUNCT
ap-1400	194	33	and	and	CCONJ
ap-1400	194	34	was	be	AUX
ap-1400	194	35	described	describe	VERB
ap-1400	194	36	analytically	analytically	ADV
ap-1400	194	37	by	by	ADP
ap-1400	194	38	kirillov	kirillov	NOUN
ap-1400	194	39	and	and	CCONJ
ap-1400	194	40	seyranian	seyranian	ADJ
ap-1400	194	41	in	in	ADP
ap-1400	194	42	[	[	X
ap-1400	194	43	27	27	NUM
ap-1400	194	44	,	,	PUNCT
ap-1400	194	45	28	28	NUM
ap-1400	194	46	]	]	PUNCT
ap-1400	194	47	.	.	PUNCT
ap-1400	195	1	moreover	moreover	ADV
ap-1400	195	2	,	,	PUNCT
ap-1400	195	3	the	the	DET
ap-1400	195	4	critical	critical	ADJ
ap-1400	195	5	load	load	NOUN
ap-1400	195	6	at	at	ADP
ap-1400	195	7	these	these	DET
ap-1400	195	8	points	point	NOUN
ap-1400	195	9	can	can	AUX
ap-1400	195	10	jump	jump	VERB
ap-1400	195	11	to	to	ADP
ap-1400	195	12	a	a	DET
ap-1400	195	13	higher	high	ADJ
ap-1400	195	14	value	value	NOUN
ap-1400	195	15	corresponding	correspond	VERB
ap-1400	195	16	to	to	ADP
ap-1400	195	17	the	the	DET
ap-1400	195	18	merging	merging	NOUN
ap-1400	195	19	of	of	ADP
ap-1400	195	20	other	other	ADJ
ap-1400	195	21	(	(	PUNCT
ap-1400	195	22	often	often	ADV
ap-1400	195	23	higher	high	ADJ
ap-1400	195	24	)	)	PUNCT
ap-1400	195	25	modes	mode	NOUN
ap-1400	195	26	,	,	PUNCT
ap-1400	195	27	and	and	CCONJ
ap-1400	195	28	is	be	AUX
ap-1400	195	29	thus	thus	ADV
ap-1400	195	30	undefined	undefined	ADJ
ap-1400	195	31	[	[	X
ap-1400	195	32	4,6,7	4,6,7	NOUN
ap-1400	195	33	]	]	PUNCT
ap-1400	195	34	.	.	PUNCT
ap-1400	196	1	nevertheless	nevertheless	ADV
ap-1400	196	2	,	,	PUNCT
ap-1400	196	3	these	these	DET
ap-1400	196	4	points	point	NOUN
ap-1400	196	5	could	could	AUX
ap-1400	196	6	be	be	AUX
ap-1400	196	7	local	local	ADJ
ap-1400	196	8	extrema	extrema	NOUN
ap-1400	196	9	of	of	ADP
ap-1400	196	10	the	the	DET
ap-1400	196	11	merit	merit	NOUN
ap-1400	196	12	functional	functional	ADJ
ap-1400	196	13	,	,	PUNCT
ap-1400	196	14	see	see	VERB
ap-1400	196	15	[	[	X
ap-1400	196	16	29	29	NUM
ap-1400	196	17	]	]	PUNCT
ap-1400	196	18	where	where	SCONJ
ap-1400	196	19	the	the	DET
ap-1400	196	20	necessary	necessary	ADJ
ap-1400	196	21	conditions	condition	NOUN
ap-1400	196	22	for	for	ADP
ap-1400	196	23	that	that	PRON
ap-1400	196	24	were	be	AUX
ap-1400	196	25	derived	derive	VERB
ap-1400	196	26	.	.	PUNCT
ap-1400	197	1	we	we	PRON
ap-1400	197	2	stress	stress	VERB
ap-1400	197	3	that	that	SCONJ
ap-1400	197	4	due	due	ADP
ap-1400	197	5	to	to	ADP
ap-1400	197	6	the	the	DET
ap-1400	197	7	finite	finite	ADJ
ap-1400	197	8	number	number	NOUN
ap-1400	197	9	of	of	ADP
ap-1400	197	10	degrees	degree	NOUN
ap-1400	197	11	of	of	ADP
ap-1400	197	12	freedom	freedom	NOUN
ap-1400	197	13	and	and	CCONJ
ap-1400	197	14	the	the	DET
ap-1400	197	15	finite	finite	ADJ
ap-1400	197	16	number	number	NOUN
ap-1400	197	17	of	of	ADP
ap-1400	197	18	control	control	NOUN
ap-1400	197	19	parameters	parameter	NOUN
ap-1400	197	20	the	the	DET
ap-1400	197	21	stability	stability	NOUN
ap-1400	197	22	boundary	boundary	NOUN
ap-1400	197	23	of	of	ADP
ap-1400	197	24	an	an	DET
ap-1400	197	25	m	m	NOUN
ap-1400	197	26	-	-	PUNCT
ap-1400	197	27	link	link	ADJ
ap-1400	197	28	ziegler	ziegler	NOUN
ap-1400	197	29	pendulum	pendulum	NOUN
ap-1400	197	30	can	can	AUX
ap-1400	197	31	be	be	AUX
ap-1400	197	32	thoroughly	thoroughly	ADV
ap-1400	197	33	analyzed	analyze	VERB
ap-1400	197	34	both	both	CCONJ
ap-1400	197	35	analytically	analytically	ADV
ap-1400	197	36	and	and	CCONJ
ap-1400	197	37	numerically	numerically	ADV
ap-1400	197	38	.	.	PUNCT
ap-1400	198	1	in	in	ADP
ap-1400	198	2	particular	particular	ADJ
ap-1400	198	3	,	,	PUNCT
ap-1400	198	4	the	the	DET
ap-1400	198	5	coordinates	coordinate	NOUN
ap-1400	198	6	of	of	ADP
ap-1400	198	7	the	the	DET
ap-1400	198	8	singular	singular	ADJ
ap-1400	198	9	points	point	NOUN
ap-1400	198	10	can	can	AUX
ap-1400	198	11	be	be	AUX
ap-1400	198	12	calculated	calculate	VERB
ap-1400	198	13	with	with	ADP
ap-1400	198	14	arbitrary	arbitrary	ADJ
ap-1400	198	15	precision	precision	NOUN
ap-1400	198	16	and	and	CCONJ
ap-1400	198	17	thus	thus	ADV
ap-1400	198	18	the	the	DET
ap-1400	198	19	issues	issue	NOUN
ap-1400	198	20	of	of	ADP
ap-1400	198	21	high	high	ADJ
ap-1400	198	22	sensitivity	sensitivity	NOUN
ap-1400	198	23	of	of	ADP
ap-1400	198	24	the	the	DET
ap-1400	198	25	critical	critical	ADJ
ap-1400	198	26	flutter	flutter	NOUN
ap-1400	198	27	load	load	NOUN
ap-1400	198	28	at	at	ADP
ap-1400	198	29	the	the	DET
ap-1400	198	30	optima	optima	PROPN
ap-1400	198	31	could	could	AUX
ap-1400	198	32	be	be	AUX
ap-1400	198	33	successfully	successfully	ADV
ap-1400	198	34	resolved	resolve	VERB
ap-1400	198	35	in	in	ADP
ap-1400	198	36	this	this	DET
ap-1400	198	37	model	model	NOUN
ap-1400	198	38	,	,	PUNCT
ap-1400	198	39	unlike	unlike	ADP
ap-1400	198	40	the	the	DET
ap-1400	198	41	optimization	optimization	NOUN
ap-1400	198	42	problems	problem	NOUN
ap-1400	198	43	for	for	ADP
ap-1400	198	44	distributed	distribute	VERB
ap-1400	198	45	systems	system	NOUN
ap-1400	198	46	.	.	PUNCT
ap-1400	199	1	the	the	DET
ap-1400	199	2	possibility	possibility	NOUN
ap-1400	199	3	to	to	PART
ap-1400	199	4	work	work	VERB
ap-1400	199	5	with	with	ADP
ap-1400	199	6	singularities	singularity	NOUN
ap-1400	199	7	related	relate	VERB
ap-1400	199	8	to	to	ADP
ap-1400	199	9	coalescence	coalescence	NOUN
ap-1400	199	10	of	of	ADP
ap-1400	199	11	more	more	ADJ
ap-1400	199	12	than	than	ADP
ap-1400	199	13	two	two	NUM
ap-1400	199	14	eigenvalues	eigenvalue	NOUN
ap-1400	199	15	allows	allow	VERB
ap-1400	199	16	us	we	PRON
ap-1400	199	17	to	to	PART
ap-1400	199	18	make	make	VERB
ap-1400	199	19	a	a	DET
ap-1400	199	20	qualitative	qualitative	ADJ
ap-1400	199	21	investigation	investigation	NOUN
ap-1400	199	22	of	of	ADP
ap-1400	199	23	the	the	DET
ap-1400	199	24	question	question	NOUN
ap-1400	199	25	‘	'	PUNCT
ap-1400	199	26	should	should	AUX
ap-1400	199	27	low	low	ADJ
ap-1400	199	28	-	-	PUNCT
ap-1400	199	29	order	order	NOUN
ap-1400	199	30	models	model	NOUN
ap-1400	199	31	be	be	AUX
ap-1400	199	32	believed	believe	VERB
ap-1400	199	33	?	?	PUNCT
ap-1400	199	34	’	'	PUNCT
ap-1400	200	1	[	[	X
ap-1400	200	2	31	31	NUM
ap-1400	200	3	]	]	PUNCT
ap-1400	200	4	.	.	PUNCT
ap-1400	201	1	although	although	SCONJ
ap-1400	201	2	two	two	NUM
ap-1400	201	3	-	-	PUNCT
ap-1400	201	4	mode	mode	NOUN
ap-1400	201	5	approximations	approximation	NOUN
ap-1400	201	6	work	work	VERB
ap-1400	201	7	well	well	ADV
ap-1400	201	8	far	far	ADV
ap-1400	201	9	from	from	ADP
ap-1400	201	10	such	such	ADJ
ap-1400	201	11	singularities	singularity	NOUN
ap-1400	201	12	,	,	PUNCT
ap-1400	201	13	in	in	ADP
ap-1400	201	14	their	their	PRON
ap-1400	201	15	vicinity	vicinity	NOUN
ap-1400	201	16	we	we	PRON
ap-1400	201	17	have	have	VERB
ap-1400	201	18	to	to	PART
ap-1400	201	19	take	take	VERB
ap-1400	201	20	into	into	ADP
ap-1400	201	21	account	account	NOUN
ap-1400	201	22	higher	high	ADJ
ap-1400	201	23	modes	mode	NOUN
ap-1400	201	24	.	.	PUNCT
ap-1400	202	1	2.3	2.3	NUM
ap-1400	202	2	damped	damped	NOUN
ap-1400	202	3	case	case	NOUN
ap-1400	202	4	in	in	ADP
ap-1400	202	5	the	the	DET
ap-1400	202	6	presence	presence	NOUN
ap-1400	202	7	of	of	ADP
ap-1400	202	8	dissipation	dissipation	NOUN
ap-1400	202	9	,	,	PUNCT
ap-1400	202	10	the	the	DET
ap-1400	202	11	equation	equation	NOUN
ap-1400	202	12	of	of	ADP
ap-1400	202	13	the	the	DET
ap-1400	202	14	ziegler	ziegler	PROPN
ap-1400	202	15	pendulum	pendulum	NOUN
ap-1400	202	16	is	be	AUX
ap-1400	202	17	mẍ+dẋ+kx	mẍ+dẋ+kx	NOUN
ap-1400	202	18	=	=	SYM
ap-1400	202	19	0	0	NUM
ap-1400	202	20	(	(	PUNCT
ap-1400	202	21	18	18	NUM
ap-1400	202	22	)	)	PUNCT
ap-1400	202	23	with	with	ADP
ap-1400	202	24	the	the	DET
ap-1400	202	25	damping	damp	VERB
ap-1400	202	26	matrix	matrix	NOUN
ap-1400	202	27	[	[	X
ap-1400	202	28	25	25	NUM
ap-1400	202	29	,	,	PUNCT
ap-1400	202	30	26	26	NUM
ap-1400	202	31	]	]	X
ap-1400	202	32	d	d	NOUN
ap-1400	202	33	=	=	SYM
ap-1400	202	34	⎛⎜⎜⎜⎜⎜⎜⎜⎝	⎛⎜⎜⎜⎜⎜⎜⎜⎝	NOUN
ap-1400	202	35	d1	d1	NOUN
ap-1400	202	36	+	+	CCONJ
ap-1400	202	37	d2	d2	PROPN
ap-1400	202	38	−d2	−d2	X
ap-1400	202	39	·	·	PUNCT
ap-1400	202	40	·	·	PUNCT
ap-1400	202	41	·	·	PUNCT
ap-1400	203	1	0	0	PUNCT
ap-1400	203	2	0	0	NUM
ap-1400	204	1	−d2	−d2	PROPN
ap-1400	204	2	d2	d2	PROPN
ap-1400	204	3	+	+	CCONJ
ap-1400	204	4	d3	d3	PROPN
ap-1400	204	5	·	·	PUNCT
ap-1400	204	6	·	·	PUNCT
ap-1400	204	7	·	·	PUNCT
ap-1400	204	8	0	0	NUM
ap-1400	204	9	0	0	NUM
ap-1400	204	10	·	·	PUNCT
ap-1400	204	11	·	·	PUNCT
ap-1400	204	12	·	·	PUNCT
ap-1400	204	13	·	·	PUNCT
ap-1400	204	14	·	·	PUNCT
ap-1400	204	15	·	·	PUNCT
ap-1400	204	16	·	·	PUNCT
ap-1400	204	17	·	·	PUNCT
ap-1400	204	18	·	·	PUNCT
ap-1400	204	19	·	·	PUNCT
ap-1400	204	20	·	·	PUNCT
ap-1400	204	21	·	·	PUNCT
ap-1400	204	22	·	·	PUNCT
ap-1400	204	23	·	·	PUNCT
ap-1400	204	24	·	·	PUNCT
ap-1400	204	25	0	0	NUM
ap-1400	204	26	0	0	NUM
ap-1400	204	27	·	·	PUNCT
ap-1400	204	28	·	·	PUNCT
ap-1400	204	29	·	·	PUNCT
ap-1400	204	30	dm−1	dm−1	NOUN
ap-1400	204	31	+	+	CCONJ
ap-1400	204	32	dm	dm	X
ap-1400	204	33	−dm−1	−dm−1	NOUN
ap-1400	204	34	0	0	NUM
ap-1400	204	35	0	0	NUM
ap-1400	204	36	·	·	PUNCT
ap-1400	204	37	·	·	PUNCT
ap-1400	204	38	·	·	PUNCT
ap-1400	204	39	−dm−1	−dm−1	X
ap-1400	204	40	dm	dm	PROPN
ap-1400	204	41	⎞⎟⎟⎟⎟⎟⎟⎟⎠	⎞⎟⎟⎟⎟⎟⎟⎟⎠	PROPN
ap-1400	204	42	.	.	PUNCT
ap-1400	205	1	(	(	PUNCT
ap-1400	205	2	19	19	NUM
ap-1400	205	3	)	)	PUNCT
ap-1400	205	4	for	for	ADP
ap-1400	205	5	the	the	DET
ap-1400	205	6	two	two	NUM
ap-1400	205	7	-	-	PUNCT
ap-1400	205	8	link	link	NOUN
ap-1400	205	9	damped	damp	VERB
ap-1400	205	10	ziegler	ziegler	PROPN
ap-1400	205	11	pendulum	pendulum	NOUN
ap-1400	205	12	with	with	ADP
ap-1400	205	13	m	m	PROPN
ap-1400	205	14	=	=	SYM
ap-1400	205	15	2	2	NUM
ap-1400	205	16	,	,	PUNCT
ap-1400	205	17	we	we	PRON
ap-1400	205	18	find	find	VERB
ap-1400	205	19	the	the	DET
ap-1400	205	20	characteristic	characteristic	ADJ
ap-1400	205	21	equation	equation	NOUN
ap-1400	205	22	a0λ	a0λ	NOUN
ap-1400	205	23	4	4	NUM
ap-1400	205	24	+	+	CCONJ
ap-1400	205	25	a1λ	a1λ	PROPN
ap-1400	205	26	3	3	NUM
ap-1400	205	27	+	+	NUM
ap-1400	205	28	a2λ	a2λ	NOUN
ap-1400	205	29	2	2	NUM
ap-1400	205	30	+	+	CCONJ
ap-1400	205	31	a3λ	a3λ	NOUN
ap-1400	205	32	+	+	NOUN
ap-1400	205	33	a4	a4	NOUN
ap-1400	205	34	=	=	SYM
ap-1400	205	35	0	0	NUM
ap-1400	205	36	.	.	PUNCT
ap-1400	206	1	(	(	PUNCT
ap-1400	206	2	20	20	NUM
ap-1400	206	3	)	)	PUNCT
ap-1400	206	4	with	with	ADP
ap-1400	206	5	the	the	DET
ap-1400	206	6	coefficients	coefficient	NOUN
ap-1400	206	7	a0	a0	NOUN
ap-1400	206	8	=	=	SYM
ap-1400	206	9	l4m1m2	l4m1m2	X
ap-1400	206	10	,	,	PUNCT
ap-1400	206	11	a1	a1	NOUN
ap-1400	206	12	=	=	PUNCT
ap-1400	206	13	l2(m1d2	l2(m1d2	PROPN
ap-1400	206	14	+	+	CCONJ
ap-1400	206	15	d1m2	d1m2	X
ap-1400	206	16	+	+	X
ap-1400	206	17	4m2d2	4m2d2	NOUN
ap-1400	206	18	)	)	PUNCT
ap-1400	206	19	,	,	PUNCT
ap-1400	206	20	a2	a2	PROPN
ap-1400	206	21	=	=	PUNCT
ap-1400	206	22	d1d2	d1d2	PUNCT
ap-1400	207	1	+	+	CCONJ
ap-1400	207	2	m1l	m1l	ADJ
ap-1400	207	3	2c2	2c2	NUM
ap-1400	208	1	+	+	CCONJ
ap-1400	208	2	4m2l	4m2l	NOUN
ap-1400	208	3	2c2	2c2	NUM
ap-1400	209	1	+	+	CCONJ
ap-1400	209	2	c1m2l	c1m2l	NUM
ap-1400	209	3	2	2	NUM
ap-1400	209	4	−	−	PROPN
ap-1400	209	5	2pl3m2	2pl3m2	NUM
ap-1400	209	6	,	,	PUNCT
ap-1400	209	7	a3	a3	NOUN
ap-1400	209	8	=	=	SYM
ap-1400	210	1	d1c2	d1c2	PROPN
ap-1400	211	1	+	+	CCONJ
ap-1400	211	2	c1d2	c1d2	NOUN
ap-1400	211	3	,	,	PUNCT
ap-1400	211	4	a4	a4	NOUN
ap-1400	211	5	=	=	SYM
ap-1400	211	6	c1c2	c1c2	X
ap-1400	211	7	.	.	PUNCT
ap-1400	211	8	(	(	PUNCT
ap-1400	211	9	21	21	NUM
ap-1400	211	10	)	)	PUNCT
ap-1400	211	11	applying	apply	VERB
ap-1400	211	12	the	the	DET
ap-1400	211	13	routh	routh	PROPN
ap-1400	211	14	-	-	PUNCT
ap-1400	211	15	hurwitz	hurwitz	PROPN
ap-1400	211	16	criterion	criterion	NOUN
ap-1400	211	17	,	,	PUNCT
ap-1400	211	18	we	we	PRON
ap-1400	211	19	find	find	VERB
ap-1400	211	20	the	the	DET
ap-1400	211	21	critical	critical	ADJ
ap-1400	211	22	flutter	flutter	NOUN
ap-1400	211	23	load	load	NOUN
ap-1400	211	24	p	p	NOUN
ap-1400	211	25	=	=	PUNCT
ap-1400	211	26	4m22(d	4m22(d	NUM
ap-1400	211	27	2	2	NUM
ap-1400	211	28	2c	2c	NUM
ap-1400	211	29	2	2	NUM
ap-1400	211	30	1	1	NUM
ap-1400	211	31	+	+	CCONJ
ap-1400	211	32	d21c	d21c	VERB
ap-1400	211	33	2	2	NUM
ap-1400	211	34	2	2	NUM
ap-1400	211	35	)	)	PUNCT
ap-1400	211	36	+	+	NUM
ap-1400	211	37	d1d2(8m2(m1	d1d2(8m2(m1	NOUN
ap-1400	211	38	+	+	CCONJ
ap-1400	211	39	2m2)c22	2m2)c22	NUM
ap-1400	211	40	+	+	CCONJ
ap-1400	211	41	(	(	PUNCT
ap-1400	211	42	c1m2	c1m2	X
ap-1400	211	43	−	−	NOUN
ap-1400	211	44	m1c2)2	m1c2)2	NOUN
ap-1400	211	45	)	)	PUNCT
ap-1400	211	46	2(m2l(4m2d2	2(m2l(4m2d2	NUM
ap-1400	211	47	+	+	PUNCT
ap-1400	212	1	d1m2	d1m2	X
ap-1400	212	2	+	+	CCONJ
ap-1400	212	3	m1d2)(c1d2	m1d2)(c1d2	ADJ
ap-1400	212	4	+	+	CCONJ
ap-1400	212	5	d1c2	d1c2	NOUN
ap-1400	212	6	)	)	PUNCT
ap-1400	212	7	+	+	CCONJ
ap-1400	212	8	1	1	NUM
ap-1400	212	9	2	2	NUM
ap-1400	212	10	d1d2	d1d2	DET
ap-1400	212	11	m2l3	m2l3	NOUN
ap-1400	212	12	.	.	PUNCT
ap-1400	213	1	(	(	PUNCT
ap-1400	213	2	22	22	NUM
ap-1400	213	3	)	)	PUNCT
ap-1400	213	4	for	for	ADP
ap-1400	213	5	c1	c1	NOUN
ap-1400	213	6	=	=	PROPN
ap-1400	213	7	c2	c2	PROPN
ap-1400	213	8	=	=	SYM
ap-1400	213	9	1	1	NUM
ap-1400	213	10	,	,	PUNCT
ap-1400	213	11	l	l	NOUN
ap-1400	213	12	=	=	SYM
ap-1400	213	13	1	1	NUM
ap-1400	213	14	,	,	PUNCT
ap-1400	213	15	m1	m1	PROPN
ap-1400	213	16	=	=	SYM
ap-1400	213	17	2	2	NUM
ap-1400	213	18	and	and	CCONJ
ap-1400	213	19	m2	m2	PROPN
ap-1400	213	20	=	=	SYM
ap-1400	213	21	1	1	NUM
ap-1400	213	22	it	it	PRON
ap-1400	213	23	was	be	AUX
ap-1400	213	24	found	find	VERB
ap-1400	213	25	to	to	PART
ap-1400	213	26	be	be	AUX
ap-1400	213	27	[	[	X
ap-1400	213	28	34	34	NUM
ap-1400	213	29	]	]	X
ap-1400	213	30	p	p	NOUN
ap-1400	213	31	=	=	PUNCT
ap-1400	213	32	4d21	4d21	NOUN
ap-1400	214	1	+	+	CCONJ
ap-1400	214	2	33d1d2	33d1d2	NUM
ap-1400	215	1	+	+	CCONJ
ap-1400	215	2	4d22	4d22	NUM
ap-1400	215	3	2(6d2	2(6d2	NUM
ap-1400	216	1	+	+	SYM
ap-1400	216	2	d1)(d2	d1)(d2	NOUN
ap-1400	216	3	+	+	CCONJ
ap-1400	216	4	d1	d1	NOUN
ap-1400	216	5	)	)	PUNCT
ap-1400	217	1	+	+	CCONJ
ap-1400	217	2	1	1	NUM
ap-1400	217	3	2	2	NUM
ap-1400	217	4	d1d2	d1d2	NOUN
ap-1400	217	5	.	.	PUNCT
ap-1400	218	1	(	(	PUNCT
ap-1400	218	2	23	23	NUM
ap-1400	218	3	)	)	PUNCT
ap-1400	218	4	equation	equation	NOUN
ap-1400	218	5	(	(	PUNCT
ap-1400	218	6	23	23	NUM
ap-1400	218	7	)	)	PUNCT
ap-1400	218	8	defines	define	VERB
ap-1400	218	9	a	a	DET
ap-1400	218	10	surface	surface	NOUN
ap-1400	218	11	with	with	ADP
ap-1400	218	12	the	the	DET
ap-1400	218	13	whitney	whitney	NOUN
ap-1400	218	14	umbrella	umbrella	NOUN
ap-1400	218	15	singularity	singularity	NOUN
ap-1400	218	16	in	in	ADP
ap-1400	218	17	the	the	DET
ap-1400	218	18	(	(	PUNCT
ap-1400	218	19	d1	d1	PROPN
ap-1400	218	20	,	,	PUNCT
ap-1400	218	21	d2	d2	PROPN
ap-1400	218	22	,	,	PUNCT
ap-1400	218	23	p	p	NOUN
ap-1400	218	24	)	)	PUNCT
ap-1400	218	25	-space	-space	NOUN
ap-1400	218	26	which	which	PRON
ap-1400	218	27	explains	explain	VERB
ap-1400	218	28	ziegler	ziegler	PROPN
ap-1400	218	29	’s	’s	PART
ap-1400	218	30	destabilization	destabilization	NOUN
ap-1400	218	31	paradox	paradox	NOUN
ap-1400	218	32	by	by	ADP
ap-1400	218	33	vanishing	vanish	VERB
ap-1400	218	34	dissipation	dissipation	NOUN
ap-1400	218	35	[	[	X
ap-1400	218	36	26	26	NUM
ap-1400	218	37	]	]	PUNCT
ap-1400	218	38	,	,	PUNCT
ap-1400	218	39	as	as	SCONJ
ap-1400	218	40	was	be	AUX
ap-1400	218	41	first	first	ADV
ap-1400	218	42	demonstrated	demonstrate	VERB
ap-1400	218	43	by	by	ADP
ap-1400	218	44	bottema	bottema	NOUN
ap-1400	218	45	already	already	ADV
ap-1400	218	46	in	in	ADP
ap-1400	218	47	1956	1956	NUM
ap-1400	219	1	[	[	X
ap-1400	219	2	32	32	NUM
ap-1400	219	3	,	,	PUNCT
ap-1400	219	4	35	35	NUM
ap-1400	219	5	]	]	PUNCT
ap-1400	219	6	.	.	PUNCT
ap-1400	220	1	in	in	ADP
ap-1400	220	2	contrast	contrast	NOUN
ap-1400	220	3	to	to	ADP
ap-1400	220	4	earlier	early	ADJ
ap-1400	220	5	studies	study	NOUN
ap-1400	220	6	,	,	PUNCT
ap-1400	220	7	e.g.	e.g.	ADV
ap-1400	220	8	[	[	X
ap-1400	220	9	32	32	NUM
ap-1400	220	10	,	,	PUNCT
ap-1400	220	11	34–36	34–36	NUM
ap-1400	220	12	]	]	PUNCT
ap-1400	220	13	,	,	PUNCT
ap-1400	220	14	we	we	PRON
ap-1400	220	15	consider	consider	VERB
ap-1400	220	16	the	the	DET
ap-1400	220	17	critical	critical	ADJ
ap-1400	220	18	flutter	flutter	NOUN
ap-1400	220	19	load	load	NOUN
ap-1400	220	20	(	(	PUNCT
ap-1400	220	21	22	22	NUM
ap-1400	220	22	)	)	PUNCT
ap-1400	220	23	as	as	ADP
ap-1400	220	24	a	a	DET
ap-1400	220	25	function	function	NOUN
ap-1400	220	26	of	of	ADP
ap-1400	220	27	the	the	DET
ap-1400	220	28	masses	masse	NOUN
ap-1400	220	29	p	p	NOUN
ap-1400	220	30	=	=	PUNCT
ap-1400	220	31	p	p	X
ap-1400	220	32	(	(	PUNCT
ap-1400	220	33	m1	m1	PROPN
ap-1400	220	34	,	,	PUNCT
ap-1400	220	35	m2	m2	PROPN
ap-1400	220	36	)	)	PUNCT
ap-1400	220	37	for	for	ADP
ap-1400	220	38	the	the	DET
ap-1400	220	39	fixed	fix	VERB
ap-1400	220	40	damping	damp	VERB
ap-1400	220	41	distribution	distribution	NOUN
ap-1400	220	42	.	.	PUNCT
ap-1400	221	1	39	39	NUM
ap-1400	221	2	acta	acta	PROPN
ap-1400	221	3	polytechnica	polytechnica	PROPN
ap-1400	221	4	vol	vol	NOUN
ap-1400	221	5	.	.	PUNCT
ap-1400	222	1	51	51	NUM
ap-1400	222	2	no	no	NOUN
ap-1400	222	3	.	.	PUNCT
ap-1400	223	1	4/2011	4/2011	NUM
ap-1400	223	2	fig	fig	NOUN
ap-1400	223	3	.	.	PUNCT
ap-1400	224	1	4	4	NUM
ap-1400	224	2	:	:	PUNCT
ap-1400	224	3	damped	damp	VERB
ap-1400	224	4	2	2	NUM
ap-1400	224	5	-	-	PUNCT
ap-1400	224	6	link	link	NOUN
ap-1400	224	7	ziegler	ziegler	NOUN
ap-1400	224	8	pendulum	pendulum	NOUN
ap-1400	224	9	with	with	ADP
ap-1400	224	10	l	l	NOUN
ap-1400	224	11	=	=	SYM
ap-1400	224	12	1	1	NUM
ap-1400	224	13	,	,	PUNCT
ap-1400	224	14	c1	c1	NOUN
ap-1400	224	15	=	=	PROPN
ap-1400	224	16	c2	c2	PROPN
ap-1400	224	17	=	=	SYM
ap-1400	225	1	1	1	NUM
ap-1400	225	2	:	:	PUNCT
ap-1400	225	3	the	the	DET
ap-1400	225	4	critical	critical	ADJ
ap-1400	225	5	flutter	flutter	NOUN
ap-1400	225	6	load	load	NOUN
ap-1400	225	7	p	p	PROPN
ap-1400	225	8	(	(	PUNCT
ap-1400	225	9	α	α	NOUN
ap-1400	225	10	)	)	PUNCT
ap-1400	225	11	as	as	ADP
ap-1400	225	12	a	a	DET
ap-1400	225	13	function	function	NOUN
ap-1400	225	14	of	of	ADP
ap-1400	225	15	the	the	DET
ap-1400	225	16	azimuth	azimuth	PROPN
ap-1400	225	17	angle	angle	NOUN
ap-1400	225	18	α	α	PROPN
ap-1400	225	19	indicating	indicate	VERB
ap-1400	225	20	the	the	DET
ap-1400	225	21	direction	direction	NOUN
ap-1400	225	22	in	in	ADP
ap-1400	225	23	the	the	DET
ap-1400	225	24	(	(	PUNCT
ap-1400	225	25	m1	m1	NOUN
ap-1400	225	26	,	,	PUNCT
ap-1400	225	27	m2)-plane	m2)-plane	NOUN
ap-1400	225	28	for	for	ADP
ap-1400	225	29	(	(	PUNCT
ap-1400	225	30	a	a	PRON
ap-1400	225	31	)	)	PUNCT
ap-1400	225	32	d1	d1	PROPN
ap-1400	225	33	=	=	SYM
ap-1400	225	34	d2	d2	PROPN
ap-1400	225	35	=	=	SYM
ap-1400	225	36	1	1	NUM
ap-1400	225	37	and	and	CCONJ
ap-1400	225	38	r	r	NOUN
ap-1400	225	39	=	=	SYM
ap-1400	225	40	1	1	NUM
ap-1400	225	41	,	,	PUNCT
ap-1400	225	42	(	(	PUNCT
ap-1400	225	43	b	b	X
ap-1400	225	44	)	)	PUNCT
ap-1400	225	45	d1	d1	NOUN
ap-1400	225	46	=	=	SYM
ap-1400	225	47	d2	d2	PROPN
ap-1400	225	48	=	=	SYM
ap-1400	225	49	1	1	NUM
ap-1400	225	50	and	and	CCONJ
ap-1400	225	51	r	r	NOUN
ap-1400	225	52	=	=	SYM
ap-1400	225	53	0.4	0.4	NUM
ap-1400	225	54	,	,	PUNCT
ap-1400	225	55	(	(	PUNCT
ap-1400	225	56	c	c	NOUN
ap-1400	225	57	)	)	PUNCT
ap-1400	225	58	d1	d1	NOUN
ap-1400	225	59	=	=	SYM
ap-1400	225	60	1	1	NUM
ap-1400	225	61	,	,	PUNCT
ap-1400	225	62	d2	d2	PROPN
ap-1400	225	63	=	=	SYM
ap-1400	225	64	0.1	0.1	NUM
ap-1400	225	65	and	and	CCONJ
ap-1400	225	66	r	r	NOUN
ap-1400	225	67	=	=	SYM
ap-1400	225	68	1	1	NUM
ap-1400	225	69	,	,	PUNCT
ap-1400	225	70	(	(	PUNCT
ap-1400	225	71	d	d	X
ap-1400	225	72	)	)	PUNCT
ap-1400	225	73	d1	d1	NOUN
ap-1400	225	74	=	=	SYM
ap-1400	225	75	1	1	NUM
ap-1400	225	76	,	,	PUNCT
ap-1400	225	77	d2	d2	PROPN
ap-1400	225	78	=	=	SYM
ap-1400	225	79	0.1	0.1	NUM
ap-1400	225	80	and	and	CCONJ
ap-1400	225	81	r	r	NOUN
ap-1400	225	82	=	=	SYM
ap-1400	225	83	0.1	0.1	NUM
ap-1400	225	84	in	in	ADP
ap-1400	225	85	figure	figure	NOUN
ap-1400	225	86	4	4	NUM
ap-1400	225	87	,	,	PUNCT
ap-1400	225	88	the	the	DET
ap-1400	225	89	stability	stability	NOUN
ap-1400	225	90	diagrams	diagram	VERB
ap-1400	225	91	for	for	ADP
ap-1400	225	92	the	the	DET
ap-1400	225	93	damped	damped	ADJ
ap-1400	225	94	two	two	NUM
ap-1400	225	95	-	-	PUNCT
ap-1400	225	96	link	link	NOUN
ap-1400	225	97	ziegler	ziegler	NOUN
ap-1400	225	98	pendulum	pendulum	NOUN
ap-1400	225	99	are	be	AUX
ap-1400	225	100	shown	show	VERB
ap-1400	225	101	in	in	ADP
ap-1400	225	102	the	the	DET
ap-1400	225	103	assumption	assumption	NOUN
ap-1400	225	104	of	of	ADP
ap-1400	225	105	c1	c1	PROPN
ap-1400	225	106	=	=	PROPN
ap-1400	225	107	c2	c2	PROPN
ap-1400	225	108	=	=	SYM
ap-1400	225	109	1	1	NUM
ap-1400	225	110	,	,	PUNCT
ap-1400	225	111	l	l	NOUN
ap-1400	225	112	=	=	SYM
ap-1400	225	113	1	1	NUM
ap-1400	225	114	,	,	PUNCT
ap-1400	225	115	m1	m1	NOUN
ap-1400	225	116	=	=	SYM
ap-1400	225	117	r	r	NOUN
ap-1400	225	118	cos	cos	PROPN
ap-1400	225	119	α	α	PROPN
ap-1400	225	120	and	and	CCONJ
ap-1400	225	121	m2	m2	PROPN
ap-1400	225	122	=	=	NOUN
ap-1400	225	123	r	r	NOUN
ap-1400	225	124	sin	sin	NOUN
ap-1400	225	125	α	α	NOUN
ap-1400	225	126	.	.	PUNCT
ap-1400	226	1	the	the	DET
ap-1400	226	2	critical	critical	ADJ
ap-1400	226	3	load	load	NOUN
ap-1400	226	4	p	p	NOUN
ap-1400	226	5	(	(	PUNCT
ap-1400	226	6	m1	m1	PROPN
ap-1400	226	7	,	,	PUNCT
ap-1400	226	8	m2	m2	PROPN
ap-1400	226	9	)	)	PUNCT
ap-1400	226	10	does	do	AUX
ap-1400	226	11	not	not	PART
ap-1400	226	12	constitute	constitute	VERB
ap-1400	226	13	a	a	DET
ap-1400	226	14	ruled	rule	VERB
ap-1400	226	15	surface	surface	NOUN
ap-1400	226	16	and	and	CCONJ
ap-1400	226	17	thus	thus	ADV
ap-1400	226	18	the	the	DET
ap-1400	226	19	function	function	NOUN
ap-1400	226	20	p	p	NOUN
ap-1400	226	21	(	(	PUNCT
ap-1400	226	22	α	α	NOUN
ap-1400	226	23	)	)	PUNCT
ap-1400	226	24	depends	depend	VERB
ap-1400	226	25	on	on	ADP
ap-1400	226	26	the	the	DET
ap-1400	226	27	radial	radial	ADJ
ap-1400	226	28	distance	distance	NOUN
ap-1400	226	29	r	r	NOUN
ap-1400	226	30	in	in	ADP
ap-1400	226	31	the	the	DET
ap-1400	226	32	(	(	PUNCT
ap-1400	226	33	m1	m1	NOUN
ap-1400	226	34	,	,	PUNCT
ap-1400	226	35	m2)-plane	m2)-plane	PROPN
ap-1400	226	36	.	.	PUNCT
ap-1400	227	1	we	we	PRON
ap-1400	227	2	see	see	VERB
ap-1400	227	3	that	that	SCONJ
ap-1400	227	4	the	the	DET
ap-1400	227	5	extrema	extrema	NOUN
ap-1400	227	6	again	again	ADV
ap-1400	227	7	correspond	correspond	VERB
ap-1400	227	8	to	to	ADP
ap-1400	227	9	the	the	DET
ap-1400	227	10	boundary	boundary	ADJ
ap-1400	227	11	points	point	NOUN
ap-1400	227	12	m1	m1	PROPN
ap-1400	227	13	=	=	PUNCT
ap-1400	227	14	0	0	NUM
ap-1400	227	15	and	and	CCONJ
ap-1400	227	16	m2	m2	PROPN
ap-1400	227	17	=	=	SYM
ap-1400	227	18	0	0	PROPN
ap-1400	227	19	,	,	PUNCT
ap-1400	227	20	although	although	SCONJ
ap-1400	227	21	the	the	DET
ap-1400	227	22	singularity	singularity	NOUN
ap-1400	227	23	at	at	ADP
ap-1400	227	24	α	α	PROPN
ap-1400	227	25	=	=	PUNCT
ap-1400	227	26	π/2	π/2	NUM
ap-1400	227	27	is	be	AUX
ap-1400	227	28	an	an	DET
ap-1400	227	29	intersection	intersection	NOUN
ap-1400	227	30	point	point	NOUN
ap-1400	227	31	.	.	PUNCT
ap-1400	228	1	nevertheless	nevertheless	ADV
ap-1400	228	2	,	,	PUNCT
ap-1400	228	3	with	with	ADP
ap-1400	228	4	an	an	DET
ap-1400	228	5	increase	increase	NOUN
ap-1400	228	6	in	in	ADP
ap-1400	228	7	the	the	DET
ap-1400	228	8	number	number	NOUN
ap-1400	228	9	of	of	ADP
ap-1400	228	10	degrees	degree	NOUN
ap-1400	228	11	of	of	ADP
ap-1400	228	12	freedom	freedom	NOUN
ap-1400	228	13	and	and	CCONJ
ap-1400	228	14	control	control	NOUN
ap-1400	228	15	parameters	parameter	NOUN
ap-1400	228	16	new	new	ADJ
ap-1400	228	17	types	type	NOUN
ap-1400	228	18	of	of	ADP
ap-1400	228	19	singularities	singularity	NOUN
ap-1400	228	20	will	will	AUX
ap-1400	228	21	appear	appear	VERB
ap-1400	228	22	.	.	PUNCT
ap-1400	229	1	the	the	DET
ap-1400	229	2	planar	planar	ADJ
ap-1400	229	3	stability	stability	NOUN
ap-1400	229	4	diagrams	diagram	NOUN
ap-1400	229	5	of	of	ADP
ap-1400	229	6	figure	figure	NOUN
ap-1400	229	7	4	4	NUM
ap-1400	229	8	depend	depend	VERB
ap-1400	229	9	on	on	ADP
ap-1400	229	10	the	the	DET
ap-1400	229	11	damping	damp	VERB
ap-1400	229	12	distribution	distribution	NOUN
ap-1400	229	13	but	but	CCONJ
ap-1400	229	14	do	do	AUX
ap-1400	229	15	not	not	PART
ap-1400	229	16	tend	tend	VERB
ap-1400	229	17	to	to	ADP
ap-1400	229	18	that	that	PRON
ap-1400	229	19	of	of	ADP
ap-1400	229	20	the	the	DET
ap-1400	229	21	undamped	undampe	VERB
ap-1400	229	22	pendulum	pendulum	NOUN
ap-1400	229	23	when	when	SCONJ
ap-1400	229	24	damping	damp	VERB
ap-1400	229	25	goes	go	VERB
ap-1400	229	26	to	to	ADP
ap-1400	229	27	zero	zero	NUM
ap-1400	229	28	(	(	PUNCT
ap-1400	229	29	destabilization	destabilization	NOUN
ap-1400	229	30	paradox	paradox	NOUN
ap-1400	229	31	[	[	X
ap-1400	229	32	32	32	NUM
ap-1400	229	33	,	,	PUNCT
ap-1400	229	34	35	35	NUM
ap-1400	229	35	,	,	PUNCT
ap-1400	229	36	36	36	NUM
ap-1400	229	37	]	]	NUM
ap-1400	229	38	)	)	PUNCT
ap-1400	229	39	.	.	PUNCT
ap-1400	230	1	2.4	2.4	NUM
ap-1400	230	2	‘	'	PUNCT
ap-1400	230	3	problema	problema	NOUN
ap-1400	230	4	novum	novum	NOUN
ap-1400	230	5	ad	ad	NOUN
ap-1400	230	6	cuius	cuius	PROPN
ap-1400	230	7	solutionem	solutionem	PROPN
ap-1400	230	8	mathematici	mathematici	PROPN
ap-1400	230	9	invitantur	invitantur	PROPN
ap-1400	230	10	’	'	PUNCT
ap-1400	230	11	‘	'	PUNCT
ap-1400	230	12	a	a	DET
ap-1400	230	13	new	new	ADJ
ap-1400	230	14	problem	problem	NOUN
ap-1400	230	15	that	that	PRON
ap-1400	230	16	mathematicians	mathematician	NOUN
ap-1400	230	17	are	be	AUX
ap-1400	230	18	invited	invite	VERB
ap-1400	230	19	to	to	PART
ap-1400	230	20	solve	solve	VERB
ap-1400	230	21	’	'	PUNCT
ap-1400	230	22	is	be	AUX
ap-1400	230	23	a	a	DET
ap-1400	230	24	translation	translation	NOUN
ap-1400	230	25	of	of	ADP
ap-1400	230	26	the	the	DET
ap-1400	230	27	latin	latin	ADJ
ap-1400	230	28	title	title	NOUN
ap-1400	230	29	of	of	ADP
ap-1400	230	30	the	the	DET
ap-1400	230	31	work	work	NOUN
ap-1400	230	32	by	by	ADP
ap-1400	230	33	j.	j.	PROPN
ap-1400	230	34	bernoulli	bernoulli	PROPN
ap-1400	230	35	published	publish	VERB
ap-1400	230	36	in	in	ADP
ap-1400	230	37	1696	1696	NUM
ap-1400	230	38	where	where	SCONJ
ap-1400	230	39	he	he	PRON
ap-1400	230	40	proposed	propose	VERB
ap-1400	230	41	the	the	DET
ap-1400	230	42	famous	famous	ADJ
ap-1400	230	43	brachistochrone	brachistochrone	NOUN
ap-1400	230	44	problem	problem	NOUN
ap-1400	230	45	[	[	X
ap-1400	230	46	37	37	NUM
ap-1400	230	47	]	]	PUNCT
ap-1400	230	48	.	.	PUNCT
ap-1400	231	1	supporting	support	VERB
ap-1400	231	2	this	this	DET
ap-1400	231	3	good	good	ADJ
ap-1400	231	4	old	old	ADJ
ap-1400	231	5	tradition	tradition	NOUN
ap-1400	231	6	,	,	PUNCT
ap-1400	231	7	we	we	PRON
ap-1400	231	8	would	would	AUX
ap-1400	231	9	like	like	VERB
ap-1400	231	10	to	to	PART
ap-1400	231	11	formulate	formulate	VERB
ap-1400	231	12	the	the	DET
ap-1400	231	13	following	follow	VERB
ap-1400	231	14	optimization	optimization	NOUN
ap-1400	231	15	problem	problem	NOUN
ap-1400	231	16	:	:	PUNCT
ap-1400	231	17	given	give	VERB
ap-1400	231	18	a	a	DET
ap-1400	231	19	circulatory	circulatory	ADJ
ap-1400	231	20	system	system	NOUN
ap-1400	231	21	(	(	PUNCT
ap-1400	231	22	1	1	NUM
ap-1400	231	23	)	)	PUNCT
ap-1400	231	24	with	with	ADP
ap-1400	231	25	matrices	matrix	NOUN
ap-1400	231	26	m	m	VERB
ap-1400	231	27	and	and	CCONJ
ap-1400	231	28	k	k	PROPN
ap-1400	231	29	defined	define	VERB
ap-1400	231	30	as	as	ADP
ap-1400	231	31	in	in	ADP
ap-1400	231	32	(	(	PUNCT
ap-1400	231	33	12	12	NUM
ap-1400	231	34	)	)	PUNCT
ap-1400	231	35	and	and	CCONJ
ap-1400	231	36	(	(	PUNCT
ap-1400	231	37	13	13	NUM
ap-1400	231	38	)	)	PUNCT
ap-1400	231	39	.	.	PUNCT
ap-1400	232	1	find	find	VERB
ap-1400	232	2	all	all	DET
ap-1400	232	3	local	local	ADJ
ap-1400	232	4	extrema	extrema	NOUN
ap-1400	232	5	,	,	PUNCT
ap-1400	232	6	the	the	DET
ap-1400	232	7	absolute	absolute	ADJ
ap-1400	232	8	maximum	maximum	NOUN
ap-1400	232	9	of	of	ADP
ap-1400	232	10	the	the	DET
ap-1400	232	11	critical	critical	ADJ
ap-1400	232	12	flutter	flutter	NOUN
ap-1400	232	13	load	load	NOUN
ap-1400	232	14	p	p	NOUN
ap-1400	232	15	,	,	PUNCT
ap-1400	232	16	and	and	CCONJ
ap-1400	232	17	the	the	DET
ap-1400	232	18	corresponding	corresponding	ADJ
ap-1400	232	19	extremal	extremal	ADJ
ap-1400	232	20	mass	mass	NOUN
ap-1400	232	21	distributions	distribution	NOUN
ap-1400	232	22	{	{	PUNCT
ap-1400	232	23	m1	m1	NOUN
ap-1400	232	24	,	,	PUNCT
ap-1400	232	25	m2	m2	PROPN
ap-1400	232	26	,	,	PUNCT
ap-1400	232	27	.	.	PUNCT
ap-1400	232	28	.	.	PUNCT
ap-1400	233	1	.	.	PUNCT
ap-1400	234	1	,	,	PUNCT
ap-1400	234	2	mm	mm	X
ap-1400	234	3	}	}	PUNCT
ap-1400	234	4	.	.	PUNCT
ap-1400	235	1	we	we	PRON
ap-1400	235	2	can	can	AUX
ap-1400	235	3	also	also	ADV
ap-1400	235	4	consider	consider	VERB
ap-1400	235	5	the	the	DET
ap-1400	235	6	problem	problem	NOUN
ap-1400	235	7	of	of	ADP
ap-1400	235	8	optimal	optimal	ADJ
ap-1400	235	9	stiffness	stiffness	ADJ
ap-1400	235	10	distribution	distribution	NOUN
ap-1400	235	11	or	or	CCONJ
ap-1400	235	12	even	even	ADV
ap-1400	235	13	vary	vary	VERB
ap-1400	235	14	both	both	CCONJ
ap-1400	235	15	stiffness	stiffness	ADJ
ap-1400	235	16	and	and	CCONJ
ap-1400	235	17	mass	mass	NOUN
ap-1400	235	18	.	.	PUNCT
ap-1400	236	1	the	the	DET
ap-1400	236	2	same	same	ADJ
ap-1400	236	3	problems	problem	NOUN
ap-1400	236	4	can	can	AUX
ap-1400	236	5	be	be	AUX
ap-1400	236	6	formulated	formulate	VERB
ap-1400	236	7	for	for	ADP
ap-1400	236	8	the	the	DET
ap-1400	236	9	damped	damped	ADJ
ap-1400	236	10	pendulum	pendulum	NOUN
ap-1400	236	11	with	with	ADP
ap-1400	236	12	the	the	DET
ap-1400	236	13	damping	damp	VERB
ap-1400	236	14	matrix	matrix	NOUN
ap-1400	236	15	(	(	PUNCT
ap-1400	236	16	19	19	NUM
ap-1400	236	17	)	)	PUNCT
ap-1400	236	18	.	.	PUNCT
ap-1400	237	1	we	we	PRON
ap-1400	237	2	expect	expect	VERB
ap-1400	237	3	that	that	SCONJ
ap-1400	237	4	both	both	PRON
ap-1400	237	5	in	in	ADP
ap-1400	237	6	the	the	DET
ap-1400	237	7	undamped	undampe	VERB
ap-1400	237	8	case	case	NOUN
ap-1400	237	9	and	and	CCONJ
ap-1400	237	10	in	in	ADP
ap-1400	237	11	the	the	DET
ap-1400	237	12	damped	damped	NOUN
ap-1400	237	13	case	case	NOUN
ap-1400	237	14	there	there	PRON
ap-1400	237	15	exists	exist	VERB
ap-1400	237	16	a	a	DET
ap-1400	237	17	class	class	NOUN
ap-1400	237	18	of	of	ADP
ap-1400	237	19	extrema	extrema	NOUN
ap-1400	237	20	corresponding	correspond	VERB
ap-1400	237	21	to	to	ADP
ap-1400	237	22	the	the	DET
ap-1400	237	23	distributions	distribution	NOUN
ap-1400	237	24	{	{	PUNCT
ap-1400	237	25	m1	m1	PROPN
ap-1400	237	26	,	,	PUNCT
ap-1400	237	27	m2	m2	PROPN
ap-1400	237	28	,	,	PUNCT
ap-1400	237	29	.	.	PUNCT
ap-1400	237	30	.	.	PUNCT
ap-1400	238	1	.	.	PUNCT
ap-1400	239	1	,	,	PUNCT
ap-1400	239	2	mm	mm	INTJ
ap-1400	239	3	}	}	PUNCT
ap-1400	239	4	with	with	ADP
ap-1400	239	5	some	some	DET
ap-1400	239	6	masses	masse	NOUN
ap-1400	239	7	mi	mi	NOUN
ap-1400	239	8	=	=	NOUN
ap-1400	239	9	0	0	PROPN
ap-1400	239	10	.	.	PUNCT
ap-1400	240	1	it	it	PRON
ap-1400	240	2	should	should	AUX
ap-1400	240	3	be	be	AUX
ap-1400	240	4	possible	possible	ADJ
ap-1400	240	5	to	to	PART
ap-1400	240	6	find	find	VERB
ap-1400	240	7	these	these	DET
ap-1400	240	8	40	40	NUM
ap-1400	240	9	acta	acta	PROPN
ap-1400	240	10	polytechnica	polytechnica	PROPN
ap-1400	240	11	vol	vol	NOUN
ap-1400	240	12	.	.	PUNCT
ap-1400	241	1	51	51	NUM
ap-1400	241	2	no	no	INTJ
ap-1400	241	3	.	.	PUNCT
ap-1400	242	1	4/2011	4/2011	NUM
ap-1400	242	2	optimal	optimal	ADJ
ap-1400	242	3	mass	mass	NOUN
ap-1400	242	4	distributions	distribution	NOUN
ap-1400	242	5	explicitly	explicitly	ADV
ap-1400	242	6	,	,	PUNCT
ap-1400	242	7	perhaps	perhaps	ADV
ap-1400	242	8	with	with	ADP
ap-1400	242	9	the	the	DET
ap-1400	242	10	use	use	NOUN
ap-1400	242	11	of	of	ADP
ap-1400	242	12	the	the	DET
ap-1400	242	13	pontryagin	pontryagin	NOUN
ap-1400	242	14	’s	’s	PART
ap-1400	242	15	maximum	maximum	ADJ
ap-1400	242	16	principle	principle	NOUN
ap-1400	242	17	.	.	PUNCT
ap-1400	243	1	it	it	PRON
ap-1400	243	2	would	would	AUX
ap-1400	243	3	be	be	AUX
ap-1400	243	4	interesting	interesting	ADJ
ap-1400	243	5	to	to	PART
ap-1400	243	6	identify	identify	VERB
ap-1400	243	7	the	the	DET
ap-1400	243	8	singularities	singularity	NOUN
ap-1400	243	9	of	of	ADP
ap-1400	243	10	the	the	DET
ap-1400	243	11	stability	stability	NOUN
ap-1400	243	12	boundary	boundary	NOUN
ap-1400	243	13	that	that	PRON
ap-1400	243	14	correspond	correspond	VERB
ap-1400	243	15	to	to	ADP
ap-1400	243	16	these	these	DET
ap-1400	243	17	extrema	extrema	NOUN
ap-1400	243	18	;	;	PUNCT
ap-1400	243	19	some	some	PRON
ap-1400	243	20	of	of	ADP
ap-1400	243	21	them	they	PRON
ap-1400	243	22	could	could	AUX
ap-1400	243	23	be	be	AUX
ap-1400	243	24	related	relate	VERB
ap-1400	243	25	to	to	PART
ap-1400	243	26	infinite	infinite	VERB
ap-1400	243	27	eigenvalues	eigenvalue	NOUN
ap-1400	243	28	λ	λ	NOUN
ap-1400	243	29	.	.	PROPN
ap-1400	243	30	on	on	ADP
ap-1400	243	31	the	the	DET
ap-1400	243	32	other	other	ADJ
ap-1400	243	33	hand	hand	NOUN
ap-1400	243	34	,	,	PUNCT
ap-1400	243	35	some	some	DET
ap-1400	243	36	local	local	ADJ
ap-1400	243	37	extrema	extrema	NOUN
ap-1400	243	38	should	should	AUX
ap-1400	243	39	exist	exist	VERB
ap-1400	243	40	with	with	ADP
ap-1400	243	41	mass	mass	ADJ
ap-1400	243	42	distributions	distribution	NOUN
ap-1400	243	43	that	that	PRON
ap-1400	243	44	do	do	AUX
ap-1400	243	45	not	not	PART
ap-1400	243	46	contain	contain	VERB
ap-1400	243	47	vanishing	vanish	VERB
ap-1400	243	48	masses	masse	NOUN
ap-1400	243	49	mi	mi	PROPN
ap-1400	243	50	.	.	PUNCT
ap-1400	244	1	it	it	PRON
ap-1400	244	2	would	would	AUX
ap-1400	244	3	be	be	AUX
ap-1400	244	4	interesting	interesting	ADJ
ap-1400	244	5	to	to	PART
ap-1400	244	6	understand	understand	VERB
ap-1400	244	7	at	at	ADP
ap-1400	244	8	which	which	PRON
ap-1400	244	9	points	point	NOUN
ap-1400	244	10	—	—	PUNCT
ap-1400	244	11	smooth	smooth	ADJ
ap-1400	244	12	or	or	CCONJ
ap-1400	244	13	non	non	ADJ
ap-1400	244	14	-	-	ADJ
ap-1400	244	15	smooth	smooth	ADJ
ap-1400	244	16	—	—	PUNCT
ap-1400	244	17	of	of	ADP
ap-1400	244	18	the	the	DET
ap-1400	244	19	stability	stability	NOUN
ap-1400	244	20	boundaries	boundary	NOUN
ap-1400	244	21	they	they	PRON
ap-1400	244	22	are	be	AUX
ap-1400	244	23	attained	attain	VERB
ap-1400	244	24	.	.	PUNCT
ap-1400	245	1	since	since	SCONJ
ap-1400	245	2	the	the	DET
ap-1400	245	3	system	system	NOUN
ap-1400	245	4	is	be	AUX
ap-1400	245	5	finite	finite	ADJ
ap-1400	245	6	-	-	ADJ
ap-1400	245	7	dimensional	dimensional	ADJ
ap-1400	245	8	and	and	CCONJ
ap-1400	245	9	contains	contain	VERB
ap-1400	245	10	a	a	DET
ap-1400	245	11	finite	finite	ADJ
ap-1400	245	12	number	number	NOUN
ap-1400	245	13	of	of	ADP
ap-1400	245	14	control	control	NOUN
ap-1400	245	15	parameters	parameter	NOUN
ap-1400	245	16	with	with	ADP
ap-1400	245	17	a	a	DET
ap-1400	245	18	clear	clear	ADJ
ap-1400	245	19	physical	physical	ADJ
ap-1400	245	20	meaning	meaning	NOUN
ap-1400	245	21	,	,	PUNCT
ap-1400	245	22	the	the	DET
ap-1400	245	23	locations	location	NOUN
ap-1400	245	24	of	of	ADP
ap-1400	245	25	the	the	DET
ap-1400	245	26	singularities	singularity	NOUN
ap-1400	245	27	corresponding	correspond	VERB
ap-1400	245	28	to	to	ADP
ap-1400	245	29	multiple	multiple	ADJ
ap-1400	245	30	eigenvalues	eigenvalue	NOUN
ap-1400	245	31	can	can	AUX
ap-1400	245	32	easily	easily	ADV
ap-1400	245	33	be	be	AUX
ap-1400	245	34	found	find	VERB
ap-1400	245	35	numerically	numerically	ADV
ap-1400	245	36	with	with	ADP
ap-1400	245	37	high	high	ADJ
ap-1400	245	38	accuracy	accuracy	NOUN
ap-1400	245	39	.	.	PUNCT
ap-1400	246	1	in	in	ADP
ap-1400	246	2	the	the	DET
ap-1400	246	3	vicinity	vicinity	NOUN
ap-1400	246	4	of	of	ADP
ap-1400	246	5	such	such	ADJ
ap-1400	246	6	points	point	NOUN
ap-1400	246	7	where	where	SCONJ
ap-1400	246	8	at	at	ADV
ap-1400	246	9	least	least	ADV
ap-1400	246	10	three	three	NUM
ap-1400	246	11	pure	pure	ADJ
ap-1400	246	12	imaginary	imaginary	ADJ
ap-1400	246	13	eigenvalues	eigenvalue	NOUN
ap-1400	246	14	couple	couple	NOUN
ap-1400	246	15	,	,	PUNCT
ap-1400	246	16	the	the	DET
ap-1400	246	17	question	question	NOUN
ap-1400	246	18	‘	'	PUNCT
ap-1400	246	19	should	should	AUX
ap-1400	246	20	low	low	ADJ
ap-1400	246	21	-	-	PUNCT
ap-1400	246	22	order	order	NOUN
ap-1400	246	23	models	model	NOUN
ap-1400	246	24	be	be	AUX
ap-1400	246	25	believed	believe	VERB
ap-1400	246	26	’	'	PUNCT
ap-1400	247	1	[	[	X
ap-1400	247	2	31	31	NUM
ap-1400	247	3	]	]	PUNCT
ap-1400	247	4	makes	make	VERB
ap-1400	247	5	sense	sense	NOUN
ap-1400	247	6	,	,	PUNCT
ap-1400	247	7	because	because	SCONJ
ap-1400	247	8	here	here	ADV
ap-1400	247	9	one	one	NUM
ap-1400	247	10	more	more	ADJ
ap-1400	247	11	degree	degree	NOUN
ap-1400	247	12	of	of	ADP
ap-1400	247	13	freedom	freedom	NOUN
ap-1400	247	14	is	be	AUX
ap-1400	247	15	crucial	crucial	ADJ
ap-1400	247	16	for	for	ADP
ap-1400	247	17	the	the	DET
ap-1400	247	18	correct	correct	ADJ
ap-1400	247	19	solution	solution	NOUN
ap-1400	247	20	.	.	PUNCT
ap-1400	248	1	knowledge	knowledge	NOUN
ap-1400	248	2	of	of	ADP
ap-1400	248	3	rigorously	rigorously	ADV
ap-1400	248	4	established	establish	VERB
ap-1400	248	5	optimal	optimal	ADJ
ap-1400	248	6	solutions	solution	NOUN
ap-1400	248	7	at	at	ADP
ap-1400	248	8	every	every	DET
ap-1400	248	9	m	m	NOUN
ap-1400	248	10	should	should	AUX
ap-1400	248	11	shed	shed	VERB
ap-1400	248	12	light	light	NOUN
ap-1400	248	13	on	on	ADP
ap-1400	248	14	the	the	DET
ap-1400	248	15	behavior	behavior	NOUN
ap-1400	248	16	of	of	ADP
ap-1400	248	17	the	the	DET
ap-1400	248	18	optimal	optimal	ADJ
ap-1400	248	19	mass	mass	NOUN
ap-1400	248	20	distributions	distribution	NOUN
ap-1400	248	21	and	and	CCONJ
ap-1400	248	22	critical	critical	ADJ
ap-1400	248	23	frequencies	frequency	NOUN
ap-1400	248	24	with	with	ADP
ap-1400	248	25	an	an	DET
ap-1400	248	26	increase	increase	NOUN
ap-1400	248	27	in	in	ADP
ap-1400	248	28	the	the	DET
ap-1400	248	29	number	number	NOUN
ap-1400	248	30	of	of	ADP
ap-1400	248	31	degrees	degree	NOUN
ap-1400	248	32	of	of	ADP
ap-1400	248	33	freedom	freedom	NOUN
ap-1400	248	34	.	.	PUNCT
ap-1400	249	1	as	as	ADP
ap-1400	249	2	a	a	DET
ap-1400	249	3	by	by	NOUN
ap-1400	249	4	-	-	PUNCT
ap-1400	249	5	product	product	NOUN
ap-1400	249	6	,	,	PUNCT
ap-1400	249	7	such	such	DET
ap-1400	249	8	a	a	DET
ap-1400	249	9	study	study	NOUN
ap-1400	249	10	will	will	AUX
ap-1400	249	11	give	give	VERB
ap-1400	249	12	an	an	DET
ap-1400	249	13	insight	insight	NOUN
ap-1400	249	14	into	into	ADP
ap-1400	249	15	the	the	DET
ap-1400	249	16	problem	problem	NOUN
ap-1400	249	17	of	of	ADP
ap-1400	249	18	dimension	dimension	NOUN
ap-1400	249	19	reduction	reduction	NOUN
ap-1400	249	20	,	,	PUNCT
ap-1400	249	21	and	and	CCONJ
ap-1400	249	22	will	will	AUX
ap-1400	249	23	serve	serve	VERB
ap-1400	249	24	as	as	ADP
ap-1400	249	25	a	a	DET
ap-1400	249	26	nice	nice	ADJ
ap-1400	249	27	playground	playground	NOUN
ap-1400	249	28	both	both	CCONJ
ap-1400	249	29	for	for	ADP
ap-1400	249	30	applying	apply	VERB
ap-1400	249	31	the	the	DET
ap-1400	249	32	existing	exist	VERB
ap-1400	249	33	methods	method	NOUN
ap-1400	249	34	of	of	ADP
ap-1400	249	35	nonsmooth	nonsmooth	ADJ
ap-1400	249	36	analysis	analysis	NOUN
ap-1400	249	37	and	and	CCONJ
ap-1400	249	38	eigenvalue	eigenvalue	ADJ
ap-1400	249	39	optimization	optimization	NOUN
ap-1400	249	40	[	[	X
ap-1400	249	41	38	38	NUM
ap-1400	249	42	–	–	PUNCT
ap-1400	249	43	40	40	NUM
ap-1400	249	44	]	]	PUNCT
ap-1400	249	45	and	and	CCONJ
ap-1400	249	46	for	for	ADP
ap-1400	249	47	developing	develop	VERB
ap-1400	249	48	them	they	PRON
ap-1400	249	49	further	far	ADV
ap-1400	249	50	in	in	ADP
ap-1400	249	51	the	the	DET
ap-1400	249	52	direction	direction	NOUN
ap-1400	249	53	of	of	ADP
ap-1400	249	54	a	a	DET
ap-1400	249	55	tighter	tight	ADJ
ap-1400	249	56	relation	relation	NOUN
ap-1400	249	57	both	both	PRON
ap-1400	249	58	with	with	ADP
ap-1400	249	59	singularity	singularity	NOUN
ap-1400	249	60	theory	theory	NOUN
ap-1400	249	61	and	and	CCONJ
ap-1400	249	62	with	with	ADP
ap-1400	249	63	the	the	DET
ap-1400	249	64	needs	need	NOUN
ap-1400	249	65	of	of	ADP
ap-1400	249	66	applications	application	NOUN
ap-1400	249	67	.	.	PUNCT
ap-1400	250	1	we	we	PRON
ap-1400	250	2	expect	expect	VERB
ap-1400	250	3	that	that	SCONJ
ap-1400	250	4	the	the	DET
ap-1400	250	5	proposed	propose	VERB
ap-1400	250	6	model	model	NOUN
ap-1400	250	7	optimization	optimization	NOUN
ap-1400	250	8	problem	problem	NOUN
ap-1400	250	9	will	will	AUX
ap-1400	250	10	yield	yield	VERB
ap-1400	250	11	useful	useful	ADJ
ap-1400	250	12	recommendations	recommendation	NOUN
ap-1400	250	13	for	for	ADP
ap-1400	250	14	improving	improve	VERB
ap-1400	250	15	the	the	DET
ap-1400	250	16	algorithms	algorithm	NOUN
ap-1400	250	17	for	for	ADP
ap-1400	250	18	optimizing	optimize	VERB
ap-1400	250	19	real	real	ADJ
ap-1400	250	20	non	non	ADJ
ap-1400	250	21	-	-	ADJ
ap-1400	250	22	conservative	conservative	ADJ
ap-1400	250	23	structures	structure	NOUN
ap-1400	250	24	in	in	ADP
ap-1400	250	25	industry	industry	NOUN
ap-1400	250	26	.	.	PUNCT
ap-1400	251	1	references	reference	NOUN
ap-1400	251	2	[	[	X
ap-1400	251	3	1	1	NUM
ap-1400	251	4	]	]	PUNCT
ap-1400	251	5	gajewski	gajewski	PROPN
ap-1400	251	6	,	,	PUNCT
ap-1400	251	7	a.	a.	NOUN
ap-1400	251	8	,	,	PUNCT
ap-1400	251	9	zyczkowski	zyczkowski	PROPN
ap-1400	251	10	,	,	PUNCT
ap-1400	251	11	m.	m.	NOUN
ap-1400	251	12	:	:	PUNCT
ap-1400	251	13	optimal	optimal	ADJ
ap-1400	251	14	structural	structural	ADJ
ap-1400	251	15	design	design	NOUN
ap-1400	251	16	under	under	ADP
ap-1400	251	17	stability	stability	NOUN
ap-1400	251	18	constraints	constraint	NOUN
ap-1400	251	19	.	.	PUNCT
ap-1400	252	1	dordrecht	dordrecht	NOUN
ap-1400	252	2	:	:	PUNCT
ap-1400	252	3	kluwer	kluwer	NOUN
ap-1400	252	4	,	,	PUNCT
ap-1400	252	5	1988	1988	NUM
ap-1400	252	6	,	,	PUNCT
ap-1400	252	7	in	in	ADP
ap-1400	252	8	particular	particular	ADJ
ap-1400	252	9	,	,	PUNCT
ap-1400	252	10	p.	p.	NOUN
ap-1400	252	11	137	137	NUM
ap-1400	252	12	.	.	PUNCT
ap-1400	253	1	[	[	X
ap-1400	253	2	2	2	NUM
ap-1400	253	3	]	]	PUNCT
ap-1400	253	4	zyczkowski	zyczkowski	PROPN
ap-1400	253	5	,	,	PUNCT
ap-1400	253	6	m.	m.	NOUN
ap-1400	253	7	(	(	PUNCT
ap-1400	253	8	ed	ed	NOUN
ap-1400	253	9	.	.	PROPN
ap-1400	253	10	):	):	PUNCT
ap-1400	253	11	structural	structural	ADJ
ap-1400	253	12	optimization	optimization	NOUN
ap-1400	253	13	under	under	ADP
ap-1400	253	14	stability	stability	NOUN
ap-1400	253	15	and	and	CCONJ
ap-1400	253	16	vibration	vibration	NOUN
ap-1400	253	17	constraints	constraint	NOUN
ap-1400	253	18	.	.	PUNCT
ap-1400	254	1	wien	wien	PROPN
ap-1400	254	2	–	–	PUNCT
ap-1400	254	3	new	new	PROPN
ap-1400	254	4	york	york	PROPN
ap-1400	254	5	:	:	PUNCT
ap-1400	254	6	springer	springer	NOUN
ap-1400	254	7	-	-	PUNCT
ap-1400	254	8	verlag	verlag	PROPN
ap-1400	254	9	,	,	PUNCT
ap-1400	254	10	1989	1989	NUM
ap-1400	254	11	.	.	PUNCT
ap-1400	255	1	[	[	X
ap-1400	255	2	3	3	NUM
ap-1400	255	3	]	]	X
ap-1400	255	4	seyranian	seyranian	NOUN
ap-1400	255	5	,	,	PUNCT
ap-1400	255	6	a.	a.	NOUN
ap-1400	255	7	p.	p.	PROPN
ap-1400	255	8	,	,	PUNCT
ap-1400	255	9	lund	lund	PROPN
ap-1400	255	10	,	,	PUNCT
ap-1400	255	11	e.	e.	PROPN
ap-1400	255	12	,	,	PUNCT
ap-1400	255	13	olhoff	olhoff	PROPN
ap-1400	255	14	,	,	PUNCT
ap-1400	255	15	n.	n.	NOUN
ap-1400	255	16	:	:	PUNCT
ap-1400	255	17	multiple	multiple	ADJ
ap-1400	255	18	eigenvalues	eigenvalue	VERB
ap-1400	255	19	in	in	ADP
ap-1400	255	20	structural	structural	ADJ
ap-1400	255	21	optimization	optimization	NOUN
ap-1400	255	22	problems	problem	NOUN
ap-1400	255	23	.	.	PUNCT
ap-1400	256	1	journal	journal	NOUN
ap-1400	256	2	of	of	ADP
ap-1400	256	3	structural	structural	ADJ
ap-1400	256	4	and	and	CCONJ
ap-1400	256	5	multidisciplinary	multidisciplinary	ADJ
ap-1400	256	6	optimization	optimization	NOUN
ap-1400	256	7	.	.	PUNCT
ap-1400	257	1	8	8	NUM
ap-1400	257	2	(	(	PUNCT
ap-1400	257	3	1994	1994	NUM
ap-1400	257	4	)	)	PUNCT
ap-1400	257	5	,	,	PUNCT
ap-1400	257	6	207–227	207–227	NUM
ap-1400	257	7	.	.	PUNCT
ap-1400	258	1	[	[	X
ap-1400	258	2	4	4	NUM
ap-1400	258	3	]	]	X
ap-1400	258	4	claudon	claudon	PROPN
ap-1400	258	5	,	,	PUNCT
ap-1400	258	6	j.	j.	PROPN
ap-1400	258	7	l.	l.	PROPN
ap-1400	258	8	:	:	PUNCT
ap-1400	258	9	characteristic	characteristic	ADJ
ap-1400	258	10	curves	curve	NOUN
ap-1400	258	11	and	and	CCONJ
ap-1400	258	12	optimum	optimum	ADJ
ap-1400	258	13	design	design	NOUN
ap-1400	258	14	of	of	ADP
ap-1400	258	15	two	two	NUM
ap-1400	258	16	structures	structure	NOUN
ap-1400	258	17	subjected	subject	VERB
ap-1400	258	18	to	to	ADP
ap-1400	258	19	circulatory	circulatory	ADJ
ap-1400	258	20	loads	load	NOUN
ap-1400	258	21	,	,	PUNCT
ap-1400	258	22	journal	journal	PROPN
ap-1400	258	23	de	de	PROPN
ap-1400	258	24	mecanique	mecanique	PROPN
ap-1400	258	25	.	.	PUNCT
ap-1400	259	1	14(3	14(3	NUM
ap-1400	259	2	)	)	PUNCT
ap-1400	259	3	(	(	PUNCT
ap-1400	259	4	1975	1975	NUM
ap-1400	259	5	)	)	PUNCT
ap-1400	259	6	,	,	PUNCT
ap-1400	260	1	531–543	531–543	NUM
ap-1400	260	2	.	.	PUNCT
ap-1400	261	1	[	[	X
ap-1400	261	2	5	5	NUM
ap-1400	261	3	]	]	X
ap-1400	261	4	sundararajan	sundararajan	NOUN
ap-1400	261	5	,	,	PUNCT
ap-1400	261	6	c.	c.	NOUN
ap-1400	261	7	:	:	PUNCT
ap-1400	261	8	optimization	optimization	NOUN
ap-1400	261	9	of	of	ADP
ap-1400	261	10	a	a	DET
ap-1400	261	11	nonconservative	nonconservative	ADJ
ap-1400	261	12	elastic	elastic	ADJ
ap-1400	261	13	system	system	NOUN
ap-1400	261	14	with	with	ADP
ap-1400	261	15	stability	stability	NOUN
ap-1400	261	16	constraint	constraint	NOUN
ap-1400	261	17	.	.	PUNCT
ap-1400	262	1	journal	journal	NOUN
ap-1400	262	2	of	of	ADP
ap-1400	262	3	optimization	optimization	NOUN
ap-1400	262	4	theory	theory	NOUN
ap-1400	262	5	and	and	CCONJ
ap-1400	262	6	applications	application	NOUN
ap-1400	262	7	.	.	PUNCT
ap-1400	263	1	16(3/4	16(3/4	NUM
ap-1400	263	2	)	)	PUNCT
ap-1400	264	1	(	(	PUNCT
ap-1400	264	2	1975	1975	NUM
ap-1400	264	3	)	)	PUNCT
ap-1400	264	4	,	,	PUNCT
ap-1400	265	1	355–378	355–378	NUM
ap-1400	265	2	.	.	PUNCT
ap-1400	266	1	[	[	X
ap-1400	266	2	6	6	NUM
ap-1400	266	3	]	]	PUNCT
ap-1400	266	4	hanaoka	hanaoka	PRON
ap-1400	266	5	,	,	PUNCT
ap-1400	266	6	m.	m.	NOUN
ap-1400	266	7	,	,	PUNCT
ap-1400	266	8	washizu	washizu	PROPN
ap-1400	266	9	,	,	PUNCT
ap-1400	266	10	k.	k.	NOUN
ap-1400	266	11	:	:	PUNCT
ap-1400	266	12	optimum	optimum	ADJ
ap-1400	266	13	design	design	NOUN
ap-1400	266	14	of	of	ADP
ap-1400	266	15	beck	beck	PROPN
ap-1400	266	16	’s	’s	PART
ap-1400	266	17	column	column	NOUN
ap-1400	266	18	.	.	PUNCT
ap-1400	267	1	computers	computer	NOUN
ap-1400	267	2	and	and	CCONJ
ap-1400	267	3	structures	structure	NOUN
ap-1400	267	4	.	.	PUNCT
ap-1400	268	1	11(6	11(6	NUM
ap-1400	268	2	)	)	PUNCT
ap-1400	268	3	(	(	PUNCT
ap-1400	268	4	1980	1980	NUM
ap-1400	268	5	)	)	PUNCT
ap-1400	269	1	473–480	473–480	NUM
ap-1400	269	2	.	.	PUNCT
ap-1400	270	1	[	[	X
ap-1400	270	2	7	7	NUM
ap-1400	270	3	]	]	X
ap-1400	270	4	kounadis	kounadi	NOUN
ap-1400	270	5	,	,	PUNCT
ap-1400	270	6	a.	a.	NOUN
ap-1400	270	7	n.	n.	PROPN
ap-1400	270	8	,	,	PUNCT
ap-1400	270	9	katsikadelis	katsikadelis	PROPN
ap-1400	270	10	,	,	PUNCT
ap-1400	270	11	j.	j.	PROPN
ap-1400	270	12	t.	t.	PROPN
ap-1400	270	13	:	:	PUNCT
ap-1400	270	14	on	on	ADP
ap-1400	270	15	the	the	DET
ap-1400	270	16	discontinuity	discontinuity	NOUN
ap-1400	270	17	of	of	ADP
ap-1400	270	18	the	the	DET
ap-1400	270	19	flutter	flutter	NOUN
ap-1400	270	20	load	load	NOUN
ap-1400	270	21	for	for	ADP
ap-1400	270	22	various	various	ADJ
ap-1400	270	23	types	type	NOUN
ap-1400	270	24	of	of	ADP
ap-1400	270	25	cantilevers	cantilever	NOUN
ap-1400	270	26	,	,	PUNCT
ap-1400	270	27	international	international	ADJ
ap-1400	270	28	journal	journal	NOUN
ap-1400	270	29	of	of	ADP
ap-1400	270	30	solids	solid	NOUN
ap-1400	270	31	and	and	CCONJ
ap-1400	270	32	structures	structure	NOUN
ap-1400	270	33	.	.	PUNCT
ap-1400	271	1	16	16	NUM
ap-1400	271	2	(	(	PUNCT
ap-1400	271	3	1980	1980	NUM
ap-1400	271	4	)	)	PUNCT
ap-1400	271	5	,	,	PUNCT
ap-1400	271	6	375–383	375–383	NUM
ap-1400	271	7	.	.	PUNCT
ap-1400	272	1	[	[	X
ap-1400	272	2	8	8	NUM
ap-1400	272	3	]	]	X
ap-1400	272	4	park	park	NOUN
ap-1400	272	5	,	,	PUNCT
ap-1400	272	6	y.	y.	PROPN
ap-1400	272	7	p.	p.	PROPN
ap-1400	272	8	,	,	PUNCT
ap-1400	272	9	mote	mote	PROPN
ap-1400	272	10	,	,	PUNCT
ap-1400	272	11	c.	c.	PROPN
ap-1400	272	12	d.	d.	PROPN
ap-1400	272	13	:	:	PUNCT
ap-1400	272	14	the	the	DET
ap-1400	272	15	maximum	maximum	PROPN
ap-1400	272	16	controlled	control	VERB
ap-1400	272	17	follower	follower	NOUN
ap-1400	272	18	force	force	NOUN
ap-1400	272	19	on	on	ADP
ap-1400	272	20	a	a	DET
ap-1400	272	21	free	free	ADJ
ap-1400	272	22	-	-	PUNCT
ap-1400	272	23	free	free	ADJ
ap-1400	272	24	beam	beam	NOUN
ap-1400	272	25	carrying	carry	VERB
ap-1400	272	26	a	a	DET
ap-1400	272	27	concentrated	concentrated	ADJ
ap-1400	272	28	mass	mass	NOUN
ap-1400	272	29	,	,	PUNCT
ap-1400	272	30	journal	journal	NOUN
ap-1400	272	31	of	of	ADP
ap-1400	272	32	sound	sound	NOUN
ap-1400	272	33	and	and	CCONJ
ap-1400	272	34	vibration	vibration	NOUN
ap-1400	272	35	.	.	PUNCT
ap-1400	273	1	98	98	NUM
ap-1400	273	2	(	(	PUNCT
ap-1400	273	3	1985	1985	NUM
ap-1400	273	4	)	)	PUNCT
ap-1400	273	5	,	,	PUNCT
ap-1400	273	6	247–256	247–256	NUM
ap-1400	273	7	.	.	PUNCT
ap-1400	274	1	[	[	X
ap-1400	274	2	9	9	NUM
ap-1400	274	3	]	]	X
ap-1400	274	4	ringertz	ringertz	NOUN
ap-1400	274	5	,	,	PUNCT
ap-1400	274	6	u.	u.	PROPN
ap-1400	274	7	:	:	PUNCT
ap-1400	274	8	on	on	ADP
ap-1400	274	9	the	the	DET
ap-1400	274	10	design	design	NOUN
ap-1400	274	11	of	of	ADP
ap-1400	274	12	beck	beck	PROPN
ap-1400	274	13	’s	’s	PART
ap-1400	274	14	column	column	NOUN
ap-1400	274	15	,	,	PUNCT
ap-1400	274	16	structural	structural	ADJ
ap-1400	274	17	optimization	optimization	NOUN
ap-1400	274	18	.	.	PUNCT
ap-1400	275	1	8(2–3	8(2–3	VERB
ap-1400	275	2	)	)	PUNCT
ap-1400	275	3	(	(	PUNCT
ap-1400	275	4	1994	1994	NUM
ap-1400	275	5	)	)	PUNCT
ap-1400	275	6	,	,	PUNCT
ap-1400	275	7	120–124	120–124	NUM
ap-1400	275	8	.	.	PUNCT
ap-1400	276	1	[	[	X
ap-1400	276	2	10	10	NUM
ap-1400	276	3	]	]	X
ap-1400	276	4	kirillov	kirillov	NOUN
ap-1400	276	5	,	,	PUNCT
ap-1400	276	6	o.	o.	PROPN
ap-1400	276	7	n.	n.	PROPN
ap-1400	276	8	,	,	PUNCT
ap-1400	276	9	seyranian	seyranian	NOUN
ap-1400	276	10	,	,	PUNCT
ap-1400	276	11	a.	a.	NOUN
ap-1400	276	12	p.	p.	NOUN
ap-1400	276	13	:	:	PUNCT
ap-1400	276	14	optimization	optimization	NOUN
ap-1400	276	15	of	of	ADP
ap-1400	276	16	stability	stability	NOUN
ap-1400	276	17	of	of	ADP
ap-1400	276	18	a	a	DET
ap-1400	276	19	flexible	flexible	ADJ
ap-1400	276	20	missile	missile	NOUN
ap-1400	276	21	under	under	ADP
ap-1400	276	22	follower	follower	NOUN
ap-1400	276	23	thrust	thrust	PROPN
ap-1400	276	24	,	,	PUNCT
ap-1400	276	25	aiaa	aiaa	PROPN
ap-1400	276	26	paper	paper	PROPN
ap-1400	276	27	98	98	NUM
ap-1400	276	28	-	-	SYM
ap-1400	276	29	4969	4969	NUM
ap-1400	276	30	,	,	PUNCT
ap-1400	276	31	(	(	PUNCT
ap-1400	276	32	1998	1998	NUM
ap-1400	276	33	)	)	PUNCT
ap-1400	276	34	,	,	PUNCT
ap-1400	276	35	2	2	NUM
ap-1400	276	36	063–2	063–2	NUM
ap-1400	276	37	073	073	NUM
ap-1400	276	38	.	.	PUNCT
ap-1400	277	1	[	[	X
ap-1400	277	2	11	11	NUM
ap-1400	277	3	]	]	PUNCT
ap-1400	277	4	kirillov	kirillov	NOUN
ap-1400	277	5	,	,	PUNCT
ap-1400	277	6	o.	o.	PROPN
ap-1400	277	7	n.	n.	NOUN
ap-1400	277	8	:	:	PUNCT
ap-1400	277	9	optimization	optimization	NOUN
ap-1400	277	10	of	of	ADP
ap-1400	277	11	stability	stability	NOUN
ap-1400	277	12	of	of	ADP
ap-1400	277	13	the	the	DET
ap-1400	277	14	flying	fly	VERB
ap-1400	277	15	bar	bar	NOUN
ap-1400	277	16	.	.	PUNCT
ap-1400	278	1	young	young	ADJ
ap-1400	278	2	scientists	scientist	NOUN
ap-1400	278	3	bulletin	bulletin	NOUN
ap-1400	278	4	.	.	PUNCT
ap-1400	279	1	applied	apply	VERB
ap-1400	279	2	mathematics	mathematic	NOUN
ap-1400	279	3	and	and	CCONJ
ap-1400	279	4	mechanics	mechanic	NOUN
ap-1400	279	5	1(1	1(1	NUM
ap-1400	279	6	)	)	PUNCT
ap-1400	279	7	(	(	PUNCT
ap-1400	279	8	1999	1999	NUM
ap-1400	279	9	)	)	PUNCT
ap-1400	279	10	,	,	PUNCT
ap-1400	279	11	64–78	64–78	NUM
ap-1400	279	12	.	.	PUNCT
ap-1400	280	1	[	[	X
ap-1400	280	2	12	12	NUM
ap-1400	280	3	]	]	PUNCT
ap-1400	280	4	kirillov	kirillov	NOUN
ap-1400	280	5	,	,	PUNCT
ap-1400	280	6	o.	o.	PROPN
ap-1400	280	7	n.	n.	PROPN
ap-1400	280	8	,	,	PUNCT
ap-1400	280	9	seyranian	seyranian	NOUN
ap-1400	280	10	,	,	PUNCT
ap-1400	280	11	a.	a.	NOUN
ap-1400	280	12	p.	p.	NOUN
ap-1400	280	13	:	:	PUNCT
ap-1400	280	14	optimization	optimization	NOUN
ap-1400	280	15	of	of	ADP
ap-1400	280	16	stability	stability	NOUN
ap-1400	280	17	of	of	ADP
ap-1400	280	18	a	a	DET
ap-1400	280	19	flying	fly	VERB
ap-1400	280	20	column	column	NOUN
ap-1400	280	21	.	.	PUNCT
ap-1400	281	1	3rd	3rd	ADJ
ap-1400	281	2	world	world	NOUN
ap-1400	281	3	congress	congress	PROPN
ap-1400	281	4	of	of	ADP
ap-1400	281	5	structural	structural	ADJ
ap-1400	281	6	and	and	CCONJ
ap-1400	281	7	multidisciplinary	multidisciplinary	ADJ
ap-1400	281	8	optimization	optimization	NOUN
ap-1400	281	9	.	.	PUNCT
ap-1400	282	1	buffalo	buffalo	PROPN
ap-1400	282	2	.	.	PUNCT
ap-1400	282	3	new	new	PROPN
ap-1400	282	4	york	york	PROPN
ap-1400	282	5	(	(	PUNCT
ap-1400	282	6	usa	usa	PROPN
ap-1400	282	7	)	)	PUNCT
ap-1400	282	8	:	:	PUNCT
ap-1400	283	1	may	may	AUX
ap-1400	283	2	17–21	17–21	NUM
ap-1400	283	3	,	,	PUNCT
ap-1400	283	4	1999	1999	NUM
ap-1400	283	5	.	.	PUNCT
ap-1400	284	1	short	short	ADJ
ap-1400	284	2	paper	paper	NOUN
ap-1400	284	3	proceedings	proceeding	NOUN
ap-1400	284	4	,	,	PUNCT
ap-1400	284	5	2	2	NUM
ap-1400	284	6	(	(	PUNCT
ap-1400	284	7	1999	1999	NUM
ap-1400	284	8	)	)	PUNCT
ap-1400	284	9	355–357	355–357	NUM
ap-1400	284	10	.	.	PUNCT
ap-1400	285	1	[	[	X
ap-1400	285	2	13	13	NUM
ap-1400	285	3	]	]	X
ap-1400	285	4	langthjem	langthjem	NOUN
ap-1400	285	5	,	,	PUNCT
ap-1400	285	6	m.	m.	NOUN
ap-1400	285	7	a.	a.	PROPN
ap-1400	285	8	,	,	PUNCT
ap-1400	285	9	sugiyama	sugiyama	NOUN
ap-1400	285	10	,	,	PUNCT
ap-1400	285	11	y.	y.	NOUN
ap-1400	285	12	:	:	PUNCT
ap-1400	285	13	optimum	optimum	ADJ
ap-1400	285	14	shape	shape	NOUN
ap-1400	285	15	design	design	NOUN
ap-1400	285	16	against	against	ADP
ap-1400	285	17	flutter	flutter	NOUN
ap-1400	285	18	of	of	ADP
ap-1400	285	19	a	a	DET
ap-1400	285	20	cantilevered	cantilevered	ADJ
ap-1400	285	21	column	column	NOUN
ap-1400	285	22	with	with	ADP
ap-1400	285	23	an	an	DET
ap-1400	285	24	end	end	NOUN
ap-1400	285	25	-	-	PUNCT
ap-1400	285	26	mass	mass	NOUN
ap-1400	285	27	of	of	ADP
ap-1400	285	28	finite	finite	ADJ
ap-1400	285	29	size	size	NOUN
ap-1400	285	30	subjected	subject	VERB
ap-1400	285	31	to	to	ADP
ap-1400	285	32	a	a	DET
ap-1400	285	33	non	non	ADJ
ap-1400	285	34	-	-	ADJ
ap-1400	285	35	conservative	conservative	ADJ
ap-1400	285	36	load	load	NOUN
ap-1400	285	37	,	,	PUNCT
ap-1400	285	38	journal	journal	NOUN
ap-1400	285	39	of	of	ADP
ap-1400	285	40	sound	sound	NOUN
ap-1400	285	41	and	and	CCONJ
ap-1400	285	42	vibration	vibration	NOUN
ap-1400	285	43	.	.	PUNCT
ap-1400	286	1	226(1	226(1	X
ap-1400	286	2	)	)	PUNCT
ap-1400	286	3	(	(	PUNCT
ap-1400	286	4	1999	1999	NUM
ap-1400	286	5	)	)	PUNCT
ap-1400	286	6	,	,	PUNCT
ap-1400	286	7	1–23	1–23	PROPN
ap-1400	286	8	.	.	PUNCT
ap-1400	287	1	41	41	NUM
ap-1400	287	2	acta	acta	PROPN
ap-1400	287	3	polytechnica	polytechnica	PROPN
ap-1400	287	4	vol	vol	NOUN
ap-1400	287	5	.	.	PUNCT
ap-1400	288	1	51	51	NUM
ap-1400	288	2	no	no	INTJ
ap-1400	288	3	.	.	PUNCT
ap-1400	288	4	4/2011	4/2011	NUM
ap-1400	289	1	[	[	X
ap-1400	289	2	14	14	NUM
ap-1400	289	3	]	]	X
ap-1400	289	4	langthjem	langthjem	NOUN
ap-1400	289	5	,	,	PUNCT
ap-1400	289	6	m.	m.	NOUN
ap-1400	289	7	a.	a.	PROPN
ap-1400	289	8	,	,	PUNCT
ap-1400	289	9	sugiyama	sugiyama	NOUN
ap-1400	289	10	,	,	PUNCT
ap-1400	289	11	y.	y.	NOUN
ap-1400	289	12	:	:	PUNCT
ap-1400	289	13	optimum	optimum	ADJ
ap-1400	289	14	design	design	NOUN
ap-1400	289	15	of	of	ADP
ap-1400	289	16	cantilevered	cantilevered	ADJ
ap-1400	289	17	columns	column	NOUN
ap-1400	289	18	under	under	ADP
ap-1400	289	19	the	the	DET
ap-1400	289	20	combined	combine	VERB
ap-1400	289	21	action	action	NOUN
ap-1400	289	22	of	of	ADP
ap-1400	289	23	conservative	conservative	ADJ
ap-1400	289	24	and	and	CCONJ
ap-1400	289	25	nonconservative	nonconservative	ADJ
ap-1400	289	26	loads	load	NOUN
ap-1400	289	27	part	part	NOUN
ap-1400	290	1	i	i	PRON
ap-1400	290	2	:	:	PUNCT
ap-1400	290	3	the	the	DET
ap-1400	290	4	undamped	undamped	ADJ
ap-1400	290	5	case	case	NOUN
ap-1400	290	6	.	.	PUNCT
ap-1400	291	1	computers	computer	NOUN
ap-1400	291	2	and	and	CCONJ
ap-1400	291	3	structures	structure	NOUN
ap-1400	291	4	.	.	PUNCT
ap-1400	292	1	74(4	74(4	X
ap-1400	292	2	)	)	PUNCT
ap-1400	292	3	(	(	PUNCT
ap-1400	292	4	2000	2000	NUM
ap-1400	292	5	)	)	PUNCT
ap-1400	292	6	,	,	PUNCT
ap-1400	292	7	385–398	385–398	NUM
ap-1400	292	8	.	.	PUNCT
ap-1400	293	1	[	[	X
ap-1400	293	2	15	15	NUM
ap-1400	293	3	]	]	X
ap-1400	293	4	langthjem	langthjem	NOUN
ap-1400	293	5	,	,	PUNCT
ap-1400	293	6	m.	m.	NOUN
ap-1400	293	7	a.	a.	PROPN
ap-1400	293	8	,	,	PUNCT
ap-1400	293	9	sugiyama	sugiyama	NOUN
ap-1400	293	10	,	,	PUNCT
ap-1400	293	11	y.	y.	NOUN
ap-1400	293	12	:	:	PUNCT
ap-1400	293	13	optimum	optimum	ADJ
ap-1400	293	14	design	design	NOUN
ap-1400	293	15	of	of	ADP
ap-1400	293	16	cantilevered	cantilevered	ADJ
ap-1400	293	17	columns	column	NOUN
ap-1400	293	18	under	under	ADP
ap-1400	293	19	the	the	DET
ap-1400	293	20	combined	combine	VERB
ap-1400	293	21	action	action	NOUN
ap-1400	293	22	of	of	ADP
ap-1400	293	23	conservative	conservative	ADJ
ap-1400	293	24	and	and	CCONJ
ap-1400	293	25	nonconservative	nonconservative	ADJ
ap-1400	293	26	loads	load	NOUN
ap-1400	293	27	part	part	NOUN
ap-1400	293	28	ii	ii	PROPN
ap-1400	293	29	:	:	PUNCT
ap-1400	293	30	the	the	DET
ap-1400	293	31	damped	damped	NOUN
ap-1400	293	32	case	case	NOUN
ap-1400	293	33	.	.	PUNCT
ap-1400	294	1	computers	computer	NOUN
ap-1400	294	2	and	and	CCONJ
ap-1400	294	3	structures	structure	NOUN
ap-1400	294	4	.	.	PUNCT
ap-1400	295	1	74(4	74(4	X
ap-1400	295	2	)	)	PUNCT
ap-1400	295	3	(	(	PUNCT
ap-1400	295	4	2000	2000	NUM
ap-1400	295	5	)	)	PUNCT
ap-1400	295	6	,	,	PUNCT
ap-1400	295	7	399–408	399–408	NUM
ap-1400	295	8	.	.	PUNCT
ap-1400	296	1	[	[	X
ap-1400	296	2	16	16	NUM
ap-1400	296	3	]	]	X
ap-1400	296	4	langthjem	langthjem	PROPN
ap-1400	296	5	,	,	PUNCT
ap-1400	296	6	m.	m.	NOUN
ap-1400	296	7	a.	a.	PROPN
ap-1400	296	8	,	,	PUNCT
ap-1400	296	9	sugiyama	sugiyama	NOUN
ap-1400	296	10	,	,	PUNCT
ap-1400	296	11	y.	y.	NOUN
ap-1400	296	12	:	:	PUNCT
ap-1400	296	13	dynamic	dynamic	ADJ
ap-1400	296	14	stability	stability	NOUN
ap-1400	296	15	of	of	ADP
ap-1400	296	16	columns	column	NOUN
ap-1400	296	17	subjected	subject	VERB
ap-1400	296	18	to	to	ADP
ap-1400	296	19	follower	follower	NOUN
ap-1400	296	20	loads	load	NOUN
ap-1400	296	21	:	:	PUNCT
ap-1400	296	22	a	a	DET
ap-1400	296	23	survey	survey	NOUN
ap-1400	296	24	.	.	PUNCT
ap-1400	297	1	journal	journal	NOUN
ap-1400	297	2	of	of	ADP
ap-1400	297	3	sound	sound	NOUN
ap-1400	297	4	and	and	CCONJ
ap-1400	297	5	vibration	vibration	NOUN
ap-1400	297	6	.	.	PUNCT
ap-1400	298	1	238	238	NUM
ap-1400	298	2	(	(	PUNCT
ap-1400	298	3	2000	2000	NUM
ap-1400	298	4	)	)	PUNCT
ap-1400	298	5	,	,	PUNCT
ap-1400	298	6	809–851	809–851	NUM
ap-1400	298	7	.	.	PUNCT
ap-1400	299	1	[	[	X
ap-1400	299	2	17	17	NUM
ap-1400	299	3	]	]	X
ap-1400	299	4	temis	temis	PROPN
ap-1400	299	5	,	,	PUNCT
ap-1400	299	6	yu	yu	PROPN
ap-1400	299	7	.	.	PROPN
ap-1400	299	8	m.	m.	PROPN
ap-1400	299	9	,	,	PUNCT
ap-1400	299	10	fedorov	fedorov	PROPN
ap-1400	299	11	,	,	PUNCT
ap-1400	299	12	i.	i.	PROPN
ap-1400	299	13	m.	m.	PROPN
ap-1400	299	14	:	:	PUNCT
ap-1400	299	15	shape	shape	VERB
ap-1400	299	16	optimization	optimization	NOUN
ap-1400	299	17	of	of	ADP
ap-1400	299	18	nonconservatively	nonconservatively	ADV
ap-1400	299	19	loaded	load	VERB
ap-1400	299	20	beams	beam	NOUN
ap-1400	299	21	with	with	ADP
ap-1400	299	22	a	a	DET
ap-1400	299	23	stability	stability	NOUN
ap-1400	299	24	criterion	criterion	NOUN
ap-1400	299	25	.	.	PUNCT
ap-1400	300	1	problems	problem	NOUN
ap-1400	300	2	of	of	ADP
ap-1400	300	3	strength	strength	NOUN
ap-1400	300	4	and	and	CCONJ
ap-1400	300	5	plasticity	plasticity	NOUN
ap-1400	300	6	.	.	PUNCT
ap-1400	301	1	69	69	NUM
ap-1400	301	2	(	(	PUNCT
ap-1400	301	3	2007	2007	NUM
ap-1400	301	4	)	)	PUNCT
ap-1400	301	5	,	,	PUNCT
ap-1400	301	6	24–37	24–37	PROPN
ap-1400	301	7	.	.	PUNCT
ap-1400	302	1	[	[	X
ap-1400	302	2	18	18	NUM
ap-1400	302	3	]	]	PUNCT
ap-1400	302	4	katsikadelis	katsikadeli	NOUN
ap-1400	302	5	,	,	PUNCT
ap-1400	302	6	j.	j.	PROPN
ap-1400	302	7	t.	t.	PROPN
ap-1400	302	8	,	,	PUNCT
ap-1400	302	9	tsiatas	tsiata	NOUN
ap-1400	302	10	,	,	PUNCT
ap-1400	302	11	g.	g.	PROPN
ap-1400	302	12	c.	c.	PROPN
ap-1400	302	13	:	:	PUNCT
ap-1400	302	14	optimum	optimum	ADJ
ap-1400	302	15	design	design	NOUN
ap-1400	302	16	of	of	ADP
ap-1400	302	17	structures	structure	NOUN
ap-1400	302	18	subjected	subject	VERB
ap-1400	302	19	to	to	ADP
ap-1400	302	20	follower	follower	NOUN
ap-1400	302	21	forces	force	NOUN
ap-1400	302	22	.	.	PUNCT
ap-1400	303	1	international	international	ADJ
ap-1400	303	2	journal	journal	PROPN
ap-1400	303	3	of	of	ADP
ap-1400	303	4	mechanical	mechanical	ADJ
ap-1400	303	5	sciences	science	NOUN
ap-1400	303	6	.	.	PUNCT
ap-1400	304	1	49	49	NUM
ap-1400	304	2	(	(	PUNCT
ap-1400	304	3	2007	2007	NUM
ap-1400	304	4	)	)	PUNCT
ap-1400	304	5	,	,	PUNCT
ap-1400	304	6	1	1	NUM
ap-1400	304	7	204–1212	204–1212	NUM
ap-1400	304	8	.	.	PUNCT
ap-1400	305	1	[	[	X
ap-1400	305	2	19	19	NUM
ap-1400	305	3	]	]	X
ap-1400	305	4	beck	beck	NOUN
ap-1400	305	5	,	,	PUNCT
ap-1400	305	6	m.	m.	NOUN
ap-1400	305	7	:	:	PUNCT
ap-1400	305	8	die	die	VERB
ap-1400	305	9	knicklast	knicklast	PROPN
ap-1400	305	10	des	des	X
ap-1400	305	11	einseitig	einseitig	PROPN
ap-1400	305	12	eingespannten	eingespannten	VERB
ap-1400	305	13	,	,	PUNCT
ap-1400	305	14	tangential	tangential	ADJ
ap-1400	305	15	gedruckten	gedruckten	VERB
ap-1400	305	16	stabes	stabe	NOUN
ap-1400	305	17	(	(	PUNCT
ap-1400	305	18	the	the	DET
ap-1400	305	19	buckling	buckle	VERB
ap-1400	305	20	load	load	NOUN
ap-1400	305	21	of	of	ADP
ap-1400	305	22	the	the	DET
ap-1400	305	23	cantilevered	cantilever	VERB
ap-1400	305	24	,	,	PUNCT
ap-1400	305	25	tangentially	tangentially	ADV
ap-1400	305	26	loaded	load	VERB
ap-1400	305	27	rod	rod	NOUN
ap-1400	305	28	)	)	PUNCT
ap-1400	305	29	.	.	PUNCT
ap-1400	306	1	zeitschrift	zeitschrift	PROPN
ap-1400	306	2	fur	fur	PROPN
ap-1400	306	3	angewandte	angewandte	PROPN
ap-1400	306	4	mathematik	mathematik	PROPN
ap-1400	306	5	und	und	PROPN
ap-1400	306	6	mechanik	mechanik	PROPN
ap-1400	306	7	.	.	PROPN
ap-1400	307	1	3	3	NUM
ap-1400	307	2	(	(	PUNCT
ap-1400	307	3	1952	1952	NUM
ap-1400	307	4	)	)	PUNCT
ap-1400	307	5	,	,	PUNCT
ap-1400	307	6	225–228	225–228	NUM
ap-1400	307	7	.	.	PUNCT
ap-1400	308	1	[	[	X
ap-1400	308	2	20	20	NUM
ap-1400	308	3	]	]	PUNCT
ap-1400	308	4	sugiyama	sugiyama	NOUN
ap-1400	308	5	,	,	PUNCT
ap-1400	308	6	y.	y.	PROPN
ap-1400	308	7	,	,	PUNCT
ap-1400	308	8	langthjem	langthjem	PROPN
ap-1400	308	9	,	,	PUNCT
ap-1400	308	10	m.	m.	NOUN
ap-1400	308	11	a.	a.	PROPN
ap-1400	308	12	,	,	PUNCT
ap-1400	308	13	ryu	ryu	ADJ
ap-1400	308	14	,	,	PUNCT
ap-1400	308	15	b.-j	b.-j	PROPN
ap-1400	308	16	.	.	PUNCT
ap-1400	308	17	:	:	PUNCT
ap-1400	308	18	realistic	realistic	ADJ
ap-1400	308	19	follower	follower	NOUN
ap-1400	308	20	forces	force	NOUN
ap-1400	308	21	.	.	PUNCT
ap-1400	309	1	journal	journal	PROPN
ap-1400	309	2	of	of	ADP
ap-1400	309	3	sound	sound	NOUN
ap-1400	309	4	and	and	CCONJ
ap-1400	309	5	vibration	vibration	NOUN
ap-1400	309	6	.	.	PUNCT
ap-1400	310	1	225	225	NUM
ap-1400	310	2	(	(	PUNCT
ap-1400	310	3	1999	1999	NUM
ap-1400	310	4	)	)	PUNCT
ap-1400	310	5	,	,	PUNCT
ap-1400	310	6	779–782	779–782	NUM
ap-1400	310	7	.	.	PUNCT
ap-1400	311	1	[	[	X
ap-1400	311	2	21	21	NUM
ap-1400	311	3	]	]	PUNCT
ap-1400	311	4	sugiyama	sugiyama	NOUN
ap-1400	311	5	,	,	PUNCT
ap-1400	311	6	y.	y.	PROPN
ap-1400	311	7	,	,	PUNCT
ap-1400	311	8	langthjem	langthjem	PROPN
ap-1400	311	9	,	,	PUNCT
ap-1400	311	10	m.	m.	NOUN
ap-1400	311	11	a.	a.	PROPN
ap-1400	311	12	,	,	PUNCT
ap-1400	311	13	ryu	ryu	ADJ
ap-1400	311	14	,	,	PUNCT
ap-1400	311	15	b.-j	b.-j	PROPN
ap-1400	311	16	.	.	PUNCT
ap-1400	311	17	:	:	PUNCT
ap-1400	311	18	beck	beck	PROPN
ap-1400	311	19	’s	’s	PART
ap-1400	311	20	column	column	NOUN
ap-1400	311	21	as	as	ADP
ap-1400	311	22	the	the	DET
ap-1400	311	23	ugly	ugly	ADJ
ap-1400	311	24	duckling	duckling	NOUN
ap-1400	311	25	.	.	PUNCT
ap-1400	312	1	journal	journal	NOUN
ap-1400	312	2	of	of	ADP
ap-1400	312	3	sound	sound	NOUN
ap-1400	312	4	and	and	CCONJ
ap-1400	312	5	vibration	vibration	NOUN
ap-1400	312	6	.	.	PUNCT
ap-1400	313	1	254	254	NUM
ap-1400	313	2	(	(	PUNCT
ap-1400	313	3	2002	2002	NUM
ap-1400	313	4	)	)	PUNCT
ap-1400	313	5	,	,	PUNCT
ap-1400	313	6	407–410	407–410	NUM
ap-1400	313	7	.	.	PUNCT
ap-1400	314	1	[	[	X
ap-1400	314	2	22	22	NUM
ap-1400	314	3	]	]	PUNCT
ap-1400	314	4	elishakoff	elishakoff	NOUN
ap-1400	314	5	,	,	PUNCT
ap-1400	314	6	:	:	PUNCT
ap-1400	314	7	controversy	controversy	NOUN
ap-1400	314	8	associated	associate	VERB
ap-1400	314	9	with	with	ADP
ap-1400	314	10	the	the	DET
ap-1400	314	11	so	so	ADV
ap-1400	314	12	-	-	PUNCT
ap-1400	314	13	called	call	VERB
ap-1400	314	14	“	"	PUNCT
ap-1400	314	15	follower	follower	NOUN
ap-1400	314	16	forces	force	NOUN
ap-1400	314	17	”	"	PUNCT
ap-1400	314	18	:	:	PUNCT
ap-1400	314	19	critical	critical	ADJ
ap-1400	314	20	overview	overview	NOUN
ap-1400	314	21	.	.	PUNCT
ap-1400	315	1	applied	apply	VERB
ap-1400	315	2	mechanics	mechanic	NOUN
ap-1400	315	3	reviews	review	NOUN
ap-1400	315	4	.	.	PUNCT
ap-1400	316	1	58	58	NUM
ap-1400	316	2	(	(	PUNCT
ap-1400	316	3	2005	2005	NUM
ap-1400	316	4	)	)	PUNCT
ap-1400	316	5	,	,	PUNCT
ap-1400	316	6	117–142	117–142	NUM
ap-1400	316	7	.	.	PUNCT
ap-1400	317	1	[	[	X
ap-1400	317	2	23	23	NUM
ap-1400	317	3	]	]	PUNCT
ap-1400	317	4	gasparini	gasparini	NOUN
ap-1400	317	5	,	,	PUNCT
ap-1400	317	6	a.	a.	NOUN
ap-1400	317	7	m.	m.	NOUN
ap-1400	317	8	,	,	PUNCT
ap-1400	317	9	saetta	saetta	PROPN
ap-1400	317	10	,	,	PUNCT
ap-1400	317	11	a.	a.	NOUN
ap-1400	317	12	v.	v.	PROPN
ap-1400	317	13	,	,	PUNCT
ap-1400	317	14	vitaliani	vitaliani	PROPN
ap-1400	317	15	,	,	PUNCT
ap-1400	317	16	r.	r.	PROPN
ap-1400	317	17	v.	v.	PROPN
ap-1400	317	18	:	:	PUNCT
ap-1400	317	19	on	on	ADP
ap-1400	317	20	the	the	DET
ap-1400	317	21	stability	stability	NOUN
ap-1400	317	22	and	and	CCONJ
ap-1400	317	23	instability	instability	NOUN
ap-1400	317	24	regions	region	NOUN
ap-1400	317	25	of	of	ADP
ap-1400	317	26	non	non	ADJ
ap-1400	317	27	-	-	ADJ
ap-1400	317	28	conservative	conservative	ADJ
ap-1400	317	29	continuous	continuous	ADJ
ap-1400	317	30	system	system	NOUN
ap-1400	317	31	under	under	ADP
ap-1400	317	32	partially	partially	ADV
ap-1400	317	33	follower	follower	NOUN
ap-1400	317	34	forces	force	NOUN
ap-1400	317	35	.	.	PUNCT
ap-1400	318	1	computer	computer	NOUN
ap-1400	318	2	methods	method	NOUN
ap-1400	318	3	in	in	ADP
ap-1400	318	4	applied	applied	ADJ
ap-1400	318	5	mechanics	mechanic	NOUN
ap-1400	318	6	and	and	CCONJ
ap-1400	318	7	engineering	engineering	NOUN
ap-1400	318	8	.	.	PUNCT
ap-1400	319	1	124	124	NUM
ap-1400	319	2	(	(	PUNCT
ap-1400	319	3	1995	1995	NUM
ap-1400	319	4	)	)	PUNCT
ap-1400	319	5	,	,	PUNCT
ap-1400	319	6	63–78	63–78	NUM
ap-1400	319	7	.	.	PUNCT
ap-1400	320	1	[	[	X
ap-1400	320	2	24	24	NUM
ap-1400	320	3	]	]	SYM
ap-1400	320	4	gallina	gallina	NOUN
ap-1400	320	5	,	,	PUNCT
ap-1400	320	6	p.	p.	NOUN
ap-1400	320	7	:	:	PUNCT
ap-1400	320	8	about	about	ADP
ap-1400	320	9	the	the	DET
ap-1400	320	10	stability	stability	NOUN
ap-1400	320	11	of	of	ADP
ap-1400	320	12	non	non	ADJ
ap-1400	320	13	-	-	ADJ
ap-1400	320	14	conservative	conservative	ADJ
ap-1400	320	15	undamped	undamped	ADJ
ap-1400	320	16	systems	system	NOUN
ap-1400	320	17	,	,	PUNCT
ap-1400	320	18	journal	journal	NOUN
ap-1400	320	19	of	of	ADP
ap-1400	320	20	sound	sound	NOUN
ap-1400	320	21	and	and	CCONJ
ap-1400	320	22	vibration	vibration	NOUN
ap-1400	320	23	.	.	PUNCT
ap-1400	321	1	262(4	262(4	X
ap-1400	321	2	)	)	PUNCT
ap-1400	321	3	(	(	PUNCT
ap-1400	321	4	2003	2003	NUM
ap-1400	321	5	)	)	PUNCT
ap-1400	321	6	,	,	PUNCT
ap-1400	322	1	977–988	977–988	NUM
ap-1400	322	2	.	.	PUNCT
ap-1400	323	1	[	[	X
ap-1400	323	2	25	25	NUM
ap-1400	323	3	]	]	PUNCT
ap-1400	323	4	lobas	lobas	PROPN
ap-1400	323	5	,	,	PUNCT
ap-1400	323	6	l.	l.	PROPN
ap-1400	323	7	g.	g.	PROPN
ap-1400	323	8	:	:	PUNCT
ap-1400	323	9	dynamic	dynamic	ADJ
ap-1400	323	10	behavior	behavior	NOUN
ap-1400	323	11	of	of	ADP
ap-1400	323	12	multilink	multilink	ADJ
ap-1400	323	13	pendulums	pendulum	NOUN
ap-1400	323	14	under	under	ADP
ap-1400	323	15	follower	follower	NOUN
ap-1400	323	16	forces	force	NOUN
ap-1400	323	17	.	.	PUNCT
ap-1400	324	1	international	international	ADJ
ap-1400	324	2	applied	apply	VERB
ap-1400	324	3	mechanics	mechanic	NOUN
ap-1400	324	4	.	.	PUNCT
ap-1400	325	1	41(6	41(6	NUM
ap-1400	325	2	)	)	PUNCT
ap-1400	325	3	(	(	PUNCT
ap-1400	325	4	2005	2005	NUM
ap-1400	325	5	)	)	PUNCT
ap-1400	325	6	,	,	PUNCT
ap-1400	325	7	587–613	587–613	NUM
ap-1400	325	8	.	.	PUNCT
ap-1400	326	1	[	[	X
ap-1400	326	2	26	26	NUM
ap-1400	326	3	]	]	X
ap-1400	326	4	ziegler	ziegler	PROPN
ap-1400	326	5	,	,	PUNCT
ap-1400	326	6	h.	h.	PROPN
ap-1400	326	7	:	:	PUNCT
ap-1400	326	8	die	die	VERB
ap-1400	326	9	stabilitätskriterien	stabilitätskriterien	SYM
ap-1400	326	10	der	der	PROPN
ap-1400	326	11	elastomechanik	elastomechanik	X
ap-1400	326	12	(	(	PUNCT
ap-1400	326	13	stability	stability	NOUN
ap-1400	326	14	criteria	criterion	NOUN
ap-1400	326	15	in	in	ADP
ap-1400	326	16	elasticity	elasticity	NOUN
ap-1400	326	17	theory	theory	NOUN
ap-1400	326	18	)	)	PUNCT
ap-1400	326	19	.	.	PUNCT
ap-1400	327	1	ingenieurarchiv	ingenieurarchiv	PROPN
ap-1400	327	2	.	.	PUNCT
ap-1400	328	1	20	20	NUM
ap-1400	328	2	(	(	PUNCT
ap-1400	328	3	1952	1952	NUM
ap-1400	328	4	)	)	PUNCT
ap-1400	328	5	,	,	PUNCT
ap-1400	329	1	49–56	49–56	NUM
ap-1400	329	2	.	.	PUNCT
ap-1400	330	1	[	[	X
ap-1400	330	2	27	27	NUM
ap-1400	330	3	]	]	PUNCT
ap-1400	330	4	kirillov	kirillov	NOUN
ap-1400	330	5	,	,	PUNCT
ap-1400	330	6	o.	o.	PROPN
ap-1400	330	7	n.	n.	PROPN
ap-1400	330	8	,	,	PUNCT
ap-1400	330	9	seyranian	seyranian	NOUN
ap-1400	330	10	,	,	PUNCT
ap-1400	330	11	a.	a.	NOUN
ap-1400	330	12	p.	p.	NOUN
ap-1400	330	13	:	:	PUNCT
ap-1400	330	14	overlapping	overlap	VERB
ap-1400	330	15	of	of	ADP
ap-1400	330	16	frequency	frequency	NOUN
ap-1400	330	17	curves	curve	NOUN
ap-1400	330	18	in	in	ADP
ap-1400	330	19	non	non	ADJ
ap-1400	330	20	-	-	ADJ
ap-1400	330	21	conservative	conservative	ADJ
ap-1400	330	22	systems	system	NOUN
ap-1400	330	23	.	.	PUNCT
ap-1400	331	1	doklady	doklady	PROPN
ap-1400	331	2	physics	physics	PROPN
ap-1400	331	3	.	.	PUNCT
ap-1400	332	1	46(3	46(3	NOUN
ap-1400	332	2	)	)	PUNCT
ap-1400	332	3	(	(	PUNCT
ap-1400	332	4	2001	2001	NUM
ap-1400	332	5	)	)	PUNCT
ap-1400	332	6	,	,	PUNCT
ap-1400	332	7	184–189	184–189	NUM
ap-1400	332	8	.	.	PUNCT
ap-1400	333	1	[	[	X
ap-1400	333	2	28	28	NUM
ap-1400	333	3	]	]	X
ap-1400	333	4	kirillov	kirillov	NOUN
ap-1400	333	5	,	,	PUNCT
ap-1400	333	6	o.	o.	PROPN
ap-1400	333	7	n.	n.	PROPN
ap-1400	333	8	,	,	PUNCT
ap-1400	333	9	seyranian	seyranian	NOUN
ap-1400	333	10	,	,	PUNCT
ap-1400	333	11	a.	a.	NOUN
ap-1400	333	12	p.	p.	NOUN
ap-1400	333	13	:	:	PUNCT
ap-1400	333	14	metamorphoses	metamorphosis	NOUN
ap-1400	333	15	of	of	ADP
ap-1400	333	16	characteristic	characteristic	ADJ
ap-1400	333	17	curves	curve	NOUN
ap-1400	333	18	in	in	ADP
ap-1400	333	19	circulatory	circulatory	ADJ
ap-1400	333	20	systems	system	NOUN
ap-1400	333	21	.	.	PUNCT
ap-1400	334	1	journal	journal	NOUN
ap-1400	334	2	of	of	ADP
ap-1400	334	3	applied	apply	VERB
ap-1400	334	4	mathematics	mathematic	NOUN
ap-1400	334	5	and	and	CCONJ
ap-1400	334	6	mechanics	mechanic	NOUN
ap-1400	334	7	.	.	PUNCT
ap-1400	335	1	66(3	66(3	NOUN
ap-1400	335	2	)	)	PUNCT
ap-1400	335	3	(	(	PUNCT
ap-1400	335	4	2002	2002	NUM
ap-1400	335	5	)	)	PUNCT
ap-1400	335	6	,	,	PUNCT
ap-1400	335	7	371–385	371–385	NUM
ap-1400	335	8	.	.	PUNCT
ap-1400	336	1	[	[	X
ap-1400	336	2	29	29	NUM
ap-1400	336	3	]	]	X
ap-1400	336	4	kirillov	kirillov	NOUN
ap-1400	336	5	,	,	PUNCT
ap-1400	336	6	o.	o.	PROPN
ap-1400	336	7	n.	n.	PROPN
ap-1400	336	8	,	,	PUNCT
ap-1400	336	9	seyranian	seyranian	NOUN
ap-1400	336	10	,	,	PUNCT
ap-1400	336	11	a.	a.	NOUN
ap-1400	336	12	p.	p.	NOUN
ap-1400	336	13	:	:	PUNCT
ap-1400	336	14	a	a	DET
ap-1400	336	15	non	non	ADJ
ap-1400	336	16	-	-	ADJ
ap-1400	336	17	smooth	smooth	ADJ
ap-1400	336	18	optimization	optimization	NOUN
ap-1400	336	19	problem	problem	NOUN
ap-1400	336	20	.	.	PUNCT
ap-1400	337	1	moscow	moscow	PROPN
ap-1400	337	2	university	university	PROPN
ap-1400	337	3	mechanics	mechanic	NOUN
ap-1400	337	4	bulletin	bulletin	NOUN
ap-1400	337	5	.	.	PUNCT
ap-1400	338	1	57(3	57(3	X
ap-1400	338	2	)	)	PUNCT
ap-1400	338	3	(	(	PUNCT
ap-1400	338	4	2002	2002	NUM
ap-1400	338	5	)	)	PUNCT
ap-1400	338	6	,	,	PUNCT
ap-1400	338	7	1–6	1–6	X
ap-1400	338	8	.	.	PUNCT
ap-1400	339	1	[	[	X
ap-1400	339	2	30	30	NUM
ap-1400	339	3	]	]	X
ap-1400	339	4	bolotin	bolotin	NOUN
ap-1400	339	5	,	,	PUNCT
ap-1400	339	6	v.	v.	PROPN
ap-1400	339	7	v.	v.	ADJ
ap-1400	339	8	:	:	PUNCT
ap-1400	339	9	non	non	ADJ
ap-1400	339	10	-	-	ADJ
ap-1400	339	11	conservative	conservative	ADJ
ap-1400	339	12	problems	problem	NOUN
ap-1400	339	13	of	of	ADP
ap-1400	339	14	the	the	DET
ap-1400	339	15	theory	theory	NOUN
ap-1400	339	16	of	of	ADP
ap-1400	339	17	elastic	elastic	ADJ
ap-1400	339	18	stability	stability	NOUN
ap-1400	339	19	.	.	PUNCT
ap-1400	340	1	moscow	moscow	PROPN
ap-1400	340	2	:	:	PUNCT
ap-1400	340	3	fizmatgiz	fizmatgiz	NOUN
ap-1400	340	4	(	(	PUNCT
ap-1400	340	5	in	in	ADP
ap-1400	340	6	russian	russian	PROPN
ap-1400	340	7	)	)	PUNCT
ap-1400	340	8	,	,	PUNCT
ap-1400	340	9	1961	1961	NUM
ap-1400	340	10	;	;	PUNCT
ap-1400	340	11	oxford	oxford	PROPN
ap-1400	340	12	:	:	PUNCT
ap-1400	340	13	pergamon	pergamon	NOUN
ap-1400	340	14	,	,	PUNCT
ap-1400	340	15	1963	1963	NUM
ap-1400	340	16	.	.	PUNCT
ap-1400	341	1	[	[	X
ap-1400	341	2	31	31	NUM
ap-1400	341	3	]	]	PUNCT
ap-1400	341	4	butlin	butlin	NOUN
ap-1400	341	5	,	,	PUNCT
ap-1400	341	6	t.	t.	PROPN
ap-1400	341	7	,	,	PUNCT
ap-1400	341	8	woodhouse	woodhouse	PROPN
ap-1400	341	9	,	,	PUNCT
ap-1400	341	10	j.	j.	PROPN
ap-1400	341	11	:	:	PUNCT
ap-1400	341	12	friction	friction	NOUN
ap-1400	341	13	-	-	PUNCT
ap-1400	341	14	induced	induce	VERB
ap-1400	341	15	vibration	vibration	NOUN
ap-1400	341	16	:	:	PUNCT
ap-1400	341	17	should	should	AUX
ap-1400	341	18	low	low	ADJ
ap-1400	341	19	-	-	PUNCT
ap-1400	341	20	order	order	NOUN
ap-1400	341	21	models	model	NOUN
ap-1400	341	22	be	be	AUX
ap-1400	341	23	believed	believe	VERB
ap-1400	341	24	?	?	PUNCT
ap-1400	342	1	journal	journal	NOUN
ap-1400	342	2	of	of	ADP
ap-1400	342	3	sound	sound	NOUN
ap-1400	342	4	and	and	CCONJ
ap-1400	342	5	vibration	vibration	NOUN
ap-1400	342	6	.	.	PUNCT
ap-1400	343	1	328	328	NUM
ap-1400	343	2	(	(	PUNCT
ap-1400	343	3	2009	2009	NUM
ap-1400	343	4	)	)	PUNCT
ap-1400	343	5	,	,	PUNCT
ap-1400	343	6	92–108	92–108	NUM
ap-1400	343	7	.	.	PUNCT
ap-1400	344	1	[	[	X
ap-1400	344	2	32	32	NUM
ap-1400	344	3	]	]	PUNCT
ap-1400	344	4	kirillov	kirillov	NOUN
ap-1400	344	5	,	,	PUNCT
ap-1400	344	6	o.	o.	PROPN
ap-1400	344	7	n.	n.	PROPN
ap-1400	344	8	,	,	PUNCT
ap-1400	344	9	verhulst	verhulst	PROPN
ap-1400	344	10	,	,	PUNCT
ap-1400	344	11	f.	f.	NOUN
ap-1400	344	12	:	:	PUNCT
ap-1400	344	13	paradoxes	paradox	NOUN
ap-1400	344	14	of	of	ADP
ap-1400	344	15	dissipation	dissipation	NOUN
ap-1400	344	16	-	-	PUNCT
ap-1400	344	17	induced	induce	VERB
ap-1400	344	18	destabilization	destabilization	NOUN
ap-1400	344	19	or	or	CCONJ
ap-1400	344	20	who	who	PRON
ap-1400	344	21	opened	open	VERB
ap-1400	344	22	whitney	whitney	PROPN
ap-1400	344	23	’s	’s	PART
ap-1400	344	24	umbrella	umbrella	NOUN
ap-1400	344	25	?	?	PUNCT
ap-1400	345	1	zeitschrift	zeitschrift	NOUN
ap-1400	345	2	fur	fur	PROPN
ap-1400	345	3	angewandte	angewandte	PROPN
ap-1400	345	4	mathematik	mathematik	PROPN
ap-1400	345	5	und	und	PROPN
ap-1400	345	6	mechanik	mechanik	PROPN
ap-1400	345	7	.	.	PUNCT
ap-1400	346	1	90(6	90(6	X
ap-1400	346	2	)	)	PUNCT
ap-1400	346	3	(	(	PUNCT
ap-1400	346	4	2010	2010	NUM
ap-1400	346	5	)	)	PUNCT
ap-1400	346	6	,	,	PUNCT
ap-1400	347	1	462–488	462–488	NUM
ap-1400	347	2	.	.	PUNCT
ap-1400	348	1	[	[	X
ap-1400	348	2	33	33	NUM
ap-1400	348	3	]	]	X
ap-1400	348	4	wang	wang	PROPN
ap-1400	348	5	,	,	PUNCT
ap-1400	348	6	g.	g.	PROPN
ap-1400	348	7	,	,	PUNCT
ap-1400	348	8	lin	lin	PROPN
ap-1400	348	9	,	,	PUNCT
ap-1400	348	10	y.	y.	PROPN
ap-1400	348	11	:	:	PUNCT
ap-1400	348	12	a	a	DET
ap-1400	348	13	new	new	ADJ
ap-1400	348	14	extension	extension	NOUN
ap-1400	348	15	of	of	ADP
ap-1400	348	16	leverrier	leverri	ADJ
ap-1400	348	17	’s	’s	PART
ap-1400	348	18	algorithm	algorithm	NOUN
ap-1400	348	19	.	.	PUNCT
ap-1400	349	1	linear	linear	ADJ
ap-1400	349	2	algebra	algebra	NOUN
ap-1400	349	3	and	and	CCONJ
ap-1400	349	4	applications	application	NOUN
ap-1400	349	5	.	.	PUNCT
ap-1400	350	1	180	180	NUM
ap-1400	350	2	(	(	PUNCT
ap-1400	350	3	1993	1993	NUM
ap-1400	350	4	)	)	PUNCT
ap-1400	350	5	,	,	PUNCT
ap-1400	350	6	227–238	227–238	NUM
ap-1400	350	7	.	.	PUNCT
ap-1400	351	1	42	42	NUM
ap-1400	351	2	acta	acta	PROPN
ap-1400	351	3	polytechnica	polytechnica	PROPN
ap-1400	351	4	vol	vol	NOUN
ap-1400	351	5	.	.	PUNCT
ap-1400	352	1	51	51	NUM
ap-1400	352	2	no	no	INTJ
ap-1400	352	3	.	.	PUNCT
ap-1400	352	4	4/2011	4/2011	NUM
ap-1400	353	1	[	[	X
ap-1400	353	2	34	34	NUM
ap-1400	353	3	]	]	X
ap-1400	353	4	herrmann	herrmann	PROPN
ap-1400	353	5	,	,	PUNCT
ap-1400	353	6	g.	g.	PROPN
ap-1400	353	7	,	,	PUNCT
ap-1400	353	8	jong	jong	PROPN
ap-1400	353	9	,	,	PUNCT
ap-1400	353	10	i.	i.	PROPN
ap-1400	353	11	c.	c.	PROPN
ap-1400	353	12	:	:	PUNCT
ap-1400	353	13	on	on	ADP
ap-1400	353	14	the	the	DET
ap-1400	353	15	destabilizing	destabilizing	ADJ
ap-1400	353	16	effect	effect	NOUN
ap-1400	353	17	of	of	ADP
ap-1400	353	18	damping	damp	VERB
ap-1400	353	19	in	in	ADP
ap-1400	353	20	nonconservative	nonconservative	ADJ
ap-1400	353	21	elastic	elastic	ADJ
ap-1400	353	22	systems	system	NOUN
ap-1400	353	23	.	.	PUNCT
ap-1400	354	1	transactions	transaction	NOUN
ap-1400	354	2	of	of	ADP
ap-1400	354	3	the	the	DET
ap-1400	354	4	asme	asme	PROPN
ap-1400	354	5	,	,	PUNCT
ap-1400	354	6	journal	journal	NOUN
ap-1400	354	7	of	of	ADP
ap-1400	354	8	applied	apply	VERB
ap-1400	354	9	mechanics	mechanic	NOUN
ap-1400	354	10	.	.	PUNCT
ap-1400	355	1	32(3	32(3	NUM
ap-1400	355	2	)	)	PUNCT
ap-1400	355	3	(	(	PUNCT
ap-1400	355	4	1965	1965	NUM
ap-1400	355	5	)	)	PUNCT
ap-1400	355	6	,	,	PUNCT
ap-1400	355	7	592–597	592–597	NUM
ap-1400	355	8	.	.	PUNCT
ap-1400	356	1	[	[	X
ap-1400	356	2	35	35	NUM
ap-1400	356	3	]	]	SYM
ap-1400	356	4	bottema	bottema	NOUN
ap-1400	356	5	,	,	PUNCT
ap-1400	356	6	o.	o.	PROPN
ap-1400	356	7	:	:	PUNCT
ap-1400	356	8	the	the	DET
ap-1400	356	9	routh	routh	PROPN
ap-1400	356	10	-	-	PUNCT
ap-1400	356	11	hurwitz	hurwitz	PROPN
ap-1400	356	12	condition	condition	NOUN
ap-1400	356	13	for	for	ADP
ap-1400	356	14	the	the	DET
ap-1400	356	15	biquadratic	biquadratic	ADJ
ap-1400	356	16	equation	equation	NOUN
ap-1400	356	17	.	.	PUNCT
ap-1400	357	1	indagationes	indagatione	NOUN
ap-1400	357	2	mathematicae	mathematicae	PROPN
ap-1400	357	3	.	.	PUNCT
ap-1400	358	1	18	18	NUM
ap-1400	358	2	(	(	PUNCT
ap-1400	358	3	1956	1956	NUM
ap-1400	358	4	)	)	PUNCT
ap-1400	358	5	,	,	PUNCT
ap-1400	358	6	403–406	403–406	NUM
ap-1400	358	7	.	.	PUNCT
ap-1400	359	1	[	[	X
ap-1400	359	2	36	36	NUM
ap-1400	359	3	]	]	PUNCT
ap-1400	359	4	kirillov	kirillov	NOUN
ap-1400	359	5	,	,	PUNCT
ap-1400	359	6	o.	o.	PROPN
ap-1400	359	7	n.	n.	NOUN
ap-1400	359	8	:	:	PUNCT
ap-1400	359	9	destabilization	destabilization	NOUN
ap-1400	359	10	paradox	paradox	NOUN
ap-1400	359	11	.	.	PUNCT
ap-1400	360	1	doklady	doklady	PROPN
ap-1400	360	2	physics	physics	PROPN
ap-1400	360	3	.	.	PUNCT
ap-1400	361	1	49	49	NUM
ap-1400	361	2	(	(	PUNCT
ap-1400	361	3	2004	2004	NUM
ap-1400	361	4	)	)	PUNCT
ap-1400	361	5	,	,	PUNCT
ap-1400	361	6	239–245	239–245	NUM
ap-1400	361	7	.	.	PUNCT
ap-1400	362	1	[	[	X
ap-1400	362	2	37	37	NUM
ap-1400	362	3	]	]	X
ap-1400	362	4	bernoulli	bernoulli	PROPN
ap-1400	362	5	,	,	PUNCT
ap-1400	362	6	j.	j.	PROPN
ap-1400	362	7	:	:	PUNCT
ap-1400	362	8	problema	problema	NOUN
ap-1400	362	9	novum	novum	PROPN
ap-1400	362	10	ad	ad	NOUN
ap-1400	362	11	cuius	cuius	PROPN
ap-1400	362	12	solutionem	solutionem	PROPN
ap-1400	362	13	mathematici	mathematici	PROPN
ap-1400	362	14	invitantur	invitantur	PROPN
ap-1400	362	15	(	(	PUNCT
ap-1400	362	16	a	a	DET
ap-1400	362	17	new	new	ADJ
ap-1400	362	18	problem	problem	NOUN
ap-1400	362	19	that	that	PRON
ap-1400	362	20	mathematicians	mathematician	NOUN
ap-1400	362	21	are	be	AUX
ap-1400	362	22	invited	invite	VERB
ap-1400	362	23	to	to	PART
ap-1400	362	24	solve	solve	VERB
ap-1400	362	25	)	)	PUNCT
ap-1400	362	26	.	.	PUNCT
ap-1400	362	27	acta	acta	PROPN
ap-1400	362	28	eruditorum	eruditorum	PROPN
ap-1400	362	29	.	.	PUNCT
ap-1400	363	1	15	15	NUM
ap-1400	363	2	(	(	PUNCT
ap-1400	363	3	1696	1696	NUM
ap-1400	363	4	)	)	PUNCT
ap-1400	363	5	,	,	PUNCT
ap-1400	363	6	264–269	264–269	NUM
ap-1400	363	7	.	.	PUNCT
ap-1400	364	1	[	[	X
ap-1400	364	2	38	38	NUM
ap-1400	364	3	]	]	SYM
ap-1400	364	4	lewis	lewis	PROPN
ap-1400	364	5	,	,	PUNCT
ap-1400	364	6	a.	a.	PROPN
ap-1400	364	7	s.	s.	PROPN
ap-1400	364	8	:	:	PUNCT
ap-1400	364	9	the	the	DET
ap-1400	364	10	mathematics	mathematic	NOUN
ap-1400	364	11	of	of	ADP
ap-1400	364	12	eigenvalue	eigenvalue	PROPN
ap-1400	364	13	optimization	optimization	NOUN
ap-1400	364	14	.	.	PUNCT
ap-1400	365	1	mathematical	mathematical	ADJ
ap-1400	365	2	programming	programming	NOUN
ap-1400	365	3	,	,	PUNCT
ap-1400	365	4	ser	ser	NOUN
ap-1400	365	5	.	.	PUNCT
ap-1400	366	1	b	b	PROPN
ap-1400	366	2	97	97	NUM
ap-1400	366	3	(	(	PUNCT
ap-1400	366	4	2003	2003	NUM
ap-1400	366	5	)	)	PUNCT
ap-1400	366	6	,	,	PUNCT
ap-1400	366	7	155–176	155–176	NUM
ap-1400	366	8	.	.	PUNCT
ap-1400	367	1	[	[	X
ap-1400	367	2	39	39	NUM
ap-1400	367	3	]	]	X
ap-1400	367	4	burke	burke	PROPN
ap-1400	367	5	,	,	PUNCT
ap-1400	367	6	j.	j.	PROPN
ap-1400	367	7	v.	v.	PROPN
ap-1400	367	8	,	,	PUNCT
ap-1400	367	9	henrion	henrion	NOUN
ap-1400	367	10	,	,	PUNCT
ap-1400	367	11	d.	d.	PROPN
ap-1400	367	12	,	,	PUNCT
ap-1400	367	13	lewis	lewis	PROPN
ap-1400	367	14	,	,	PUNCT
ap-1400	367	15	a.	a.	PROPN
ap-1400	367	16	s.	s.	PROPN
ap-1400	367	17	,	,	PUNCT
ap-1400	367	18	overton	overton	PROPN
ap-1400	367	19	,	,	PUNCT
ap-1400	367	20	m.	m.	NOUN
ap-1400	367	21	l.	l.	PROPN
ap-1400	367	22	:	:	PUNCT
ap-1400	367	23	stabilization	stabilization	NOUN
ap-1400	367	24	via	via	ADP
ap-1400	367	25	nonsmooth	nonsmooth	NOUN
ap-1400	367	26	,	,	PUNCT
ap-1400	367	27	nonconvex	nonconvex	NOUN
ap-1400	367	28	optimization	optimization	NOUN
ap-1400	367	29	.	.	PUNCT
ap-1400	368	1	ieee	ieee	PROPN
ap-1400	368	2	transations	transation	NOUN
ap-1400	368	3	on	on	ADP
ap-1400	368	4	automatic	automatic	ADJ
ap-1400	368	5	control	control	NOUN
ap-1400	368	6	.	.	PUNCT
ap-1400	369	1	51(11	51(11	NUM
ap-1400	369	2	)	)	PUNCT
ap-1400	369	3	(	(	PUNCT
ap-1400	369	4	2006	2006	NUM
ap-1400	369	5	)	)	PUNCT
ap-1400	369	6	,	,	PUNCT
ap-1400	369	7	1	1	NUM
ap-1400	369	8	760–1769	760–1769	NUM
ap-1400	369	9	.	.	PUNCT
ap-1400	370	1	[	[	X
ap-1400	370	2	40	40	NUM
ap-1400	370	3	]	]	PUNCT
ap-1400	370	4	ledyaev	ledyaev	PROPN
ap-1400	370	5	,	,	PUNCT
ap-1400	370	6	yu	yu	PROPN
ap-1400	370	7	.	.	PUNCT
ap-1400	370	8	s.	s.	PROPN
ap-1400	370	9	,	,	PUNCT
ap-1400	370	10	zhu	zhu	PROPN
ap-1400	370	11	,	,	PUNCT
ap-1400	370	12	q.	q.	PROPN
ap-1400	370	13	j.	j.	PROPN
ap-1400	370	14	:	:	PUNCT
ap-1400	370	15	nonsmooth	nonsmooth	VERB
ap-1400	370	16	analysis	analysis	NOUN
ap-1400	370	17	on	on	ADP
ap-1400	370	18	smooth	smooth	ADJ
ap-1400	370	19	manifolds	manifold	NOUN
ap-1400	370	20	.	.	PUNCT
ap-1400	371	1	transactions	transaction	NOUN
ap-1400	371	2	of	of	ADP
ap-1400	371	3	the	the	DET
ap-1400	371	4	american	american	PROPN
ap-1400	371	5	mathematical	mathematical	PROPN
ap-1400	371	6	society	society	NOUN
ap-1400	371	7	.	.	PUNCT
ap-1400	372	1	359(8	359(8	NUM
ap-1400	372	2	)	)	PUNCT
ap-1400	372	3	(	(	PUNCT
ap-1400	372	4	2007	2007	NUM
ap-1400	372	5	)	)	PUNCT
ap-1400	372	6	,	,	PUNCT
ap-1400	372	7	3	3	NUM
ap-1400	372	8	687–3732	687–3732	NUM
ap-1400	372	9	.	.	PUNCT
ap-1400	373	1	oleg	oleg	PROPN
ap-1400	373	2	n.	n.	PROPN
ap-1400	373	3	kirillov	kirillov	PROPN
ap-1400	373	4	e	e	NOUN
ap-1400	373	5	-	-	NOUN
ap-1400	373	6	mail	mail	NOUN
ap-1400	373	7	:	:	PUNCT
ap-1400	373	8	o.kirillov@hzdr.de	o.kirillov@hzdr.de	NUM
ap-1400	373	9	magneto	magneto	ADJ
ap-1400	373	10	-	-	PUNCT
ap-1400	373	11	hydrodynamics	hydrodynamic	NOUN
ap-1400	373	12	division	division	NOUN
ap-1400	373	13	(	(	PUNCT
ap-1400	373	14	fwsh	fwsh	NOUN
ap-1400	373	15	)	)	PUNCT
ap-1400	373	16	helmholtz	helmholtz	NOUN
ap-1400	373	17	-	-	PUNCT
ap-1400	373	18	zentrum	zentrum	PROPN
ap-1400	373	19	dresden	dresden	PROPN
ap-1400	373	20	-	-	PUNCT
ap-1400	373	21	rossendorf	rossendorf	PROPN
ap-1400	373	22	p.o	p.o	PROPN
ap-1400	373	23	.	.	PROPN
ap-1400	373	24	box	box	PROPN
ap-1400	373	25	510119	510119	NUM
ap-1400	373	26	,	,	PUNCT
ap-1400	373	27	d-01314	d-01314	PROPN
ap-1400	373	28	dresden	dresden	PROPN
ap-1400	373	29	,	,	PUNCT
ap-1400	373	30	germany	germany	PROPN
ap-1400	373	31	43	43	NUM