id	sid	tid	token	lemma	pos
ap-616	1	1	ap04-bittnar1.vp	ap04-bittnar1.vp	PROPN
ap-616	1	2	1	1	NUM
ap-616	1	3	introduction	introduction	NOUN
ap-616	1	4	it	it	PRON
ap-616	1	5	is	be	AUX
ap-616	1	6	well	well	ADV
ap-616	1	7	-	-	PUNCT
ap-616	1	8	known	know	VERB
ap-616	1	9	that	that	SCONJ
ap-616	1	10	the	the	DET
ap-616	1	11	verlet	verlet	ADJ
ap-616	1	12	algorithm	algorithm	NOUN
ap-616	1	13	(	(	PUNCT
ap-616	1	14	explicit	explicit	ADJ
ap-616	1	15	newmark	newmark	NOUN
ap-616	1	16	for	for	ADP
ap-616	1	17	a	a	DET
ap-616	1	18	certain	certain	ADJ
ap-616	1	19	choice	choice	NOUN
ap-616	1	20	of	of	ADP
ap-616	1	21	its	its	PRON
ap-616	1	22	parameters	parameter	NOUN
ap-616	1	23	)	)	PUNCT
ap-616	1	24	may	may	AUX
ap-616	1	25	be	be	AUX
ap-616	1	26	written	write	VERB
ap-616	1	27	as	as	ADP
ap-616	1	28	a	a	DET
ap-616	1	29	composition	composition	NOUN
ap-616	1	30	of	of	ADP
ap-616	1	31	two	two	NUM
ap-616	1	32	first	first	ADJ
ap-616	1	33	order	order	NOUN
ap-616	1	34	algorithms	algorithm	NOUN
ap-616	1	35	,	,	PUNCT
ap-616	1	36	the	the	DET
ap-616	1	37	symplectic	symplectic	PROPN
ap-616	1	38	euler	euler	NOUN
ap-616	1	39	and	and	CCONJ
ap-616	1	40	its	its	PRON
ap-616	1	41	adjoint	adjoint	NOUN
ap-616	2	1	[	[	X
ap-616	2	2	2	2	NUM
ap-616	2	3	]	]	PUNCT
ap-616	2	4	.	.	PUNCT
ap-616	3	1	what	what	PRON
ap-616	3	2	is	be	AUX
ap-616	3	3	perhaps	perhaps	ADV
ap-616	3	4	less	less	ADV
ap-616	3	5	known	known	ADJ
ap-616	3	6	is	be	AUX
ap-616	3	7	that	that	SCONJ
ap-616	3	8	there	there	PRON
ap-616	3	9	is	be	VERB
ap-616	3	10	an	an	DET
ap-616	3	11	interpretation	interpretation	NOUN
ap-616	3	12	of	of	ADP
ap-616	3	13	this	this	DET
ap-616	3	14	composition	composition	NOUN
ap-616	3	15	in	in	ADP
ap-616	3	16	terms	term	NOUN
ap-616	3	17	of	of	ADP
ap-616	3	18	an	an	DET
ap-616	3	19	approximation	approximation	NOUN
ap-616	3	20	of	of	ADP
ap-616	3	21	the	the	DET
ap-616	3	22	midpoint	midpoint	NOUN
ap-616	3	23	rule	rule	NOUN
ap-616	3	24	,	,	PUNCT
ap-616	3	25	which	which	PRON
ap-616	3	26	is	be	AUX
ap-616	3	27	of	of	ADP
ap-616	3	28	course	course	NOUN
ap-616	3	29	implicit	implicit	ADJ
ap-616	3	30	in	in	ADP
ap-616	3	31	the	the	DET
ap-616	3	32	evaluation	evaluation	NOUN
ap-616	3	33	of	of	ADP
ap-616	3	34	the	the	DET
ap-616	3	35	forcing	force	VERB
ap-616	3	36	impulse	impulse	NOUN
ap-616	3	37	.	.	PUNCT
ap-616	4	1	our	our	PRON
ap-616	4	2	goal	goal	NOUN
ap-616	4	3	in	in	ADP
ap-616	4	4	this	this	DET
ap-616	4	5	brief	brief	ADJ
ap-616	4	6	note	note	NOUN
ap-616	4	7	is	be	AUX
ap-616	4	8	to	to	PART
ap-616	4	9	point	point	VERB
ap-616	4	10	out	out	ADP
ap-616	4	11	that	that	SCONJ
ap-616	4	12	this	this	DET
ap-616	4	13	mechanically	mechanically	ADV
ap-616	4	14	inspired	inspire	VERB
ap-616	4	15	derivation	derivation	NOUN
ap-616	4	16	yields	yield	VERB
ap-616	4	17	the	the	DET
ap-616	4	18	well	well	ADV
ap-616	4	19	-	-	PUNCT
ap-616	4	20	known	know	VERB
ap-616	4	21	second	second	ADJ
ap-616	4	22	order	order	NOUN
ap-616	4	23	explicit	explicit	ADJ
ap-616	4	24	verlet	verlet	NOUN
ap-616	4	25	algorithm	algorithm	NOUN
ap-616	4	26	in	in	ADP
ap-616	4	27	the	the	DET
ap-616	4	28	vector	vector	NOUN
ap-616	4	29	space	space	NOUN
ap-616	4	30	setting	setting	NOUN
ap-616	4	31	,	,	PUNCT
ap-616	4	32	and	and	CCONJ
ap-616	4	33	also	also	ADV
ap-616	4	34	an	an	DET
ap-616	4	35	extremely	extremely	ADV
ap-616	4	36	accurate	accurate	ADJ
ap-616	4	37	integrator	integrator	NOUN
ap-616	4	38	for	for	ADP
ap-616	4	39	rigid	rigid	ADJ
ap-616	4	40	body	body	NOUN
ap-616	4	41	rotations	rotation	NOUN
ap-616	4	42	when	when	SCONJ
ap-616	4	43	the	the	DET
ap-616	4	44	midpoint	midpoint	NOUN
ap-616	4	45	rule	rule	NOUN
ap-616	4	46	is	be	AUX
ap-616	4	47	interpreted	interpret	VERB
ap-616	4	48	in	in	ADP
ap-616	4	49	the	the	DET
ap-616	4	50	lie	lie	NOUN
ap-616	4	51	sense	sense	NOUN
ap-616	4	52	.	.	PUNCT
ap-616	5	1	2	2	NUM
ap-616	5	2	vector	vector	NOUN
ap-616	5	3	space	space	NOUN
ap-616	5	4	midpoint	midpoint	NOUN
ap-616	5	5	rule	rule	NOUN
ap-616	5	6	approximation	approximation	NOUN
ap-616	5	7	let	let	VERB
ap-616	5	8	us	we	PRON
ap-616	5	9	write	write	VERB
ap-616	5	10	the	the	DET
ap-616	5	11	initial	initial	ADJ
ap-616	5	12	value	value	NOUN
ap-616	5	13	problem	problem	NOUN
ap-616	5	14	for	for	ADP
ap-616	5	15	a	a	DET
ap-616	5	16	mechanical	mechanical	ADJ
ap-616	5	17	system	system	NOUN
ap-616	5	18	with	with	ADP
ap-616	5	19	configuration	configuration	NOUN
ap-616	5	20	u	u	PROPN
ap-616	5	21	�	�	PROPN
ap-616	5	22	�	�	PROPN
ap-616	5	23	n	n	NOUN
ap-616	5	24	in	in	ADP
ap-616	5	25	a	a	DET
ap-616	5	26	fairly	fairly	ADV
ap-616	5	27	general	general	ADJ
ap-616	5	28	form	form	NOUN
ap-616	5	29	as	as	ADP
ap-616	5	30	�	�	PROPN
ap-616	5	31	,	,	PUNCT
ap-616	5	32	(	(	PUNCT
ap-616	5	33	)	)	PUNCT
ap-616	5	34	�	�	PROPN
ap-616	5	35	,	,	PUNCT
ap-616	5	36	(	(	PUNCT
ap-616	5	37	)	)	PUNCT
ap-616	6	1	p	p	NOUN
ap-616	6	2	f	f	PROPN
ap-616	7	1	p	p	X
ap-616	7	2	p	p	X
ap-616	7	3	u	u	NOUN
ap-616	7	4	m	m	PROPN
ap-616	7	5	p	p	NOUN
ap-616	7	6	u	u	X
ap-616	7	7	u	u	PROPN
ap-616	7	8	�	�	PROPN
ap-616	7	9	�	�	PROPN
ap-616	7	10	�	�	PROPN
ap-616	7	11	�	�	PROPN
ap-616	7	12	�	�	PROPN
ap-616	7	13	0	0	NUM
ap-616	7	14	0	0	NUM
ap-616	7	15	0	0	NUM
ap-616	7	16	1	1	NUM
ap-616	7	17	0	0	NUM
ap-616	7	18	,	,	PUNCT
ap-616	7	19	where	where	SCONJ
ap-616	7	20	�	�	PROPN
ap-616	7	21	p	p	PROPN
ap-616	7	22	is	be	AUX
ap-616	7	23	the	the	DET
ap-616	7	24	rate	rate	NOUN
ap-616	7	25	of	of	ADP
ap-616	7	26	linear	linear	PROPN
ap-616	7	27	momentum	momentum	NOUN
ap-616	7	28	,	,	PUNCT
ap-616	7	29	and	and	CCONJ
ap-616	7	30	f	f	PROPN
ap-616	7	31	f	f	PROPN
ap-616	7	32	u	u	X
ap-616	7	33	�	�	PROPN
ap-616	7	34	(	(	PUNCT
ap-616	7	35	,	,	PUNCT
ap-616	7	36	)	)	PUNCT
ap-616	7	37	t	t	PROPN
ap-616	7	38	is	be	AUX
ap-616	7	39	the	the	DET
ap-616	7	40	applied	applied	ADJ
ap-616	7	41	force	force	NOUN
ap-616	7	42	.	.	PUNCT
ap-616	8	1	for	for	ADP
ap-616	8	2	simplicity	simplicity	NOUN
ap-616	8	3	we	we	PRON
ap-616	8	4	shall	shall	AUX
ap-616	8	5	assume	assume	VERB
ap-616	8	6	p	p	PROPN
ap-616	8	7	mv	mv	PROPN
ap-616	8	8	�	�	PROPN
ap-616	8	9	,	,	PUNCT
ap-616	8	10	where	where	SCONJ
ap-616	8	11	m	m	NOUN
ap-616	8	12	is	be	AUX
ap-616	8	13	a	a	DET
ap-616	8	14	time	time	NOUN
ap-616	8	15	-	-	PUNCT
ap-616	8	16	independent	independent	ADJ
ap-616	8	17	mass	mass	NOUN
ap-616	8	18	matrix	matrix	NOUN
ap-616	8	19	,	,	PUNCT
ap-616	8	20	and	and	CCONJ
ap-616	8	21	v	v	NOUN
ap-616	8	22	is	be	AUX
ap-616	8	23	the	the	DET
ap-616	8	24	velocity	velocity	NOUN
ap-616	8	25	.	.	PUNCT
ap-616	9	1	the	the	DET
ap-616	9	2	midpoint	midpoint	NOUN
ap-616	9	3	approximation	approximation	NOUN
ap-616	9	4	of	of	ADP
ap-616	9	5	the	the	DET
ap-616	9	6	second	second	ADJ
ap-616	9	7	equation	equation	NOUN
ap-616	9	8	is	be	AUX
ap-616	9	9	u	u	NOUN
ap-616	9	10	u	u	NOUN
ap-616	9	11	m	m	VERB
ap-616	9	12	p	p	NOUN
ap-616	9	13	(	(	PUNCT
ap-616	9	14	)	)	PUNCT
ap-616	9	15	(	(	PUNCT
ap-616	9	16	)	)	PUNCT
ap-616	9	17	t	t	NOUN
ap-616	9	18	t	t	PROPN
ap-616	9	19	t	t	PROPN
ap-616	9	20	t	t	PROPN
ap-616	9	21	t	t	PROPN
ap-616	9	22	t	t	PROPN
ap-616	9	23	�	�	PROPN
ap-616	9	24	�	�	PROPN
ap-616	9	25	�	�	PROPN
ap-616	9	26	�	�	PROPN
ap-616	9	27	�	�	PROPN
ap-616	9	28	�	�	PROPN
ap-616	9	29	�	�	PROPN
ap-616	9	30	�	�	PROPN
ap-616	9	31	�	�	PROPN
ap-616	9	32	�	�	PROPN
ap-616	9	33	�	�	PROPN
ap-616	9	34	�	�	PROPN
ap-616	9	35	1	1	NUM
ap-616	9	36	2	2	NUM
ap-616	9	37	,	,	PUNCT
ap-616	9	38	where	where	SCONJ
ap-616	9	39	p	p	PROPN
ap-616	9	40	p	p	X
ap-616	9	41	u	u	NOUN
ap-616	9	42	(	(	PUNCT
ap-616	9	43	)	)	PUNCT
ap-616	9	44	(	(	PUNCT
ap-616	9	45	(	(	PUNCT
ap-616	9	46	)	)	PUNCT
ap-616	9	47	,	,	PUNCT
ap-616	9	48	)	)	PUNCT
ap-616	9	49	t	t	PROPN
ap-616	9	50	t	t	PROPN
ap-616	9	51	t	t	PROPN
ap-616	9	52	t	t	PROPN
ap-616	9	53	t	t	PROPN
ap-616	9	54	t	t	PROPN
ap-616	9	55	�	�	PROPN
ap-616	9	56	�	�	PROPN
ap-616	9	57	�	�	PROPN
ap-616	9	58	�	�	PROPN
ap-616	9	59	�	�	PROPN
ap-616	9	60	�	�	PROPN
ap-616	9	61	�	�	PROPN
ap-616	9	62	2	2	NUM
ap-616	9	63	2	2	NUM
ap-616	9	64	2	2	NUM
ap-616	9	65	makes	make	VERB
ap-616	9	66	this	this	DET
ap-616	9	67	formula	formula	NOUN
ap-616	9	68	implicit	implicit	NOUN
ap-616	9	69	.	.	PUNCT
ap-616	10	1	to	to	PART
ap-616	10	2	approximate	approximate	VERB
ap-616	10	3	the	the	DET
ap-616	10	4	midpoint	midpoint	NOUN
ap-616	10	5	momentum	momentum	NOUN
ap-616	10	6	,	,	PUNCT
ap-616	10	7	we	we	PRON
ap-616	10	8	may	may	AUX
ap-616	10	9	use	use	VERB
ap-616	10	10	the	the	DET
ap-616	10	11	equation	equation	NOUN
ap-616	10	12	of	of	ADP
ap-616	10	13	motion	motion	NOUN
ap-616	10	14	in	in	ADP
ap-616	10	15	integral	integral	ADJ
ap-616	10	16	form	form	NOUN
ap-616	10	17	,	,	PUNCT
ap-616	10	18	p	p	X
ap-616	10	19	p	p	X
ap-616	10	20	f	f	X
ap-616	10	21	(	(	PUNCT
ap-616	10	22	)	)	PUNCT
ap-616	10	23	(	(	PUNCT
ap-616	10	24	)	)	PUNCT
ap-616	10	25	(	(	PUNCT
ap-616	10	26	)	)	PUNCT
ap-616	10	27	t	t	PROPN
ap-616	10	28	h	h	NOUN
ap-616	10	29	t	t	PROPN
ap-616	10	30	t	t	PROPN
ap-616	10	31	t	t	PROPN
ap-616	10	32	h	h	PROPN
ap-616	10	33	�	�	PROPN
ap-616	10	34	�	�	PROPN
ap-616	10	35	�	�	PROPN
ap-616	10	36	�	�	PROPN
ap-616	10	37	�	�	PROPN
ap-616	10	38	�	�	PROPN
ap-616	10	39	�	�	PROPN
ap-616	10	40	d	d	PROPN
ap-616	10	41	,	,	PUNCT
ap-616	10	42	and	and	CCONJ
ap-616	10	43	numerically	numerically	ADV
ap-616	10	44	evaluate	evaluate	VERB
ap-616	10	45	the	the	DET
ap-616	10	46	impulse	impulse	ADJ
ap-616	10	47	integral	integral	NOUN
ap-616	10	48	.	.	PUNCT
ap-616	11	1	this	this	PRON
ap-616	11	2	we	we	PRON
ap-616	11	3	propose	propose	VERB
ap-616	11	4	to	to	PART
ap-616	11	5	treat	treat	VERB
ap-616	11	6	by	by	ADP
ap-616	11	7	recourse	recourse	NOUN
ap-616	11	8	to	to	ADP
ap-616	11	9	the	the	DET
ap-616	11	10	concept	concept	NOUN
ap-616	11	11	of	of	ADP
ap-616	11	12	concentrated	concentrated	ADJ
ap-616	11	13	,	,	PUNCT
ap-616	11	14	discrete	discrete	ADJ
ap-616	11	15	impulses	impulse	NOUN
ap-616	11	16	delivered	deliver	VERB
ap-616	11	17	at	at	ADP
ap-616	11	18	pre	pre	ADJ
ap-616	11	19	-	-	ADJ
ap-616	11	20	selected	select	VERB
ap-616	11	21	time	time	NOUN
ap-616	11	22	instants	instant	NOUN
ap-616	11	23	.	.	PUNCT
ap-616	12	1	in	in	ADP
ap-616	12	2	particular	particular	ADJ
ap-616	12	3	,	,	PUNCT
ap-616	12	4	the	the	DET
ap-616	12	5	impulse	impulse	NOUN
ap-616	12	6	may	may	AUX
ap-616	12	7	be	be	AUX
ap-616	12	8	delivered	deliver	VERB
ap-616	12	9	at	at	ADP
ap-616	12	10	the	the	DET
ap-616	12	11	end	end	NOUN
ap-616	12	12	of	of	ADP
ap-616	12	13	the	the	DET
ap-616	12	14	time	time	NOUN
ap-616	12	15	step	step	NOUN
ap-616	12	16	,	,	PUNCT
ap-616	12	17	in	in	ADP
ap-616	12	18	which	which	DET
ap-616	12	19	case	case	NOUN
ap-616	12	20	f	f	X
ap-616	12	21	0	0	NUM
ap-616	12	22	(	(	PUNCT
ap-616	12	23	)	)	PUNCT
ap-616	12	24	�	�	PROPN
ap-616	12	25	�	�	PROPN
ap-616	12	26	d	d	PROPN
ap-616	12	27	t	t	PROPN
ap-616	12	28	t	t	PROPN
ap-616	12	29	t	t	PROPN
ap-616	12	30	�	�	PROPN
ap-616	12	31	�	�	PROPN
ap-616	12	32	�	�	PROPN
ap-616	12	33	2	2	NUM
ap-616	12	34	.	.	PUNCT
ap-616	13	1	on	on	ADP
ap-616	13	2	the	the	DET
ap-616	13	3	other	other	ADJ
ap-616	13	4	hand	hand	NOUN
ap-616	13	5	,	,	PUNCT
ap-616	13	6	the	the	DET
ap-616	13	7	impulse	impulse	NOUN
ap-616	13	8	may	may	AUX
ap-616	13	9	be	be	AUX
ap-616	13	10	imposed	impose	VERB
ap-616	13	11	at	at	ADP
ap-616	13	12	the	the	DET
ap-616	13	13	beginning	beginning	NOUN
ap-616	13	14	of	of	ADP
ap-616	13	15	the	the	DET
ap-616	13	16	time	time	NOUN
ap-616	13	17	step	step	NOUN
ap-616	13	18	,	,	PUNCT
ap-616	13	19	and	and	CCONJ
ap-616	13	20	f	f	PROPN
ap-616	13	21	f	f	PROPN
ap-616	13	22	(	(	PUNCT
ap-616	13	23	)	)	PUNCT
ap-616	13	24	(	(	PUNCT
ap-616	13	25	)	)	PUNCT
ap-616	13	26	�	�	PROPN
ap-616	13	27	�	�	PROPN
ap-616	13	28	d	d	PROPN
ap-616	13	29	t	t	PROPN
ap-616	13	30	t	t	PROPN
ap-616	13	31	t	t	PROPN
ap-616	13	32	t	t	PROPN
ap-616	13	33	t	t	PROPN
ap-616	13	34	�	�	PROPN
ap-616	13	35	�	�	PROPN
ap-616	13	36	�	�	PROPN
ap-616	13	37	�	�	PROPN
ap-616	13	38	2	2	NUM
ap-616	13	39	.	.	PUNCT
ap-616	14	1	therefore	therefore	ADV
ap-616	14	2	,	,	PUNCT
ap-616	14	3	we	we	PRON
ap-616	14	4	obtain	obtain	VERB
ap-616	14	5	two	two	NUM
ap-616	14	6	algorithms	algorithm	NOUN
ap-616	14	7	.	.	PUNCT
ap-616	15	1	the	the	DET
ap-616	15	2	first	first	ADJ
ap-616	15	3	one	one	NUM
ap-616	15	4	,	,	PUNCT
ap-616	15	5	�	�	PROPN
ap-616	15	6	�	�	PROPN
ap-616	15	7	t	t	PROPN
ap-616	15	8	,	,	PUNCT
ap-616	15	9	may	may	AUX
ap-616	15	10	be	be	AUX
ap-616	15	11	recognized	recognize	VERB
ap-616	15	12	as	as	ADP
ap-616	15	13	the	the	DET
ap-616	15	14	symplectic	symplectic	PROPN
ap-616	15	15	euler	euler	NOUN
ap-616	15	16	method	method	NOUN
ap-616	15	17	,	,	PUNCT
ap-616	15	18	and	and	CCONJ
ap-616	15	19	the	the	DET
ap-616	15	20	second	second	ADJ
ap-616	15	21	,	,	PUNCT
ap-616	15	22	�	�	PROPN
ap-616	15	23	�	�	PROPN
ap-616	15	24	t	t	PROPN
ap-616	15	25	*	*	PUNCT
ap-616	15	26	,	,	PUNCT
ap-616	15	27	as	as	ADP
ap-616	15	28	its	its	PRON
ap-616	15	29	adjoint	adjoint	NOUN
ap-616	15	30	.	.	PUNCT
ap-616	16	1	�	�	PROPN
ap-616	16	2	�	�	PROPN
ap-616	16	3	�	�	PROPN
ap-616	16	4	�	�	PROPN
ap-616	16	5	�	�	PROPN
ap-616	16	6	�	�	PROPN
ap-616	16	7	t	t	PROPN
ap-616	16	8	t	t	PROPN
ap-616	16	9	t	t	PROPN
ap-616	16	10	t	t	PROPN
ap-616	16	11	t	t	PROPN
ap-616	16	12	t	t	PROPN
ap-616	16	13	t	t	PROPN
ap-616	16	14	t	t	PROPN
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ap-616	16	16	t	t	PROPN
ap-616	16	17	t	t	PROPN
ap-616	16	18	t	t	PROPN
ap-616	16	19	t	t	PROPN
ap-616	16	20	p	p	X
ap-616	16	21	u	u	PROPN
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ap-616	16	35	�	�	PROPN
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ap-616	16	46	1	1	NUM
ap-616	16	47	�	�	PROPN
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ap-616	16	49	�	�	PROPN
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ap-616	16	51	�	�	PROPN
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ap-616	16	53	�	�	PROPN
ap-616	16	54	�	�	PROPN
ap-616	16	55	t	t	PROPN
ap-616	16	56	(	(	PUNCT
ap-616	16	57	symplectic	symplectic	PROPN
ap-616	16	58	euler	euler	PROPN
ap-616	16	59	)	)	PUNCT
ap-616	16	60	�	�	PROPN
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ap-616	16	65	�	�	PROPN
ap-616	16	66	�	�	PROPN
ap-616	17	1	t	t	PROPN
ap-616	17	2	t	t	PROPN
ap-616	17	3	t	t	PROPN
ap-616	17	4	t	t	PROPN
ap-616	17	5	t	t	PROPN
ap-616	17	6	t	t	PROPN
ap-616	17	7	t	t	PROPN
ap-616	17	8	t	t	PROPN
ap-616	17	9	t	t	PROPN
ap-616	17	10	t	t	PROPN
ap-616	17	11	t	t	PROPN
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ap-616	17	13	t	t	PROPN
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ap-616	17	15	p	p	X
ap-616	17	16	u	u	X
ap-616	17	17	p	p	NOUN
ap-616	17	18	u	u	NOUN
ap-616	17	19	p	p	PROPN
ap-616	17	20	f	f	PROPN
ap-616	17	21	u	u	PROPN
ap-616	17	22	m	m	PROPN
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ap-616	17	25	�	�	PROPN
ap-616	17	26	�	�	PROPN
ap-616	17	27	�	�	PROPN
ap-616	17	28	�	�	PROPN
ap-616	17	29	�	�	PROPN
ap-616	17	30	�	�	PROPN
ap-616	17	31	�	�	PROPN
ap-616	17	32	�	�	PROPN
ap-616	17	33	�	�	PROPN
ap-616	17	34	�	�	PROPN
ap-616	17	35	�	�	PROPN
ap-616	17	36	�	�	PROPN
ap-616	17	37	�	�	PROPN
ap-616	17	38	�	�	PROPN
ap-616	17	39	�	�	PROPN
ap-616	17	40	�	�	PROPN
ap-616	17	41	�	�	PROPN
ap-616	17	42	�	�	PROPN
ap-616	17	43	�	�	PROPN
ap-616	17	44	�	�	PROPN
ap-616	17	45	�	�	PROPN
ap-616	17	46	�	�	PROPN
ap-616	17	47	1p	1p	PROPN
ap-616	17	48	t	t	PROPN
ap-616	17	49	(	(	PUNCT
ap-616	17	50	symplectic	symplectic	PROPN
ap-616	17	51	euler	euler	PROPN
ap-616	17	52	adjoint	adjoint	PROPN
ap-616	17	53	)	)	PUNCT
ap-616	17	54	.	.	PUNCT
ap-616	18	1	these	these	DET
ap-616	18	2	algorithms	algorithm	NOUN
ap-616	18	3	are	be	AUX
ap-616	18	4	symplectic	symplectic	ADJ
ap-616	18	5	[	[	X
ap-616	18	6	2	2	NUM
ap-616	18	7	]	]	PUNCT
ap-616	18	8	,	,	PUNCT
ap-616	18	9	and	and	CCONJ
ap-616	18	10	momentum	momentum	NOUN
ap-616	18	11	conserving	conserving	NOUN
ap-616	18	12	.	.	PUNCT
ap-616	19	1	their	their	PRON
ap-616	19	2	accuracy	accuracy	NOUN
ap-616	19	3	is	be	AUX
ap-616	19	4	only	only	ADV
ap-616	19	5	linear	linear	ADJ
ap-616	19	6	in	in	ADP
ap-616	19	7	the	the	DET
ap-616	19	8	time	time	NOUN
ap-616	19	9	step	step	NOUN
ap-616	19	10	,	,	PUNCT
ap-616	19	11	but	but	CCONJ
ap-616	19	12	their	their	PRON
ap-616	19	13	composition	composition	NOUN
ap-616	19	14	preserves	preserve	VERB
ap-616	19	15	both	both	DET
ap-616	19	16	symplecticity	symplecticity	NOUN
ap-616	19	17	and	and	CCONJ
ap-616	19	18	momentum	momentum	NOUN
ap-616	19	19	conservation	conservation	NOUN
ap-616	19	20	and	and	CCONJ
ap-616	19	21	yields	yield	NOUN
ap-616	19	22	a	a	DET
ap-616	19	23	second	second	ADJ
ap-616	19	24	order	order	NOUN
ap-616	19	25	accurate	accurate	ADJ
ap-616	19	26	algorithm	algorithm	NOUN
ap-616	19	27	.	.	PUNCT
ap-616	20	1	that	that	DET
ap-616	20	2	algorithm	algorithm	NOUN
ap-616	20	3	may	may	AUX
ap-616	20	4	be	be	AUX
ap-616	20	5	recognized	recognize	VERB
ap-616	20	6	as	as	ADP
ap-616	20	7	the	the	DET
ap-616	20	8	well	well	ADV
ap-616	20	9	-	-	PUNCT
ap-616	20	10	known	know	VERB
ap-616	20	11	verlet	verlet	NOUN
ap-616	20	12	(	(	PUNCT
ap-616	20	13	explicit	explicit	ADJ
ap-616	20	14	newmark	newmark	NOUN
ap-616	20	15	with	with	ADP
ap-616	20	16	�	�	PROPN
ap-616	20	17	�	�	PROPN
ap-616	20	18	1	1	NUM
ap-616	20	19	2	2	NUM
ap-616	20	20	)	)	PUNCT
ap-616	20	21	�	�	PROPN
ap-616	20	22	�	�	PROPN
ap-616	20	23	�	�	PROPN
ap-616	20	24	�	�	PROPN
ap-616	20	25	�	�	PROPN
ap-616	20	26	�	�	PROPN
ap-616	20	27	t	t	PROPN
ap-616	20	28	t	t	PROPN
ap-616	20	29	t	t	PROPN
ap-616	20	30	�	�	PROPN
ap-616	20	31	2	2	NUM
ap-616	20	32	2	2	NUM
ap-616	20	33	*	*	PUNCT
ap-616	20	34	�	�	PROPN
ap-616	20	35	(	(	PUNCT
ap-616	20	36	verlet	verlet	PROPN
ap-616	20	37	)	)	PUNCT
ap-616	20	38	.	.	PUNCT
ap-616	21	1	3	3	NUM
ap-616	21	2	midpoint	midpoint	NOUN
ap-616	21	3	rule	rule	NOUN
ap-616	21	4	approximation	approximation	NOUN
ap-616	21	5	on	on	ADP
ap-616	21	6	the	the	DET
ap-616	21	7	rotation	rotation	NOUN
ap-616	21	8	group	group	NOUN
ap-616	21	9	now	now	ADV
ap-616	21	10	we	we	PRON
ap-616	21	11	shall	shall	AUX
ap-616	21	12	discuss	discuss	VERB
ap-616	21	13	the	the	DET
ap-616	21	14	dynamics	dynamic	NOUN
ap-616	21	15	of	of	ADP
ap-616	21	16	rigid	rigid	ADJ
ap-616	21	17	bodies	body	NOUN
ap-616	21	18	rotating	rotate	VERB
ap-616	21	19	about	about	ADP
ap-616	21	20	a	a	DET
ap-616	21	21	fixed	fix	VERB
ap-616	21	22	point	point	NOUN
ap-616	21	23	.	.	PUNCT
ap-616	22	1	(	(	PUNCT
ap-616	22	2	more	more	ADJ
ap-616	22	3	detail	detail	NOUN
ap-616	22	4	is	be	AUX
ap-616	22	5	available	available	ADJ
ap-616	22	6	in	in	ADP
ap-616	22	7	reference	reference	NOUN
ap-616	22	8	[	[	X
ap-616	22	9	3	3	NUM
ap-616	22	10	]	]	PUNCT
ap-616	22	11	.	.	PUNCT
ap-616	22	12	)	)	PUNCT
ap-616	23	1	the	the	DET
ap-616	23	2	initial	initial	ADJ
ap-616	23	3	value	value	NOUN
ap-616	23	4	problem	problem	NOUN
ap-616	23	5	may	may	AUX
ap-616	23	6	be	be	AUX
ap-616	23	7	written	write	VERB
ap-616	23	8	in	in	ADP
ap-616	23	9	the	the	DET
ap-616	23	10	convected	convected	ADJ
ap-616	23	11	description	description	NOUN
ap-616	23	12	(	(	PUNCT
ap-616	23	13	body	body	NOUN
ap-616	23	14	frame	frame	NOUN
ap-616	23	15	)	)	PUNCT
ap-616	23	16	as	as	SCONJ
ap-616	23	17	�	�	PROPN
ap-616	23	18	�	�	PROPN
ap-616	23	19	�	�	PROPN
ap-616	23	20	,	,	PUNCT
ap-616	23	21	(	(	PUNCT
ap-616	23	22	)	)	PUNCT
ap-616	23	23	�	�	PROPN
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ap-616	23	25	�	�	PROPN
ap-616	23	26	�	�	PROPN
ap-616	23	27	�	�	PROPN
ap-616	23	28	�	�	PROPN
ap-616	23	29	�	�	PROPN
ap-616	23	30	�	�	PROPN
ap-616	23	31	�	�	PROPN
ap-616	23	32	�	�	PROPN
ap-616	23	33	skew	skew	NOUN
ap-616	23	34	i	i	PRON
ap-616	23	35	t1	t1	VERB
ap-616	23	36	00	00	PUNCT
ap-616	23	37	�	�	PROPN
ap-616	23	38	�	�	PROPN
ap-616	23	39	r	r	NOUN
ap-616	23	40	r	r	NOUN
ap-616	24	1	i	i	NOUN
ap-616	24	2	r	r	NOUN
ap-616	24	3	r	r	PROPN
ap-616	24	4	�	�	PROPN
ap-616	24	5	�	�	PROPN
ap-616	24	6	�	�	PROPN
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ap-616	24	8	1	1	NUM
ap-616	24	9	00	00	NUM
ap-616	24	10	�	�	PROPN
ap-616	24	11	,	,	PUNCT
ap-616	24	12	(	(	PUNCT
ap-616	24	13	)	)	PUNCT
ap-616	24	14	,	,	PUNCT
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ap-616	24	16	�	�	PROPN
ap-616	24	17	�	�	PROPN
ap-616	24	18	is	be	AUX
ap-616	24	19	the	the	DET
ap-616	24	20	rate	rate	NOUN
ap-616	24	21	of	of	ADP
ap-616	24	22	body	body	NOUN
ap-616	24	23	frame	frame	NOUN
ap-616	24	24	angular	angular	ADJ
ap-616	24	25	momentum	momentum	NOUN
ap-616	24	26	,	,	PUNCT
ap-616	24	27	r	r	NOUN
ap-616	24	28	is	be	AUX
ap-616	24	29	the	the	DET
ap-616	24	30	rotation	rotation	NOUN
ap-616	24	31	tensor	tensor	NOUN
ap-616	24	32	,	,	PUNCT
ap-616	24	33	t	t	PROPN
ap-616	24	34	is	be	AUX
ap-616	24	35	the	the	DET
ap-616	24	36	applied	apply	VERB
ap-616	24	37	torque	torque	NOUN
ap-616	24	38	in	in	ADP
ap-616	24	39	the	the	DET
ap-616	24	40	body	body	NOUN
ap-616	24	41	frame	frame	NOUN
ap-616	24	42	,	,	PUNCT
ap-616	24	43	skew	skew	VERB
ap-616	24	44	[	[	X
ap-616	24	45	�	�	X
ap-616	24	46	]	]	PUNCT
ap-616	24	47	is	be	AUX
ap-616	24	48	defined	define	VERB
ap-616	24	49	by	by	ADP
ap-616	24	50	skew	skew	NOUN
ap-616	24	51	[	[	PUNCT
ap-616	24	52	]	]	X
ap-616	24	53	h	h	NOUN
ap-616	24	54	h	h	NOUN
ap-616	24	55	0	0	NUM
ap-616	24	56	�	�	PROPN
ap-616	24	57	�	�	PROPN
ap-616	24	58	,	,	PUNCT
ap-616	24	59	and	and	CCONJ
ap-616	24	60	i	i	PRON
ap-616	24	61	is	be	AUX
ap-616	24	62	the	the	DET
ap-616	24	63	time	time	NOUN
ap-616	24	64	-	-	PUNCT
ap-616	24	65	inde	inde	VERB
ap-616	24	66	©	©	PROPN
ap-616	24	67	czech	czech	PROPN
ap-616	24	68	technical	technical	PROPN
ap-616	24	69	university	university	PROPN
ap-616	24	70	publishing	publishing	NOUN
ap-616	24	71	house	house	NOUN
ap-616	24	72	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-616	24	73	51	51	NUM
ap-616	24	74	acta	acta	PROPN
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ap-616	24	76	vol	vol	NOUN
ap-616	24	77	.	.	PROPN
ap-616	25	1	44	44	NUM
ap-616	25	2	no	no	NOUN
ap-616	25	3	.	.	PUNCT
ap-616	26	1	5–6/2004	5–6/2004	NUM
ap-616	26	2	explicit	explicit	ADJ
ap-616	26	3	time	time	NOUN
ap-616	26	4	integrators	integrator	NOUN
ap-616	26	5	for	for	ADP
ap-616	26	6	nonlinear	nonlinear	ADJ
ap-616	26	7	dynamics	dynamic	NOUN
ap-616	26	8	derived	derive	VERB
ap-616	26	9	from	from	ADP
ap-616	26	10	the	the	DET
ap-616	26	11	midpoint	midpoint	NOUN
ap-616	26	12	rule	rule	NOUN
ap-616	26	13	p.	p.	PROPN
ap-616	26	14	krysl	krysl	NOUN
ap-616	26	15	we	we	PRON
ap-616	26	16	address	address	VERB
ap-616	26	17	the	the	DET
ap-616	26	18	design	design	NOUN
ap-616	26	19	of	of	ADP
ap-616	26	20	time	time	NOUN
ap-616	26	21	integrators	integrator	NOUN
ap-616	26	22	for	for	ADP
ap-616	26	23	mechanical	mechanical	ADJ
ap-616	26	24	systems	system	NOUN
ap-616	26	25	that	that	PRON
ap-616	26	26	are	be	AUX
ap-616	26	27	explicit	explicit	ADJ
ap-616	26	28	in	in	ADP
ap-616	26	29	the	the	DET
ap-616	26	30	forcing	force	VERB
ap-616	26	31	evaluations	evaluation	NOUN
ap-616	26	32	.	.	PUNCT
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ap-616	27	2	starting	starting	NOUN
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ap-616	27	4	is	be	AUX
ap-616	27	5	the	the	DET
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ap-616	27	10	in	in	ADP
ap-616	27	11	the	the	DET
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ap-616	27	13	form	form	NOUN
ap-616	27	14	for	for	ADP
ap-616	27	15	the	the	DET
ap-616	27	16	vector	vector	NOUN
ap-616	27	17	space	space	NOUN
ap-616	27	18	setting	setting	NOUN
ap-616	27	19	,	,	PUNCT
ap-616	27	20	or	or	CCONJ
ap-616	27	21	in	in	ADP
ap-616	27	22	the	the	DET
ap-616	27	23	lie	lie	NOUN
ap-616	27	24	form	form	NOUN
ap-616	27	25	for	for	ADP
ap-616	27	26	the	the	DET
ap-616	27	27	rotation	rotation	NOUN
ap-616	27	28	group	group	NOUN
ap-616	27	29	.	.	PUNCT
ap-616	28	1	by	by	ADP
ap-616	28	2	introducing	introduce	VERB
ap-616	28	3	discrete	discrete	ADJ
ap-616	28	4	,	,	PUNCT
ap-616	28	5	concentrated	concentrated	ADJ
ap-616	28	6	impulses	impulse	NOUN
ap-616	28	7	we	we	PRON
ap-616	28	8	can	can	AUX
ap-616	28	9	approximate	approximate	VERB
ap-616	28	10	the	the	DET
ap-616	28	11	forcing	forcing	NOUN
ap-616	28	12	impressed	impress	VERB
ap-616	28	13	upon	upon	SCONJ
ap-616	28	14	the	the	DET
ap-616	28	15	system	system	NOUN
ap-616	28	16	over	over	ADP
ap-616	28	17	the	the	DET
ap-616	28	18	time	time	NOUN
ap-616	28	19	step	step	NOUN
ap-616	28	20	,	,	PUNCT
ap-616	28	21	and	and	CCONJ
ap-616	28	22	thus	thus	ADV
ap-616	28	23	arrive	arrive	VERB
ap-616	28	24	at	at	ADP
ap-616	28	25	first	first	ADJ
ap-616	28	26	-	-	PUNCT
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ap-616	28	28	integrators	integrator	NOUN
ap-616	28	29	.	.	PUNCT
ap-616	29	1	these	these	PRON
ap-616	29	2	can	can	AUX
ap-616	29	3	then	then	ADV
ap-616	29	4	be	be	AUX
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ap-616	29	6	to	to	PART
ap-616	29	7	yield	yield	VERB
ap-616	29	8	a	a	DET
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ap-616	29	10	order	order	NOUN
ap-616	29	11	integrator	integrator	NOUN
ap-616	29	12	with	with	ADP
ap-616	29	13	very	very	ADV
ap-616	29	14	desirable	desirable	ADJ
ap-616	29	15	properties	property	NOUN
ap-616	29	16	:	:	PUNCT
ap-616	29	17	symplecticity	symplecticity	NOUN
ap-616	29	18	and	and	CCONJ
ap-616	29	19	momentum	momentum	NOUN
ap-616	29	20	conservation	conservation	NOUN
ap-616	29	21	.	.	PUNCT
ap-616	30	1	keywords	keyword	NOUN
ap-616	30	2	:	:	PUNCT
ap-616	30	3	time	time	NOUN
ap-616	30	4	integration	integration	NOUN
ap-616	30	5	,	,	PUNCT
ap-616	30	6	rigid	rigid	ADJ
ap-616	30	7	body	body	NOUN
ap-616	30	8	motion	motion	NOUN
ap-616	30	9	,	,	PUNCT
ap-616	30	10	midpoint	midpoint	NOUN
ap-616	30	11	rule	rule	NOUN
ap-616	30	12	,	,	PUNCT
ap-616	30	13	symplectic	symplectic	PROPN
ap-616	30	14	euler	euler	PROPN
ap-616	30	15	,	,	PUNCT
ap-616	30	16	verlet	verlet	NOUN
ap-616	30	17	,	,	PUNCT
ap-616	30	18	newmark	newmark	NOUN
ap-616	30	19	,	,	PUNCT
ap-616	30	20	midpoint	midpoint	NOUN
ap-616	30	21	lie	lie	NOUN
ap-616	30	22	algorithm	algorithm	NOUN
ap-616	30	23	.	.	PUNCT
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ap-616	31	2	tensor	tensor	NOUN
ap-616	31	3	of	of	ADP
ap-616	31	4	inertia	inertia	NOUN
ap-616	31	5	in	in	ADP
ap-616	31	6	the	the	DET
ap-616	31	7	body	body	NOUN
ap-616	31	8	frame	frame	NOUN
ap-616	31	9	.	.	PUNCT
ap-616	32	1	the	the	DET
ap-616	32	2	second	second	ADJ
ap-616	32	3	equation	equation	NOUN
ap-616	32	4	is	be	AUX
ap-616	32	5	not	not	PART
ap-616	32	6	in	in	ADP
ap-616	32	7	a	a	DET
ap-616	32	8	form	form	NOUN
ap-616	32	9	suitable	suitable	ADJ
ap-616	32	10	for	for	ADP
ap-616	32	11	midpoint	midpoint	NOUN
ap-616	32	12	discretization	discretization	NOUN
ap-616	32	13	,	,	PUNCT
ap-616	32	14	because	because	SCONJ
ap-616	32	15	the	the	DET
ap-616	32	16	rotation	rotation	NOUN
ap-616	32	17	tensor	tensor	NOUN
ap-616	32	18	constitutes	constitute	VERB
ap-616	32	19	points	point	NOUN
ap-616	32	20	of	of	ADP
ap-616	32	21	the	the	DET
ap-616	32	22	lie	lie	NOUN
ap-616	32	23	group	group	NOUN
ap-616	32	24	so(3	so(3	PROPN
ap-616	32	25	)	)	PUNCT
ap-616	32	26	,	,	PUNCT
ap-616	32	27	which	which	PRON
ap-616	32	28	is	be	AUX
ap-616	32	29	not	not	PART
ap-616	32	30	a	a	DET
ap-616	32	31	vector	vector	NOUN
ap-616	32	32	space	space	NOUN
ap-616	32	33	and	and	CCONJ
ap-616	32	34	linear	linear	ADJ
ap-616	32	35	combinations	combination	NOUN
ap-616	32	36	are	be	AUX
ap-616	32	37	not	not	PART
ap-616	32	38	legal	legal	ADJ
ap-616	32	39	operations	operation	NOUN
ap-616	32	40	on	on	ADP
ap-616	32	41	the	the	DET
ap-616	32	42	rotation	rotation	NOUN
ap-616	32	43	tensors	tensor	NOUN
ap-616	32	44	.	.	PUNCT
ap-616	33	1	to	to	PART
ap-616	33	2	transform	transform	VERB
ap-616	33	3	the	the	DET
ap-616	33	4	initial	initial	ADJ
ap-616	33	5	value	value	NOUN
ap-616	33	6	problem	problem	NOUN
ap-616	33	7	to	to	ADP
ap-616	33	8	a	a	DET
ap-616	33	9	form	form	NOUN
ap-616	33	10	suitable	suitable	ADJ
ap-616	33	11	for	for	ADP
ap-616	33	12	our	our	PRON
ap-616	33	13	purposes	purpose	NOUN
ap-616	33	14	,	,	PUNCT
ap-616	33	15	we	we	PRON
ap-616	33	16	shall	shall	AUX
ap-616	33	17	introduce	introduce	VERB
ap-616	33	18	the	the	DET
ap-616	33	19	rotation	rotation	NOUN
ap-616	33	20	vector	vector	NOUN
ap-616	33	21	representation	representation	NOUN
ap-616	33	22	of	of	ADP
ap-616	33	23	the	the	DET
ap-616	33	24	rotation	rotation	NOUN
ap-616	33	25	tensor	tensor	NOUN
ap-616	33	26	.	.	PUNCT
ap-616	34	1	the	the	DET
ap-616	34	2	equation	equation	NOUN
ap-616	34	3	of	of	ADP
ap-616	34	4	motion	motion	NOUN
ap-616	34	5	is	be	AUX
ap-616	34	6	written	write	VERB
ap-616	34	7	in	in	ADP
ap-616	34	8	the	the	DET
ap-616	34	9	spatial	spatial	ADJ
ap-616	34	10	frame	frame	NOUN
ap-616	34	11	as	as	ADP
ap-616	34	12	�	�	PROPN
ap-616	34	13	�	�	PROPN
ap-616	34	14	�	�	PROPN
ap-616	34	15	rt	rt	PROPN
ap-616	34	16	,	,	PUNCT
ap-616	34	17	where	where	SCONJ
ap-616	34	18	�	�	PROPN
ap-616	34	19	�	�	PROPN
ap-616	34	20	is	be	AUX
ap-616	34	21	the	the	DET
ap-616	34	22	rate	rate	NOUN
ap-616	34	23	of	of	ADP
ap-616	34	24	the	the	DET
ap-616	34	25	spatial	spatial	ADJ
ap-616	34	26	angular	angular	ADJ
ap-616	34	27	momentum	momentum	NOUN
ap-616	34	28	,	,	PUNCT
ap-616	34	29	and	and	CCONJ
ap-616	34	30	consequently	consequently	ADV
ap-616	34	31	the	the	DET
ap-616	34	32	equation	equation	NOUN
ap-616	34	33	of	of	ADP
ap-616	34	34	motion	motion	NOUN
ap-616	34	35	may	may	AUX
ap-616	34	36	be	be	AUX
ap-616	34	37	written	write	VERB
ap-616	34	38	in	in	ADP
ap-616	34	39	integral	integral	ADJ
ap-616	34	40	form	form	NOUN
ap-616	34	41	as	as	ADP
ap-616	34	42	�	�	PROPN
ap-616	34	43	�	�	PROPN
ap-616	34	44	�	�	PROPN
ap-616	34	45	�	�	PROPN
ap-616	34	46	�	�	PROPN
ap-616	34	47	(	(	PUNCT
ap-616	34	48	)	)	PUNCT
ap-616	34	49	exp	exp	NOUN
ap-616	34	50	[	[	PUNCT
ap-616	34	51	]	]	X
ap-616	34	52	(	(	PUNCT
ap-616	34	53	)	)	PUNCT
ap-616	34	54	(	(	PUNCT
ap-616	34	55	)	)	PUNCT
ap-616	34	56	(	(	PUNCT
ap-616	34	57	)	)	PUNCT
ap-616	34	58	(	(	PUNCT
ap-616	34	59	)	)	PUNCT
ap-616	34	60	t	t	NOUN
ap-616	34	61	t	t	X
ap-616	34	62	tt	tt	PROPN
ap-616	34	63	t	t	PROPN
ap-616	34	64	t	t	PROPN
ap-616	34	65	�	�	PROPN
ap-616	34	66	�	�	PROPN
ap-616	34	67	�	�	PROPN
ap-616	34	68	�	�	PROPN
ap-616	34	69	�	�	PROPN
ap-616	34	70	�	�	PROPN
ap-616	34	71	�	�	PROPN
ap-616	34	72	�	�	PROPN
ap-616	34	73	�	�	PROPN
ap-616	34	74	�	�	PROPN
ap-616	34	75	�	�	PROPN
ap-616	34	76	skew	skew	NOUN
ap-616	34	77	d0	d0	NOUN
ap-616	34	78	0	0	NUM
ap-616	35	1	r	r	NOUN
ap-616	35	2	r	r	NOUN
ap-616	35	3	t	t	PROPN
ap-616	35	4	�	�	PROPN
ap-616	35	5	�	�	PROPN
ap-616	35	6	�	�	PROPN
ap-616	35	7	�	�	PROPN
ap-616	35	8	where	where	SCONJ
ap-616	35	9	�	�	PROPN
ap-616	35	10	�	�	PROPN
ap-616	35	11	exp	exp	NOUN
ap-616	35	12	[	[	PUNCT
ap-616	35	13	]	]	X
ap-616	35	14	(	(	PUNCT
ap-616	35	15	)	)	PUNCT
ap-616	35	16	(	(	PUNCT
ap-616	35	17	)	)	PUNCT
ap-616	35	18	�	�	PROPN
ap-616	35	19	�	�	PROPN
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ap-616	35	21	�	�	PROPN
ap-616	35	22	r	r	PROPN
ap-616	35	23	rt	rt	PROPN
ap-616	35	24	t	t	PROPN
ap-616	35	25	t0	t0	PROPN
ap-616	35	26	is	be	AUX
ap-616	35	27	the	the	DET
ap-616	35	28	incremental	incremental	ADJ
ap-616	35	29	rotation	rotation	NOUN
ap-616	35	30	through	through	ADP
ap-616	35	31	vector	vector	PROPN
ap-616	35	32	�	�	PROPN
ap-616	35	33	.	.	PUNCT
ap-616	36	1	upon	upon	SCONJ
ap-616	36	2	time	time	NOUN
ap-616	36	3	differentiation	differentiation	NOUN
ap-616	36	4	and	and	CCONJ
ap-616	36	5	identification	identification	NOUN
ap-616	36	6	with	with	ADP
ap-616	36	7	the	the	DET
ap-616	36	8	original	original	ADJ
ap-616	36	9	differential	differential	NOUN
ap-616	36	10	equation	equation	NOUN
ap-616	36	11	of	of	ADP
ap-616	36	12	motion	motion	NOUN
ap-616	36	13	,	,	PUNCT
ap-616	36	14	we	we	PRON
ap-616	36	15	obtain	obtain	VERB
ap-616	36	16	�	�	PROPN
ap-616	36	17	(	(	PUNCT
ap-616	36	18	exp	exp	NOUN
ap-616	36	19	)	)	PUNCT
ap-616	36	20	[	[	PUNCT
ap-616	36	21	]	]	X
ap-616	36	22	�	�	PROPN
ap-616	36	23	�	�	PROPN
ap-616	36	24	�	�	PROPN
ap-616	36	25	�	�	PROPN
ap-616	36	26	�	�	PROPN
ap-616	36	27	�	�	PROPN
ap-616	36	28	�	�	PROPN
ap-616	36	29	d	d	NOUN
ap-616	36	30	skew	skew	NOUN
ap-616	36	31	1	1	NUM
ap-616	36	32	1i	1i	NOUN
ap-616	36	33	,	,	PUNCT
ap-616	36	34	where	where	SCONJ
ap-616	36	35	d	d	PROPN
ap-616	36	36	skewexp	skewexp	NOUN
ap-616	36	37	(	(	PUNCT
ap-616	36	38	)	)	PUNCT
ap-616	36	39	[	[	PUNCT
ap-616	36	40	]	]	X
ap-616	36	41	�	�	PROPN
ap-616	36	42	�	�	PROPN
ap-616	36	43	�	�	PROPN
ap-616	36	44	is	be	AUX
ap-616	36	45	the	the	DET
ap-616	36	46	differential	differential	NOUN
ap-616	36	47	of	of	ADP
ap-616	36	48	the	the	DET
ap-616	36	49	exponential	exponential	ADJ
ap-616	36	50	map	map	NOUN
ap-616	36	51	.	.	PUNCT
ap-616	37	1	the	the	DET
ap-616	37	2	initial	initial	ADJ
ap-616	37	3	value	value	NOUN
ap-616	37	4	problem	problem	NOUN
ap-616	37	5	may	may	AUX
ap-616	37	6	therefore	therefore	ADV
ap-616	37	7	be	be	AUX
ap-616	37	8	rewritten	rewrite	VERB
ap-616	37	9	as	as	ADP
ap-616	37	10	�	�	PROPN
ap-616	37	11	,	,	PUNCT
ap-616	37	12	(	(	PUNCT
ap-616	37	13	)	)	PUNCT
ap-616	37	14	�	�	PROPN
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ap-616	37	16	�	�	PROPN
ap-616	37	17	�	�	PROPN
ap-616	37	18	�	�	PROPN
ap-616	37	19	�	�	PROPN
ap-616	37	20	�	�	PROPN
ap-616	37	21	�	�	PROPN
ap-616	37	22	�	�	PROPN
ap-616	37	23	�	�	PROPN
ap-616	37	24	�	�	PROPN
ap-616	37	25	�	�	PROPN
ap-616	37	26	�	�	PROPN
ap-616	37	27	�	�	PROPN
ap-616	37	28	�	�	PROPN
ap-616	37	29	�	�	PROPN
ap-616	37	30	skew	skew	NOUN
ap-616	37	31	i	i	PROPN
ap-616	37	32	t1	t1	VERB
ap-616	37	33	00	00	NUM
ap-616	37	34	,	,	PUNCT
ap-616	37	35	�	�	PROPN
ap-616	37	36	(	(	PUNCT
ap-616	37	37	exp	exp	NOUN
ap-616	37	38	)	)	PUNCT
ap-616	37	39	(	(	PUNCT
ap-616	37	40	)	)	PUNCT
ap-616	37	41	[	[	PUNCT
ap-616	37	42	]	]	X
ap-616	37	43	�	�	PROPN
ap-616	37	44	�	�	PROPN
ap-616	37	45	�	�	PROPN
ap-616	37	46	�	�	PROPN
ap-616	37	47	�	�	PROPN
ap-616	37	48	�	�	PROPN
ap-616	37	49	�	�	PROPN
ap-616	37	50	�	�	PROPN
ap-616	37	51	�	�	PROPN
ap-616	37	52	d	d	PROPN
ap-616	37	53	,	,	PUNCT
ap-616	37	54	skew	skew	ADJ
ap-616	37	55	1	1	NUM
ap-616	37	56	1	1	NUM
ap-616	37	57	0i	0i	NOUN
ap-616	37	58	0	0	NUM
ap-616	37	59	.	.	PUNCT
ap-616	38	1	the	the	DET
ap-616	38	2	midpoint	midpoint	NOUN
ap-616	38	3	approximation	approximation	NOUN
ap-616	38	4	applied	apply	VERB
ap-616	38	5	to	to	ADP
ap-616	38	6	the	the	DET
ap-616	38	7	second	second	ADJ
ap-616	38	8	equation	equation	NOUN
ap-616	38	9	yields	yield	NOUN
ap-616	38	10	(	(	PUNCT
ap-616	38	11	�	�	PROPN
ap-616	38	12	t	t	PROPN
ap-616	38	13	�	�	PROPN
ap-616	38	14	0	0	NUM
ap-616	38	15	)	)	PUNCT
ap-616	38	16	�	�	PROPN
ap-616	38	17	�	�	PROPN
ap-616	38	18	�	�	PROPN
ap-616	38	19	t	t	PROPN
ap-616	38	20	t	t	PROPN
ap-616	38	21	t	t	PROPN
ap-616	38	22	tt	tt	PROPN
ap-616	38	23	t	t	PROPN
ap-616	38	24	�	�	PROPN
ap-616	38	25	�	�	PROPN
ap-616	38	26	�	�	PROPN
ap-616	38	27	�	�	PROPN
ap-616	38	28	�	�	PROPN
ap-616	38	29	�	�	PROPN
ap-616	38	30	�	�	PROPN
ap-616	38	31	�	�	PROPN
ap-616	38	32	�	�	PROPN
ap-616	38	33	�	�	PROPN
ap-616	38	34	�	�	PROPN
ap-616	38	35	�	�	PROPN
ap-616	38	36	�	�	PROPN
ap-616	38	37	�	�	PROPN
ap-616	38	38	�	�	PROPN
ap-616	38	39	d	d	NOUN
ap-616	38	40	skew	skew	NOUN
ap-616	38	41	exp	exp	NOUN
ap-616	38	42	[	[	PUNCT
ap-616	38	43	]	]	X
ap-616	38	44	1	1	NUM
ap-616	38	45	2	2	NUM
ap-616	38	46	1	1	NUM
ap-616	38	47	1	1	NUM
ap-616	38	48	2i	2i	NUM
ap-616	38	49	which	which	PRON
ap-616	38	50	may	may	AUX
ap-616	38	51	be	be	AUX
ap-616	38	52	simplified	simplify	VERB
ap-616	38	53	by	by	ADP
ap-616	38	54	noting	note	VERB
ap-616	38	55	d	d	PROPN
ap-616	38	56	skew	skew	NOUN
ap-616	38	57	exp	exp	NOUN
ap-616	38	58	[	[	PUNCT
ap-616	38	59	]	]	X
ap-616	38	60	�	�	PROPN
ap-616	38	61	�	�	PROPN
ap-616	38	62	�	�	PROPN
ap-616	38	63	�	�	PROPN
ap-616	38	64	�	�	PROPN
ap-616	38	65	1	1	NUM
ap-616	38	66	2	2	NUM
ap-616	38	67	�	�	PROPN
ap-616	38	68	�	�	PROPN
ap-616	38	69	�	�	PROPN
ap-616	38	70	t	t	PROPN
ap-616	38	71	t	t	PROPN
ap-616	38	72	t	t	PROPN
ap-616	38	73	t	t	PROPN
ap-616	38	74	t	t	PROPN
ap-616	38	75	t	t	PROPN
ap-616	38	76	�	�	PROPN
ap-616	38	77	�	�	PROPN
ap-616	38	78	�	�	PROPN
ap-616	38	79	to	to	PART
ap-616	38	80	give	give	VERB
ap-616	38	81	1	1	NUM
ap-616	38	82	2	2	NUM
ap-616	38	83	�	�	PROPN
ap-616	38	84	�	�	PROPN
ap-616	38	85	�	�	PROPN
ap-616	38	86	t	t	PROPN
ap-616	38	87	t	t	PROPN
ap-616	38	88	t	t	PROPN
ap-616	38	89	t	t	PROPN
ap-616	38	90	ti	ti	PROPN
ap-616	38	91	�	�	PROPN
ap-616	38	92	�	�	PROPN
ap-616	38	93	�	�	PROPN
ap-616	38	94	�	�	PROPN
ap-616	38	95	�	�	PROPN
ap-616	38	96	.	.	PUNCT
ap-616	39	1	this	this	DET
ap-616	39	2	equation	equation	NOUN
ap-616	39	3	needs	need	VERB
ap-616	39	4	to	to	PART
ap-616	39	5	be	be	AUX
ap-616	39	6	solved	solve	VERB
ap-616	39	7	for	for	ADP
ap-616	39	8	the	the	DET
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ap-616	39	10	vector	vector	NOUN
ap-616	39	11	.	.	PUNCT
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ap-616	40	2	,	,	PUNCT
ap-616	40	3	as	as	ADP
ap-616	40	4	for	for	ADP
ap-616	40	5	the	the	DET
ap-616	40	6	vector	vector	NOUN
ap-616	40	7	space	space	NOUN
ap-616	40	8	setting	set	VERB
ap-616	40	9	we	we	PRON
ap-616	40	10	get	get	VERB
ap-616	40	11	two	two	NUM
ap-616	40	12	different	different	ADJ
ap-616	40	13	algorithms	algorithm	NOUN
ap-616	40	14	,	,	PUNCT
ap-616	40	15	depending	depend	VERB
ap-616	40	16	on	on	ADP
ap-616	40	17	the	the	DET
ap-616	40	18	chosen	choose	VERB
ap-616	40	19	approximation	approximation	NOUN
ap-616	40	20	of	of	ADP
ap-616	40	21	�	�	PROPN
ap-616	40	22	t	t	PROPN
ap-616	40	23	t	t	PROPN
ap-616	40	24	�	�	PROPN
ap-616	40	25	�	�	PROPN
ap-616	40	26	2	2	NUM
ap-616	40	27	.	.	PUNCT
ap-616	41	1	for	for	SCONJ
ap-616	41	2	the	the	DET
ap-616	41	3	impulse	impulse	NOUN
ap-616	41	4	applied	apply	VERB
ap-616	41	5	at	at	ADP
ap-616	41	6	the	the	DET
ap-616	41	7	beginning	beginning	NOUN
ap-616	41	8	of	of	ADP
ap-616	41	9	the	the	DET
ap-616	41	10	time	time	NOUN
ap-616	41	11	step	step	NOUN
ap-616	41	12	we	we	PRON
ap-616	41	13	obtain	obtain	VERB
ap-616	41	14	the	the	DET
ap-616	41	15	so(3	so(3	NOUN
ap-616	41	16	)	)	PUNCT
ap-616	41	17	counterpart	counterpart	NOUN
ap-616	41	18	of	of	ADP
ap-616	41	19	the	the	DET
ap-616	41	20	symplectic	symplectic	PROPN
ap-616	41	21	euler	euler	PROPN
ap-616	41	22	integrator	integrator	NOUN
ap-616	41	23	:	:	PUNCT
ap-616	42	1	�	�	PROPN
ap-616	42	2	�	�	PROPN
ap-616	42	3	�	�	PROPN
ap-616	42	4	�	�	PROPN
ap-616	42	5	�	�	PROPN
ap-616	42	6	�	�	PROPN
ap-616	42	7	�	�	PROPN
ap-616	42	8	�	�	PROPN
ap-616	42	9	t	t	PROPN
ap-616	42	10	t	t	PROPN
ap-616	42	11	t	t	PROPN
ap-616	42	12	t	t	PROPN
ap-616	42	13	t	t	PROPN
ap-616	42	14	t	t	PROPN
ap-616	42	15	t	t	PROPN
ap-616	42	16	t	t	PROPN
ap-616	42	17	t	t	NOUN
ap-616	42	18	r	r	NOUN
ap-616	42	19	r	r	PROPN
ap-616	42	20	�	�	PROPN
ap-616	42	21	�	�	PROPN
ap-616	42	22	�	�	PROPN
ap-616	42	23	�	�	PROPN
ap-616	42	24	�	�	PROPN
ap-616	42	25	�	�	PROPN
ap-616	42	26	�	�	PROPN
ap-616	42	27	�	�	PROPN
ap-616	42	28	�	�	PROPN
ap-616	42	29	�	�	PROPN
ap-616	42	30	�	�	PROPN
ap-616	42	31	�	�	PROPN
ap-616	42	32	�	�	PROPN
ap-616	42	33	�	�	PROPN
ap-616	42	34	�	�	PROPN
ap-616	42	35	�	�	PROPN
ap-616	42	36	exp	exp	NOUN
ap-616	42	37	[	[	PUNCT
ap-616	42	38	)	)	PUNCT
ap-616	42	39	]	]	X
ap-616	42	40	skew	skew	ADJ
ap-616	42	41	(	(	PUNCT
ap-616	42	42	(	(	PUNCT
ap-616	42	43	)	)	PUNCT
ap-616	42	44	exp	exp	NOUN
ap-616	42	45	[	[	PUNCT
ap-616	42	46	)	)	PUNCT
ap-616	42	47	]	]	PUNCT
ap-616	42	48	�	�	PROPN
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ap-616	42	50	t	t	PROPN
ap-616	42	51	t	t	PROPN
ap-616	42	52	t	t	PROPN
ap-616	42	53	t	t	PROPN
ap-616	42	54	t	t	PROPN
ap-616	42	55	t	t	PROPN
ap-616	42	56	�	�	PROPN
ap-616	42	57	�	�	PROPN
ap-616	42	58	�	�	PROPN
ap-616	42	59	�	�	PROPN
ap-616	42	60	�	�	PROPN
ap-616	42	61	�	�	PROPN
ap-616	42	62	�	�	PROPN
ap-616	42	63	�	�	PROPN
ap-616	42	64	�	�	PROPN
ap-616	42	65	�	�	PROPN
ap-616	42	66	t	t	PROPN
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ap-616	42	68	skew	skew	PROPN
ap-616	42	69	(	(	PUNCT
ap-616	42	70	,	,	PUNCT
ap-616	42	71	where	where	SCONJ
ap-616	42	72	�	�	PROPN
ap-616	42	73	t	t	PROPN
ap-616	42	74	t	t	PROPN
ap-616	42	75	�	�	PROPN
ap-616	42	76	�	�	PROPN
ap-616	42	77	solves	solve	VERB
ap-616	42	78	1	1	NUM
ap-616	42	79	�	�	PROPN
ap-616	42	80	�	�	PROPN
ap-616	42	81	�	�	PROPN
ap-616	42	82	�	�	PROPN
ap-616	42	83	t	t	PROPN
ap-616	42	84	tt	tt	PROPN
ap-616	42	85	t	t	PROPN
ap-616	42	86	t	t	PROPN
ap-616	42	87	t	t	PROPN
ap-616	42	88	t	t	PROPN
ap-616	42	89	ti	ti	PROPN
ap-616	42	90	t	t	PROPN
ap-616	42	91	�	�	PROPN
ap-616	42	92	�	�	PROPN
ap-616	42	93	�	�	PROPN
ap-616	42	94	�	�	PROPN
ap-616	42	95	�	�	PROPN
ap-616	42	96	�	�	PROPN
ap-616	42	97	�	�	PROPN
ap-616	42	98	�	�	PROPN
ap-616	42	99	�	�	PROPN
ap-616	42	100	�	�	PROPN
ap-616	42	101	�	�	PROPN
ap-616	42	102	�	�	PROPN
ap-616	42	103	�	�	PROPN
ap-616	42	104	�	�	PROPN
ap-616	42	105	�	�	PROPN
ap-616	42	106	�	�	PROPN
ap-616	42	107	�	�	PROPN
ap-616	42	108	�	�	PROPN
ap-616	42	109	exp	exp	NOUN
ap-616	42	110	(	(	PUNCT
ap-616	42	111	)	)	PUNCT
ap-616	42	112	skew	skew	NOUN
ap-616	42	113	1	1	NUM
ap-616	42	114	2	2	NUM
ap-616	42	115	.	.	PUNCT
ap-616	43	1	on	on	ADP
ap-616	43	2	the	the	DET
ap-616	43	3	other	other	ADJ
ap-616	43	4	hand	hand	NOUN
ap-616	43	5	,	,	PUNCT
ap-616	43	6	the	the	DET
ap-616	43	7	total	total	ADJ
ap-616	43	8	torque	torque	NOUN
ap-616	43	9	impulse	impulse	NOUN
ap-616	43	10	applied	apply	VERB
ap-616	43	11	at	at	ADP
ap-616	43	12	the	the	DET
ap-616	43	13	end	end	NOUN
ap-616	43	14	of	of	ADP
ap-616	43	15	the	the	DET
ap-616	43	16	time	time	NOUN
ap-616	43	17	step	step	NOUN
ap-616	43	18	yields	yield	VERB
ap-616	43	19	the	the	DET
ap-616	43	20	adjoint	adjoint	PROPN
ap-616	43	21	method	method	PROPN
ap-616	43	22	�	�	PROPN
ap-616	43	23	�	�	PROPN
ap-616	43	24	�	�	PROPN
ap-616	43	25	�	�	PROPN
ap-616	43	26	�	�	PROPN
ap-616	43	27	�	�	PROPN
ap-616	43	28	�	�	PROPN
ap-616	43	29	�	�	PROPN
ap-616	44	1	t	t	PROPN
ap-616	44	2	t	t	PROPN
ap-616	44	3	t	t	PROPN
ap-616	44	4	t	t	PROPN
ap-616	44	5	t	t	PROPN
ap-616	44	6	t	t	PROPN
ap-616	44	7	t	t	PROPN
ap-616	44	8	t	t	PROPN
ap-616	44	9	t	t	PROPN
ap-616	44	10	*	*	SYM
ap-616	44	11	exp	exp	PROPN
ap-616	44	12	[	[	PUNCT
ap-616	44	13	)	)	PUNCT
ap-616	44	14	r	r	NOUN
ap-616	44	15	r	r	NOUN
ap-616	44	16	�	�	PROPN
ap-616	44	17	�	�	PROPN
ap-616	44	18	�	�	PROPN
ap-616	44	19	�	�	PROPN
ap-616	44	20	�	�	PROPN
ap-616	44	21	�	�	PROPN
ap-616	44	22	�	�	PROPN
ap-616	44	23	�	�	PROPN
ap-616	44	24	�	�	PROPN
ap-616	44	25	�	�	PROPN
ap-616	44	26	�	�	PROPN
ap-616	44	27	�	�	PROPN
ap-616	44	28	�	�	PROPN
ap-616	44	29	�	�	PROPN
ap-616	44	30	�	�	PROPN
ap-616	44	31	�	�	PROPN
ap-616	44	32	skew	skew	NOUN
ap-616	44	33	(	(	PUNCT
ap-616	44	34	]	]	X
ap-616	44	35	(	(	PUNCT
ap-616	44	36	)	)	PUNCT
ap-616	44	37	exp	exp	NOUN
ap-616	44	38	[	[	PUNCT
ap-616	44	39	)	)	PUNCT
ap-616	44	40	]	]	PUNCT
ap-616	44	41	�	�	PROPN
ap-616	44	42	�	�	PROPN
ap-616	44	43	t	t	PROPN
ap-616	44	44	t	t	PROPN
ap-616	44	45	t	t	PROPN
ap-616	44	46	t	t	PROPN
ap-616	44	47	t	t	PROPN
ap-616	44	48	t	t	PROPN
ap-616	44	49	t	t	PROPN
ap-616	44	50	�	�	PROPN
ap-616	44	51	�	�	PROPN
ap-616	44	52	�	�	PROPN
ap-616	44	53	�	�	PROPN
ap-616	44	54	�	�	PROPN
ap-616	44	55	�	�	PROPN
ap-616	44	56	�	�	PROPN
ap-616	44	57	�	�	PROPN
ap-616	44	58	�	�	PROPN
ap-616	44	59	�	�	PROPN
ap-616	44	60	�	�	PROPN
ap-616	44	61	�	�	PROPN
ap-616	44	62	t	t	PROPN
ap-616	44	63	r	r	NOUN
ap-616	44	64	skew	skew	PROPN
ap-616	44	65	(	(	PUNCT
ap-616	44	66	,	,	PUNCT
ap-616	44	67	where	where	SCONJ
ap-616	44	68	�	�	PROPN
ap-616	44	69	t	t	PROPN
ap-616	44	70	t	t	PROPN
ap-616	44	71	�	�	PROPN
ap-616	44	72	�	�	PROPN
ap-616	44	73	solves	solve	VERB
ap-616	44	74	1	1	NUM
ap-616	44	75	�	�	PROPN
ap-616	44	76	�	�	PROPN
ap-616	44	77	�	�	PROPN
ap-616	44	78	t	t	PROPN
ap-616	44	79	t	t	PROPN
ap-616	44	80	t	t	PROPN
ap-616	44	81	t	t	PROPN
ap-616	44	82	t	t	PROPN
ap-616	44	83	ti	ti	PROPN
ap-616	44	84	�	�	PROPN
ap-616	44	85	�	�	PROPN
ap-616	44	86	�	�	PROPN
ap-616	44	87	�	�	PROPN
ap-616	44	88	�	�	PROPN
ap-616	44	89	�	�	PROPN
ap-616	44	90	�	�	PROPN
ap-616	44	91	�	�	PROPN
ap-616	44	92	�	�	PROPN
ap-616	44	93	�	�	PROPN
ap-616	44	94	�	�	PROPN
ap-616	44	95	�	�	PROPN
ap-616	44	96	�	�	PROPN
ap-616	44	97	�	�	PROPN
ap-616	44	98	�	�	PROPN
ap-616	44	99	�	�	PROPN
ap-616	44	100	�	�	PROPN
ap-616	44	101	exp	exp	NOUN
ap-616	44	102	skew	skew	NOUN
ap-616	44	103	1	1	NUM
ap-616	44	104	2	2	NUM
ap-616	44	105	.	.	PUNCT
ap-616	45	1	both	both	DET
ap-616	45	2	algorithms	algorithm	NOUN
ap-616	45	3	are	be	AUX
ap-616	45	4	first	first	ADJ
ap-616	45	5	-	-	PUNCT
ap-616	45	6	order	order	NOUN
ap-616	45	7	,	,	PUNCT
ap-616	45	8	symplectic	symplectic	NOUN
ap-616	45	9	,	,	PUNCT
ap-616	45	10	and	and	CCONJ
ap-616	45	11	momentum	momentum	NOUN
ap-616	45	12	conserving	conserving	NOUN
ap-616	45	13	.	.	PUNCT
ap-616	46	1	as	as	ADP
ap-616	46	2	before	before	ADV
ap-616	46	3	,	,	PUNCT
ap-616	46	4	the	the	DET
ap-616	46	5	composition	composition	NOUN
ap-616	46	6	of	of	ADP
ap-616	46	7	these	these	DET
ap-616	46	8	two	two	NUM
ap-616	46	9	algorithms	algorithm	NOUN
ap-616	46	10	in	in	ADP
ap-616	46	11	one	one	NUM
ap-616	46	12	time	time	NOUN
ap-616	46	13	step	step	NOUN
ap-616	46	14	provides	provide	VERB
ap-616	46	15	us	we	PRON
ap-616	46	16	with	with	ADP
ap-616	46	17	a	a	DET
ap-616	46	18	second	second	ADJ
ap-616	46	19	order	order	NOUN
ap-616	46	20	accurate	accurate	ADJ
ap-616	46	21	algorithm	algorithm	NOUN
ap-616	46	22	,	,	PUNCT
ap-616	46	23	which	which	PRON
ap-616	46	24	is	be	AUX
ap-616	46	25	an	an	DET
ap-616	46	26	analogy	analogy	NOUN
ap-616	46	27	of	of	ADP
ap-616	46	28	the	the	DET
ap-616	46	29	verlet	verlet	NOUN
ap-616	46	30	(	(	PUNCT
ap-616	46	31	explicit	explicit	ADJ
ap-616	46	32	newmark	newmark	NOUN
ap-616	46	33	with	with	ADP
ap-616	46	34	�	�	PROPN
ap-616	46	35	�	�	PROPN
ap-616	46	36	1	1	NUM
ap-616	46	37	2	2	NUM
ap-616	46	38	)	)	PUNCT
ap-616	46	39	algorithm	algorithm	NOUN
ap-616	46	40	for	for	ADP
ap-616	46	41	the	the	DET
ap-616	46	42	vector	vector	NOUN
ap-616	46	43	space	space	NOUN
ap-616	46	44	dynamics	dynamic	NOUN
ap-616	46	45	�	�	PROPN
ap-616	46	46	�	�	PROPN
ap-616	46	47	�	�	PROPN
ap-616	46	48	�	�	PROPN
ap-616	46	49	�	�	PROPN
ap-616	46	50	�	�	PROPN
ap-616	46	51	t	t	PROPN
ap-616	46	52	t	t	PROPN
ap-616	46	53	t	t	PROPN
ap-616	46	54	�	�	PROPN
ap-616	46	55	2	2	NUM
ap-616	46	56	2	2	NUM
ap-616	46	57	*	*	PUNCT
ap-616	46	58	�	�	PROPN
ap-616	46	59	.	.	PUNCT
ap-616	47	1	52	52	NUM
ap-616	47	2	©	©	PROPN
ap-616	47	3	czech	czech	PROPN
ap-616	47	4	technical	technical	PROPN
ap-616	47	5	university	university	PROPN
ap-616	47	6	publishing	publishing	NOUN
ap-616	47	7	house	house	NOUN
ap-616	47	8	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-616	47	9	acta	acta	PROPN
ap-616	47	10	polytechnica	polytechnica	PROPN
ap-616	47	11	vol	vol	NOUN
ap-616	47	12	.	.	PROPN
ap-616	48	1	44	44	NUM
ap-616	48	2	no	no	NOUN
ap-616	48	3	.	.	PUNCT
ap-616	49	1	5–6/2004	5–6/2004	NUM
ap-616	49	2	fig	fig	NOUN
ap-616	49	3	.	.	PUNCT
ap-616	50	1	1	1	NUM
ap-616	50	2	:	:	PUNCT
ap-616	50	3	fast	fast	ADJ
ap-616	50	4	lagrangian	lagrangian	ADJ
ap-616	50	5	top	top	NOUN
ap-616	50	6	;	;	PUNCT
ap-616	50	7	on	on	ADP
ap-616	50	8	the	the	DET
ap-616	50	9	left	left	ADJ
ap-616	50	10	hand	hand	NOUN
ap-616	50	11	side	side	NOUN
ap-616	50	12	convergence	convergence	NOUN
ap-616	50	13	in	in	ADP
ap-616	50	14	the	the	DET
ap-616	50	15	norm	norm	NOUN
ap-616	50	16	of	of	ADP
ap-616	50	17	the	the	DET
ap-616	50	18	error	error	NOUN
ap-616	50	19	in	in	ADP
ap-616	50	20	body	body	NOUN
ap-616	50	21	-	-	PUNCT
ap-616	50	22	frame	frame	NOUN
ap-616	50	23	angular	angular	ADJ
ap-616	50	24	momentum	momentum	NOUN
ap-616	50	25	;	;	PUNCT
ap-616	50	26	on	on	ADP
ap-616	50	27	the	the	DET
ap-616	50	28	right	right	ADJ
ap-616	50	29	hand	hand	NOUN
ap-616	50	30	side	side	NOUN
ap-616	50	31	convergence	convergence	NOUN
ap-616	50	32	in	in	ADP
ap-616	50	33	the	the	DET
ap-616	50	34	norm	norm	NOUN
ap-616	50	35	of	of	ADP
ap-616	50	36	the	the	DET
ap-616	50	37	error	error	NOUN
ap-616	50	38	in	in	ADP
ap-616	50	39	the	the	DET
ap-616	50	40	attitude	attitude	NOUN
ap-616	50	41	matrix	matrix	NOUN
ap-616	50	42	:	:	PUNCT
ap-616	50	43	akw	akw	PROPN
ap-616	50	44	:	:	PUNCT
ap-616	50	45	implicit	implicit	ADJ
ap-616	50	46	midpoint	midpoint	NOUN
ap-616	50	47	rule	rule	NOUN
ap-616	50	48	of	of	ADP
ap-616	50	49	austin	austin	PROPN
ap-616	50	50	,	,	PUNCT
ap-616	50	51	krishnaprasad	krishnaprasad	ADJ
ap-616	50	52	,	,	PUNCT
ap-616	50	53	[	[	X
ap-616	50	54	1	1	NUM
ap-616	50	55	]	]	PUNCT
ap-616	50	56	:	:	PUNCT
ap-616	50	57	sw	sw	PROPN
ap-616	50	58	:	:	PUNCT
ap-616	50	59	simo	simo	PROPN
ap-616	50	60	and	and	CCONJ
ap-616	50	61	wong	wong	PROPN
ap-616	51	1	[	[	X
ap-616	51	2	5	5	NUM
ap-616	51	3	]	]	PUNCT
ap-616	51	4	;	;	PUNCT
ap-616	51	5	nmb	nmb	NOUN
ap-616	51	6	:	:	PUNCT
ap-616	51	7	krysl	krysl	PROPN
ap-616	51	8	,	,	PUNCT
ap-616	51	9	endres	endres	PROPN
ap-616	51	10	newmark	newmark	PROPN
ap-616	51	11	algorithm	algorithm	PROPN
ap-616	52	1	[	[	X
ap-616	52	2	4	4	NUM
ap-616	52	3	]	]	PUNCT
ap-616	52	4	;	;	PUNCT
ap-616	52	5	liemid[1	liemid[1	X
ap-616	52	6	]	]	X
ap-616	52	7	:	:	PUNCT
ap-616	52	8	implicit	implicit	ADJ
ap-616	52	9	midpoint	midpoint	NOUN
ap-616	52	10	lie	lie	NOUN
ap-616	52	11	:	:	PUNCT
ap-616	52	12	liemid[e1	liemid[e1	PROPN
ap-616	52	13	]	]	PUNCT
ap-616	52	14	:	:	PUNCT
ap-616	52	15	adjoint	adjoint	NOUN
ap-616	52	16	of	of	ADP
ap-616	52	17	the	the	DET
ap-616	52	18	symplectic	symplectic	PROPN
ap-616	52	19	euler	euler	NOUN
ap-616	52	20	(	(	PUNCT
ap-616	52	21	explicit	explicit	ADJ
ap-616	52	22	midpoint	midpoint	NOUN
ap-616	52	23	lie	lie	NOUN
ap-616	52	24	variant	variant	NOUN
ap-616	52	25	1	1	NUM
ap-616	52	26	)	)	PUNCT
ap-616	52	27	;	;	PUNCT
ap-616	53	1	liemid[e2	liemid[e2	PROPN
ap-616	53	2	]	]	PUNCT
ap-616	53	3	:	:	PUNCT
ap-616	53	4	symplectic	symplectic	PROPN
ap-616	53	5	euler	euler	PROPN
ap-616	53	6	(	(	PUNCT
ap-616	53	7	explicit	explicit	ADJ
ap-616	53	8	midpoint	midpoint	NOUN
ap-616	53	9	lie	lie	NOUN
ap-616	53	10	variant	variant	NOUN
ap-616	53	11	2	2	NUM
ap-616	53	12	)	)	PUNCT
ap-616	53	13	;	;	PUNCT
ap-616	53	14	liemid[ea	liemid[ea	NOUN
ap-616	53	15	]	]	X
ap-616	53	16	:	:	PUNCT
ap-616	53	17	alternating	alternate	VERB
ap-616	53	18	explicit	explicit	ADJ
ap-616	53	19	midpoint	midpoint	NOUN
ap-616	53	20	lie	lie	NOUN
ap-616	53	21	method	method	NOUN
ap-616	53	22	.	.	PUNCT
ap-616	54	1	the	the	DET
ap-616	54	2	above	above	ADJ
ap-616	54	3	algorithms	algorithm	NOUN
ap-616	54	4	have	have	AUX
ap-616	54	5	been	be	AUX
ap-616	54	6	called	call	VERB
ap-616	54	7	the	the	DET
ap-616	54	8	explicit	explicit	ADJ
ap-616	54	9	midpoint	midpoint	NOUN
ap-616	54	10	lie	lie	NOUN
ap-616	54	11	variant	variant	NOUN
ap-616	54	12	2	2	NUM
ap-616	54	13	and	and	CCONJ
ap-616	54	14	1	1	NUM
ap-616	54	15	respectively	respectively	ADV
ap-616	54	16	,	,	PUNCT
ap-616	54	17	and	and	CCONJ
ap-616	54	18	the	the	DET
ap-616	54	19	alternating	alternate	VERB
ap-616	54	20	midpoint	midpoint	NOUN
ap-616	54	21	lie	lie	NOUN
ap-616	54	22	algorithm	algorithm	NOUN
ap-616	54	23	in	in	ADP
ap-616	54	24	reference	reference	NOUN
ap-616	54	25	[	[	X
ap-616	54	26	3	3	NUM
ap-616	54	27	]	]	PUNCT
ap-616	54	28	.	.	PUNCT
ap-616	55	1	it	it	PRON
ap-616	55	2	bears	bear	VERB
ap-616	55	3	emphasis	emphasis	NOUN
ap-616	55	4	that	that	SCONJ
ap-616	55	5	these	these	DET
ap-616	55	6	algorithms	algorithm	NOUN
ap-616	55	7	are	be	AUX
ap-616	55	8	not	not	PART
ap-616	55	9	simply	simply	ADV
ap-616	55	10	the	the	DET
ap-616	55	11	symplectic	symplectic	PROPN
ap-616	55	12	euler	euler	NOUN
ap-616	55	13	and	and	CCONJ
ap-616	55	14	its	its	PRON
ap-616	55	15	adjoint	adjoint	NOUN
ap-616	55	16	.	.	PUNCT
ap-616	56	1	they	they	PRON
ap-616	56	2	all	all	PRON
ap-616	56	3	reduce	reduce	VERB
ap-616	56	4	to	to	ADP
ap-616	56	5	the	the	DET
ap-616	56	6	full	full	ADJ
ap-616	56	7	midpoint	midpoint	NOUN
ap-616	56	8	lie	lie	NOUN
ap-616	56	9	algorithm	algorithm	NOUN
ap-616	56	10	for	for	ADP
ap-616	56	11	torque	torque	NOUN
ap-616	56	12	-	-	PUNCT
ap-616	56	13	free	free	ADJ
ap-616	56	14	motion	motion	NOUN
ap-616	56	15	,	,	PUNCT
ap-616	56	16	and	and	CCONJ
ap-616	56	17	it	it	PRON
ap-616	56	18	is	be	AUX
ap-616	56	19	only	only	ADV
ap-616	56	20	the	the	DET
ap-616	56	21	approximation	approximation	NOUN
ap-616	56	22	of	of	ADP
ap-616	56	23	the	the	DET
ap-616	56	24	midpoint	midpoint	NOUN
ap-616	56	25	momentum	momentum	NOUN
ap-616	56	26	evaluation	evaluation	NOUN
ap-616	56	27	that	that	PRON
ap-616	56	28	distinguishes	distinguish	VERB
ap-616	56	29	them	they	PRON
ap-616	56	30	from	from	ADP
ap-616	56	31	the	the	DET
ap-616	56	32	implicit	implicit	ADJ
ap-616	56	33	midpoint	midpoint	NOUN
ap-616	56	34	lie	lie	NOUN
ap-616	56	35	rule	rule	NOUN
ap-616	56	36	.	.	PUNCT
ap-616	57	1	4	4	NUM
ap-616	57	2	example	example	NOUN
ap-616	57	3	the	the	DET
ap-616	57	4	accuracy	accuracy	NOUN
ap-616	57	5	of	of	ADP
ap-616	57	6	the	the	DET
ap-616	57	7	explicit	explicit	ADJ
ap-616	57	8	midpoint	midpoint	NOUN
ap-616	57	9	lie	lie	NOUN
ap-616	57	10	algorithms	algorithms	NOUN
ap-616	57	11	is	be	AUX
ap-616	57	12	rather	rather	ADV
ap-616	57	13	remarkable	remarkable	ADJ
ap-616	57	14	,	,	PUNCT
ap-616	57	15	as	as	SCONJ
ap-616	57	16	may	may	AUX
ap-616	57	17	be	be	AUX
ap-616	57	18	seen	see	VERB
ap-616	57	19	in	in	ADP
ap-616	57	20	fig	fig	NOUN
ap-616	57	21	.	.	PUNCT
ap-616	58	1	1	1	X
ap-616	58	2	.	.	X
ap-616	58	3	we	we	PRON
ap-616	58	4	show	show	VERB
ap-616	58	5	convergence	convergence	NOUN
ap-616	58	6	graphs	graph	NOUN
ap-616	58	7	for	for	ADP
ap-616	58	8	the	the	DET
ap-616	58	9	fast	fast	ADJ
ap-616	58	10	spinning	spinning	NOUN
ap-616	58	11	heavy	heavy	ADJ
ap-616	58	12	top	top	NOUN
ap-616	58	13	(	(	PUNCT
ap-616	58	14	the	the	DET
ap-616	58	15	kinetic	kinetic	ADJ
ap-616	58	16	energy	energy	NOUN
ap-616	58	17	is	be	AUX
ap-616	58	18	dominant	dominant	ADJ
ap-616	58	19	,	,	PUNCT
ap-616	58	20	and	and	CCONJ
ap-616	58	21	a	a	DET
ap-616	58	22	numerical	numerical	ADJ
ap-616	58	23	method	method	NOUN
ap-616	58	24	has	have	VERB
ap-616	58	25	to	to	PART
ap-616	58	26	deal	deal	VERB
ap-616	58	27	effectively	effectively	ADV
ap-616	58	28	with	with	ADP
ap-616	58	29	precession	precession	NOUN
ap-616	58	30	and	and	CCONJ
ap-616	58	31	nutation	nutation	NOUN
ap-616	58	32	which	which	PRON
ap-616	58	33	are	be	AUX
ap-616	58	34	motions	motion	NOUN
ap-616	58	35	of	of	ADP
ap-616	58	36	distinct	distinct	ADJ
ap-616	58	37	frequencies	frequency	NOUN
ap-616	58	38	)	)	PUNCT
ap-616	58	39	.	.	PUNCT
ap-616	59	1	even	even	ADV
ap-616	59	2	the	the	DET
ap-616	59	3	first	first	ADJ
ap-616	59	4	-	-	PUNCT
ap-616	59	5	order	order	NOUN
ap-616	59	6	methods	method	NOUN
ap-616	59	7	perform	perform	VERB
ap-616	59	8	very	very	ADV
ap-616	59	9	well	well	ADV
ap-616	59	10	for	for	ADP
ap-616	59	11	larger	large	ADJ
ap-616	59	12	time	time	NOUN
ap-616	59	13	steps	step	NOUN
ap-616	59	14	,	,	PUNCT
ap-616	59	15	and	and	CCONJ
ap-616	59	16	the	the	DET
ap-616	59	17	present	present	ADJ
ap-616	59	18	alternating	alternate	VERB
ap-616	59	19	midpoint	midpoint	NOUN
ap-616	59	20	lie	lie	NOUN
ap-616	59	21	algorithm	algorithm	NOUN
ap-616	59	22	is	be	AUX
ap-616	59	23	the	the	DET
ap-616	59	24	strongest	strong	ADJ
ap-616	59	25	performer	performer	NOUN
ap-616	59	26	out	out	ADP
ap-616	59	27	of	of	ADP
ap-616	59	28	a	a	DET
ap-616	59	29	selection	selection	NOUN
ap-616	59	30	of	of	ADP
ap-616	59	31	the	the	DET
ap-616	59	32	best	good	ADJ
ap-616	59	33	currently	currently	ADV
ap-616	59	34	available	available	ADJ
ap-616	59	35	implicit	implicit	ADJ
ap-616	59	36	and	and	CCONJ
ap-616	59	37	explicit	explicit	ADJ
ap-616	59	38	algorithms	algorithm	NOUN
ap-616	59	39	,	,	PUNCT
ap-616	59	40	including	include	VERB
ap-616	59	41	the	the	DET
ap-616	59	42	implicit	implicit	ADJ
ap-616	59	43	midpoint	midpoint	NOUN
ap-616	59	44	lie	lie	NOUN
ap-616	59	45	method	method	NOUN
ap-616	59	46	.	.	PUNCT
ap-616	60	1	5	5	NUM
ap-616	60	2	conclusions	conclusion	NOUN
ap-616	60	3	we	we	PRON
ap-616	60	4	have	have	AUX
ap-616	60	5	presented	present	VERB
ap-616	60	6	an	an	DET
ap-616	60	7	approach	approach	NOUN
ap-616	60	8	to	to	ADP
ap-616	60	9	the	the	DET
ap-616	60	10	construction	construction	NOUN
ap-616	60	11	of	of	ADP
ap-616	60	12	rigid	rigid	ADJ
ap-616	60	13	body	body	NOUN
ap-616	60	14	integrators	integrator	NOUN
ap-616	60	15	,	,	PUNCT
ap-616	60	16	in	in	ADP
ap-616	60	17	particular	particular	ADJ
ap-616	60	18	for	for	ADP
ap-616	60	19	general	general	ADJ
ap-616	60	20	3	3	NUM
ap-616	60	21	-	-	PUNCT
ap-616	60	22	d	d	NOUN
ap-616	60	23	rotations	rotation	NOUN
ap-616	60	24	,	,	PUNCT
ap-616	60	25	that	that	PRON
ap-616	60	26	are	be	AUX
ap-616	60	27	explicit	explicit	ADJ
ap-616	60	28	in	in	ADP
ap-616	60	29	the	the	DET
ap-616	60	30	evaluation	evaluation	NOUN
ap-616	60	31	of	of	ADP
ap-616	60	32	the	the	DET
ap-616	60	33	forcing	forcing	ADJ
ap-616	60	34	,	,	PUNCT
ap-616	60	35	momentum	momentum	NOUN
ap-616	60	36	-	-	PUNCT
ap-616	60	37	conserving	conserve	VERB
ap-616	60	38	,	,	PUNCT
ap-616	60	39	and	and	CCONJ
ap-616	60	40	symplectic	symplectic	ADJ
ap-616	60	41	.	.	PUNCT
ap-616	61	1	the	the	DET
ap-616	61	2	starting	starting	NOUN
ap-616	61	3	point	point	NOUN
ap-616	61	4	is	be	AUX
ap-616	61	5	the	the	DET
ap-616	61	6	midpoint	midpoint	NOUN
ap-616	61	7	(	(	PUNCT
ap-616	61	8	implicit	implicit	ADJ
ap-616	61	9	)	)	PUNCT
ap-616	61	10	rule	rule	NOUN
ap-616	61	11	,	,	PUNCT
ap-616	61	12	which	which	PRON
ap-616	61	13	is	be	AUX
ap-616	61	14	then	then	ADV
ap-616	61	15	treated	treat	VERB
ap-616	61	16	with	with	ADP
ap-616	61	17	numerical	numerical	ADJ
ap-616	61	18	integration	integration	NOUN
ap-616	61	19	of	of	ADP
ap-616	61	20	the	the	DET
ap-616	61	21	forcing	forcing	NOUN
ap-616	61	22	with	with	ADP
ap-616	61	23	concentrated	concentrated	ADJ
ap-616	61	24	impulses	impulse	NOUN
ap-616	61	25	.	.	PUNCT
ap-616	62	1	the	the	DET
ap-616	62	2	resulting	result	VERB
ap-616	62	3	algorithms	algorithm	NOUN
ap-616	62	4	conserve	conserve	VERB
ap-616	62	5	momentum	momentum	NOUN
ap-616	62	6	,	,	PUNCT
ap-616	62	7	are	be	AUX
ap-616	62	8	symplectic	symplectic	ADJ
ap-616	62	9	,	,	PUNCT
ap-616	62	10	first	first	ADJ
ap-616	62	11	-	-	PUNCT
ap-616	62	12	order	order	NOUN
ap-616	62	13	,	,	PUNCT
ap-616	62	14	and	and	CCONJ
ap-616	62	15	they	they	PRON
ap-616	62	16	are	be	AUX
ap-616	62	17	adjoint	adjoint	VERB
ap-616	62	18	.	.	PUNCT
ap-616	63	1	consequently	consequently	ADV
ap-616	63	2	,	,	PUNCT
ap-616	63	3	their	their	PRON
ap-616	63	4	composition	composition	NOUN
ap-616	63	5	leads	lead	VERB
ap-616	63	6	to	to	ADP
ap-616	63	7	a	a	DET
ap-616	63	8	second	second	ADJ
ap-616	63	9	order	order	NOUN
ap-616	63	10	algorithm	algorithm	NOUN
ap-616	63	11	,	,	PUNCT
ap-616	63	12	which	which	PRON
ap-616	63	13	may	may	AUX
ap-616	63	14	be	be	AUX
ap-616	63	15	readily	readily	ADV
ap-616	63	16	interpreted	interpret	VERB
ap-616	63	17	as	as	ADP
ap-616	63	18	a	a	DET
ap-616	63	19	verlet	verlet	NOUN
ap-616	63	20	(	(	PUNCT
ap-616	63	21	explicit	explicit	ADJ
ap-616	63	22	newmark	newmark	NOUN
ap-616	63	23	)	)	PUNCT
ap-616	63	24	integrator	integrator	NOUN
ap-616	63	25	,	,	PUNCT
ap-616	63	26	both	both	CCONJ
ap-616	63	27	in	in	ADP
ap-616	63	28	the	the	DET
ap-616	63	29	vector	vector	NOUN
ap-616	63	30	space	space	NOUN
ap-616	63	31	setting	setting	NOUN
ap-616	63	32	,	,	PUNCT
ap-616	63	33	and	and	CCONJ
ap-616	63	34	in	in	ADP
ap-616	63	35	the	the	DET
ap-616	63	36	setting	setting	NOUN
ap-616	63	37	of	of	ADP
ap-616	63	38	the	the	DET
ap-616	63	39	special	special	ADJ
ap-616	63	40	orthogonal	orthogonal	ADJ
ap-616	63	41	group	group	NOUN
ap-616	63	42	of	of	ADP
ap-616	63	43	rotations	rotation	NOUN
ap-616	63	44	.	.	PUNCT
ap-616	64	1	(	(	PUNCT
ap-616	64	2	we	we	PRON
ap-616	64	3	would	would	AUX
ap-616	64	4	like	like	VERB
ap-616	64	5	to	to	PART
ap-616	64	6	suggest	suggest	VERB
ap-616	64	7	as	as	ADP
ap-616	64	8	an	an	DET
ap-616	64	9	appropriate	appropriate	ADJ
ap-616	64	10	name	name	NOUN
ap-616	64	11	explicit	explicit	ADJ
ap-616	64	12	midpoint	midpoint	NOUN
ap-616	64	13	lie	lie	NOUN
ap-616	64	14	algorithm	algorithm	NOUN
ap-616	64	15	for	for	ADP
ap-616	64	16	the	the	DET
ap-616	64	17	latter	latter	ADJ
ap-616	64	18	.	.	PUNCT
ap-616	64	19	)	)	PUNCT
ap-616	65	1	for	for	ADP
ap-616	65	2	rotational	rotational	ADJ
ap-616	65	3	dynamics	dynamic	NOUN
ap-616	65	4	,	,	PUNCT
ap-616	65	5	this	this	DET
ap-616	65	6	integrator	integrator	NOUN
ap-616	65	7	is	be	AUX
ap-616	65	8	a	a	DET
ap-616	65	9	new	new	ADJ
ap-616	65	10	addition	addition	NOUN
ap-616	65	11	to	to	ADP
ap-616	65	12	the	the	DET
ap-616	65	13	lineup	lineup	NOUN
ap-616	65	14	of	of	ADP
ap-616	65	15	current	current	ADJ
ap-616	65	16	high	high	ADJ
ap-616	65	17	performance	performance	NOUN
ap-616	65	18	algorithms	algorithm	NOUN
ap-616	65	19	,	,	PUNCT
ap-616	65	20	and	and	CCONJ
ap-616	65	21	in	in	ADP
ap-616	65	22	fact	fact	NOUN
ap-616	65	23	numerical	numerical	ADJ
ap-616	65	24	evidence	evidence	NOUN
ap-616	65	25	suggests	suggest	VERB
ap-616	65	26	that	that	SCONJ
ap-616	65	27	it	it	PRON
ap-616	65	28	is	be	AUX
ap-616	65	29	the	the	DET
ap-616	65	30	best	good	ADJ
ap-616	65	31	second	second	ADJ
ap-616	65	32	-	-	PUNCT
ap-616	65	33	order	order	NOUN
ap-616	65	34	integrator	integrator	NOUN
ap-616	65	35	to	to	ADP
ap-616	65	36	date	date	NOUN
ap-616	65	37	.	.	PUNCT
ap-616	66	1	applications	application	NOUN
ap-616	66	2	abound	abound	VERB
ap-616	66	3	:	:	PUNCT
ap-616	66	4	molecular	molecular	ADJ
ap-616	66	5	dynamics	dynamic	NOUN
ap-616	66	6	,	,	PUNCT
ap-616	66	7	micro	micro	ADJ
ap-616	66	8	magnetics	magnetic	NOUN
ap-616	66	9	,	,	PUNCT
ap-616	66	10	rigid	rigid	ADJ
ap-616	66	11	body	body	NOUN
ap-616	66	12	dynamics	dynamic	NOUN
ap-616	66	13	,	,	PUNCT
ap-616	66	14	finite	finite	ADJ
ap-616	66	15	element	element	NOUN
ap-616	66	16	dynamics	dynamic	NOUN
ap-616	66	17	of	of	ADP
ap-616	66	18	deformable	deformable	ADJ
ap-616	66	19	solids	solid	NOUN
ap-616	66	20	.	.	PUNCT
ap-616	67	1	acknowledgment	acknowledgment	NOUN
ap-616	67	2	support	support	NOUN
ap-616	67	3	for	for	ADP
ap-616	67	4	this	this	DET
ap-616	67	5	research	research	NOUN
ap-616	67	6	by	by	ADP
ap-616	67	7	a	a	DET
ap-616	67	8	hughes	hughes	PROPN
ap-616	67	9	-	-	PUNCT
ap-616	67	10	christensen	christensen	PROPN
ap-616	67	11	award	award	PROPN
ap-616	67	12	is	be	AUX
ap-616	67	13	gratefully	gratefully	ADV
ap-616	67	14	acknowledged	acknowledge	VERB
ap-616	67	15	.	.	PUNCT
ap-616	68	1	references	reference	NOUN
ap-616	68	2	[	[	X
ap-616	68	3	1	1	X
ap-616	68	4	]	]	PUNCT
ap-616	68	5	austin	austin	PROPN
ap-616	68	6	m.	m.	PROPN
ap-616	68	7	,	,	PUNCT
ap-616	68	8	krishnaprasad	krishnaprasad	PROPN
ap-616	68	9	p.	p.	PROPN
ap-616	68	10	s.	s.	PROPN
ap-616	68	11	,	,	PUNCT
ap-616	68	12	wang	wang	PROPN
ap-616	68	13	l.	l.	PROPN
ap-616	68	14	s.	s.	PROPN
ap-616	68	15	:	:	PUNCT
ap-616	68	16	“	"	PUNCT
ap-616	68	17	almost	almost	ADV
ap-616	68	18	lie	lie	NOUN
ap-616	68	19	-	-	PUNCT
ap-616	68	20	poisson	poisson	NOUN
ap-616	68	21	integrators	integrator	NOUN
ap-616	68	22	for	for	ADP
ap-616	68	23	the	the	DET
ap-616	68	24	rigid	rigid	ADJ
ap-616	68	25	body	body	NOUN
ap-616	68	26	.	.	PUNCT
ap-616	68	27	”	"	PUNCT
ap-616	69	1	journal	journal	NOUN
ap-616	69	2	of	of	ADP
ap-616	69	3	computational	computational	ADJ
ap-616	69	4	physics	physics	NOUN
ap-616	69	5	,	,	PUNCT
ap-616	69	6	vol	vol	NOUN
ap-616	69	7	.	.	PROPN
ap-616	70	1	107	107	NUM
ap-616	70	2	(	(	PUNCT
ap-616	70	3	1993	1993	NUM
ap-616	70	4	)	)	PUNCT
ap-616	70	5	,	,	PUNCT
ap-616	71	1	p.	p.	NOUN
ap-616	71	2	105–117	105–117	NUM
ap-616	71	3	.	.	PUNCT
ap-616	72	1	[	[	X
ap-616	72	2	2	2	NUM
ap-616	72	3	]	]	PUNCT
ap-616	72	4	hairer	hairer	PROPN
ap-616	72	5	e.	e.	PROPN
ap-616	72	6	,	,	PUNCT
ap-616	72	7	lubich	lubich	PROPN
ap-616	72	8	c.	c.	PROPN
ap-616	72	9	,	,	PUNCT
ap-616	72	10	wanner	wanner	NOUN
ap-616	72	11	g.	g.	PROPN
ap-616	72	12	:	:	PUNCT
ap-616	72	13	“	"	PUNCT
ap-616	72	14	geometric	geometric	ADJ
ap-616	72	15	numerical	numerical	ADJ
ap-616	72	16	integration	integration	NOUN
ap-616	72	17	.	.	PUNCT
ap-616	73	1	structure	structure	NOUN
ap-616	73	2	-	-	PUNCT
ap-616	73	3	preserving	preserve	VERB
ap-616	73	4	algorithms	algorithm	NOUN
ap-616	73	5	for	for	ADP
ap-616	73	6	ordinary	ordinary	ADJ
ap-616	73	7	differential	differential	ADJ
ap-616	73	8	equations	equation	NOUN
ap-616	73	9	.	.	PUNCT
ap-616	73	10	”	"	PUNCT
ap-616	74	1	springer	springer	NOUN
ap-616	74	2	series	series	NOUN
ap-616	74	3	in	in	ADP
ap-616	74	4	comput	comput	NOUN
ap-616	74	5	.	.	PUNCT
ap-616	75	1	mathematics	mathematic	NOUN
ap-616	75	2	,	,	PUNCT
ap-616	75	3	springer	springer	NOUN
ap-616	75	4	-	-	PUNCT
ap-616	75	5	verlag	verlag	PROPN
ap-616	75	6	,	,	PUNCT
ap-616	75	7	vol	vol	NOUN
ap-616	75	8	.	.	PROPN
ap-616	75	9	31	31	NUM
ap-616	75	10	(	(	PUNCT
ap-616	75	11	2002	2002	NUM
ap-616	75	12	)	)	PUNCT
ap-616	75	13	.	.	PUNCT
ap-616	76	1	[	[	X
ap-616	76	2	3	3	X
ap-616	76	3	]	]	X
ap-616	76	4	krysl	krysl	NOUN
ap-616	76	5	p.	p.	NOUN
ap-616	76	6	:	:	PUNCT
ap-616	76	7	“	"	PUNCT
ap-616	76	8	explicit	explicit	ADJ
ap-616	76	9	momentum	momentum	NOUN
ap-616	76	10	-	-	PUNCT
ap-616	76	11	conserving	conserve	VERB
ap-616	76	12	integrator	integrator	NOUN
ap-616	76	13	for	for	ADP
ap-616	76	14	dynamics	dynamic	NOUN
ap-616	76	15	of	of	ADP
ap-616	76	16	rigid	rigid	ADJ
ap-616	76	17	bodies	body	NOUN
ap-616	76	18	approximating	approximate	VERB
ap-616	76	19	the	the	DET
ap-616	76	20	midpoint	midpoint	NOUN
ap-616	76	21	lie	lie	NOUN
ap-616	76	22	algorithm	algorithm	NOUN
ap-616	76	23	.	.	PUNCT
ap-616	76	24	”	"	PUNCT
ap-616	77	1	international	international	ADJ
ap-616	77	2	journal	journal	NOUN
ap-616	77	3	for	for	ADP
ap-616	77	4	numerical	numerical	ADJ
ap-616	77	5	methods	method	NOUN
ap-616	77	6	in	in	ADP
ap-616	77	7	engineering	engineering	NOUN
ap-616	77	8	,	,	PUNCT
ap-616	77	9	(	(	PUNCT
ap-616	77	10	2004	2004	NUM
ap-616	77	11	)	)	PUNCT
ap-616	77	12	,	,	PUNCT
ap-616	77	13	submitted	submit	VERB
ap-616	77	14	.	.	PUNCT
ap-616	78	1	[	[	X
ap-616	78	2	4	4	NUM
ap-616	78	3	]	]	X
ap-616	78	4	krysl	krysl	PROPN
ap-616	78	5	p.	p.	PROPN
ap-616	78	6	,	,	PUNCT
ap-616	78	7	endres	endres	PROPN
ap-616	78	8	l.	l.	PROPN
ap-616	78	9	:	:	PUNCT
ap-616	78	10	“	"	PUNCT
ap-616	78	11	explicit	explicit	ADJ
ap-616	78	12	newmark	newmark	NOUN
ap-616	78	13	/	/	SYM
ap-616	78	14	verlet	verlet	NOUN
ap-616	78	15	algorithm	algorithm	NOUN
ap-616	78	16	for	for	ADP
ap-616	78	17	time	time	NOUN
ap-616	78	18	integration	integration	NOUN
ap-616	78	19	of	of	ADP
ap-616	78	20	the	the	DET
ap-616	78	21	rotational	rotational	ADJ
ap-616	78	22	dynamics	dynamic	NOUN
ap-616	78	23	of	of	ADP
ap-616	78	24	rigid	rigid	ADJ
ap-616	78	25	bodies	body	NOUN
ap-616	78	26	.	.	PUNCT
ap-616	78	27	”	"	PUNCT
ap-616	79	1	international	international	ADJ
ap-616	79	2	journal	journal	NOUN
ap-616	79	3	for	for	ADP
ap-616	79	4	numerical	numerical	ADJ
ap-616	79	5	methods	method	NOUN
ap-616	79	6	in	in	ADP
ap-616	79	7	engineering	engineering	NOUN
ap-616	79	8	,	,	PUNCT
ap-616	79	9	(	(	PUNCT
ap-616	79	10	2004	2004	NUM
ap-616	79	11	)	)	PUNCT
ap-616	79	12	,	,	PUNCT
ap-616	79	13	submitted	submit	VERB
ap-616	79	14	.	.	PUNCT
ap-616	80	1	[	[	X
ap-616	80	2	5	5	X
ap-616	80	3	]	]	PUNCT
ap-616	80	4	simo	simo	PROPN
ap-616	80	5	j.	j.	PROPN
ap-616	80	6	c.	c.	PROPN
ap-616	80	7	,	,	PUNCT
ap-616	80	8	wong	wong	PROPN
ap-616	80	9	k.	k.	PROPN
ap-616	80	10	k.	k.	PROPN
ap-616	80	11	:	:	PUNCT
ap-616	80	12	“	"	PUNCT
ap-616	80	13	unconditionally	unconditionally	ADV
ap-616	80	14	stable	stable	ADJ
ap-616	80	15	algorithms	algorithm	NOUN
ap-616	80	16	for	for	ADP
ap-616	80	17	rigid	rigid	ADJ
ap-616	80	18	body	body	NOUN
ap-616	80	19	dynamics	dynamic	NOUN
ap-616	80	20	that	that	PRON
ap-616	80	21	exactly	exactly	ADV
ap-616	80	22	preserve	preserve	VERB
ap-616	80	23	energy	energy	NOUN
ap-616	80	24	and	and	CCONJ
ap-616	80	25	momentum	momentum	NOUN
ap-616	80	26	.	.	PUNCT
ap-616	80	27	”	"	PUNCT
ap-616	81	1	international	international	ADJ
ap-616	81	2	journal	journal	NOUN
ap-616	81	3	for	for	ADP
ap-616	81	4	numerical	numerical	ADJ
ap-616	81	5	methods	method	NOUN
ap-616	81	6	in	in	ADP
ap-616	81	7	engineering	engineering	NOUN
ap-616	81	8	,	,	PUNCT
ap-616	81	9	vol	vol	NOUN
ap-616	81	10	.	.	PROPN
ap-616	81	11	31	31	NUM
ap-616	81	12	(	(	PUNCT
ap-616	81	13	1991	1991	NUM
ap-616	81	14	)	)	PUNCT
ap-616	81	15	,	,	PUNCT
ap-616	81	16	p.	p.	NOUN
ap-616	81	17	19–52	19–52	NUM
ap-616	81	18	.	.	PUNCT
ap-616	82	1	petr	petr	PROPN
ap-616	82	2	krysl	krysl	PROPN
ap-616	82	3	e	e	PROPN
ap-616	83	1	-	-	NOUN
ap-616	83	2	mail	mail	NOUN
ap-616	83	3	:	:	PUNCT
ap-616	83	4	pkrysl@ucsd.edu	pkrysl@ucsd.edu	PROPN
ap-616	83	5	university	university	PROPN
ap-616	83	6	of	of	ADP
ap-616	83	7	california	california	PROPN
ap-616	83	8	san	san	PROPN
ap-616	83	9	diego	diego	PROPN
ap-616	83	10	la	la	PROPN
ap-616	83	11	jolla	jolla	PROPN
ap-616	83	12	california	california	PROPN
ap-616	83	13	92093	92093	NUM
ap-616	83	14	-	-	SYM
ap-616	83	15	0085	0085	NUM
ap-616	83	16	,	,	PUNCT
ap-616	83	17	usa	usa	PROPN
ap-616	83	18	©	©	PROPN
ap-616	83	19	czech	czech	PROPN
ap-616	83	20	technical	technical	PROPN
ap-616	83	21	university	university	PROPN
ap-616	83	22	publishing	publishing	NOUN
ap-616	83	23	house	house	NOUN
ap-616	83	24	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-616	83	25	53	53	NUM
ap-616	83	26	acta	acta	PROPN
ap-616	83	27	polytechnica	polytechnica	PROPN
ap-616	83	28	vol	vol	NOUN
ap-616	83	29	.	.	PROPN
ap-616	84	1	44	44	NUM
ap-616	84	2	no	no	NOUN
ap-616	84	3	.	.	PUNCT
ap-616	85	1	5–6/2004	5–6/2004	NUM