id	sid	tid	token	lemma	pos
ajst-27746	1	1	academic	academic	ADJ
ajst-27746	1	2	journal	journal	NOUN
ajst-27746	1	3	of	of	ADP
ajst-27746	1	4	science	science	NOUN
ajst-27746	1	5	and	and	CCONJ
ajst-27746	1	6	technology	technology	NOUN
ajst-27746	1	7	issn	issn	NOUN
ajst-27746	1	8	:	:	PUNCT
ajst-27746	1	9	2771	2771	NUM
ajst-27746	1	10	-	-	SYM
ajst-27746	1	11	3032	3032	NUM
ajst-27746	1	12	|	|	NOUN
ajst-27746	1	13	vol	vol	NOUN
ajst-27746	1	14	.	.	PROPN
ajst-27746	1	15	13	13	NUM
ajst-27746	1	16	,	,	PUNCT
ajst-27746	1	17	no	no	INTJ
ajst-27746	1	18	.	.	NOUN
ajst-27746	1	19	2	2	NUM
ajst-27746	1	20	,	,	PUNCT
ajst-27746	1	21	2024	2024	NUM
ajst-27746	1	22	302	302	NUM
ajst-27746	1	23	research	research	NOUN
ajst-27746	1	24	on	on	ADP
ajst-27746	1	25	complex	complex	ADJ
ajst-27746	1	26	motion	motion	NOUN
ajst-27746	1	27	path	path	NOUN
ajst-27746	1	28	optimisation	optimisation	NOUN
ajst-27746	1	29	based	base	VERB
ajst-27746	1	30	on	on	ADP
ajst-27746	1	31	pde	pde	NOUN
ajst-27746	1	32	constraints	constraint	NOUN
ajst-27746	1	33	and	and	CCONJ
ajst-27746	1	34	deeponet	deeponet	NOUN
ajst-27746	1	35	neural	neural	ADJ
ajst-27746	1	36	network	network	NOUN
ajst-27746	1	37	models	model	NOUN
ajst-27746	1	38	yuhao	yuhao	PROPN
ajst-27746	1	39	fang1	fang1	PROPN
ajst-27746	1	40	,	,	PUNCT
ajst-27746	1	41	†	†	PROPN
ajst-27746	1	42	,	,	PUNCT
ajst-27746	1	43	*	*	PROPN
ajst-27746	1	44	,	,	PUNCT
ajst-27746	1	45	yixuan	yixuan	PROPN
ajst-27746	1	46	wang1	wang1	PROPN
ajst-27746	1	47	,	,	PUNCT
ajst-27746	1	48	†	†	PROPN
ajst-27746	1	49	,	,	PUNCT
ajst-27746	1	50	zhenyuan	zhenyuan	PROPN
ajst-27746	1	51	wei2	wei2	PROPN
ajst-27746	1	52	,	,	PUNCT
ajst-27746	1	53	†	†	PROPN
ajst-27746	1	54	1faculty	1faculty	NUM
ajst-27746	1	55	of	of	ADP
ajst-27746	1	56	engineering	engineering	NOUN
ajst-27746	1	57	,	,	PUNCT
ajst-27746	1	58	shenzhen	shenzhen	PROPN
ajst-27746	1	59	msu	msu	PROPN
ajst-27746	1	60	-	-	PUNCT
ajst-27746	1	61	bit	bit	NOUN
ajst-27746	1	62	university	university	NOUN
ajst-27746	1	63	,	,	PUNCT
ajst-27746	1	64	shenzhen	shenzhen	PROPN
ajst-27746	1	65	,	,	PUNCT
ajst-27746	1	66	china	china	PROPN
ajst-27746	1	67	2faculty	2faculty	NUM
ajst-27746	1	68	of	of	ADP
ajst-27746	1	69	computational	computational	ADJ
ajst-27746	1	70	mathematics	mathematic	NOUN
ajst-27746	1	71	and	and	CCONJ
ajst-27746	1	72	cybernetics	cybernetic	NOUN
ajst-27746	1	73	,	,	PUNCT
ajst-27746	1	74	shenzhen	shenzhen	PROPN
ajst-27746	1	75	msu	msu	PROPN
ajst-27746	1	76	-	-	PUNCT
ajst-27746	1	77	bit	bit	NOUN
ajst-27746	1	78	university	university	NOUN
ajst-27746	1	79	,	,	PUNCT
ajst-27746	1	80	shenzhen	shenzhen	PROPN
ajst-27746	1	81	,	,	PUNCT
ajst-27746	1	82	china	china	PROPN
ajst-27746	1	83	†	†	PROPN
ajst-27746	2	1	these	these	DET
ajst-27746	2	2	authors	author	NOUN
ajst-27746	2	3	also	also	ADV
ajst-27746	2	4	contributed	contribute	VERB
ajst-27746	2	5	equally	equally	ADV
ajst-27746	2	6	to	to	ADP
ajst-27746	2	7	this	this	DET
ajst-27746	2	8	work	work	NOUN
ajst-27746	2	9	*	*	PUNCT
ajst-27746	2	10	corresponding	correspond	VERB
ajst-27746	2	11	author	author	NOUN
ajst-27746	2	12	:	:	PUNCT
ajst-27746	2	13	fangyuhao@gmail.com	fangyuhao@gmail.com	X
ajst-27746	2	14	abstract	abstract	ADJ
ajst-27746	2	15	:	:	PUNCT
ajst-27746	2	16	aiming	aim	VERB
ajst-27746	2	17	at	at	ADP
ajst-27746	2	18	the	the	DET
ajst-27746	2	19	key	key	ADJ
ajst-27746	2	20	motion	motion	NOUN
ajst-27746	2	21	path	path	NOUN
ajst-27746	2	22	and	and	CCONJ
ajst-27746	2	23	speed	speed	NOUN
ajst-27746	2	24	control	control	NOUN
ajst-27746	2	25	problem	problem	NOUN
ajst-27746	2	26	in	in	ADP
ajst-27746	2	27	a	a	DET
ajst-27746	2	28	traditional	traditional	ADJ
ajst-27746	2	29	folk	folk	NOUN
ajst-27746	2	30	performance	performance	NOUN
ajst-27746	2	31	,	,	PUNCT
ajst-27746	2	32	this	this	DET
ajst-27746	2	33	paper	paper	NOUN
ajst-27746	2	34	designs	design	VERB
ajst-27746	2	35	a	a	DET
ajst-27746	2	36	comprehensive	comprehensive	ADJ
ajst-27746	2	37	optimization	optimization	NOUN
ajst-27746	2	38	scheme	scheme	NOUN
ajst-27746	2	39	.	.	PUNCT
ajst-27746	3	1	combined	combine	VERB
ajst-27746	3	2	with	with	ADP
ajst-27746	3	3	the	the	DET
ajst-27746	3	4	constraints	constraint	NOUN
ajst-27746	3	5	of	of	ADP
ajst-27746	3	6	partial	partial	ADJ
ajst-27746	3	7	differential	differential	NOUN
ajst-27746	3	8	equation	equation	NOUN
ajst-27746	3	9	(	(	PUNCT
ajst-27746	3	10	pde	pde	NOUN
ajst-27746	3	11	)	)	PUNCT
ajst-27746	3	12	,	,	PUNCT
ajst-27746	3	13	the	the	DET
ajst-27746	3	14	position	position	NOUN
ajst-27746	3	15	and	and	CCONJ
ajst-27746	3	16	velocity	velocity	NOUN
ajst-27746	3	17	changes	change	NOUN
ajst-27746	3	18	of	of	ADP
ajst-27746	3	19	each	each	DET
ajst-27746	3	20	time	time	NOUN
ajst-27746	3	21	node	node	NOUN
ajst-27746	3	22	are	be	AUX
ajst-27746	3	23	calculated	calculate	VERB
ajst-27746	3	24	to	to	PART
ajst-27746	3	25	ensure	ensure	VERB
ajst-27746	3	26	the	the	DET
ajst-27746	3	27	smoothness	smoothness	NOUN
ajst-27746	3	28	of	of	ADP
ajst-27746	3	29	the	the	DET
ajst-27746	3	30	motion	motion	NOUN
ajst-27746	3	31	and	and	CCONJ
ajst-27746	3	32	the	the	DET
ajst-27746	3	33	rationality	rationality	NOUN
ajst-27746	3	34	of	of	ADP
ajst-27746	3	35	the	the	DET
ajst-27746	3	36	speed	speed	NOUN
ajst-27746	3	37	.	.	PUNCT
ajst-27746	4	1	in	in	ADP
ajst-27746	4	2	order	order	NOUN
ajst-27746	4	3	to	to	PART
ajst-27746	4	4	further	far	ADV
ajst-27746	4	5	improve	improve	VERB
ajst-27746	4	6	the	the	DET
ajst-27746	4	7	optimization	optimization	NOUN
ajst-27746	4	8	effect	effect	NOUN
ajst-27746	4	9	,	,	PUNCT
ajst-27746	4	10	alternate	alternate	ADJ
ajst-27746	4	11	direction	direction	NOUN
ajst-27746	4	12	multiplier	multipli	ADJ
ajst-27746	4	13	method	method	NOUN
ajst-27746	4	14	(	(	PUNCT
ajst-27746	4	15	admm	admm	VERB
ajst-27746	4	16	)	)	PUNCT
ajst-27746	4	17	and	and	CCONJ
ajst-27746	4	18	deeponet	deeponet	NOUN
ajst-27746	4	19	neural	neural	ADJ
ajst-27746	4	20	network	network	NOUN
ajst-27746	4	21	model	model	NOUN
ajst-27746	4	22	are	be	AUX
ajst-27746	4	23	introduced	introduce	VERB
ajst-27746	4	24	to	to	PART
ajst-27746	4	25	realize	realize	VERB
ajst-27746	4	26	the	the	DET
ajst-27746	4	27	fine	fine	ADJ
ajst-27746	4	28	adjustment	adjustment	NOUN
ajst-27746	4	29	of	of	ADP
ajst-27746	4	30	path	path	NOUN
ajst-27746	4	31	planning	planning	NOUN
ajst-27746	4	32	and	and	CCONJ
ajst-27746	4	33	speed	speed	NOUN
ajst-27746	4	34	control	control	NOUN
ajst-27746	4	35	.	.	PUNCT
ajst-27746	5	1	the	the	DET
ajst-27746	5	2	results	result	NOUN
ajst-27746	5	3	show	show	VERB
ajst-27746	5	4	that	that	SCONJ
ajst-27746	5	5	this	this	DET
ajst-27746	5	6	scheme	scheme	NOUN
ajst-27746	5	7	not	not	PART
ajst-27746	5	8	only	only	ADV
ajst-27746	5	9	improves	improve	VERB
ajst-27746	5	10	the	the	DET
ajst-27746	5	11	performance	performance	NOUN
ajst-27746	5	12	's	's	PART
ajst-27746	5	13	appreciation	appreciation	NOUN
ajst-27746	5	14	,	,	PUNCT
ajst-27746	5	15	but	but	CCONJ
ajst-27746	5	16	also	also	ADV
ajst-27746	5	17	significantly	significantly	ADV
ajst-27746	5	18	enhances	enhance	VERB
ajst-27746	5	19	the	the	DET
ajst-27746	5	20	execution	execution	NOUN
ajst-27746	5	21	's	's	PART
ajst-27746	5	22	accuracy	accuracy	NOUN
ajst-27746	5	23	and	and	CCONJ
ajst-27746	5	24	operability	operability	NOUN
ajst-27746	5	25	.	.	PUNCT
ajst-27746	6	1	keywords	keyword	NOUN
ajst-27746	6	2	:	:	PUNCT
ajst-27746	6	3	path	path	NOUN
ajst-27746	6	4	planning	planning	NOUN
ajst-27746	6	5	,	,	PUNCT
ajst-27746	6	6	admm	admm	NOUN
ajst-27746	6	7	algorithm	algorithm	NOUN
ajst-27746	6	8	,	,	PUNCT
ajst-27746	6	9	deeponet	deeponet	NOUN
ajst-27746	6	10	,	,	PUNCT
ajst-27746	6	11	pde	pde	NOUN
ajst-27746	6	12	.	.	PUNCT
ajst-27746	7	1	1	1	X
ajst-27746	7	2	.	.	X
ajst-27746	7	3	introduction	introduction	NOUN
ajst-27746	7	4	the	the	DET
ajst-27746	7	5	purpose	purpose	NOUN
ajst-27746	7	6	of	of	ADP
ajst-27746	7	7	this	this	DET
ajst-27746	7	8	study	study	NOUN
ajst-27746	7	9	is	be	AUX
ajst-27746	7	10	to	to	PART
ajst-27746	7	11	solve	solve	VERB
ajst-27746	7	12	the	the	DET
ajst-27746	7	13	problem	problem	NOUN
ajst-27746	7	14	of	of	ADP
ajst-27746	7	15	path	path	NOUN
ajst-27746	7	16	planning	planning	NOUN
ajst-27746	7	17	and	and	CCONJ
ajst-27746	7	18	speed	speed	NOUN
ajst-27746	7	19	control	control	NOUN
ajst-27746	7	20	of	of	ADP
ajst-27746	7	21	performing	perform	VERB
ajst-27746	7	22	teams	team	NOUN
ajst-27746	7	23	in	in	ADP
ajst-27746	7	24	complex	complex	ADJ
ajst-27746	7	25	paths	path	NOUN
ajst-27746	7	26	through	through	ADP
ajst-27746	7	27	mathematical	mathematical	ADJ
ajst-27746	7	28	modeling	modeling	NOUN
ajst-27746	7	29	and	and	CCONJ
ajst-27746	7	30	numerical	numerical	ADJ
ajst-27746	7	31	optimization	optimization	NOUN
ajst-27746	8	1	[	[	X
ajst-27746	8	2	1	1	NUM
ajst-27746	8	3	]	]	PUNCT
ajst-27746	8	4	.	.	PUNCT
ajst-27746	9	1	we	we	PRON
ajst-27746	9	2	deeply	deeply	ADV
ajst-27746	9	3	analyze	analyze	VERB
ajst-27746	9	4	the	the	DET
ajst-27746	9	5	motion	motion	NOUN
ajst-27746	9	6	characteristics	characteristic	NOUN
ajst-27746	9	7	of	of	ADP
ajst-27746	9	8	each	each	DET
ajst-27746	9	9	component	component	NOUN
ajst-27746	9	10	in	in	ADP
ajst-27746	9	11	the	the	DET
ajst-27746	9	12	performance	performance	NOUN
ajst-27746	9	13	process	process	NOUN
ajst-27746	9	14	,	,	PUNCT
ajst-27746	9	15	build	build	VERB
ajst-27746	9	16	an	an	DET
ajst-27746	9	17	accurate	accurate	ADJ
ajst-27746	9	18	motion	motion	NOUN
ajst-27746	9	19	model	model	NOUN
ajst-27746	9	20	,	,	PUNCT
ajst-27746	9	21	and	and	CCONJ
ajst-27746	9	22	calculate	calculate	VERB
ajst-27746	9	23	the	the	DET
ajst-27746	9	24	position	position	NOUN
ajst-27746	9	25	and	and	CCONJ
ajst-27746	9	26	speed	speed	NOUN
ajst-27746	9	27	changes	change	NOUN
ajst-27746	9	28	of	of	ADP
ajst-27746	9	29	each	each	DET
ajst-27746	9	30	time	time	NOUN
ajst-27746	9	31	node	node	NOUN
ajst-27746	9	32	combined	combine	VERB
ajst-27746	9	33	with	with	ADP
ajst-27746	9	34	pde	pde	NOUN
ajst-27746	9	35	constraints	constraint	NOUN
ajst-27746	9	36	[	[	X
ajst-27746	9	37	2	2	NUM
ajst-27746	9	38	]	]	PUNCT
ajst-27746	9	39	.	.	PUNCT
ajst-27746	10	1	on	on	ADP
ajst-27746	10	2	this	this	DET
ajst-27746	10	3	basis	basis	NOUN
ajst-27746	10	4	,	,	PUNCT
ajst-27746	10	5	alternate	alternate	ADJ
ajst-27746	10	6	direction	direction	NOUN
ajst-27746	10	7	multiplier	multipli	ADJ
ajst-27746	10	8	method	method	NOUN
ajst-27746	10	9	(	(	PUNCT
ajst-27746	10	10	admm	admm	VERB
ajst-27746	10	11	)	)	PUNCT
ajst-27746	11	1	[	[	X
ajst-27746	11	2	3	3	NUM
ajst-27746	11	3	]	]	PUNCT
ajst-27746	11	4	and	and	CCONJ
ajst-27746	11	5	deeponet	deeponet	NOUN
ajst-27746	11	6	neural	neural	ADJ
ajst-27746	11	7	network	network	NOUN
ajst-27746	11	8	model	model	NOUN
ajst-27746	11	9	were	be	AUX
ajst-27746	11	10	further	far	ADV
ajst-27746	11	11	introduced	introduce	VERB
ajst-27746	11	12	to	to	PART
ajst-27746	11	13	optimize	optimize	VERB
ajst-27746	11	14	the	the	DET
ajst-27746	11	15	path	path	NOUN
ajst-27746	11	16	planning	planning	NOUN
ajst-27746	11	17	and	and	CCONJ
ajst-27746	11	18	speed	speed	NOUN
ajst-27746	11	19	control	control	NOUN
ajst-27746	11	20	[	[	X
ajst-27746	11	21	4	4	NUM
ajst-27746	11	22	]	]	PUNCT
ajst-27746	11	23	,	,	PUNCT
ajst-27746	11	24	in	in	ADP
ajst-27746	11	25	order	order	NOUN
ajst-27746	11	26	to	to	PART
ajst-27746	11	27	achieve	achieve	VERB
ajst-27746	11	28	the	the	DET
ajst-27746	11	29	best	good	ADJ
ajst-27746	11	30	performance	performance	NOUN
ajst-27746	11	31	effect	effect	NOUN
ajst-27746	11	32	.	.	PUNCT
ajst-27746	12	1	2	2	X
ajst-27746	12	2	.	.	X
ajst-27746	12	3	the	the	DET
ajst-27746	12	4	establishment	establishment	NOUN
ajst-27746	12	5	and	and	CCONJ
ajst-27746	12	6	analysis	analysis	NOUN
ajst-27746	12	7	of	of	ADP
ajst-27746	12	8	spiral	spiral	ADJ
ajst-27746	12	9	motion	motion	NOUN
ajst-27746	12	10	model	model	NOUN
ajst-27746	12	11	based	base	VERB
ajst-27746	12	12	on	on	ADP
ajst-27746	12	13	the	the	DET
ajst-27746	12	14	complex	complex	ADJ
ajst-27746	12	15	movement	movement	NOUN
ajst-27746	12	16	trajectory	trajectory	NOUN
ajst-27746	12	17	,	,	PUNCT
ajst-27746	12	18	this	this	DET
ajst-27746	12	19	paper	paper	NOUN
ajst-27746	12	20	takes	take	VERB
ajst-27746	12	21	the	the	DET
ajst-27746	12	22	dragon	dragon	NOUN
ajst-27746	12	23	dance	dance	NOUN
ajst-27746	12	24	activity	activity	NOUN
ajst-27746	12	25	as	as	ADP
ajst-27746	12	26	an	an	DET
ajst-27746	12	27	example	example	NOUN
ajst-27746	12	28	to	to	PART
ajst-27746	12	29	analyze	analyze	VERB
ajst-27746	12	30	,	,	PUNCT
ajst-27746	12	31	aiming	aim	VERB
ajst-27746	12	32	at	at	ADP
ajst-27746	12	33	the	the	DET
ajst-27746	12	34	situation	situation	NOUN
ajst-27746	12	35	that	that	SCONJ
ajst-27746	12	36	the	the	DET
ajst-27746	12	37	movement	movement	NOUN
ajst-27746	12	38	theme	theme	NOUN
ajst-27746	12	39	is	be	AUX
ajst-27746	12	40	rotated	rotate	VERB
ajst-27746	12	41	clockwise	clockwise	NOUN
ajst-27746	12	42	along	along	ADP
ajst-27746	12	43	the	the	DET
ajst-27746	12	44	isometric	isometric	ADJ
ajst-27746	12	45	spiral	spiral	NOUN
ajst-27746	12	46	,	,	PUNCT
ajst-27746	12	47	it	it	PRON
ajst-27746	12	48	is	be	AUX
ajst-27746	12	49	necessary	necessary	ADJ
ajst-27746	12	50	to	to	PART
ajst-27746	12	51	establish	establish	VERB
ajst-27746	12	52	a	a	DET
ajst-27746	12	53	mathematical	mathematical	ADJ
ajst-27746	12	54	model	model	NOUN
ajst-27746	12	55	to	to	PART
ajst-27746	12	56	describe	describe	VERB
ajst-27746	12	57	the	the	DET
ajst-27746	12	58	whole	whole	ADJ
ajst-27746	12	59	movement	movement	NOUN
ajst-27746	12	60	process	process	NOUN
ajst-27746	12	61	.	.	PUNCT
ajst-27746	13	1	based	base	VERB
ajst-27746	13	2	on	on	ADP
ajst-27746	13	3	the	the	DET
ajst-27746	13	4	pitch	pitch	NOUN
ajst-27746	13	5	and	and	CCONJ
ajst-27746	13	6	the	the	DET
ajst-27746	13	7	speed	speed	NOUN
ajst-27746	13	8	of	of	ADP
ajst-27746	13	9	the	the	DET
ajst-27746	13	10	handle	handle	NOUN
ajst-27746	13	11	in	in	ADP
ajst-27746	13	12	front	front	NOUN
ajst-27746	13	13	of	of	ADP
ajst-27746	13	14	the	the	DET
ajst-27746	13	15	dragon	dragon	NOUN
ajst-27746	13	16	head	head	NOUN
ajst-27746	13	17	,	,	PUNCT
ajst-27746	13	18	the	the	DET
ajst-27746	13	19	position	position	NOUN
ajst-27746	13	20	and	and	CCONJ
ajst-27746	13	21	speed	speed	NOUN
ajst-27746	13	22	per	per	ADP
ajst-27746	13	23	second	second	NOUN
ajst-27746	13	24	of	of	ADP
ajst-27746	13	25	each	each	DET
ajst-27746	13	26	segment	segment	NOUN
ajst-27746	13	27	of	of	ADP
ajst-27746	13	28	the	the	DET
ajst-27746	13	29	dragon	dragon	NOUN
ajst-27746	13	30	dance	dance	NOUN
ajst-27746	13	31	team	team	NOUN
ajst-27746	13	32	were	be	AUX
ajst-27746	13	33	calculated	calculate	VERB
ajst-27746	13	34	.	.	PUNCT
ajst-27746	14	1	in	in	ADP
ajst-27746	14	2	the	the	DET
ajst-27746	14	3	whole	whole	ADJ
ajst-27746	14	4	process	process	NOUN
ajst-27746	14	5	of	of	ADP
ajst-27746	14	6	the	the	DET
ajst-27746	14	7	dragon	dragon	NOUN
ajst-27746	14	8	dance	dance	NOUN
ajst-27746	14	9	team	team	NOUN
ajst-27746	14	10	moving	move	VERB
ajst-27746	14	11	along	along	ADP
ajst-27746	14	12	the	the	DET
ajst-27746	14	13	spiral	spiral	ADJ
ajst-27746	14	14	line	line	NOUN
ajst-27746	14	15	,	,	PUNCT
ajst-27746	14	16	in	in	ADP
ajst-27746	14	17	order	order	NOUN
ajst-27746	14	18	to	to	PART
ajst-27746	14	19	accurately	accurately	ADV
ajst-27746	14	20	describe	describe	VERB
ajst-27746	14	21	the	the	DET
ajst-27746	14	22	trajectory	trajectory	NOUN
ajst-27746	14	23	,	,	PUNCT
ajst-27746	14	24	the	the	DET
ajst-27746	14	25	position	position	NOUN
ajst-27746	14	26	of	of	ADP
ajst-27746	14	27	the	the	DET
ajst-27746	14	28	center	center	NOUN
ajst-27746	14	29	of	of	ADP
ajst-27746	14	30	the	the	DET
ajst-27746	14	31	front	front	ADJ
ajst-27746	14	32	handle	handle	NOUN
ajst-27746	14	33	of	of	ADP
ajst-27746	14	34	the	the	DET
ajst-27746	14	35	board	board	NOUN
ajst-27746	14	36	is	be	AUX
ajst-27746	14	37	calculated	calculate	VERB
ajst-27746	14	38	by	by	ADP
ajst-27746	14	39	geometric	geometric	ADJ
ajst-27746	14	40	modeling	modeling	NOUN
ajst-27746	14	41	section	section	NOUN
ajst-27746	14	42	by	by	ADP
ajst-27746	14	43	section	section	NOUN
ajst-27746	14	44	.	.	PUNCT
ajst-27746	15	1	these	these	DET
ajst-27746	15	2	positions	position	NOUN
ajst-27746	15	3	depend	depend	VERB
ajst-27746	15	4	on	on	ADP
ajst-27746	15	5	the	the	DET
ajst-27746	15	6	distance	distance	NOUN
ajst-27746	15	7	between	between	ADP
ajst-27746	15	8	the	the	DET
ajst-27746	15	9	boards	board	NOUN
ajst-27746	15	10	and	and	CCONJ
ajst-27746	15	11	their	their	PRON
ajst-27746	15	12	changes	change	NOUN
ajst-27746	15	13	in	in	ADP
ajst-27746	15	14	position	position	NOUN
ajst-27746	15	15	relative	relative	ADJ
ajst-27746	15	16	to	to	ADP
ajst-27746	15	17	the	the	DET
ajst-27746	15	18	spiral	spiral	NOUN
ajst-27746	15	19	,	,	PUNCT
ajst-27746	15	20	especially	especially	ADV
ajst-27746	15	21	the	the	DET
ajst-27746	15	22	connection	connection	NOUN
ajst-27746	15	23	between	between	ADP
ajst-27746	15	24	the	the	DET
ajst-27746	15	25	body	body	NOUN
ajst-27746	15	26	and	and	CCONJ
ajst-27746	15	27	the	the	DET
ajst-27746	15	28	tail	tail	NOUN
ajst-27746	15	29	of	of	ADP
ajst-27746	15	30	the	the	DET
ajst-27746	15	31	dragon	dragon	NOUN
ajst-27746	15	32	.	.	PUNCT
ajst-27746	16	1	to	to	ADP
ajst-27746	16	2	this	this	DET
ajst-27746	16	3	end	end	NOUN
ajst-27746	16	4	,	,	PUNCT
ajst-27746	16	5	we	we	PRON
ajst-27746	16	6	use	use	VERB
ajst-27746	16	7	differential	differential	ADJ
ajst-27746	16	8	equations	equation	NOUN
ajst-27746	16	9	and	and	CCONJ
ajst-27746	16	10	wave	wave	NOUN
ajst-27746	16	11	equations	equation	NOUN
ajst-27746	16	12	to	to	PART
ajst-27746	16	13	analyze	analyze	VERB
ajst-27746	16	14	its	its	PRON
ajst-27746	16	15	motion	motion	NOUN
ajst-27746	16	16	patterns	pattern	NOUN
ajst-27746	16	17	,	,	PUNCT
ajst-27746	16	18	trajectories	trajectory	NOUN
ajst-27746	16	19	and	and	CCONJ
ajst-27746	16	20	velocity	velocity	NOUN
ajst-27746	16	21	changes	change	NOUN
ajst-27746	16	22	.	.	PUNCT
ajst-27746	17	1	2.1	2.1	NUM
ajst-27746	17	2	.	.	PUNCT
ajst-27746	18	1	the	the	DET
ajst-27746	18	2	helix	helix	ADJ
ajst-27746	18	3	model	model	NOUN
ajst-27746	18	4	is	be	AUX
ajst-27746	18	5	established	establish	VERB
ajst-27746	18	6	the	the	DET
ajst-27746	18	7	faucet	faucet	NOUN
ajst-27746	18	8	is	be	AUX
ajst-27746	18	9	rotated	rotate	VERB
ajst-27746	18	10	clockwise	clockwise	NOUN
ajst-27746	18	11	along	along	ADP
ajst-27746	18	12	the	the	DET
ajst-27746	18	13	isometric	isometric	ADJ
ajst-27746	18	14	helix	helix	NOUN
ajst-27746	18	15	and	and	CCONJ
ajst-27746	18	16	the	the	DET
ajst-27746	18	17	position	position	NOUN
ajst-27746	18	18	is	be	AUX
ajst-27746	18	19	determined	determine	VERB
ajst-27746	18	20	by	by	ADP
ajst-27746	18	21	time	time	NOUN
ajst-27746	18	22	𝑡.	𝑡.	VERB
ajst-27746	18	23	the	the	DET
ajst-27746	18	24	polar	polar	ADJ
ajst-27746	18	25	coordinate	coordinate	NOUN
ajst-27746	18	26	equation	equation	NOUN
ajst-27746	18	27	of	of	ADP
ajst-27746	18	28	the	the	DET
ajst-27746	18	29	helix	helix	NOUN
ajst-27746	18	30	can	can	AUX
ajst-27746	18	31	be	be	AUX
ajst-27746	18	32	expressed	express	VERB
ajst-27746	18	33	as	as	ADP
ajst-27746	18	34	[	[	X
ajst-27746	18	35	5	5	NUM
ajst-27746	18	36	]	]	X
ajst-27746	18	37	:	:	PUNCT
ajst-27746	18	38			NOUN
ajst-27746	18	39			PUNCT
ajst-27746	18	40	0	0	NUM
ajst-27746	18	41	2	2	NUM
ajst-27746	18	42	p	p	NOUN
ajst-27746	18	43	r	r	NOUN
ajst-27746	18	44	r	r	NOUN
ajst-27746	18	45			PROPN
ajst-27746	18	46			PROPN
ajst-27746	19	1			PROPN
ajst-27746	19	2			PUNCT
ajst-27746	19	3	(	(	PUNCT
ajst-27746	19	4	1	1	NUM
ajst-27746	19	5	)	)	PUNCT
ajst-27746	20	1	where	where	SCONJ
ajst-27746	20	2	,	,	PUNCT
ajst-27746	20	3	𝑟	𝑟	PRON
ajst-27746	20	4	is	be	AUX
ajst-27746	20	5	the	the	DET
ajst-27746	20	6	starting	starting	NOUN
ajst-27746	20	7	radius	radius	NOUN
ajst-27746	20	8	;	;	PUNCT
ajst-27746	20	9	𝑝	𝑝	NOUN
ajst-27746	20	10	is	be	AUX
ajst-27746	20	11	pitch	pitch	NOUN
ajst-27746	20	12	;	;	PUNCT
ajst-27746	20	13	𝜃	𝜃	X
ajst-27746	20	14	is	be	AUX
ajst-27746	20	15	the	the	DET
ajst-27746	20	16	polar	polar	ADJ
ajst-27746	20	17	angle	angle	NOUN
ajst-27746	20	18	,	,	PUNCT
ajst-27746	20	19	which	which	PRON
ajst-27746	20	20	varies	vary	VERB
ajst-27746	20	21	with	with	ADP
ajst-27746	20	22	time	time	NOUN
ajst-27746	20	23	.	.	PUNCT
ajst-27746	21	1	parametric	parametric	ADJ
ajst-27746	21	2	equation	equation	NOUN
ajst-27746	21	3	of	of	ADP
ajst-27746	21	4	a	a	DET
ajst-27746	21	5	helix	helix	NOUN
ajst-27746	21	6	:	:	PUNCT
ajst-27746	21	7	a	a	DET
ajst-27746	21	8	helix	helix	NOUN
ajst-27746	21	9	is	be	AUX
ajst-27746	21	10	a	a	DET
ajst-27746	21	11	twodimensional	twodimensional	ADJ
ajst-27746	21	12	curve	curve	NOUN
ajst-27746	21	13	that	that	PRON
ajst-27746	21	14	can	can	AUX
ajst-27746	21	15	be	be	AUX
ajst-27746	21	16	described	describe	VERB
ajst-27746	21	17	by	by	ADP
ajst-27746	21	18	a	a	DET
ajst-27746	21	19	parametric	parametric	ADJ
ajst-27746	21	20	equation	equation	NOUN
ajst-27746	21	21	,	,	PUNCT
ajst-27746	21	22	the	the	DET
ajst-27746	21	23	two	two	NUM
ajst-27746	21	24	main	main	ADJ
ajst-27746	21	25	variables	variable	NOUN
ajst-27746	21	26	of	of	ADP
ajst-27746	21	27	a	a	DET
ajst-27746	21	28	helix	helix	NOUN
ajst-27746	21	29	are	be	AUX
ajst-27746	21	30	the	the	DET
ajst-27746	21	31	radius	radius	NOUN
ajst-27746	21	32	and	and	CCONJ
ajst-27746	21	33	the	the	DET
ajst-27746	21	34	angle	angle	NOUN
ajst-27746	21	35	.	.	PUNCT
ajst-27746	22	1	the	the	DET
ajst-27746	22	2	false	false	ADJ
ajst-27746	22	3	faucet	faucet	NOUN
ajst-27746	22	4	moves	move	NOUN
ajst-27746	22	5	along	along	ADP
ajst-27746	22	6	the	the	DET
ajst-27746	22	7	helix	helix	NOUN
ajst-27746	22	8	,	,	PUNCT
ajst-27746	22	9	and	and	CCONJ
ajst-27746	22	10	the	the	DET
ajst-27746	22	11	position	position	NOUN
ajst-27746	22	12	is	be	AUX
ajst-27746	22	13	determined	determine	VERB
ajst-27746	22	14	by	by	ADP
ajst-27746	22	15	time	time	NOUN
ajst-27746	22	16	.	.	PUNCT
ajst-27746	23	1	the	the	DET
ajst-27746	23	2	equation	equation	NOUN
ajst-27746	23	3	for	for	ADP
ajst-27746	23	4	the	the	DET
ajst-27746	23	5	helix	helix	NOUN
ajst-27746	23	6	can	can	AUX
ajst-27746	23	7	be	be	AUX
ajst-27746	23	8	expressed	express	VERB
ajst-27746	23	9	as	as	ADP
ajst-27746	23	10	:	:	PUNCT
ajst-27746	23	11			NOUN
ajst-27746	23	12			PROPN
ajst-27746	23	13			NOUN
ajst-27746	23	14			PUNCT
ajst-27746	23	15			NOUN
ajst-27746	23	16			NOUN
ajst-27746	24	1			PUNCT
ajst-27746	24	2			NOUN
ajst-27746	24	3			SYM
ajst-27746	24	4			NOUN
ajst-27746	24	5			PUNCT
ajst-27746	24	6			NOUN
ajst-27746	24	7			NOUN
ajst-27746	24	8			PUNCT
ajst-27746	24	9	cos	cos	PROPN
ajst-27746	24	10	sin	sin	PROPN
ajst-27746	24	11	x	x	PUNCT
ajst-27746	24	12	t	t	NOUN
ajst-27746	24	13	r	r	NOUN
ajst-27746	24	14	t	t	PROPN
ajst-27746	24	15	t	t	X
ajst-27746	25	1	y	y	PROPN
ajst-27746	25	2	t	t	PROPN
ajst-27746	25	3	r	r	NOUN
ajst-27746	25	4	t	t	PROPN
ajst-27746	25	5	t	t	NOUN
ajst-27746	25	6			X
ajst-27746	25	7			PROPN
ajst-27746	25	8			X
ajst-27746	25	9			VERB
ajst-27746	25	10			NUM
ajst-27746	25	11			NOUN
ajst-27746	25	12	(	(	PUNCT
ajst-27746	25	13	2	2	NUM
ajst-27746	25	14	)	)	PUNCT
ajst-27746	25	15	where	where	SCONJ
ajst-27746	25	16	,	,	PUNCT
ajst-27746	25	17	𝑥	𝑥	PROPN
ajst-27746	25	18	represents	represent	VERB
ajst-27746	25	19	the	the	DET
ajst-27746	25	20	coordinates	coordinate	NOUN
ajst-27746	25	21	of	of	ADP
ajst-27746	25	22	the	the	DET
ajst-27746	25	23	movement	movement	NOUN
ajst-27746	25	24	of	of	ADP
ajst-27746	25	25	the	the	DET
ajst-27746	25	26	faucet	faucet	NOUN
ajst-27746	25	27	on	on	ADP
ajst-27746	25	28	the	the	DET
ajst-27746	25	29	coordinate	coordinate	NOUN
ajst-27746	25	30	axis	axis	NOUN
ajst-27746	25	31	𝑥	𝑥	NOUN
ajst-27746	25	32	;	;	PUNCT
ajst-27746	25	33	𝑦	𝑦	PRON
ajst-27746	25	34	represents	represent	VERB
ajst-27746	25	35	the	the	DET
ajst-27746	25	36	coordinates	coordinate	NOUN
ajst-27746	25	37	of	of	ADP
ajst-27746	25	38	the	the	DET
ajst-27746	25	39	movement	movement	NOUN
ajst-27746	25	40	of	of	ADP
ajst-27746	25	41	the	the	DET
ajst-27746	25	42	faucet	faucet	NOUN
ajst-27746	25	43	on	on	ADP
ajst-27746	25	44	the	the	DET
ajst-27746	25	45	coordinate	coordinate	NOUN
ajst-27746	25	46	axis	axis	NOUN
ajst-27746	25	47	𝑦.	𝑦.	VERB
ajst-27746	25	48	the	the	DET
ajst-27746	25	49	speed	speed	NOUN
ajst-27746	25	50	at	at	ADP
ajst-27746	25	51	which	which	PRON
ajst-27746	25	52	the	the	DET
ajst-27746	25	53	faucet	faucet	NOUN
ajst-27746	25	54	is	be	AUX
ajst-27746	25	55	moving	move	VERB
ajst-27746	25	56	along	along	ADP
ajst-27746	25	57	a	a	DET
ajst-27746	25	58	spiral	spiral	ADJ
ajst-27746	25	59	1	1	NUM
ajst-27746	25	60	m	m	NOUN
ajst-27746	25	61	/	/	SYM
ajst-27746	25	62	s.	s.	PROPN
ajst-27746	25	63	in	in	ADP
ajst-27746	25	64	order	order	NOUN
ajst-27746	25	65	to	to	PART
ajst-27746	25	66	calculate	calculate	VERB
ajst-27746	25	67	the	the	DET
ajst-27746	25	68	position	position	NOUN
ajst-27746	25	69	of	of	ADP
ajst-27746	25	70	the	the	DET
ajst-27746	25	71	faucet	faucet	NOUN
ajst-27746	25	72	,	,	PUNCT
ajst-27746	25	73	it	it	PRON
ajst-27746	25	74	is	be	AUX
ajst-27746	25	75	necessary	necessary	ADJ
ajst-27746	25	76	to	to	PART
ajst-27746	25	77	know	know	VERB
ajst-27746	25	78	the	the	DET
ajst-27746	25	79	radius	radius	NOUN
ajst-27746	25	80	and	and	CCONJ
ajst-27746	25	81	angle	angle	NOUN
ajst-27746	25	82	of	of	ADP
ajst-27746	25	83	the	the	DET
ajst-27746	25	84	helix	helix	NOUN
ajst-27746	25	85	.	.	PUNCT
ajst-27746	26	1	radius	radius	NOUN
ajst-27746	26	2	change	change	NOUN
ajst-27746	26	3	:	:	PUNCT
ajst-27746	26	4	set	set	VERB
ajst-27746	26	5	the	the	DET
ajst-27746	26	6	initial	initial	ADJ
ajst-27746	26	7	radius	radius	NOUN
ajst-27746	26	8	of	of	ADP
ajst-27746	26	9	the	the	DET
ajst-27746	26	10	helix	helix	NOUN
ajst-27746	26	11	as	as	ADP
ajst-27746	26	12	𝑟	𝑟	X
ajst-27746	26	13	0	0	NUM
ajst-27746	26	14	,	,	PUNCT
ajst-27746	26	15	the	the	DET
ajst-27746	26	16	time	time	NOUN
ajst-27746	26	17	as	as	ADP
ajst-27746	26	18	𝑡	𝑡	NOUN
ajst-27746	26	19	,	,	PUNCT
ajst-27746	26	20	and	and	CCONJ
ajst-27746	26	21	the	the	DET
ajst-27746	26	22	pitch	pitch	NOUN
ajst-27746	26	23	of	of	ADP
ajst-27746	26	24	the	the	DET
ajst-27746	26	25	helix	helix	NOUN
ajst-27746	26	26	as	as	ADP
ajst-27746	26	27	ℎ.	ℎ.	ADJ
ajst-27746	26	28	radius	radius	NOUN
ajst-27746	26	29	of	of	ADP
ajst-27746	26	30	the	the	DET
ajst-27746	26	31	helix	helix	NOUN
ajst-27746	26	32	per	per	ADP
ajst-27746	26	33	second	second	ADJ
ajst-27746	26	34	:	:	PUNCT
ajst-27746	26	35			NOUN
ajst-27746	26	36			PROPN
ajst-27746	26	37	head	head	NOUN
ajst-27746	26	38	0	0	NUM
ajst-27746	26	39	2	2	NUM
ajst-27746	26	40	v	v	NOUN
ajst-27746	26	41	r	r	NOUN
ajst-27746	26	42	t	t	NOUN
ajst-27746	26	43	r	r	NOUN
ajst-27746	26	44	t	t	NOUN
ajst-27746	26	45			PROPN
ajst-27746	26	46			PROPN
ajst-27746	26	47			PUNCT
ajst-27746	26	48	(	(	PUNCT
ajst-27746	26	49	3	3	NUM
ajst-27746	26	50	)	)	PUNCT
ajst-27746	26	51	303	303	NUM
ajst-27746	26	52	among	among	ADP
ajst-27746	26	53	them	they	PRON
ajst-27746	26	54	,	,	PUNCT
ajst-27746	26	55	𝑣head	𝑣head	VERB
ajst-27746	26	56	the	the	DET
ajst-27746	26	57	speed	speed	NOUN
ajst-27746	26	58	of	of	ADP
ajst-27746	26	59	the	the	DET
ajst-27746	26	60	head	head	NOUN
ajst-27746	26	61	.	.	PUNCT
ajst-27746	27	1	angle	angle	NOUN
ajst-27746	27	2	change	change	NOUN
ajst-27746	27	3	:	:	PUNCT
ajst-27746	27	4	the	the	DET
ajst-27746	27	5	angular	angular	ADJ
ajst-27746	27	6	speed	speed	NOUN
ajst-27746	27	7	of	of	ADP
ajst-27746	27	8	movement	movement	NOUN
ajst-27746	27	9	of	of	ADP
ajst-27746	27	10	the	the	DET
ajst-27746	27	11	faucet	faucet	NOUN
ajst-27746	27	12	on	on	ADP
ajst-27746	27	13	the	the	DET
ajst-27746	27	14	helix	helix	NOUN
ajst-27746	27	15	is	be	AUX
ajst-27746	27	16	:	:	PUNCT
ajst-27746	27	17			NOUN
ajst-27746	27	18			SYM
ajst-27746	27	19			NOUN
ajst-27746	27	20			PROPN
ajst-27746	27	21	head	head	NOUN
ajst-27746	27	22	0	0	NUM
ajst-27746	27	23	v	v	ADP
ajst-27746	27	24	t	t	NOUN
ajst-27746	27	25	t	t	NOUN
ajst-27746	27	26	r	r	NOUN
ajst-27746	27	27	t	t	PROPN
ajst-27746	27	28			PROPN
ajst-27746	27	29			PROPN
ajst-27746	27	30			PROPN
ajst-27746	27	31	(	(	PUNCT
ajst-27746	27	32	4	4	X
ajst-27746	27	33	)	)	PUNCT
ajst-27746	27	34	position	position	NOUN
ajst-27746	27	35	of	of	ADP
ajst-27746	27	36	the	the	DET
ajst-27746	27	37	faucet	faucet	NOUN
ajst-27746	27	38	:	:	PUNCT
ajst-27746	27	39	according	accord	VERB
ajst-27746	27	40	to	to	ADP
ajst-27746	27	41	the	the	DET
ajst-27746	27	42	helix	helix	ADJ
ajst-27746	27	43	equation	equation	NOUN
ajst-27746	27	44	,	,	PUNCT
ajst-27746	27	45	the	the	DET
ajst-27746	27	46	two	two	NUM
ajst-27746	27	47	-	-	PUNCT
ajst-27746	27	48	dimensional	dimensional	ADJ
ajst-27746	27	49	plane	plane	NOUN
ajst-27746	27	50	position	position	NOUN
ajst-27746	27	51	𝑥	𝑥	NOUN
ajst-27746	27	52	,	,	PUNCT
ajst-27746	27	53	𝑦	𝑦	NOUN
ajst-27746	27	54	of	of	ADP
ajst-27746	27	55	the	the	DET
ajst-27746	27	56	faucet	faucet	NOUN
ajst-27746	27	57	at	at	ADP
ajst-27746	27	58	the	the	DET
ajst-27746	27	59	moment	moment	NOUN
ajst-27746	27	60	of	of	ADP
ajst-27746	27	61	time	time	NOUN
ajst-27746	27	62	𝑡	𝑡	PROPN
ajst-27746	27	63	is	be	AUX
ajst-27746	27	64	:	:	PUNCT
ajst-27746	27	65			NOUN
ajst-27746	27	66			SYM
ajst-27746	27	67			NOUN
ajst-27746	27	68			PUNCT
ajst-27746	27	69			NOUN
ajst-27746	27	70			NOUN
ajst-27746	28	1			PUNCT
ajst-27746	28	2			NOUN
ajst-27746	28	3			SYM
ajst-27746	28	4			NOUN
ajst-27746	28	5			PUNCT
ajst-27746	28	6			NOUN
ajst-27746	28	7			NOUN
ajst-27746	28	8			PROPN
ajst-27746	28	9	head	head	NOUN
ajst-27746	28	10	head	head	NOUN
ajst-27746	28	11	cos	cos	PROPN
ajst-27746	28	12	sin	sin	PROPN
ajst-27746	28	13	x	x	X
ajst-27746	28	14	t	t	NOUN
ajst-27746	28	15	r	r	NOUN
ajst-27746	28	16	t	t	PROPN
ajst-27746	28	17	t	t	X
ajst-27746	28	18	y	y	PROPN
ajst-27746	28	19	t	t	PROPN
ajst-27746	28	20	r	r	NOUN
ajst-27746	28	21	t	t	PROPN
ajst-27746	28	22	t	t	NOUN
ajst-27746	28	23			X
ajst-27746	28	24			PROPN
ajst-27746	28	25			X
ajst-27746	28	26			VERB
ajst-27746	28	27			NUM
ajst-27746	28	28			NOUN
ajst-27746	28	29	(	(	PUNCT
ajst-27746	28	30	5	5	NUM
ajst-27746	28	31	)	)	PUNCT
ajst-27746	28	32	rigid	rigid	ADJ
ajst-27746	28	33	constraint	constraint	NOUN
ajst-27746	28	34	model	model	NOUN
ajst-27746	28	35	:	:	PUNCT
ajst-27746	28	36	using	use	VERB
ajst-27746	28	37	the	the	DET
ajst-27746	28	38	directional	directional	ADJ
ajst-27746	28	39	angle	angle	NOUN
ajst-27746	28	40	𝜃	𝜃	X
ajst-27746	28	41	𝑡	𝑡	NOUN
ajst-27746	28	42	and	and	CCONJ
ajst-27746	28	43	the	the	DET
ajst-27746	28	44	rigid	rigid	ADJ
ajst-27746	28	45	rod	rod	NOUN
ajst-27746	28	46	length	length	NOUN
ajst-27746	28	47	𝐿	𝐿	PROPN
ajst-27746	28	48	,	,	PUNCT
ajst-27746	28	49	the	the	DET
ajst-27746	28	50	position	position	NOUN
ajst-27746	28	51	of	of	ADP
ajst-27746	28	52	the	the	DET
ajst-27746	28	53	first	first	ADJ
ajst-27746	28	54	section	section	NOUN
ajst-27746	28	55	𝑖	𝑖	SYM
ajst-27746	28	56	board	board	NOUN
ajst-27746	28	57	can	can	AUX
ajst-27746	28	58	be	be	AUX
ajst-27746	28	59	derived	derive	VERB
ajst-27746	28	60	from	from	ADP
ajst-27746	28	61	the	the	DET
ajst-27746	28	62	position	position	NOUN
ajst-27746	28	63	of	of	ADP
ajst-27746	28	64	the	the	DET
ajst-27746	28	65	previous	previous	ADJ
ajst-27746	28	66	section	section	NOUN
ajst-27746	28	67	:	:	PUNCT
ajst-27746	29	1			NOUN
ajst-27746	29	2			SYM
ajst-27746	29	3			NOUN
ajst-27746	29	4			PUNCT
ajst-27746	29	5			NOUN
ajst-27746	29	6			NOUN
ajst-27746	30	1			PUNCT
ajst-27746	30	2			NOUN
ajst-27746	30	3			SYM
ajst-27746	30	4			NOUN
ajst-27746	30	5			PUNCT
ajst-27746	30	6			NOUN
ajst-27746	31	1			NOUN
ajst-27746	32	1			PROPN
ajst-27746	32	2	1	1	NUM
ajst-27746	32	3	1	1	NUM
ajst-27746	32	4	1	1	NUM
ajst-27746	32	5	1	1	NUM
ajst-27746	32	6	cos	cos	PROPN
ajst-27746	32	7	sin	sin	NOUN
ajst-27746	33	1	i	i	PRON
ajst-27746	33	2	i	i	PRON
ajst-27746	34	1	i	i	PRON
ajst-27746	34	2	i	i	PRON
ajst-27746	35	1	i	i	PRON
ajst-27746	36	1	i	i	VERB
ajst-27746	36	2	x	x	VERB
ajst-27746	36	3	t	t	NOUN
ajst-27746	36	4	x	x	X
ajst-27746	37	1	t	t	PROPN
ajst-27746	37	2	l	l	NOUN
ajst-27746	37	3	t	t	PROPN
ajst-27746	37	4	y	y	PROPN
ajst-27746	37	5	t	t	PROPN
ajst-27746	37	6	y	y	PROPN
ajst-27746	37	7	t	t	PROPN
ajst-27746	37	8	l	l	PROPN
ajst-27746	37	9	t	t	X
ajst-27746	37	10			PROPN
ajst-27746	38	1			X
ajst-27746	38	2			PROPN
ajst-27746	38	3			PROPN
ajst-27746	38	4			PROPN
ajst-27746	38	5			PROPN
ajst-27746	38	6			NUM
ajst-27746	38	7			NOUN
ajst-27746	38	8			NUM
ajst-27746	38	9			NUM
ajst-27746	38	10			NOUN
ajst-27746	38	11			NUM
ajst-27746	38	12	(	(	PUNCT
ajst-27746	38	13	6	6	NUM
ajst-27746	38	14	)	)	PUNCT
ajst-27746	38	15	this	this	DET
ajst-27746	38	16	method	method	NOUN
ajst-27746	38	17	of	of	ADP
ajst-27746	38	18	calculation	calculation	NOUN
ajst-27746	38	19	ensures	ensure	VERB
ajst-27746	38	20	that	that	SCONJ
ajst-27746	38	21	the	the	DET
ajst-27746	38	22	section	section	NOUN
ajst-27746	38	23	𝑖	𝑖	SYM
ajst-27746	38	24	is	be	AUX
ajst-27746	38	25	always	always	ADV
ajst-27746	38	26	kept	keep	VERB
ajst-27746	38	27	at	at	ADP
ajst-27746	38	28	a	a	DET
ajst-27746	38	29	distance	distance	NOUN
ajst-27746	38	30	𝑖	𝑖	SYM
ajst-27746	38	31	1	1	NUM
ajst-27746	38	32	from	from	ADP
ajst-27746	38	33	the	the	DET
ajst-27746	38	34	section	section	NOUN
ajst-27746	38	35	as	as	ADP
ajst-27746	38	36	𝑖	𝑖	X
ajst-27746	38	37	1	1	NUM
ajst-27746	38	38	.	.	PUNCT
ajst-27746	39	1	the	the	DET
ajst-27746	39	2	wave	wave	NOUN
ajst-27746	39	3	equation	equation	NOUN
ajst-27746	39	4	:	:	PUNCT
ajst-27746	39	5	since	since	SCONJ
ajst-27746	39	6	the	the	DET
ajst-27746	39	7	movement	movement	NOUN
ajst-27746	39	8	of	of	ADP
ajst-27746	39	9	each	each	DET
ajst-27746	39	10	stage	stage	NOUN
ajst-27746	39	11	of	of	ADP
ajst-27746	39	12	the	the	DET
ajst-27746	39	13	dragon	dragon	NOUN
ajst-27746	39	14	's	's	PART
ajst-27746	39	15	body	body	NOUN
ajst-27746	39	16	is	be	AUX
ajst-27746	39	17	lagging	lag	VERB
ajst-27746	39	18	behind	behind	ADP
ajst-27746	39	19	that	that	PRON
ajst-27746	39	20	of	of	ADP
ajst-27746	39	21	the	the	DET
ajst-27746	39	22	previous	previous	ADJ
ajst-27746	39	23	stage	stage	NOUN
ajst-27746	39	24	,	,	PUNCT
ajst-27746	39	25	this	this	DET
ajst-27746	39	26	effect	effect	NOUN
ajst-27746	39	27	can	can	AUX
ajst-27746	39	28	be	be	AUX
ajst-27746	39	29	described	describe	VERB
ajst-27746	39	30	by	by	ADP
ajst-27746	39	31	the	the	DET
ajst-27746	39	32	wave	wave	NOUN
ajst-27746	39	33	equation	equation	NOUN
ajst-27746	39	34	.	.	PUNCT
ajst-27746	40	1	over	over	ADP
ajst-27746	40	2	time	time	NOUN
ajst-27746	40	3	,	,	PUNCT
ajst-27746	40	4	the	the	DET
ajst-27746	40	5	movement	movement	NOUN
ajst-27746	40	6	of	of	ADP
ajst-27746	40	7	the	the	DET
ajst-27746	40	8	dragon	dragon	NOUN
ajst-27746	40	9	head	head	NOUN
ajst-27746	40	10	is	be	AUX
ajst-27746	40	11	gradually	gradually	ADV
ajst-27746	40	12	transmitted	transmit	VERB
ajst-27746	40	13	to	to	ADP
ajst-27746	40	14	the	the	DET
ajst-27746	40	15	dragon	dragon	NOUN
ajst-27746	40	16	body	body	NOUN
ajst-27746	40	17	and	and	CCONJ
ajst-27746	40	18	tail	tail	NOUN
ajst-27746	40	19	like	like	ADP
ajst-27746	40	20	a	a	DET
ajst-27746	40	21	wave	wave	NOUN
ajst-27746	40	22	.	.	PUNCT
ajst-27746	41	1	this	this	DET
ajst-27746	41	2	wave	wave	NOUN
ajst-27746	41	3	effect	effect	NOUN
ajst-27746	41	4	makes	make	VERB
ajst-27746	41	5	the	the	DET
ajst-27746	41	6	dragon	dragon	NOUN
ajst-27746	41	7	dance	dance	NOUN
ajst-27746	41	8	team	team	NOUN
ajst-27746	41	9	's	's	PART
ajst-27746	41	10	movement	movement	NOUN
ajst-27746	41	11	on	on	ADP
ajst-27746	41	12	the	the	DET
ajst-27746	41	13	spiral	spiral	ADJ
ajst-27746	41	14	line	line	NOUN
ajst-27746	41	15	appear	appear	VERB
ajst-27746	41	16	a	a	DET
ajst-27746	41	17	curved	curved	ADJ
ajst-27746	41	18	s	s	ADV
ajst-27746	41	19	-	-	PUNCT
ajst-27746	41	20	shaped	shape	VERB
ajst-27746	41	21	motion	motion	NOUN
ajst-27746	41	22	.	.	PUNCT
ajst-27746	42	1	the	the	DET
ajst-27746	42	2	angle	angle	NOUN
ajst-27746	42	3	of	of	ADP
ajst-27746	42	4	each	each	DET
ajst-27746	42	5	board	board	NOUN
ajst-27746	42	6	of	of	ADP
ajst-27746	42	7	the	the	DET
ajst-27746	42	8	dragon	dragon	NOUN
ajst-27746	42	9	body	body	NOUN
ajst-27746	42	10	and	and	CCONJ
ajst-27746	42	11	tail	tail	NOUN
ajst-27746	42	12	lags	lag	VERB
ajst-27746	42	13	behind	behind	ADP
ajst-27746	42	14	the	the	DET
ajst-27746	42	15	dragon	dragon	NOUN
ajst-27746	42	16	head	head	NOUN
ajst-27746	42	17	.	.	PUNCT
ajst-27746	43	1	assume	assume	VERB
ajst-27746	43	2	that	that	SCONJ
ajst-27746	43	3	the	the	DET
ajst-27746	43	4	length	length	NOUN
ajst-27746	43	5	of	of	ADP
ajst-27746	43	6	each	each	DET
ajst-27746	43	7	board	board	NOUN
ajst-27746	43	8	boarding	boarding	NOUN
ajst-27746	43	9	is	be	AUX
ajst-27746	43	10	𝐿	𝐿	PROPN
ajst-27746	43	11	220	220	NUM
ajst-27746	43	12	cm	cm	NOUN
ajst-27746	43	13	,	,	PUNCT
ajst-27746	43	14	and	and	CCONJ
ajst-27746	43	15	the	the	DET
ajst-27746	43	16	relative	relative	ADJ
ajst-27746	43	17	position	position	NOUN
ajst-27746	43	18	of	of	ADP
ajst-27746	43	19	the	the	DET
ajst-27746	43	20	position	position	NOUN
ajst-27746	43	21	of	of	ADP
ajst-27746	43	22	the	the	DET
ajst-27746	43	23	first	first	ADJ
ajst-27746	43	24	board	board	NOUN
ajst-27746	43	25	𝑖	𝑖	SYM
ajst-27746	43	26	boarding	boarding	NOUN
ajst-27746	43	27	and	and	CCONJ
ajst-27746	43	28	the	the	DET
ajst-27746	43	29	head	head	NOUN
ajst-27746	43	30	is	be	AUX
ajst-27746	43	31	:	:	PUNCT
ajst-27746	43	32			NOUN
ajst-27746	44	1			SYM
ajst-27746	44	2			NOUN
ajst-27746	44	3			SYM
ajst-27746	44	4			NOUN
ajst-27746	44	5			SYM
ajst-27746	44	6			NOUN
ajst-27746	44	7			PROPN
ajst-27746	44	8	lag	lag	VERB
ajst-27746	45	1	i	i	PRON
ajst-27746	45	2	i	i	VERB
ajst-27746	46	1	r	r	NOUN
ajst-27746	46	2	t	t	NOUN
ajst-27746	46	3	r	r	NOUN
ajst-27746	46	4	t	t	NOUN
ajst-27746	47	1	i	i	PRON
ajst-27746	47	2	l	l	PROPN
ajst-27746	47	3	t	t	NOUN
ajst-27746	47	4	t	t	X
ajst-27746	47	5	i	i	NOUN
ajst-27746	47	6			PROPN
ajst-27746	47	7			PROPN
ajst-27746	47	8			ADP
ajst-27746	48	1			PROPN
ajst-27746	48	2			NOUN
ajst-27746	48	3			ADP
ajst-27746	48	4			NUM
ajst-27746	48	5			PROPN
ajst-27746	48	6			NOUN
ajst-27746	48	7			NOUN
ajst-27746	48	8	(	(	PUNCT
ajst-27746	48	9	7	7	NUM
ajst-27746	48	10	)	)	PUNCT
ajst-27746	48	11	where	where	SCONJ
ajst-27746	48	12	𝜃	𝜃	NOUN
ajst-27746	48	13	is	be	AUX
ajst-27746	48	14	the	the	DET
ajst-27746	48	15	angular	angular	ADJ
ajst-27746	48	16	lag	lag	NOUN
ajst-27746	48	17	value	value	NOUN
ajst-27746	48	18	of	of	ADP
ajst-27746	48	19	each	each	DET
ajst-27746	48	20	section	section	NOUN
ajst-27746	48	21	board	board	NOUN
ajst-27746	48	22	,	,	PUNCT
ajst-27746	48	23	which	which	PRON
ajst-27746	48	24	is	be	AUX
ajst-27746	48	25	defined	define	VERB
ajst-27746	48	26	as	as	ADP
ajst-27746	48	27	a	a	DET
ajst-27746	48	28	fixed	fix	VERB
ajst-27746	48	29	value	value	NOUN
ajst-27746	48	30	.	.	PUNCT
ajst-27746	49	1	the	the	DET
ajst-27746	49	2	two	two	NUM
ajst-27746	49	3	-	-	PUNCT
ajst-27746	49	4	dimensional	dimensional	ADJ
ajst-27746	49	5	plane	plane	NOUN
ajst-27746	49	6	position	position	NOUN
ajst-27746	49	7	𝑥	𝑥	X
ajst-27746	49	8	,	,	PUNCT
ajst-27746	49	9	𝑦	𝑦	NOUN
ajst-27746	49	10	of	of	ADP
ajst-27746	49	11	the	the	DET
ajst-27746	49	12	first	first	ADJ
ajst-27746	49	13	section	section	NOUN
ajst-27746	49	14	𝑖	𝑖	SYM
ajst-27746	49	15	board	board	NOUN
ajst-27746	49	16	boarding	boarding	NOUN
ajst-27746	49	17	at	at	ADP
ajst-27746	49	18	the	the	DET
ajst-27746	49	19	time	time	NOUN
ajst-27746	49	20	moment	moment	NOUN
ajst-27746	49	21	𝑡	𝑡	PROPN
ajst-27746	49	22	is	be	AUX
ajst-27746	49	23	:	:	PUNCT
ajst-27746	49	24			NOUN
ajst-27746	49	25			SYM
ajst-27746	49	26			NOUN
ajst-27746	49	27			PUNCT
ajst-27746	49	28			NOUN
ajst-27746	49	29			NOUN
ajst-27746	50	1			PUNCT
ajst-27746	50	2			NOUN
ajst-27746	50	3			SYM
ajst-27746	50	4			NOUN
ajst-27746	50	5			PUNCT
ajst-27746	50	6			NOUN
ajst-27746	50	7			NOUN
ajst-27746	50	8			PROPN
ajst-27746	50	9	cos	cos	PROPN
ajst-27746	50	10	,	,	PUNCT
ajst-27746	50	11	sin	sin	NOUN
ajst-27746	50	12	.	.	PUNCT
ajst-27746	51	1	i	i	PRON
ajst-27746	51	2	i	i	PRON
ajst-27746	52	1	i	i	PRON
ajst-27746	52	2	i	i	PRON
ajst-27746	53	1	i	i	PRON
ajst-27746	54	1	i	i	INTJ
ajst-27746	54	2	x	x	VERB
ajst-27746	55	1	t	t	NOUN
ajst-27746	55	2	r	r	NOUN
ajst-27746	55	3	t	t	NOUN
ajst-27746	55	4	t	t	X
ajst-27746	55	5	y	y	PROPN
ajst-27746	55	6	t	t	PROPN
ajst-27746	55	7	r	r	NOUN
ajst-27746	55	8	t	t	PROPN
ajst-27746	55	9	t	t	NOUN
ajst-27746	55	10			X
ajst-27746	55	11			PROPN
ajst-27746	55	12			X
ajst-27746	55	13			VERB
ajst-27746	55	14			NUM
ajst-27746	55	15			NOUN
ajst-27746	55	16	(	(	PUNCT
ajst-27746	55	17	8)	8)	NUM
ajst-27746	55	18			NOUN
ajst-27746	55	19			SYM
ajst-27746	55	20			NOUN
ajst-27746	55	21			SYM
ajst-27746	55	22			NOUN
ajst-27746	55	23			PUNCT
ajst-27746	55	24			NOUN
ajst-27746	55	25			NOUN
ajst-27746	55	26	2	2	NUM
ajst-27746	55	27	2	2	NUM
ajst-27746	55	28	2	2	NUM
ajst-27746	55	29	2	2	NUM
ajst-27746	55	30	2	2	NUM
ajst-27746	55	31	2	2	NUM
ajst-27746	55	32	2	2	NUM
ajst-27746	55	33	2	2	NUM
ajst-27746	55	34	2	2	NUM
ajst-27746	55	35	2	2	NUM
ajst-27746	55	36	,	,	PUNCT
ajst-27746	55	37	,	,	PUNCT
ajst-27746	55	38	,	,	PUNCT
ajst-27746	55	39	,	,	PUNCT
ajst-27746	55	40	,	,	PUNCT
ajst-27746	55	41	,	,	PUNCT
ajst-27746	55	42	x	x	X
ajst-27746	55	43	s	s	PROPN
ajst-27746	55	44	t	t	X
ajst-27746	55	45	x	x	SYM
ajst-27746	56	1	s	s	PROPN
ajst-27746	56	2	t	t	X
ajst-27746	56	3	c	c	PROPN
ajst-27746	56	4	t	t	PROPN
ajst-27746	56	5	s	s	PROPN
ajst-27746	56	6	y	y	PROPN
ajst-27746	56	7	s	s	PROPN
ajst-27746	56	8	t	t	PROPN
ajst-27746	56	9	y	y	PROPN
ajst-27746	56	10	s	s	PROPN
ajst-27746	56	11	t	t	PROPN
ajst-27746	56	12	c	c	PROPN
ajst-27746	56	13	t	t	PROPN
ajst-27746	56	14	s	s	PROPN
ajst-27746	56	15			PROPN
ajst-27746	56	16			ADJ
ajst-27746	56	17			NOUN
ajst-27746	56	18			ADJ
ajst-27746	56	19			ADJ
ajst-27746	56	20			NUM
ajst-27746	56	21			ADJ
ajst-27746	56	22			PROPN
ajst-27746	56	23			NOUN
ajst-27746	56	24			PROPN
ajst-27746	56	25			X
ajst-27746	56	26	(	(	PUNCT
ajst-27746	56	27	9	9	NUM
ajst-27746	56	28	)	)	PUNCT
ajst-27746	56	29	where	where	SCONJ
ajst-27746	56	30	,	,	PUNCT
ajst-27746	56	31	𝑥	𝑥	PROPN
ajst-27746	56	32	𝑠	𝑠	PROPN
ajst-27746	56	33	,	,	PUNCT
ajst-27746	56	34	𝑡	𝑡	PROPN
ajst-27746	56	35	and	and	CCONJ
ajst-27746	56	36	𝑦	𝑦	PROPN
ajst-27746	56	37	𝑠	𝑠	PROPN
ajst-27746	56	38	,	,	PUNCT
ajst-27746	56	39	𝑡	𝑡	PROPN
ajst-27746	56	40	respectively	respectively	ADV
ajst-27746	56	41	represents	represent	VERB
ajst-27746	56	42	the	the	DET
ajst-27746	56	43	horizontal	horizontal	ADJ
ajst-27746	56	44	and	and	CCONJ
ajst-27746	56	45	vertical	vertical	ADJ
ajst-27746	56	46	coordinates	coordinate	NOUN
ajst-27746	56	47	of	of	ADP
ajst-27746	56	48	the	the	DET
ajst-27746	56	49	dragon	dragon	NOUN
ajst-27746	56	50	body	body	NOUN
ajst-27746	56	51	in	in	ADP
ajst-27746	56	52	space	space	NOUN
ajst-27746	56	53	position	position	NOUN
ajst-27746	56	54	𝑠	𝑠	PROPN
ajst-27746	56	55	and	and	CCONJ
ajst-27746	56	56	time	time	NOUN
ajst-27746	56	57	𝑡	𝑡	PROPN
ajst-27746	56	58	,	,	PUNCT
ajst-27746	56	59	is	be	AUX
ajst-27746	56	60	the	the	DET
ajst-27746	56	61	wave	wave	NOUN
ajst-27746	56	62	speed	speed	NOUN
ajst-27746	56	63	,	,	PUNCT
ajst-27746	56	64	𝑐	𝑐	PROPN
ajst-27746	56	65	represents	represent	VERB
ajst-27746	56	66	the	the	DET
ajst-27746	56	67	speed	speed	NOUN
ajst-27746	56	68	of	of	ADP
ajst-27746	56	69	the	the	DET
ajst-27746	56	70	dragon	dragon	NOUN
ajst-27746	56	71	dance	dance	NOUN
ajst-27746	56	72	team	team	NOUN
ajst-27746	56	73	.	.	PUNCT
ajst-27746	57	1	wave	wave	NOUN
ajst-27746	57	2	speed	speed	NOUN
ajst-27746	57	3	𝑐	𝑐	PROPN
ajst-27746	57	4	:	:	PUNCT
ajst-27746	57	5	the	the	DET
ajst-27746	57	6	wave	wave	NOUN
ajst-27746	57	7	speed	speed	NOUN
ajst-27746	57	8	can	can	AUX
ajst-27746	57	9	be	be	AUX
ajst-27746	57	10	estimated	estimate	VERB
ajst-27746	57	11	by	by	ADP
ajst-27746	57	12	the	the	DET
ajst-27746	57	13	speed	speed	NOUN
ajst-27746	57	14	of	of	ADP
ajst-27746	57	15	the	the	DET
ajst-27746	57	16	dragon	dragon	NOUN
ajst-27746	57	17	head	head	NOUN
ajst-27746	57	18	and	and	CCONJ
ajst-27746	57	19	the	the	DET
ajst-27746	57	20	physical	physical	ADJ
ajst-27746	57	21	parameters	parameter	NOUN
ajst-27746	57	22	of	of	ADP
ajst-27746	57	23	the	the	DET
ajst-27746	57	24	dragon	dragon	NOUN
ajst-27746	57	25	body	body	NOUN
ajst-27746	57	26	(	(	PUNCT
ajst-27746	57	27	such	such	ADJ
ajst-27746	57	28	as	as	ADP
ajst-27746	57	29	the	the	DET
ajst-27746	57	30	length	length	NOUN
ajst-27746	57	31	of	of	ADP
ajst-27746	57	32	the	the	DET
ajst-27746	57	33	board	board	NOUN
ajst-27746	57	34	,	,	PUNCT
ajst-27746	57	35	the	the	DET
ajst-27746	57	36	rigidity	rigidity	NOUN
ajst-27746	57	37	of	of	ADP
ajst-27746	57	38	the	the	DET
ajst-27746	57	39	connection	connection	NOUN
ajst-27746	57	40	)	)	PUNCT
ajst-27746	57	41	.	.	PUNCT
ajst-27746	58	1	the	the	DET
ajst-27746	58	2	speed	speed	NOUN
ajst-27746	58	3	of	of	ADP
ajst-27746	58	4	the	the	DET
ajst-27746	58	5	head	head	NOUN
ajst-27746	58	6	determines	determine	VERB
ajst-27746	58	7	the	the	DET
ajst-27746	58	8	propagation	propagation	NOUN
ajst-27746	58	9	speed	speed	NOUN
ajst-27746	58	10	of	of	ADP
ajst-27746	58	11	the	the	DET
ajst-27746	58	12	wave	wave	NOUN
ajst-27746	58	13	,	,	PUNCT
ajst-27746	58	14	and	and	CCONJ
ajst-27746	58	15	the	the	DET
ajst-27746	58	16	wave	wave	NOUN
ajst-27746	58	17	speed	speed	NOUN
ajst-27746	58	18	also	also	ADV
ajst-27746	58	19	affects	affect	VERB
ajst-27746	58	20	the	the	DET
ajst-27746	58	21	overall	overall	ADJ
ajst-27746	58	22	shape	shape	NOUN
ajst-27746	58	23	of	of	ADP
ajst-27746	58	24	the	the	DET
ajst-27746	58	25	dragon	dragon	NOUN
ajst-27746	58	26	dance	dance	NOUN
ajst-27746	58	27	team	team	NOUN
ajst-27746	58	28	when	when	SCONJ
ajst-27746	58	29	it	it	PRON
ajst-27746	58	30	enters	enter	VERB
ajst-27746	58	31	the	the	DET
ajst-27746	58	32	plate	plate	NOUN
ajst-27746	58	33	.	.	PUNCT
ajst-27746	59	1	wave	wave	NOUN
ajst-27746	59	2	equation	equation	NOUN
ajst-27746	59	3	is	be	AUX
ajst-27746	59	4	used	use	VERB
ajst-27746	59	5	here	here	ADV
ajst-27746	59	6	to	to	PART
ajst-27746	59	7	simulate	simulate	VERB
ajst-27746	59	8	the	the	DET
ajst-27746	59	9	wave	wave	NOUN
ajst-27746	59	10	and	and	CCONJ
ajst-27746	59	11	delay	delay	VERB
ajst-27746	59	12	effects	effect	NOUN
ajst-27746	59	13	of	of	ADP
ajst-27746	59	14	the	the	DET
ajst-27746	59	15	dragon	dragon	NOUN
ajst-27746	59	16	's	's	PART
ajst-27746	59	17	body	body	NOUN
ajst-27746	59	18	and	and	CCONJ
ajst-27746	59	19	tail	tail	NOUN
ajst-27746	59	20	.	.	PUNCT
ajst-27746	60	1	as	as	SCONJ
ajst-27746	60	2	shown	show	VERB
ajst-27746	60	3	in	in	ADP
ajst-27746	60	4	figure	figure	NOUN
ajst-27746	60	5	1	1	NUM
ajst-27746	60	6	,	,	PUNCT
ajst-27746	60	7	the	the	DET
ajst-27746	60	8	motion	motion	NOUN
ajst-27746	60	9	of	of	ADP
ajst-27746	60	10	each	each	DET
ajst-27746	60	11	part	part	NOUN
ajst-27746	60	12	of	of	ADP
ajst-27746	60	13	the	the	DET
ajst-27746	60	14	dragon	dragon	NOUN
ajst-27746	60	15	dance	dance	NOUN
ajst-27746	60	16	team	team	NOUN
ajst-27746	60	17	(	(	PUNCT
ajst-27746	60	18	head	head	NOUN
ajst-27746	60	19	,	,	PUNCT
ajst-27746	60	20	body	body	NOUN
ajst-27746	60	21	,	,	PUNCT
ajst-27746	60	22	tail	tail	NOUN
ajst-27746	60	23	)	)	PUNCT
ajst-27746	60	24	in	in	ADP
ajst-27746	60	25	time	time	NOUN
ajst-27746	60	26	𝑡	𝑡	NOUN
ajst-27746	60	27	and	and	CCONJ
ajst-27746	60	28	space	space	NOUN
ajst-27746	60	29	position	position	NOUN
ajst-27746	60	30	𝑠	𝑠	PROPN
ajst-27746	60	31	(	(	PUNCT
ajst-27746	60	32	where	where	SCONJ
ajst-27746	60	33	the	the	DET
ajst-27746	60	34	coordinates	coordinate	NOUN
ajst-27746	60	35	𝑐	𝑐	PRON
ajst-27746	60	36	represent	represent	VERB
ajst-27746	60	37	the	the	DET
ajst-27746	60	38	direction	direction	NOUN
ajst-27746	60	39	of	of	ADP
ajst-27746	60	40	the	the	DET
ajst-27746	60	41	dragon	dragon	NOUN
ajst-27746	60	42	's	's	PART
ajst-27746	60	43	length	length	NOUN
ajst-27746	60	44	)	)	PUNCT
ajst-27746	60	45	can	can	AUX
ajst-27746	60	46	be	be	AUX
ajst-27746	60	47	described	describe	VERB
ajst-27746	60	48	by	by	ADP
ajst-27746	60	49	the	the	DET
ajst-27746	60	50	position	position	NOUN
ajst-27746	60	51	field	field	NOUN
ajst-27746	60	52	𝑥	𝑥	X
ajst-27746	60	53	𝑠	𝑠	PROPN
ajst-27746	60	54	,	,	PUNCT
ajst-27746	60	55	𝑡	𝑡	PROPN
ajst-27746	60	56	and	and	CCONJ
ajst-27746	60	57	𝑦	𝑦	PROPN
ajst-27746	60	58	𝑠	𝑠	PROPN
ajst-27746	60	59	,	,	PUNCT
ajst-27746	60	60	𝑡	𝑡	X
ajst-27746	60	61	[	[	X
ajst-27746	60	62	6	6	NUM
ajst-27746	60	63	]	]	PUNCT
ajst-27746	60	64	.	.	PUNCT
ajst-27746	61	1	the	the	DET
ajst-27746	61	2	equation	equation	NOUN
ajst-27746	61	3	for	for	ADP
ajst-27746	61	4	the	the	DET
ajst-27746	61	5	movement	movement	NOUN
ajst-27746	61	6	of	of	ADP
ajst-27746	61	7	the	the	DET
ajst-27746	61	8	dragon	dragon	NOUN
ajst-27746	61	9	head	head	NOUN
ajst-27746	61	10	is	be	AUX
ajst-27746	61	11	:	:	PUNCT
ajst-27746	61	12	2	2	NUM
ajst-27746	61	13	2	2	NUM
ajst-27746	61	14	(	(	PUNCT
ajst-27746	61	15	)	)	PUNCT
ajst-27746	62	1	d	d	X
ajst-27746	62	2	v	v	X
ajst-27746	62	3	dt	dt	X
ajst-27746	62	4	a	a	PRON
ajst-27746	62	5	a	a	PRON
ajst-27746	62	6			X
ajst-27746	62	7			X
ajst-27746	62	8			PROPN
ajst-27746	62	9			ADJ
ajst-27746	62	10			PROPN
ajst-27746	62	11	(	(	PUNCT
ajst-27746	62	12	10	10	NUM
ajst-27746	62	13	)	)	PUNCT
ajst-27746	62	14	figure	figure	NOUN
ajst-27746	62	15	1	1	NUM
ajst-27746	62	16	.	.	PUNCT
ajst-27746	62	17	example	example	NOUN
ajst-27746	62	18	of	of	ADP
ajst-27746	62	19	the	the	DET
ajst-27746	62	20	position	position	NOUN
ajst-27746	62	21	of	of	ADP
ajst-27746	62	22	the	the	DET
ajst-27746	62	23	disc	disc	NOUN
ajst-27746	62	24	entry	entry	NOUN
ajst-27746	62	25	spiral	spiral	NOUN
ajst-27746	62	26	304	304	NUM
ajst-27746	62	27	after	after	SCONJ
ajst-27746	62	28	it	it	PRON
ajst-27746	62	29	is	be	AUX
ajst-27746	62	30	discretized	discretize	VERB
ajst-27746	62	31	,	,	PUNCT
ajst-27746	62	32	the	the	DET
ajst-27746	62	33	value	value	NOUN
ajst-27746	62	34	of	of	ADP
ajst-27746	62	35	the	the	DET
ajst-27746	62	36	polar	polar	ADJ
ajst-27746	62	37	angle	angle	NOUN
ajst-27746	62	38	𝜃	𝜃	NOUN
ajst-27746	62	39	in	in	ADP
ajst-27746	62	40	each	each	DET
ajst-27746	62	41	time	time	NOUN
ajst-27746	62	42	step	step	NOUN
ajst-27746	62	43	is	be	AUX
ajst-27746	62	44	computed	compute	VERB
ajst-27746	62	45	iteratively	iteratively	ADV
ajst-27746	62	46	by	by	ADP
ajst-27746	62	47	runge	runge	NOUN
ajst-27746	62	48	kutta	kutta	NOUN
ajst-27746	62	49	method	method	NOUN
ajst-27746	62	50	,	,	PUNCT
ajst-27746	62	51	and	and	CCONJ
ajst-27746	62	52	then	then	ADV
ajst-27746	62	53	the	the	DET
ajst-27746	62	54	radial	radial	ADJ
ajst-27746	62	55	distance	distance	NOUN
ajst-27746	62	56	𝑟	𝑟	NOUN
ajst-27746	62	57	and	and	CCONJ
ajst-27746	62	58	position	position	NOUN
ajst-27746	62	59	of	of	ADP
ajst-27746	62	60	the	the	DET
ajst-27746	62	61	faucet	faucet	PROPN
ajst-27746	62	62	𝑥	𝑥	PROPN
ajst-27746	62	63	,	,	PUNCT
ajst-27746	62	64	𝑦	𝑦	PRON
ajst-27746	62	65	are	be	AUX
ajst-27746	62	66	obtained	obtain	VERB
ajst-27746	62	67	.	.	PUNCT
ajst-27746	63	1	2.2	2.2	NUM
ajst-27746	63	2	.	.	PUNCT
ajst-27746	63	3	spiral	spiral	ADJ
ajst-27746	63	4	model	model	NOUN
ajst-27746	63	5	solution	solution	NOUN
ajst-27746	63	6	in	in	ADP
ajst-27746	63	7	order	order	NOUN
ajst-27746	63	8	to	to	PART
ajst-27746	63	9	calculate	calculate	VERB
ajst-27746	63	10	the	the	DET
ajst-27746	63	11	position	position	NOUN
ajst-27746	63	12	and	and	CCONJ
ajst-27746	63	13	velocity	velocity	NOUN
ajst-27746	63	14	of	of	ADP
ajst-27746	63	15	each	each	DET
ajst-27746	63	16	handle	handle	NOUN
ajst-27746	63	17	at	at	ADP
ajst-27746	63	18	the	the	DET
ajst-27746	63	19	moment	moment	NOUN
ajst-27746	63	20	in	in	ADP
ajst-27746	63	21	time	time	NOUN
ajst-27746	63	22	𝑡	𝑡	PROPN
ajst-27746	63	23	,	,	PUNCT
ajst-27746	63	24	we	we	PRON
ajst-27746	63	25	need	need	VERB
ajst-27746	63	26	to	to	PART
ajst-27746	63	27	take	take	VERB
ajst-27746	63	28	the	the	DET
ajst-27746	63	29	derivative	derivative	NOUN
ajst-27746	63	30	of	of	ADP
ajst-27746	63	31	𝑟	𝑟	NOUN
ajst-27746	63	32	0	0	PUNCT
ajst-27746	63	33	and	and	CCONJ
ajst-27746	63	34	𝜃	𝜃	X
ajst-27746	63	35	respectively	respectively	ADV
ajst-27746	63	36	with	with	ADP
ajst-27746	63	37	respect	respect	NOUN
ajst-27746	63	38	to	to	ADP
ajst-27746	63	39	time	time	NOUN
ajst-27746	63	40	𝑡.	𝑡.	VERB
ajst-27746	63	41	the	the	DET
ajst-27746	63	42	steps	step	NOUN
ajst-27746	63	43	are	be	AUX
ajst-27746	63	44	as	as	SCONJ
ajst-27746	63	45	follows	follow	VERB
ajst-27746	63	46	:	:	PUNCT
ajst-27746	63	47	calculation	calculation	NOUN
ajst-27746	63	48	of	of	ADP
ajst-27746	63	49	the	the	DET
ajst-27746	63	50	faucet	faucet	NOUN
ajst-27746	63	51	:	:	PUNCT
ajst-27746	63	52	speed	speed	NOUN
ajst-27746	63	53	is	be	AUX
ajst-27746	63	54	the	the	DET
ajst-27746	63	55	derivative	derivative	NOUN
ajst-27746	63	56	of	of	ADP
ajst-27746	63	57	position	position	NOUN
ajst-27746	63	58	with	with	ADP
ajst-27746	63	59	respect	respect	NOUN
ajst-27746	63	60	to	to	ADP
ajst-27746	63	61	time	time	NOUN
ajst-27746	63	62	.	.	PUNCT
ajst-27746	64	1	velocity	velocity	NOUN
ajst-27746	64	2	in	in	ADP
ajst-27746	64	3	the	the	DET
ajst-27746	64	4	polar	polar	ADJ
ajst-27746	64	5	coordinate	coordinate	NOUN
ajst-27746	64	6	system	system	NOUN
ajst-27746	64	7	can	can	AUX
ajst-27746	64	8	be	be	AUX
ajst-27746	64	9	decomposed	decompose	VERB
ajst-27746	64	10	into	into	ADP
ajst-27746	64	11	radial	radial	ADJ
ajst-27746	64	12	velocity	velocity	NOUN
ajst-27746	64	13	and	and	CCONJ
ajst-27746	64	14	angular	angular	ADJ
ajst-27746	64	15	velocity	velocity	NOUN
ajst-27746	64	16	.	.	PUNCT
ajst-27746	65	1	radial	radial	ADJ
ajst-27746	65	2	velocity	velocity	NOUN
ajst-27746	65	3	,	,	PUNCT
ajst-27746	65	4	radial	radial	ADJ
ajst-27746	65	5	velocity	velocity	NOUN
ajst-27746	65	6	is	be	AUX
ajst-27746	65	7	the	the	DET
ajst-27746	65	8	time	time	NOUN
ajst-27746	65	9	derivative	derivative	NOUN
ajst-27746	65	10	of	of	ADP
ajst-27746	65	11	the	the	DET
ajst-27746	65	12	position	position	NOUN
ajst-27746	65	13	:	:	PUNCT
ajst-27746	65	14	𝑣	𝑣	PRON
ajst-27746	65	15	had	have	AUX
ajst-27746	65	16	,	,	PUNCT
ajst-27746	65	17	which	which	PRON
ajst-27746	65	18	can	can	AUX
ajst-27746	65	19	be	be	AUX
ajst-27746	65	20	obtained	obtain	VERB
ajst-27746	65	21	by	by	ADP
ajst-27746	65	22	simplification	simplification	NOUN
ajst-27746	65	23	𝑣	𝑣	X
ajst-27746	65	24	.	.	PUNCT
ajst-27746	66	1	since	since	SCONJ
ajst-27746	66	2	𝑟	𝑟	X
ajst-27746	66	3	𝜃	𝜃	X
ajst-27746	66	4	it	it	PRON
ajst-27746	66	5	changes	change	VERB
ajst-27746	66	6	over	over	ADP
ajst-27746	66	7	time	time	NOUN
ajst-27746	66	8	,	,	PUNCT
ajst-27746	66	9	we	we	PRON
ajst-27746	66	10	need	need	VERB
ajst-27746	66	11	to	to	PART
ajst-27746	66	12	update	update	VERB
ajst-27746	66	13	recursively	recursively	ADV
ajst-27746	66	14	according	accord	VERB
ajst-27746	66	15	to	to	ADP
ajst-27746	66	16	the	the	DET
ajst-27746	66	17	relationship	relationship	NOUN
ajst-27746	66	18	between	between	ADP
ajst-27746	66	19	𝜃	𝜃	NOUN
ajst-27746	66	20	and	and	CCONJ
ajst-27746	66	21	𝑡.	𝑡.	VERB
ajst-27746	66	22	total	total	ADJ
ajst-27746	66	23	velocity	velocity	NOUN
ajst-27746	66	24	:	:	PUNCT
ajst-27746	66	25	the	the	DET
ajst-27746	66	26	total	total	ADJ
ajst-27746	66	27	velocity	velocity	NOUN
ajst-27746	66	28	of	of	ADP
ajst-27746	66	29	the	the	DET
ajst-27746	66	30	faucet	faucet	NOUN
ajst-27746	66	31	is	be	AUX
ajst-27746	66	32	the	the	DET
ajst-27746	66	33	combined	combined	ADJ
ajst-27746	66	34	velocity	velocity	NOUN
ajst-27746	66	35	of	of	ADP
ajst-27746	66	36	the	the	DET
ajst-27746	66	37	radial	radial	ADJ
ajst-27746	66	38	velocity	velocity	NOUN
ajst-27746	66	39	and	and	CCONJ
ajst-27746	66	40	the	the	DET
ajst-27746	66	41	tangential	tangential	ADJ
ajst-27746	66	42	velocity	velocity	NOUN
ajst-27746	66	43	:	:	PUNCT
ajst-27746	66	44			NOUN
ajst-27746	66	45			SYM
ajst-27746	66	46	2	2	NUM
ajst-27746	66	47	2	2	NUM
ajst-27746	66	48	head	head	NOUN
ajst-27746	66	49	rv	rv	PROPN
ajst-27746	66	50	t	t	PROPN
ajst-27746	66	51	v	v	PROPN
ajst-27746	66	52	v	v	PROPN
ajst-27746	66	53			X
ajst-27746	66	54	(	(	PUNCT
ajst-27746	66	55	11	11	NUM
ajst-27746	66	56	)	)	PUNCT
ajst-27746	66	57	calculation	calculation	NOUN
ajst-27746	66	58	of	of	ADP
ajst-27746	66	59	the	the	DET
ajst-27746	66	60	speed	speed	NOUN
ajst-27746	66	61	of	of	ADP
ajst-27746	66	62	the	the	DET
ajst-27746	66	63	dragon	dragon	NOUN
ajst-27746	66	64	body	body	NOUN
ajst-27746	66	65	and	and	CCONJ
ajst-27746	66	66	tail	tail	NOUN
ajst-27746	66	67	:	:	PUNCT
ajst-27746	66	68	similarly	similarly	ADV
ajst-27746	66	69	,	,	PUNCT
ajst-27746	66	70	the	the	DET
ajst-27746	66	71	speed	speed	NOUN
ajst-27746	66	72	of	of	ADP
ajst-27746	66	73	the	the	DET
ajst-27746	66	74	𝑖	𝑖	PROPN
ajst-27746	66	75	section	section	NOUN
ajst-27746	66	76	board	board	NOUN
ajst-27746	66	77	is	be	AUX
ajst-27746	66	78	also	also	ADV
ajst-27746	66	79	synthesized	synthesize	VERB
ajst-27746	66	80	from	from	ADP
ajst-27746	66	81	the	the	DET
ajst-27746	66	82	radial	radial	ADJ
ajst-27746	66	83	and	and	CCONJ
ajst-27746	66	84	tangential	tangential	ADJ
ajst-27746	66	85	velocity	velocity	NOUN
ajst-27746	66	86	,	,	PUNCT
ajst-27746	66	87	the	the	DET
ajst-27746	66	88	formula	formula	NOUN
ajst-27746	66	89	is	be	AUX
ajst-27746	66	90	similar	similar	ADJ
ajst-27746	66	91	to	to	ADP
ajst-27746	66	92	the	the	DET
ajst-27746	66	93	speed	speed	NOUN
ajst-27746	66	94	of	of	ADP
ajst-27746	66	95	the	the	DET
ajst-27746	66	96	dragon	dragon	NOUN
ajst-27746	66	97	head	head	NOUN
ajst-27746	66	98	,	,	PUNCT
ajst-27746	66	99	just	just	ADV
ajst-27746	66	100	replace	replace	VERB
ajst-27746	66	101	the	the	DET
ajst-27746	66	102	radius	radius	NOUN
ajst-27746	66	103	𝑟	𝑟	CCONJ
ajst-27746	66	104	𝑡	𝑡	NOUN
ajst-27746	66	105	and	and	CCONJ
ajst-27746	66	106	angle	angle	NOUN
ajst-27746	66	107	with	with	ADP
ajst-27746	66	108	the	the	DET
ajst-27746	66	109	corresponding	corresponding	ADJ
ajst-27746	66	110	sum	sum	NOUN
ajst-27746	66	111	𝜃	𝜃	X
ajst-27746	66	112	𝑡	𝑡	NOUN
ajst-27746	66	113	.	.	PUNCT
ajst-27746	67	1	but	but	CCONJ
ajst-27746	67	2	pay	pay	VERB
ajst-27746	67	3	attention	attention	NOUN
ajst-27746	67	4	to	to	ADP
ajst-27746	67	5	the	the	DET
ajst-27746	67	6	additional	additional	ADJ
ajst-27746	67	7	lag	lag	NOUN
ajst-27746	67	8	of	of	ADP
ajst-27746	67	9	the	the	DET
ajst-27746	67	10	handle	handle	NOUN
ajst-27746	67	11	behind	behind	ADP
ajst-27746	67	12	the	the	DET
ajst-27746	67	13	dragon	dragon	NOUN
ajst-27746	67	14	's	's	PART
ajst-27746	67	15	tail	tail	NOUN
ajst-27746	67	16	.	.	PUNCT
ajst-27746	68	1	boundary	boundary	ADJ
ajst-27746	68	2	conditions	condition	NOUN
ajst-27746	68	3	and	and	CCONJ
ajst-27746	68	4	initial	initial	ADJ
ajst-27746	68	5	conditions	condition	NOUN
ajst-27746	68	6	:	:	PUNCT
ajst-27746	68	7	the	the	DET
ajst-27746	68	8	boundary	boundary	ADJ
ajst-27746	68	9	conditions	condition	NOUN
ajst-27746	68	10	of	of	ADP
ajst-27746	68	11	the	the	DET
ajst-27746	68	12	faucet	faucet	NOUN
ajst-27746	68	13	:	:	PUNCT
ajst-27746	68	14	the	the	DET
ajst-27746	68	15	speed	speed	NOUN
ajst-27746	68	16	1	1	NUM
ajst-27746	68	17	m	m	NOUN
ajst-27746	68	18	/	/	SYM
ajst-27746	68	19	s	s	X
ajst-27746	68	20	at	at	ADP
ajst-27746	68	21	which	which	PRON
ajst-27746	68	22	the	the	DET
ajst-27746	68	23	handle	handle	NOUN
ajst-27746	68	24	of	of	ADP
ajst-27746	68	25	the	the	DET
ajst-27746	68	26	faucet	faucet	NOUN
ajst-27746	68	27	moves	move	NOUN
ajst-27746	68	28	along	along	ADP
ajst-27746	68	29	the	the	DET
ajst-27746	68	30	helix	helix	NOUN
ajst-27746	68	31	,	,	PUNCT
ajst-27746	68	32	and	and	CCONJ
ajst-27746	68	33	the	the	DET
ajst-27746	68	34	position	position	NOUN
ajst-27746	68	35	is	be	AUX
ajst-27746	68	36	controlled	control	VERB
ajst-27746	68	37	by	by	ADP
ajst-27746	68	38	the	the	DET
ajst-27746	68	39	equation	equation	NOUN
ajst-27746	68	40	of	of	ADP
ajst-27746	68	41	the	the	DET
ajst-27746	68	42	helix	helix	NOUN
ajst-27746	68	43	.	.	PUNCT
ajst-27746	69	1	at	at	ADP
ajst-27746	69	2	this	this	DET
ajst-27746	69	3	point	point	NOUN
ajst-27746	69	4	:	:	PUNCT
ajst-27746	69	5			NOUN
ajst-27746	69	6			PUNCT
ajst-27746	69	7			PROPN
ajst-27746	69	8			NOUN
ajst-27746	69	9			PUNCT
ajst-27746	69	10			PROPN
ajst-27746	69	11			NOUN
ajst-27746	70	1			PUNCT
ajst-27746	70	2			NOUN
ajst-27746	70	3			PUNCT
ajst-27746	70	4			NOUN
ajst-27746	70	5			NOUN
ajst-27746	71	1			PUNCT
ajst-27746	71	2			PROPN
ajst-27746	71	3			NOUN
ajst-27746	71	4			PROPN
ajst-27746	71	5	0	0	NUM
ajst-27746	71	6	,	,	PUNCT
ajst-27746	71	7	cos	cos	PROPN
ajst-27746	71	8	0	0	PROPN
ajst-27746	71	9	,	,	PUNCT
ajst-27746	71	10	sin	sin	NOUN
ajst-27746	71	11	x	x	X
ajst-27746	71	12	t	t	NOUN
ajst-27746	71	13	r	r	NOUN
ajst-27746	71	14	t	t	PROPN
ajst-27746	71	15	t	t	X
ajst-27746	71	16	y	y	PROPN
ajst-27746	71	17	t	t	PROPN
ajst-27746	71	18	r	r	NOUN
ajst-27746	71	19	t	t	PROPN
ajst-27746	71	20	t	t	NOUN
ajst-27746	71	21			X
ajst-27746	71	22			X
ajst-27746	71	23			PROPN
ajst-27746	71	24			PROPN
ajst-27746	71	25			X
ajst-27746	71	26			VERB
ajst-27746	71	27			NUM
ajst-27746	71	28			NOUN
ajst-27746	71	29	(	(	PUNCT
ajst-27746	71	30	12	12	NUM
ajst-27746	71	31	)	)	PUNCT
ajst-27746	71	32	among	among	ADP
ajst-27746	71	33	them	they	PRON
ajst-27746	71	34	,	,	PUNCT
ajst-27746	71	35	𝜃	𝜃	NUM
ajst-27746	71	36	𝑡	𝑡	NOUN
ajst-27746	71	37	is	be	AUX
ajst-27746	71	38	the	the	DET
ajst-27746	71	39	polar	polar	ADJ
ajst-27746	71	40	angle	angle	NOUN
ajst-27746	71	41	of	of	ADP
ajst-27746	71	42	the	the	DET
ajst-27746	71	43	time	time	NOUN
ajst-27746	71	44	moment	moment	NOUN
ajst-27746	71	45	faucet	faucet	PROPN
ajst-27746	71	46	𝑡	𝑡	PROPN
ajst-27746	71	47	.	.	PUNCT
ajst-27746	72	1	from	from	ADP
ajst-27746	72	2	the	the	DET
ajst-27746	72	3	speed	speed	NOUN
ajst-27746	72	4	of	of	ADP
ajst-27746	72	5	the	the	DET
ajst-27746	72	6	faucet	faucet	NOUN
ajst-27746	72	7	𝑣head	𝑣head	VERB
ajst-27746	72	8	1	1	NUM
ajst-27746	72	9	m	m	PROPN
ajst-27746	72	10	/	/	SYM
ajst-27746	72	11	s	s	PROPN
ajst-27746	72	12	,	,	PUNCT
ajst-27746	72	13	the	the	DET
ajst-27746	72	14	angular	angular	ADJ
ajst-27746	72	15	velocity	velocity	NOUN
ajst-27746	72	16	can	can	AUX
ajst-27746	72	17	be	be	AUX
ajst-27746	72	18	obtained	obtain	VERB
ajst-27746	72	19	:	:	PUNCT
ajst-27746	72	20			PROPN
ajst-27746	72	21			PROPN
ajst-27746	73	1			PROPN
ajst-27746	73	2			NOUN
ajst-27746	73	3	head	head	NOUN
ajst-27746	73	4	0	0	NUM
ajst-27746	73	5	,	,	PUNCT
ajst-27746	73	6	0	0	NUM
ajst-27746	73	7	vd	vd	NOUN
ajst-27746	73	8	dt	dt	X
ajst-27746	73	9	r	r	NOUN
ajst-27746	73	10	t	t	NOUN
ajst-27746	73	11			X
ajst-27746	73	12			X
ajst-27746	73	13			PROPN
ajst-27746	73	14			X
ajst-27746	74	1			PROPN
ajst-27746	75	1			PROPN
ajst-27746	75	2	(	(	PUNCT
ajst-27746	75	3	13	13	NUM
ajst-27746	75	4	)	)	PUNCT
ajst-27746	75	5	this	this	PRON
ajst-27746	75	6	can	can	AUX
ajst-27746	75	7	be	be	AUX
ajst-27746	75	8	obtained	obtain	VERB
ajst-27746	75	9	from	from	ADP
ajst-27746	75	10	these	these	DET
ajst-27746	75	11	assumptions	assumption	NOUN
ajst-27746	75	12	𝜃	𝜃	NUM
ajst-27746	75	13	𝑡	𝑡	NOUN
ajst-27746	75	14	.	.	PUNCT
ajst-27746	76	1	the	the	DET
ajst-27746	76	2	boundary	boundary	ADJ
ajst-27746	76	3	condition	condition	NOUN
ajst-27746	76	4	of	of	ADP
ajst-27746	76	5	the	the	DET
ajst-27746	76	6	dragon	dragon	NOUN
ajst-27746	76	7	's	's	PART
ajst-27746	76	8	tail	tail	NOUN
ajst-27746	76	9	:	:	PUNCT
ajst-27746	76	10	the	the	DET
ajst-27746	76	11	movement	movement	NOUN
ajst-27746	76	12	of	of	ADP
ajst-27746	76	13	the	the	DET
ajst-27746	76	14	dragon	dragon	NOUN
ajst-27746	76	15	's	's	PART
ajst-27746	76	16	tail	tail	NOUN
ajst-27746	76	17	lags	lag	VERB
ajst-27746	76	18	behind	behind	ADP
ajst-27746	76	19	the	the	DET
ajst-27746	76	20	movement	movement	NOUN
ajst-27746	76	21	of	of	ADP
ajst-27746	76	22	the	the	DET
ajst-27746	76	23	dragon	dragon	NOUN
ajst-27746	76	24	and	and	CCONJ
ajst-27746	76	25	is	be	AUX
ajst-27746	76	26	affected	affect	VERB
ajst-27746	76	27	by	by	ADP
ajst-27746	76	28	the	the	DET
ajst-27746	76	29	fluctuations	fluctuation	NOUN
ajst-27746	76	30	transmitted	transmit	VERB
ajst-27746	76	31	by	by	ADP
ajst-27746	76	32	the	the	DET
ajst-27746	76	33	dragon	dragon	NOUN
ajst-27746	76	34	's	's	PART
ajst-27746	76	35	body	body	NOUN
ajst-27746	76	36	.	.	PUNCT
ajst-27746	77	1	its	its	PRON
ajst-27746	77	2	position	position	NOUN
ajst-27746	77	3	can	can	AUX
ajst-27746	77	4	be	be	AUX
ajst-27746	77	5	solved	solve	VERB
ajst-27746	77	6	by	by	ADP
ajst-27746	77	7	the	the	DET
ajst-27746	77	8	wave	wave	NOUN
ajst-27746	77	9	equation	equation	NOUN
ajst-27746	77	10	.	.	PUNCT
ajst-27746	78	1	initial	initial	ADJ
ajst-27746	78	2	condition	condition	NOUN
ajst-27746	78	3	:	:	PUNCT
ajst-27746	78	4	at	at	ADP
ajst-27746	78	5	time	time	NOUN
ajst-27746	78	6	𝑡	𝑡	PROPN
ajst-27746	78	7	0	0	NUM
ajst-27746	78	8	,	,	PUNCT
ajst-27746	78	9	the	the	DET
ajst-27746	78	10	whole	whole	ADJ
ajst-27746	78	11	dragon	dragon	NOUN
ajst-27746	78	12	is	be	AUX
ajst-27746	78	13	in	in	ADP
ajst-27746	78	14	the	the	DET
ajst-27746	78	15	form	form	NOUN
ajst-27746	78	16	of	of	ADP
ajst-27746	78	17	the	the	DET
ajst-27746	78	18	initial	initial	ADJ
ajst-27746	78	19	helix	helix	NOUN
ajst-27746	78	20	,	,	PUNCT
ajst-27746	78	21	and	and	CCONJ
ajst-27746	78	22	the	the	DET
ajst-27746	78	23	initial	initial	ADJ
ajst-27746	78	24	velocity	velocity	NOUN
ajst-27746	78	25	is	be	AUX
ajst-27746	78	26	zero	zero	NUM
ajst-27746	78	27	.	.	PUNCT
ajst-27746	79	1			NOUN
ajst-27746	79	2			PUNCT
ajst-27746	79	3			NOUN
ajst-27746	80	1			NOUN
ajst-27746	80	2			PUNCT
ajst-27746	80	3			PROPN
ajst-27746	80	4			NOUN
ajst-27746	81	1			PUNCT
ajst-27746	81	2			NOUN
ajst-27746	81	3			PUNCT
ajst-27746	81	4			NOUN
ajst-27746	81	5			NOUN
ajst-27746	81	6			PUNCT
ajst-27746	81	7			PROPN
ajst-27746	81	8			NOUN
ajst-27746	82	1			PUNCT
ajst-27746	82	2			NOUN
ajst-27746	82	3			PUNCT
ajst-27746	82	4			NOUN
ajst-27746	82	5			PROPN
ajst-27746	82	6	,	,	PUNCT
ajst-27746	82	7	0	0	NUM
ajst-27746	82	8	cos	cos	PROPN
ajst-27746	82	9	,	,	PUNCT
ajst-27746	82	10	,	,	PUNCT
ajst-27746	82	11	0	0	NUM
ajst-27746	82	12	sin	sin	NOUN
ajst-27746	82	13	,	,	PUNCT
ajst-27746	82	14	0	0	NUM
ajst-27746	82	15	,	,	PUNCT
ajst-27746	82	16	0	0	NUM
ajst-27746	82	17	0	0	NUM
ajst-27746	82	18	,	,	PUNCT
ajst-27746	82	19	0	0	NUM
ajst-27746	82	20	s	s	PART
ajst-27746	82	21	r	r	NOUN
ajst-27746	82	22	s	s	NOUN
ajst-27746	82	23	s	s	X
ajst-27746	82	24	y	y	NOUN
ajst-27746	82	25	s	s	NOUN
ajst-27746	82	26	r	r	NOUN
ajst-27746	82	27	s	s	NOUN
ajst-27746	82	28	s	s	X
ajst-27746	82	29	x	x	SYM
ajst-27746	82	30	s	s	PROPN
ajst-27746	82	31	y	y	PROPN
ajst-27746	82	32	s	s	PROPN
ajst-27746	82	33	t	t	PROPN
ajst-27746	82	34	t	t	NOUN
ajst-27746	82	35			PROPN
ajst-27746	82	36			PROPN
ajst-27746	82	37			PROPN
ajst-27746	82	38			PROPN
ajst-27746	82	39			PROPN
ajst-27746	82	40			ADJ
ajst-27746	82	41			PROPN
ajst-27746	82	42			PROPN
ajst-27746	82	43			PROPN
ajst-27746	82	44			ADJ
ajst-27746	82	45			NOUN
ajst-27746	82	46	(	(	PUNCT
ajst-27746	82	47	14	14	NUM
ajst-27746	82	48	)	)	PUNCT
ajst-27746	82	49	in	in	ADP
ajst-27746	82	50	order	order	NOUN
ajst-27746	82	51	to	to	PART
ajst-27746	82	52	solve	solve	VERB
ajst-27746	82	53	the	the	DET
ajst-27746	82	54	partial	partial	ADJ
ajst-27746	82	55	differential	differential	NOUN
ajst-27746	82	56	equation	equation	NOUN
ajst-27746	82	57	of	of	ADP
ajst-27746	82	58	the	the	DET
ajst-27746	82	59	dragon	dragon	NOUN
ajst-27746	82	60	dance	dance	PROPN
ajst-27746	82	61	team	team	NOUN
ajst-27746	82	62	movement	movement	NOUN
ajst-27746	82	63	,	,	PUNCT
ajst-27746	82	64	we	we	PRON
ajst-27746	82	65	use	use	VERB
ajst-27746	82	66	the	the	DET
ajst-27746	82	67	finite	finite	ADJ
ajst-27746	82	68	difference	difference	NOUN
ajst-27746	82	69	method	method	NOUN
ajst-27746	82	70	to	to	PART
ajst-27746	82	71	discretize	discretize	VERB
ajst-27746	82	72	and	and	CCONJ
ajst-27746	82	73	numerically	numerically	ADV
ajst-27746	82	74	integrate	integrate	VERB
ajst-27746	82	75	the	the	DET
ajst-27746	82	76	partial	partial	ADJ
ajst-27746	82	77	differential	differential	NOUN
ajst-27746	82	78	equation	equation	NOUN
ajst-27746	82	79	,	,	PUNCT
ajst-27746	82	80	and	and	CCONJ
ajst-27746	82	81	gradually	gradually	ADV
ajst-27746	82	82	solve	solve	VERB
ajst-27746	82	83	the	the	DET
ajst-27746	82	84	position	position	NOUN
ajst-27746	82	85	and	and	CCONJ
ajst-27746	82	86	speed	speed	NOUN
ajst-27746	82	87	of	of	ADP
ajst-27746	82	88	each	each	DET
ajst-27746	82	89	moment	moment	NOUN
ajst-27746	82	90	[	[	X
ajst-27746	82	91	7	7	NUM
ajst-27746	82	92	]	]	PUNCT
ajst-27746	82	93	.	.	PUNCT
ajst-27746	83	1	this	this	DET
ajst-27746	83	2	method	method	NOUN
ajst-27746	83	3	discretizes	discretize	VERB
ajst-27746	83	4	the	the	DET
ajst-27746	83	5	continuous	continuous	ADJ
ajst-27746	83	6	space	space	NOUN
ajst-27746	83	7	and	and	CCONJ
ajst-27746	83	8	time	time	NOUN
ajst-27746	83	9	and	and	CCONJ
ajst-27746	83	10	converts	convert	VERB
ajst-27746	83	11	the	the	DET
ajst-27746	83	12	pde	pde	NOUN
ajst-27746	83	13	into	into	ADP
ajst-27746	83	14	a	a	DET
ajst-27746	83	15	difference	difference	NOUN
ajst-27746	83	16	equation	equation	NOUN
ajst-27746	83	17	that	that	PRON
ajst-27746	83	18	can	can	AUX
ajst-27746	83	19	be	be	AUX
ajst-27746	83	20	solved	solve	VERB
ajst-27746	83	21	by	by	ADP
ajst-27746	83	22	a	a	DET
ajst-27746	83	23	computer	computer	NOUN
ajst-27746	83	24	algorithm	algorithm	NOUN
ajst-27746	83	25	to	to	PART
ajst-27746	83	26	get	get	VERB
ajst-27746	83	27	the	the	DET
ajst-27746	83	28	position	position	NOUN
ajst-27746	83	29	and	and	CCONJ
ajst-27746	83	30	velocity	velocity	NOUN
ajst-27746	83	31	of	of	ADP
ajst-27746	83	32	each	each	DET
ajst-27746	83	33	moment	moment	NOUN
ajst-27746	83	34	by	by	ADP
ajst-27746	83	35	discretizing	discretizing	ADJ
ajst-27746	83	36	time	time	NOUN
ajst-27746	83	37	and	and	CCONJ
ajst-27746	83	38	space	space	NOUN
ajst-27746	83	39	,	,	PUNCT
ajst-27746	83	40	an	an	DET
ajst-27746	83	41	approximate	approximate	ADJ
ajst-27746	83	42	equation	equation	NOUN
ajst-27746	83	43	in	in	ADP
ajst-27746	83	44	the	the	DET
ajst-27746	83	45	following	follow	VERB
ajst-27746	83	46	format	format	NOUN
ajst-27746	83	47	is	be	AUX
ajst-27746	83	48	obtained	obtain	VERB
ajst-27746	83	49	using	use	VERB
ajst-27746	83	50	the	the	DET
ajst-27746	83	51	finite	finite	ADJ
ajst-27746	83	52	difference	difference	NOUN
ajst-27746	83	53	method	method	NOUN
ajst-27746	83	54	:	:	PUNCT
ajst-27746	84	1			NOUN
ajst-27746	84	2			SYM
ajst-27746	84	3	2	2	NUM
ajst-27746	84	4	1	1	NUM
ajst-27746	84	5	1	1	NUM
ajst-27746	84	6	1	1	NUM
ajst-27746	84	7	1	1	NUM
ajst-27746	84	8	δ	δ	NOUN
ajst-27746	84	9	2	2	NUM
ajst-27746	84	10	2	2	NUM
ajst-27746	84	11	δ	δ	PROPN
ajst-27746	84	12	n	n	CCONJ
ajst-27746	84	13	n	n	CCONJ
ajst-27746	84	14	n	n	CCONJ
ajst-27746	84	15	n	n	CCONJ
ajst-27746	84	16	n	n	CCONJ
ajst-27746	84	17	n	n	NOUN
ajst-27746	84	18	i	i	PRON
ajst-27746	85	1	i	i	PRON
ajst-27746	85	2	i	i	PRON
ajst-27746	86	1	i	i	PRON
ajst-27746	86	2	i	i	PRON
ajst-27746	87	1	i	i	VERB
ajst-27746	87	2	c	c	VERB
ajst-27746	88	1	t	t	X
ajst-27746	88	2	u	u	X
ajst-27746	88	3	u	u	X
ajst-27746	88	4	u	u	X
ajst-27746	88	5	u	u	X
ajst-27746	88	6	u	u	X
ajst-27746	88	7	u	u	X
ajst-27746	88	8	x	x	X
ajst-27746	88	9			PROPN
ajst-27746	88	10			PROPN
ajst-27746	88	11			VERB
ajst-27746	88	12			PROPN
ajst-27746	88	13			PROPN
ajst-27746	88	14			X
ajst-27746	89	1			PROPN
ajst-27746	89	2			VERB
ajst-27746	89	3			NOUN
ajst-27746	89	4			PROPN
ajst-27746	89	5			CCONJ
ajst-27746	89	6			PROPN
ajst-27746	89	7			NOUN
ajst-27746	89	8	(	(	PUNCT
ajst-27746	89	9	15	15	NUM
ajst-27746	89	10	)	)	PUNCT
ajst-27746	89	11	where	where	SCONJ
ajst-27746	89	12	:	:	PUNCT
ajst-27746	89	13	𝑢	𝑢	PRON
ajst-27746	89	14	is	be	AUX
ajst-27746	89	15	the	the	DET
ajst-27746	89	16	displacement	displacement	NOUN
ajst-27746	89	17	of	of	ADP
ajst-27746	89	18	the	the	DET
ajst-27746	89	19	section	section	NOUN
ajst-27746	89	20	board	board	PROPN
ajst-27746	89	21	𝑖	𝑖	ADP
ajst-27746	89	22	boarding	boarding	NOUN
ajst-27746	89	23	in	in	ADP
ajst-27746	89	24	the	the	DET
ajst-27746	89	25	first	first	ADJ
ajst-27746	89	26	time	time	NOUN
ajst-27746	89	27	step	step	NOUN
ajst-27746	89	28	𝑛	𝑛	PROPN
ajst-27746	89	29	;	;	PUNCT
ajst-27746	89	30	𝛥𝑡	𝛥𝑡	PROPN
ajst-27746	89	31	is	be	AUX
ajst-27746	89	32	the	the	DET
ajst-27746	89	33	time	time	NOUN
ajst-27746	89	34	step	step	NOUN
ajst-27746	89	35	length	length	NOUN
ajst-27746	89	36	,	,	PUNCT
ajst-27746	90	1	𝛥𝑥	𝛥𝑥	PROPN
ajst-27746	90	2	is	be	AUX
ajst-27746	90	3	the	the	DET
ajst-27746	90	4	space	space	NOUN
ajst-27746	90	5	step	step	NOUN
ajst-27746	90	6	length	length	NOUN
ajst-27746	90	7	.	.	PUNCT
ajst-27746	91	1	3	3	X
ajst-27746	91	2	.	.	X
ajst-27746	91	3	dynamic	dynamic	ADJ
ajst-27746	91	4	collision	collision	NOUN
ajst-27746	91	5	detection	detection	NOUN
ajst-27746	91	6	model	model	NOUN
ajst-27746	91	7	based	base	VERB
ajst-27746	91	8	on	on	ADP
ajst-27746	91	9	the	the	DET
ajst-27746	91	10	spiral	spiral	ADJ
ajst-27746	91	11	motion	motion	NOUN
ajst-27746	91	12	model	model	NOUN
ajst-27746	91	13	established	establish	VERB
ajst-27746	91	14	above	above	ADV
ajst-27746	91	15	,	,	PUNCT
ajst-27746	91	16	this	this	DET
ajst-27746	91	17	chapter	chapter	NOUN
ajst-27746	91	18	needs	need	VERB
ajst-27746	91	19	to	to	PART
ajst-27746	91	20	determine	determine	VERB
ajst-27746	91	21	the	the	DET
ajst-27746	91	22	end	end	NOUN
ajst-27746	91	23	time	time	NOUN
ajst-27746	91	24	of	of	ADP
ajst-27746	91	25	the	the	DET
ajst-27746	91	26	dragon	dragon	NOUN
ajst-27746	91	27	dance	dance	PROPN
ajst-27746	91	28	team	team	NOUN
ajst-27746	91	29	's	's	PART
ajst-27746	91	30	disc	disc	NOUN
ajst-27746	91	31	entry	entry	NOUN
ajst-27746	91	32	,	,	PUNCT
ajst-27746	91	33	so	so	SCONJ
ajst-27746	91	34	that	that	SCONJ
ajst-27746	91	35	there	there	PRON
ajst-27746	91	36	is	be	VERB
ajst-27746	91	37	no	no	DET
ajst-27746	91	38	collision	collision	NOUN
ajst-27746	91	39	between	between	ADP
ajst-27746	91	40	boards	board	NOUN
ajst-27746	91	41	.	.	PUNCT
ajst-27746	92	1	as	as	SCONJ
ajst-27746	92	2	shown	show	VERB
ajst-27746	92	3	in	in	ADP
ajst-27746	92	4	figure	figure	NOUN
ajst-27746	92	5	2	2	NUM
ajst-27746	92	6	,	,	PUNCT
ajst-27746	92	7	by	by	ADP
ajst-27746	92	8	simulating	simulate	VERB
ajst-27746	92	9	the	the	DET
ajst-27746	92	10	relative	relative	ADJ
ajst-27746	92	11	motion	motion	NOUN
ajst-27746	92	12	trajectory	trajectory	NOUN
ajst-27746	92	13	between	between	ADP
ajst-27746	92	14	boards	board	NOUN
ajst-27746	92	15	and	and	CCONJ
ajst-27746	92	16	boards	board	NOUN
ajst-27746	92	17	,	,	PUNCT
ajst-27746	92	18	the	the	DET
ajst-27746	92	19	limit	limit	NOUN
ajst-27746	92	20	time	time	NOUN
ajst-27746	92	21	of	of	ADP
ajst-27746	92	22	the	the	DET
ajst-27746	92	23	dragon	dragon	NOUN
ajst-27746	92	24	dance	dance	NOUN
ajst-27746	92	25	team	team	NOUN
ajst-27746	92	26	's	's	PART
ajst-27746	92	27	disc	disc	NOUN
ajst-27746	92	28	entry	entry	NOUN
ajst-27746	92	29	is	be	AUX
ajst-27746	92	30	found	find	VERB
ajst-27746	92	31	without	without	ADP
ajst-27746	92	32	collision	collision	NOUN
ajst-27746	92	33	.	.	PUNCT
ajst-27746	93	1	step	step	NOUN
ajst-27746	93	2	1	1	NUM
ajst-27746	93	3	:	:	PUNCT
ajst-27746	93	4	calculate	calculate	VERB
ajst-27746	93	5	the	the	DET
ajst-27746	93	6	distance	distance	NOUN
ajst-27746	93	7	between	between	ADP
ajst-27746	93	8	adjacent	adjacent	ADJ
ajst-27746	93	9	nodes	node	NOUN
ajst-27746	93	10	.	.	PUNCT
ajst-27746	94	1	we	we	PRON
ajst-27746	94	2	need	need	VERB
ajst-27746	94	3	to	to	PART
ajst-27746	94	4	calculate	calculate	VERB
ajst-27746	94	5	the	the	DET
ajst-27746	94	6	distance	distance	NOUN
ajst-27746	94	7	between	between	ADP
ajst-27746	94	8	each	each	DET
ajst-27746	94	9	pair	pair	NOUN
ajst-27746	94	10	of	of	ADP
ajst-27746	94	11	adjacent	adjacent	ADJ
ajst-27746	94	12	nodes	node	NOUN
ajst-27746	94	13	𝑖	𝑖	NOUN
ajst-27746	94	14	and	and	CCONJ
ajst-27746	94	15	𝑖	𝑖	DET
ajst-27746	94	16	1	1	NUM
ajst-27746	94	17	.	.	PUNCT
ajst-27746	95	1	the	the	DET
ajst-27746	95	2	distance	distance	NOUN
ajst-27746	95	3	formula	formula	NOUN
ajst-27746	95	4	based	base	VERB
ajst-27746	95	5	on	on	ADP
ajst-27746	95	6	polar	polar	ADJ
ajst-27746	95	7	coordinates	coordinate	NOUN
ajst-27746	95	8	is	be	AUX
ajst-27746	95	9	:	:	PUNCT
ajst-27746	95	10			NOUN
ajst-27746	95	11			SYM
ajst-27746	95	12			NOUN
ajst-27746	95	13			PUNCT
ajst-27746	95	14			NOUN
ajst-27746	95	15			NOUN
ajst-27746	96	1			PUNCT
ajst-27746	96	2			NOUN
ajst-27746	96	3			SYM
ajst-27746	96	4			NOUN
ajst-27746	96	5			PUNCT
ajst-27746	96	6			NOUN
ajst-27746	97	1			NOUN
ajst-27746	97	2			PROPN
ajst-27746	97	3	22	22	NUM
ajst-27746	97	4	1	1	NUM
ajst-27746	97	5	1i	1i	NOUN
ajst-27746	98	1	i	i	PRON
ajst-27746	98	2	i	i	PRON
ajst-27746	99	1	i	i	PRON
ajst-27746	99	2	i	i	PRON
ajst-27746	100	1	i	i	PROPN
ajst-27746	100	2	d	d	PROPN
ajst-27746	100	3	t	t	PROPN
ajst-27746	101	1	r	r	NOUN
ajst-27746	101	2	t	t	NOUN
ajst-27746	101	3	r	r	NOUN
ajst-27746	101	4	t	t	NOUN
ajst-27746	101	5	r	r	NOUN
ajst-27746	101	6	t	t	PROPN
ajst-27746	101	7	t	t	NOUN
ajst-27746	101	8	t	t	NOUN
ajst-27746	101	9			PROPN
ajst-27746	101	10			PROPN
ajst-27746	101	11			PROPN
ajst-27746	101	12			VERB
ajst-27746	101	13			PROPN
ajst-27746	101	14			NOUN
ajst-27746	101	15	(	(	PUNCT
ajst-27746	101	16	16	16	NUM
ajst-27746	101	17	)	)	PUNCT
ajst-27746	101	18	where	where	SCONJ
ajst-27746	101	19	,	,	PUNCT
ajst-27746	101	20	𝑟	𝑟	DET
ajst-27746	101	21	𝑡	𝑡	PROPN
ajst-27746	101	22	is	be	AUX
ajst-27746	101	23	the	the	DET
ajst-27746	101	24	radial	radial	ADJ
ajst-27746	101	25	position	position	NOUN
ajst-27746	101	26	of	of	ADP
ajst-27746	101	27	the	the	DET
ajst-27746	101	28	time	time	NOUN
ajst-27746	101	29	point	point	NOUN
ajst-27746	101	30	𝑡	𝑡	PROPN
ajst-27746	101	31	and	and	CCONJ
ajst-27746	101	32	𝜃	𝜃	DET
ajst-27746	101	33	𝑡	𝑡	NOUN
ajst-27746	101	34	is	be	AUX
ajst-27746	101	35	the	the	DET
ajst-27746	101	36	polar	polar	ADJ
ajst-27746	101	37	angle	angle	NOUN
ajst-27746	101	38	of	of	ADP
ajst-27746	101	39	the	the	DET
ajst-27746	101	40	node	node	NOUN
ajst-27746	101	41	.	.	PUNCT
ajst-27746	102	1	step	step	NOUN
ajst-27746	102	2	2	2	NUM
ajst-27746	102	3	:	:	PUNCT
ajst-27746	102	4	judgment	judgment	NOUN
ajst-27746	102	5	of	of	ADP
ajst-27746	102	6	collision	collision	NOUN
ajst-27746	102	7	condition	condition	NOUN
ajst-27746	102	8	.	.	PUNCT
ajst-27746	103	1	if	if	SCONJ
ajst-27746	103	2	for	for	ADP
ajst-27746	103	3	any	any	DET
ajst-27746	103	4	𝑖	𝑖	NOUN
ajst-27746	103	5	,	,	PUNCT
ajst-27746	103	6	there	there	PRON
ajst-27746	103	7	is	be	VERB
ajst-27746	103	8	𝑑	𝑑	PROPN
ajst-27746	103	9	𝑡	𝑡	PROPN
ajst-27746	103	10	𝐿min	𝐿min	PROPN
ajst-27746	103	11	30	30	NUM
ajst-27746	103	12	cm	cm	NOUN
ajst-27746	103	13	,	,	PUNCT
ajst-27746	103	14	then	then	ADV
ajst-27746	103	15	it	it	PRON
ajst-27746	103	16	is	be	AUX
ajst-27746	103	17	considered	consider	VERB
ajst-27746	103	18	that	that	SCONJ
ajst-27746	103	19	the	the	DET
ajst-27746	103	20	node	node	PROPN
ajst-27746	103	21	𝑖	𝑖	NOUN
ajst-27746	103	22	and	and	CCONJ
ajst-27746	103	23	𝑖	𝑖	ADP
ajst-27746	103	24	1	1	NUM
ajst-27746	103	25	the	the	DET
ajst-27746	103	26	collision	collision	NOUN
ajst-27746	103	27	occurred	occur	VERB
ajst-27746	103	28	.	.	PUNCT
ajst-27746	104	1	in	in	ADP
ajst-27746	104	2	this	this	DET
ajst-27746	104	3	case	case	NOUN
ajst-27746	104	4	,	,	PUNCT
ajst-27746	104	5	record	record	VERB
ajst-27746	104	6	the	the	DET
ajst-27746	104	7	time	time	NOUN
ajst-27746	104	8	𝑡collision	𝑡collision	NOUN
ajst-27746	104	9	。	。	PUNCT
ajst-27746	104	10	when	when	SCONJ
ajst-27746	104	11	the	the	DET
ajst-27746	104	12	collision	collision	NOUN
ajst-27746	104	13	occurred	occur	VERB
ajst-27746	104	14	and	and	CCONJ
ajst-27746	104	15	the	the	DET
ajst-27746	104	16	location	location	NOUN
ajst-27746	104	17	and	and	CCONJ
ajst-27746	104	18	number	number	NOUN
ajst-27746	104	19	of	of	ADP
ajst-27746	104	20	the	the	DET
ajst-27746	104	21	collision	collision	NOUN
ajst-27746	104	22	node	node	VERB
ajst-27746	104	23	𝑥	𝑥	PRON
ajst-27746	104	24	,	,	PUNCT
ajst-27746	104	25	𝑦	𝑦	NOUN
ajst-27746	104	26	.	.	PUNCT
ajst-27746	105	1	305	305	NUM
ajst-27746	105	2	figure	figure	NOUN
ajst-27746	105	3	2	2	NUM
ajst-27746	105	4	.	.	PUNCT
ajst-27746	105	5	an	an	DET
ajst-27746	105	6	example	example	NOUN
ajst-27746	105	7	of	of	ADP
ajst-27746	105	8	the	the	DET
ajst-27746	105	9	position	position	NOUN
ajst-27746	105	10	of	of	ADP
ajst-27746	105	11	the	the	DET
ajst-27746	105	12	disc	disc	NOUN
ajst-27746	105	13	entry	entry	NOUN
ajst-27746	105	14	spiral	spiral	ADJ
ajst-27746	105	15	step	step	NOUN
ajst-27746	105	16	3	3	NUM
ajst-27746	105	17	:	:	PUNCT
ajst-27746	105	18	output	output	NOUN
ajst-27746	105	19	at	at	ADP
ajst-27746	105	20	the	the	DET
ajst-27746	105	21	time	time	NOUN
ajst-27746	105	22	of	of	ADP
ajst-27746	105	23	collision	collision	NOUN
ajst-27746	105	24	.	.	PUNCT
ajst-27746	106	1	using	use	VERB
ajst-27746	106	2	the	the	DET
ajst-27746	106	3	discretization	discretization	NOUN
ajst-27746	106	4	method	method	NOUN
ajst-27746	106	5	,	,	PUNCT
ajst-27746	106	6	update	update	VERB
ajst-27746	106	7	the	the	DET
ajst-27746	106	8	motion	motion	NOUN
ajst-27746	106	9	of	of	ADP
ajst-27746	106	10	each	each	DET
ajst-27746	106	11	node	node	NOUN
ajst-27746	106	12	by	by	ADP
ajst-27746	106	13	time	time	NOUN
ajst-27746	106	14	step	step	NOUN
ajst-27746	106	15	δ𝑡	δ𝑡	NOUN
ajst-27746	106	16	.	.	PUNCT
ajst-27746	107	1	at	at	ADP
ajst-27746	107	2	each	each	DET
ajst-27746	107	3	time	time	NOUN
ajst-27746	107	4	step	step	NOUN
ajst-27746	107	5	,	,	PUNCT
ajst-27746	107	6	we	we	PRON
ajst-27746	107	7	update	update	VERB
ajst-27746	107	8	the	the	DET
ajst-27746	107	9	specific	specific	ADJ
ajst-27746	107	10	position	position	NOUN
ajst-27746	107	11	of	of	ADP
ajst-27746	107	12	each	each	DET
ajst-27746	107	13	node	node	NOUN
ajst-27746	107	14	according	accord	VERB
ajst-27746	107	15	to	to	ADP
ajst-27746	107	16	the	the	DET
ajst-27746	107	17	changes	change	NOUN
ajst-27746	107	18	in	in	ADP
ajst-27746	107	19	the	the	DET
ajst-27746	107	20	polar	polar	ADJ
ajst-27746	107	21	angle	angle	NOUN
ajst-27746	107	22	and	and	CCONJ
ajst-27746	107	23	radial	radial	ADJ
ajst-27746	107	24	position	position	NOUN
ajst-27746	107	25	.	.	PUNCT
ajst-27746	108	1	the	the	DET
ajst-27746	108	2	position	position	NOUN
ajst-27746	108	3	update	update	NOUN
ajst-27746	108	4	formula	formula	NOUN
ajst-27746	108	5	:	:	PUNCT
ajst-27746	108	6			NOUN
ajst-27746	108	7			SYM
ajst-27746	108	8			NOUN
ajst-27746	108	9			SYM
ajst-27746	108	10			NOUN
ajst-27746	108	11			SYM
ajst-27746	108	12			NOUN
ajst-27746	108	13			NUM
ajst-27746	108	14	head	head	NOUN
ajst-27746	108	15	head	head	NOUN
ajst-27746	108	16	lag	lag	VERB
ajst-27746	108	17	,	,	PUNCT
ajst-27746	108	18	i	i	PRON
ajst-27746	108	19	i	i	VERB
ajst-27746	109	1	r	r	NOUN
ajst-27746	109	2	t	t	NOUN
ajst-27746	109	3	r	r	NOUN
ajst-27746	109	4	t	t	NOUN
ajst-27746	110	1	i	i	PRON
ajst-27746	110	2	l	l	PROPN
ajst-27746	110	3	t	t	NOUN
ajst-27746	110	4	t	t	X
ajst-27746	110	5	i	i	NOUN
ajst-27746	110	6			PROPN
ajst-27746	110	7			PROPN
ajst-27746	110	8			X
ajst-27746	111	1			PROPN
ajst-27746	111	2			NOUN
ajst-27746	111	3			PROPN
ajst-27746	112	1			NUM
ajst-27746	112	2			NUM
ajst-27746	112	3			PROPN
ajst-27746	112	4			PROPN
ajst-27746	112	5	(	(	PUNCT
ajst-27746	112	6	17	17	NUM
ajst-27746	112	7	)	)	PUNCT
ajst-27746	112	8	thus	thus	ADV
ajst-27746	112	9	,	,	PUNCT
ajst-27746	112	10	the	the	DET
ajst-27746	112	11	output	output	NOUN
ajst-27746	112	12	of	of	ADP
ajst-27746	112	13	the	the	DET
ajst-27746	112	14	position	position	NOUN
ajst-27746	112	15	at	at	ADP
ajst-27746	112	16	this	this	DET
ajst-27746	112	17	time	time	NOUN
ajst-27746	112	18	is	be	AUX
ajst-27746	112	19	obtained	obtain	VERB
ajst-27746	112	20	and	and	CCONJ
ajst-27746	112	21	the	the	DET
ajst-27746	112	22	position	position	NOUN
ajst-27746	112	23	information	information	NOUN
ajst-27746	112	24	of	of	ADP
ajst-27746	112	25	the	the	DET
ajst-27746	112	26	dragon	dragon	NOUN
ajst-27746	112	27	dance	dance	NOUN
ajst-27746	112	28	team	team	NOUN
ajst-27746	112	29	is	be	AUX
ajst-27746	112	30	obtained	obtain	VERB
ajst-27746	112	31	at	at	ADP
ajst-27746	112	32	this	this	DET
ajst-27746	112	33	time	time	NOUN
ajst-27746	112	34	.	.	PUNCT
ajst-27746	113	1	where	where	SCONJ
ajst-27746	113	2	l	l	NOUN
ajst-27746	113	3	is	be	AUX
ajst-27746	113	4	the	the	DET
ajst-27746	113	5	fixed	fix	VERB
ajst-27746	113	6	distance	distance	NOUN
ajst-27746	113	7	of	of	ADP
ajst-27746	113	8	adjacent	adjacent	ADJ
ajst-27746	113	9	nodes	node	NOUN
ajst-27746	113	10	and	and	CCONJ
ajst-27746	113	11	𝜃	𝜃	DET
ajst-27746	113	12	the	the	DET
ajst-27746	113	13	angle	angle	NOUN
ajst-27746	113	14	difference	difference	NOUN
ajst-27746	113	15	of	of	ADP
ajst-27746	113	16	node	node	NOUN
ajst-27746	113	17	lag	lag	NOUN
ajst-27746	113	18	.	.	PUNCT
ajst-27746	114	1	the	the	DET
ajst-27746	114	2	speed	speed	NOUN
ajst-27746	114	3	can	can	AUX
ajst-27746	114	4	be	be	AUX
ajst-27746	114	5	obtained	obtain	VERB
ajst-27746	114	6	by	by	ADP
ajst-27746	114	7	calculating	calculate	VERB
ajst-27746	114	8	the	the	DET
ajst-27746	114	9	difference	difference	NOUN
ajst-27746	114	10	in	in	ADP
ajst-27746	114	11	position	position	NOUN
ajst-27746	114	12	of	of	ADP
ajst-27746	114	13	each	each	DET
ajst-27746	114	14	node	node	NOUN
ajst-27746	114	15	between	between	ADP
ajst-27746	114	16	the	the	DET
ajst-27746	114	17	two	two	NUM
ajst-27746	114	18	time	time	NOUN
ajst-27746	114	19	steps	step	NOUN
ajst-27746	114	20	.	.	PUNCT
ajst-27746	115	1	for	for	ADP
ajst-27746	115	2	each	each	DET
ajst-27746	115	3	time	time	NOUN
ajst-27746	115	4	step	step	NOUN
ajst-27746	115	5	𝑡	𝑡	PROPN
ajst-27746	115	6	,	,	PUNCT
ajst-27746	115	7	the	the	DET
ajst-27746	115	8	speed	speed	NOUN
ajst-27746	115	9	can	can	AUX
ajst-27746	115	10	be	be	AUX
ajst-27746	115	11	approximated	approximate	VERB
ajst-27746	115	12	by	by	ADP
ajst-27746	115	13	:	:	PUNCT
ajst-27746	115	14			PROPN
ajst-27746	115	15			PROPN
ajst-27746	115	16			NOUN
ajst-27746	115	17			SYM
ajst-27746	115	18			NOUN
ajst-27746	115	19			SYM
ajst-27746	115	20			NOUN
ajst-27746	115	21			SYM
ajst-27746	115	22			NOUN
ajst-27746	115	23			PUNCT
ajst-27746	115	24			NOUN
ajst-27746	115	25			PUNCT
ajst-27746	116	1	δ	δ	PROPN
ajst-27746	116	2	δ	δ	PROPN
ajst-27746	116	3	δ	δ	NOUN
ajst-27746	116	4	δi	δi	VERB
ajst-27746	117	1	i	i	PRON
ajst-27746	117	2	i	i	PRON
ajst-27746	118	1	i	i	PRON
ajst-27746	119	1	i	i	INTJ
ajst-27746	120	1	i	i	VERB
ajst-27746	121	1	r	r	NOUN
ajst-27746	121	2	t	t	NOUN
ajst-27746	121	3	t	t	NOUN
ajst-27746	121	4	r	r	NOUN
ajst-27746	121	5	t	t	PROPN
ajst-27746	121	6	v	v	NOUN
ajst-27746	121	7	t	t	PROPN
ajst-27746	121	8	t	t	PROPN
ajst-27746	121	9	t	t	PROPN
ajst-27746	121	10	t	t	PROPN
ajst-27746	121	11	t	t	PROPN
ajst-27746	121	12	v	v	ADP
ajst-27746	121	13	t	t	X
ajst-27746	121	14	t	t	NOUN
ajst-27746	121	15			PROPN
ajst-27746	121	16			PROPN
ajst-27746	121	17			PROPN
ajst-27746	121	18			PUNCT
ajst-27746	121	19			PROPN
ajst-27746	121	20			NOUN
ajst-27746	121	21			NOUN
ajst-27746	121	22			PUNCT
ajst-27746	121	23			NOUN
ajst-27746	121	24			NOUN
ajst-27746	121	25	(	(	PUNCT
ajst-27746	121	26	18	18	NUM
ajst-27746	121	27	)	)	PUNCT
ajst-27746	121	28	4	4	NUM
ajst-27746	121	29	.	.	X
ajst-27746	122	1	pitch	pitch	NOUN
ajst-27746	122	2	turning	turn	VERB
ajst-27746	122	3	space	space	NOUN
ajst-27746	122	4	model	model	NOUN
ajst-27746	122	5	in	in	ADP
ajst-27746	122	6	order	order	NOUN
ajst-27746	122	7	to	to	PART
ajst-27746	122	8	ensure	ensure	VERB
ajst-27746	122	9	that	that	SCONJ
ajst-27746	122	10	the	the	DET
ajst-27746	122	11	front	front	ADJ
ajst-27746	122	12	handle	handle	NOUN
ajst-27746	122	13	of	of	ADP
ajst-27746	122	14	the	the	DET
ajst-27746	122	15	faucet	faucet	NOUN
ajst-27746	122	16	can	can	AUX
ajst-27746	122	17	be	be	AUX
ajst-27746	122	18	disc	disc	VERB
ajst-27746	122	19	into	into	ADP
ajst-27746	122	20	the	the	DET
ajst-27746	122	21	boundary	boundary	NOUN
ajst-27746	122	22	of	of	ADP
ajst-27746	122	23	the	the	DET
ajst-27746	122	24	turning	turn	VERB
ajst-27746	122	25	space	space	NOUN
ajst-27746	122	26	,	,	PUNCT
ajst-27746	122	27	the	the	DET
ajst-27746	122	28	minimum	minimum	ADJ
ajst-27746	122	29	pitch	pitch	NOUN
ajst-27746	122	30	is	be	AUX
ajst-27746	122	31	designed	design	VERB
ajst-27746	122	32	.	.	PUNCT
ajst-27746	123	1	at	at	ADP
ajst-27746	123	2	the	the	DET
ajst-27746	123	3	same	same	ADJ
ajst-27746	123	4	time	time	NOUN
ajst-27746	123	5	,	,	PUNCT
ajst-27746	123	6	the	the	DET
ajst-27746	123	7	overall	overall	ADJ
ajst-27746	123	8	path	path	NOUN
ajst-27746	123	9	planning	planning	NOUN
ajst-27746	123	10	is	be	AUX
ajst-27746	123	11	optimized	optimize	VERB
ajst-27746	123	12	globally	globally	ADV
ajst-27746	123	13	,	,	PUNCT
ajst-27746	123	14	the	the	DET
ajst-27746	123	15	movement	movement	NOUN
ajst-27746	123	16	model	model	NOUN
ajst-27746	123	17	of	of	ADP
ajst-27746	123	18	the	the	DET
ajst-27746	123	19	dragon	dragon	NOUN
ajst-27746	123	20	is	be	AUX
ajst-27746	123	21	extended	extend	VERB
ajst-27746	123	22	,	,	PUNCT
ajst-27746	123	23	the	the	DET
ajst-27746	123	24	movement	movement	NOUN
ajst-27746	123	25	of	of	ADP
ajst-27746	123	26	the	the	DET
ajst-27746	123	27	dragon	dragon	NOUN
ajst-27746	123	28	body	body	NOUN
ajst-27746	123	29	and	and	CCONJ
ajst-27746	123	30	the	the	DET
ajst-27746	123	31	dragon	dragon	NOUN
ajst-27746	123	32	tail	tail	NOUN
ajst-27746	123	33	is	be	AUX
ajst-27746	123	34	included	include	VERB
ajst-27746	123	35	,	,	PUNCT
ajst-27746	123	36	and	and	CCONJ
ajst-27746	123	37	a	a	DET
ajst-27746	123	38	complete	complete	ADJ
ajst-27746	123	39	three	three	NUM
ajst-27746	123	40	-	-	PUNCT
ajst-27746	123	41	dimensional	dimensional	ADJ
ajst-27746	123	42	path	path	NOUN
ajst-27746	123	43	planning	planning	NOUN
ajst-27746	123	44	model	model	NOUN
ajst-27746	123	45	is	be	AUX
ajst-27746	123	46	constructed	construct	VERB
ajst-27746	123	47	.	.	PUNCT
ajst-27746	124	1	by	by	ADP
ajst-27746	124	2	analyzing	analyze	VERB
ajst-27746	124	3	the	the	DET
ajst-27746	124	4	relationship	relationship	NOUN
ajst-27746	124	5	between	between	ADP
ajst-27746	124	6	the	the	DET
ajst-27746	124	7	position	position	NOUN
ajst-27746	124	8	and	and	CCONJ
ajst-27746	124	9	speed	speed	NOUN
ajst-27746	124	10	of	of	ADP
ajst-27746	124	11	each	each	DET
ajst-27746	124	12	node	node	NOUN
ajst-27746	124	13	at	at	ADP
ajst-27746	124	14	different	different	ADJ
ajst-27746	124	15	time	time	NOUN
ajst-27746	124	16	points	point	NOUN
ajst-27746	124	17	,	,	PUNCT
ajst-27746	124	18	the	the	DET
ajst-27746	124	19	path	path	NOUN
ajst-27746	124	20	length	length	NOUN
ajst-27746	124	21	and	and	CCONJ
ajst-27746	124	22	speed	speed	NOUN
ajst-27746	124	23	control	control	NOUN
ajst-27746	124	24	are	be	AUX
ajst-27746	124	25	further	far	ADV
ajst-27746	124	26	optimized	optimize	VERB
ajst-27746	124	27	,	,	PUNCT
ajst-27746	124	28	and	and	CCONJ
ajst-27746	124	29	unnecessary	unnecessary	ADJ
ajst-27746	124	30	route	route	NOUN
ajst-27746	124	31	detour	detour	NOUN
ajst-27746	124	32	or	or	CCONJ
ajst-27746	124	33	sudden	sudden	ADJ
ajst-27746	124	34	change	change	NOUN
ajst-27746	124	35	is	be	AUX
ajst-27746	124	36	avoided	avoid	VERB
ajst-27746	124	37	.	.	PUNCT
ajst-27746	125	1	4.1	4.1	NUM
ajst-27746	125	2	.	.	PUNCT
ajst-27746	126	1	u	u	NOUN
ajst-27746	126	2	-	-	ADJ
ajst-27746	126	3	turn	turn	ADJ
ajst-27746	126	4	space	space	NOUN
ajst-27746	126	5	model	model	NOUN
ajst-27746	126	6	establishment	establishment	NOUN
ajst-27746	126	7	based	base	VERB
ajst-27746	126	8	on	on	ADP
ajst-27746	126	9	the	the	DET
ajst-27746	126	10	above	above	ADJ
ajst-27746	126	11	complex	complex	ADJ
ajst-27746	126	12	path	path	NOUN
ajst-27746	126	13	model	model	NOUN
ajst-27746	126	14	,	,	PUNCT
ajst-27746	126	15	a	a	DET
ajst-27746	126	16	dragon	dragon	NOUN
ajst-27746	126	17	dance	dance	NOUN
ajst-27746	126	18	path	path	NOUN
ajst-27746	126	19	optimization	optimization	NOUN
ajst-27746	126	20	and	and	CCONJ
ajst-27746	126	21	constraint	constraint	NOUN
ajst-27746	126	22	analysis	analysis	NOUN
ajst-27746	126	23	model	model	NOUN
ajst-27746	126	24	is	be	AUX
ajst-27746	126	25	established	establish	VERB
ajst-27746	126	26	:	:	PUNCT
ajst-27746	126	27	assuming	assume	VERB
ajst-27746	126	28	that	that	SCONJ
ajst-27746	126	29	the	the	DET
ajst-27746	126	30	movement	movement	NOUN
ajst-27746	126	31	of	of	ADP
ajst-27746	126	32	the	the	DET
ajst-27746	126	33	dragon	dragon	NOUN
ajst-27746	126	34	head	head	NOUN
ajst-27746	126	35	is	be	AUX
ajst-27746	126	36	uniform	uniform	ADJ
ajst-27746	126	37	,	,	PUNCT
ajst-27746	126	38	the	the	DET
ajst-27746	126	39	polar	polar	ADJ
ajst-27746	126	40	diameter	diameter	NOUN
ajst-27746	126	41	𝑟	𝑟	X
ajst-27746	126	42	𝜃	𝜃	NOUN
ajst-27746	126	43	and	and	CCONJ
ajst-27746	126	44	polar	polar	ADJ
ajst-27746	126	45	angle	angle	NOUN
ajst-27746	127	1	𝜃	𝜃	X
ajst-27746	127	2	change	change	NOUN
ajst-27746	127	3	with	with	ADP
ajst-27746	127	4	time	time	NOUN
ajst-27746	127	5	.	.	PUNCT
ajst-27746	128	1	the	the	DET
ajst-27746	128	2	objective	objective	ADJ
ajst-27746	128	3	function	function	NOUN
ajst-27746	128	4	can	can	AUX
ajst-27746	128	5	be	be	AUX
ajst-27746	128	6	defined	define	VERB
ajst-27746	128	7	as	as	ADP
ajst-27746	128	8	:	:	PUNCT
ajst-27746	128	9	end	end	NOUN
ajst-27746	128	10	2	2	NUM
ajst-27746	128	11	2	2	NUM
ajst-27746	128	12	2	2	NUM
ajst-27746	128	13	0	0	NUM
ajst-27746	128	14	min	min	PROPN
ajst-27746	129	1	t	t	PROPN
ajst-27746	129	2	dr	dr	PROPN
ajst-27746	129	3	d	d	PROPN
ajst-27746	129	4	r	r	NOUN
ajst-27746	129	5	dt	dt	NOUN
ajst-27746	129	6	dt	dt	NOUN
ajst-27746	129	7	dt	dt	PROPN
ajst-27746	130	1			PROPN
ajst-27746	130	2			PROPN
ajst-27746	130	3			NOUN
ajst-27746	130	4			NOUN
ajst-27746	131	1			PROPN
ajst-27746	131	2			PROPN
ajst-27746	131	3			PROPN
ajst-27746	132	1			PROPN
ajst-27746	132	2			PROPN
ajst-27746	132	3			PROPN
ajst-27746	132	4			PROPN
ajst-27746	132	5	(	(	PUNCT
ajst-27746	132	6	19	19	NUM
ajst-27746	132	7	)	)	PUNCT
ajst-27746	132	8	determining	determine	VERB
ajst-27746	132	9	the	the	DET
ajst-27746	132	10	minimum	minimum	ADJ
ajst-27746	132	11	pitch	pitch	NOUN
ajst-27746	132	12	so	so	SCONJ
ajst-27746	132	13	that	that	SCONJ
ajst-27746	132	14	the	the	DET
ajst-27746	132	15	front	front	ADJ
ajst-27746	132	16	handle	handle	NOUN
ajst-27746	132	17	of	of	ADP
ajst-27746	132	18	the	the	DET
ajst-27746	132	19	faucet	faucet	NOUN
ajst-27746	132	20	can	can	AUX
ajst-27746	132	21	follow	follow	VERB
ajst-27746	132	22	the	the	DET
ajst-27746	132	23	corresponding	correspond	VERB
ajst-27746	132	24	spiral	spiral	ADJ
ajst-27746	132	25	disc	disc	NOUN
ajst-27746	132	26	into	into	ADP
ajst-27746	132	27	the	the	DET
ajst-27746	132	28	boundary	boundary	NOUN
ajst-27746	132	29	of	of	ADP
ajst-27746	132	30	the	the	DET
ajst-27746	132	31	turning	turn	VERB
ajst-27746	132	32	space	space	NOUN
ajst-27746	132	33	can	can	AUX
ajst-27746	132	34	be	be	AUX
ajst-27746	132	35	viewed	view	VERB
ajst-27746	132	36	as	as	ADP
ajst-27746	132	37	a	a	DET
ajst-27746	132	38	path	path	NOUN
ajst-27746	132	39	optimization	optimization	NOUN
ajst-27746	132	40	problem	problem	NOUN
ajst-27746	132	41	,	,	PUNCT
ajst-27746	132	42	with	with	ADP
ajst-27746	132	43	the	the	DET
ajst-27746	132	44	goal	goal	NOUN
ajst-27746	132	45	of	of	ADP
ajst-27746	132	46	minimizing	minimize	VERB
ajst-27746	132	47	the	the	DET
ajst-27746	132	48	path	path	NOUN
ajst-27746	132	49	length	length	NOUN
ajst-27746	132	50	or	or	CCONJ
ajst-27746	132	51	turning	turn	VERB
ajst-27746	132	52	time	time	NOUN
ajst-27746	132	53	of	of	ADP
ajst-27746	132	54	the	the	DET
ajst-27746	132	55	faucet	faucet	NOUN
ajst-27746	132	56	from	from	ADP
ajst-27746	132	57	the	the	DET
ajst-27746	132	58	starting	starting	NOUN
ajst-27746	132	59	point	point	NOUN
ajst-27746	132	60	to	to	ADP
ajst-27746	132	61	the	the	DET
ajst-27746	132	62	turning	turn	VERB
ajst-27746	132	63	space	space	NOUN
ajst-27746	132	64	.	.	PUNCT
ajst-27746	133	1	in	in	ADP
ajst-27746	133	2	this	this	DET
ajst-27746	133	3	condition	condition	NOUN
ajst-27746	133	4	,	,	PUNCT
ajst-27746	133	5	the	the	DET
ajst-27746	133	6	following	follow	VERB
ajst-27746	133	7	constraints	constraint	NOUN
ajst-27746	133	8	exist	exist	VERB
ajst-27746	133	9	:	:	PUNCT
ajst-27746	133	10	u	u	ADJ
ajst-27746	133	11	-	-	NOUN
ajst-27746	133	12	turn	turn	ADJ
ajst-27746	133	13	space	space	NOUN
ajst-27746	133	14	constraint	constraint	NOUN
ajst-27746	133	15	:	:	PUNCT
ajst-27746	133	16	the	the	DET
ajst-27746	133	17	faucet	faucet	NOUN
ajst-27746	133	18	must	must	AUX
ajst-27746	133	19	stop	stop	VERB
ajst-27746	133	20	at	at	ADP
ajst-27746	133	21	the	the	DET
ajst-27746	133	22	boundary	boundary	NOUN
ajst-27746	133	23	of	of	ADP
ajst-27746	133	24	u	u	NOUN
ajst-27746	133	25	-	-	NOUN
ajst-27746	133	26	turn	turn	NOUN
ajst-27746	133	27	space	space	NOUN
ajst-27746	133	28	,	,	PUNCT
ajst-27746	133	29	and	and	CCONJ
ajst-27746	133	30	the	the	DET
ajst-27746	133	31	radius	radius	NOUN
ajst-27746	133	32	of	of	ADP
ajst-27746	133	33	the	the	DET
ajst-27746	133	34	faucet	faucet	NOUN
ajst-27746	133	35	can	can	AUX
ajst-27746	133	36	not	not	PART
ajst-27746	133	37	exceed	exceed	VERB
ajst-27746	133	38	the	the	DET
ajst-27746	133	39	radius	radius	NOUN
ajst-27746	133	40	of	of	ADP
ajst-27746	133	41	u	u	NOUN
ajst-27746	133	42	-	-	NOUN
ajst-27746	133	43	turn	turn	NOUN
ajst-27746	133	44	space	space	NOUN
ajst-27746	133	45	:	:	PUNCT
ajst-27746	133	46			NOUN
ajst-27746	133	47			SYM
ajst-27746	133	48			NOUN
ajst-27746	133	49			NOUN
ajst-27746	133	50	0	0	NUM
ajst-27746	133	51	2	2	NUM
ajst-27746	133	52	4.5	4.5	NUM
ajst-27746	133	53	m	m	NOUN
ajst-27746	133	54	p	p	NOUN
ajst-27746	133	55	r	r	NOUN
ajst-27746	133	56	r	r	NOUN
ajst-27746	133	57	r	r	NOUN
ajst-27746	133	58			NOUN
ajst-27746	133	59			X
ajst-27746	133	60			PROPN
ajst-27746	133	61			X
ajst-27746	133	62			ADP
ajst-27746	134	1			PRON
ajst-27746	134	2			NOUN
ajst-27746	134	3			NUM
ajst-27746	134	4			NUM
ajst-27746	134	5			NUM
ajst-27746	134	6	(	(	PUNCT
ajst-27746	134	7	20	20	NUM
ajst-27746	134	8	)	)	PUNCT
ajst-27746	134	9	motion	motion	NOUN
ajst-27746	134	10	smoothness	smoothness	NOUN
ajst-27746	134	11	constraint	constraint	NOUN
ajst-27746	134	12	:	:	PUNCT
ajst-27746	134	13	centripetal	centripetal	ADJ
ajst-27746	134	14	acceleration	acceleration	NOUN
ajst-27746	134	15	and	and	CCONJ
ajst-27746	134	16	velocity	velocity	NOUN
ajst-27746	134	17	constraint	constraint	NOUN
ajst-27746	134	18	:	:	PUNCT
ajst-27746	134	19	with	with	ADP
ajst-27746	134	20	the	the	DET
ajst-27746	134	21	change	change	NOUN
ajst-27746	134	22	of	of	ADP
ajst-27746	134	23	path	path	NOUN
ajst-27746	134	24	radius	radius	NOUN
ajst-27746	134	25	,	,	PUNCT
ajst-27746	134	26	the	the	DET
ajst-27746	134	27	board	board	NOUN
ajst-27746	134	28	in	in	ADP
ajst-27746	134	29	the	the	DET
ajst-27746	134	30	dragon	dragon	NOUN
ajst-27746	134	31	dance	dance	NOUN
ajst-27746	134	32	team	team	NOUN
ajst-27746	134	33	will	will	AUX
ajst-27746	134	34	be	be	AUX
ajst-27746	134	35	subject	subject	ADJ
ajst-27746	134	36	to	to	ADP
ajst-27746	134	37	different	different	ADJ
ajst-27746	134	38	acceleration	acceleration	NOUN
ajst-27746	134	39	,	,	PUNCT
ajst-27746	134	40	resulting	result	VERB
ajst-27746	134	41	in	in	ADP
ajst-27746	134	42	complicated	complicated	ADJ
ajst-27746	134	43	motion	motion	NOUN
ajst-27746	134	44	equation	equation	NOUN
ajst-27746	134	45	.	.	PUNCT
ajst-27746	135	1	because	because	SCONJ
ajst-27746	135	2	the	the	DET
ajst-27746	135	3	movement	movement	NOUN
ajst-27746	135	4	of	of	ADP
ajst-27746	135	5	the	the	DET
ajst-27746	135	6	dragon	dragon	NOUN
ajst-27746	135	7	head	head	NOUN
ajst-27746	135	8	is	be	AUX
ajst-27746	135	9	smooth	smooth	ADJ
ajst-27746	135	10	,	,	PUNCT
ajst-27746	135	11	the	the	DET
ajst-27746	135	12	centripetal	centripetal	ADJ
ajst-27746	135	13	acceleration	acceleration	NOUN
ajst-27746	135	14	can	can	AUX
ajst-27746	135	15	not	not	PART
ajst-27746	135	16	exceed	exceed	VERB
ajst-27746	135	17	a	a	DET
ajst-27746	135	18	certain	certain	ADJ
ajst-27746	135	19	upper	upper	ADJ
ajst-27746	135	20	limit	limit	NOUN
ajst-27746	135	21	𝑎	𝑎	NOUN
ajst-27746	135	22	,	,	PUNCT
ajst-27746	135	23	and	and	CCONJ
ajst-27746	135	24	the	the	DET
ajst-27746	135	25	centripetal	centripetal	ADJ
ajst-27746	135	26	acceleration	acceleration	NOUN
ajst-27746	135	27	of	of	ADP
ajst-27746	135	28	each	each	DET
ajst-27746	135	29	board	board	NOUN
ajst-27746	135	30	is	be	AUX
ajst-27746	135	31	required	require	VERB
ajst-27746	135	32	not	not	PART
ajst-27746	135	33	to	to	PART
ajst-27746	135	34	exceed	exceed	VERB
ajst-27746	135	35	,	,	PUNCT
ajst-27746	135	36	that	that	PRON
ajst-27746	135	37	is	be	AUX
ajst-27746	135	38	𝑎	𝑎	PRON
ajst-27746	135	39	,	,	PUNCT
ajst-27746	135	40	the	the	DET
ajst-27746	135	41	centripetal	centripetal	ADJ
ajst-27746	135	42	acceleration	acceleration	NOUN
ajst-27746	135	43	is	be	AUX
ajst-27746	135	44	:	:	PUNCT
ajst-27746	135	45	2	2	NUM
ajst-27746	135	46	head	head	NOUN
ajst-27746	135	47	maxc	maxc	NOUN
ajst-27746	135	48	v	v	ADP
ajst-27746	135	49	a	a	DET
ajst-27746	135	50	a	a	DET
ajst-27746	135	51	a	a	DET
ajst-27746	135	52	b	b	NOUN
ajst-27746	135	53			NUM
ajst-27746	135	54			NOUN
ajst-27746	135	55			PUNCT
ajst-27746	135	56	(	(	PUNCT
ajst-27746	135	57	21	21	NUM
ajst-27746	135	58	)	)	PUNCT
ajst-27746	135	59	at	at	ADP
ajst-27746	135	60	the	the	DET
ajst-27746	135	61	same	same	ADJ
ajst-27746	135	62	time	time	NOUN
ajst-27746	135	63	,	,	PUNCT
ajst-27746	135	64	in	in	ADP
ajst-27746	135	65	order	order	NOUN
ajst-27746	135	66	to	to	PART
ajst-27746	135	67	ensure	ensure	VERB
ajst-27746	135	68	the	the	DET
ajst-27746	135	69	smooth	smooth	ADJ
ajst-27746	135	70	movement	movement	NOUN
ajst-27746	135	71	of	of	ADP
ajst-27746	135	72	the	the	DET
ajst-27746	135	73	dragon	dragon	NOUN
ajst-27746	135	74	dance	dance	NOUN
ajst-27746	135	75	team	team	NOUN
ajst-27746	135	76	,	,	PUNCT
ajst-27746	135	77	the	the	DET
ajst-27746	135	78	smoothness	smoothness	ADJ
ajst-27746	135	79	regularization	regularization	NOUN
ajst-27746	135	80	constraint	constraint	NOUN
ajst-27746	135	81	is	be	AUX
ajst-27746	135	82	introduced	introduce	VERB
ajst-27746	135	83	.	.	PUNCT
ajst-27746	136	1	the	the	DET
ajst-27746	136	2	angular	angular	ADJ
ajst-27746	136	3	velocity	velocity	NOUN
ajst-27746	136	4	and	and	CCONJ
ajst-27746	136	5	angular	angular	ADJ
ajst-27746	136	6	acceleration	acceleration	NOUN
ajst-27746	136	7	of	of	ADP
ajst-27746	136	8	the	the	DET
ajst-27746	136	9	dragon	dragon	NOUN
ajst-27746	136	10	head	head	NOUN
ajst-27746	136	11	are	be	AUX
ajst-27746	136	12	expressed	express	VERB
ajst-27746	136	13	as	as	SCONJ
ajst-27746	136	14	follows	follow	VERB
ajst-27746	136	15	:	:	PUNCT
ajst-27746	136	16	head	head	NOUN
ajst-27746	136	17	2	2	NUM
ajst-27746	136	18	2	2	NUM
ajst-27746	136	19	(	(	PUNCT
ajst-27746	136	20	)	)	PUNCT
ajst-27746	136	21	vd	vd	NOUN
ajst-27746	137	1	dt	dt	PROPN
ajst-27746	137	2	b	b	PROPN
ajst-27746	137	3	a	a	DET
ajst-27746	137	4	b	b	NOUN
ajst-27746	137	5			X
ajst-27746	137	6			PROPN
ajst-27746	137	7			PROPN
ajst-27746	137	8			PROPN
ajst-27746	137	9			X
ajst-27746	137	10	(	(	PUNCT
ajst-27746	137	11	22	22	NUM
ajst-27746	137	12	)	)	PUNCT
ajst-27746	137	13	306	306	NUM
ajst-27746	137	14	the	the	DET
ajst-27746	137	15	angular	angular	ADJ
ajst-27746	137	16	acceleration	acceleration	NOUN
ajst-27746	137	17	is	be	AUX
ajst-27746	137	18	:	:	PUNCT
ajst-27746	137	19			NOUN
ajst-27746	137	20			SYM
ajst-27746	137	21			NOUN
ajst-27746	137	22			PROPN
ajst-27746	137	23	22	22	NUM
ajst-27746	137	24	head	head	NOUN
ajst-27746	137	25	3/22	3/22	NUM
ajst-27746	137	26	2	2	NUM
ajst-27746	137	27	2	2	NUM
ajst-27746	137	28	(	(	PUNCT
ajst-27746	137	29	)	)	PUNCT
ajst-27746	137	30	v	v	ADP
ajst-27746	137	31	b	b	PROPN
ajst-27746	137	32	a	a	PRON
ajst-27746	137	33	bd	bd	PROPN
ajst-27746	137	34	dt	dt	PROPN
ajst-27746	137	35	b	b	PROPN
ajst-27746	137	36	a	a	DET
ajst-27746	137	37	b	b	X
ajst-27746	137	38			X
ajst-27746	137	39			PROPN
ajst-27746	137	40			PROPN
ajst-27746	137	41			PROPN
ajst-27746	137	42			PROPN
ajst-27746	137	43			ADV
ajst-27746	137	44			X
ajst-27746	137	45	(	(	PUNCT
ajst-27746	137	46	23	23	NUM
ajst-27746	137	47	)	)	PUNCT
ajst-27746	137	48	for	for	SCONJ
ajst-27746	137	49	the	the	DET
ajst-27746	137	50	speed	speed	NOUN
ajst-27746	137	51	𝑣head	𝑣head	VERB
ajst-27746	137	52	in	in	ADP
ajst-27746	137	53	the	the	DET
ajst-27746	137	54	formula	formula	NOUN
ajst-27746	137	55	,	,	PUNCT
ajst-27746	137	56	because	because	SCONJ
ajst-27746	137	57	the	the	DET
ajst-27746	137	58	faucet	faucet	NOUN
ajst-27746	137	59	speed	speed	NOUN
ajst-27746	137	60	can	can	AUX
ajst-27746	137	61	not	not	PART
ajst-27746	137	62	exceed	exceed	VERB
ajst-27746	137	63	1	1	NUM
ajst-27746	137	64	m	m	NOUN
ajst-27746	137	65	/	/	SYM
ajst-27746	137	66	s	s	PART
ajst-27746	137	67	,	,	PUNCT
ajst-27746	137	68	so	so	CCONJ
ajst-27746	137	69	there	there	PRON
ajst-27746	137	70	is	be	VERB
ajst-27746	137	71	𝑣head	𝑣head	ADJ
ajst-27746	137	72	1	1	NUM
ajst-27746	137	73	m	m	PROPN
ajst-27746	137	74	/	/	SYM
ajst-27746	137	75	s	s	PROPN
ajst-27746	137	76	,	,	PUNCT
ajst-27746	137	77	so	so	ADV
ajst-27746	137	78	the	the	DET
ajst-27746	137	79	requirement	requirement	NOUN
ajst-27746	137	80	𝑎angular	𝑎angular	ADJ
ajst-27746	137	81	.	.	PUNCT
ajst-27746	138	1	no	no	DET
ajst-27746	138	2	collision	collision	NOUN
ajst-27746	138	3	constraint	constraint	NOUN
ajst-27746	138	4	:	:	PUNCT
ajst-27746	138	5	the	the	DET
ajst-27746	138	6	dragon	dragon	NOUN
ajst-27746	138	7	head	head	NOUN
ajst-27746	138	8	can	can	AUX
ajst-27746	138	9	not	not	PART
ajst-27746	138	10	collide	collide	VERB
ajst-27746	138	11	with	with	ADP
ajst-27746	138	12	the	the	DET
ajst-27746	138	13	dragon	dragon	NOUN
ajst-27746	138	14	body	body	NOUN
ajst-27746	138	15	or	or	CCONJ
ajst-27746	138	16	tail	tail	NOUN
ajst-27746	138	17	in	in	ADP
ajst-27746	138	18	the	the	DET
ajst-27746	138	19	process	process	NOUN
ajst-27746	138	20	of	of	ADP
ajst-27746	138	21	turning	turn	VERB
ajst-27746	138	22	,	,	PUNCT
ajst-27746	138	23	so	so	SCONJ
ajst-27746	138	24	it	it	PRON
ajst-27746	138	25	is	be	AUX
ajst-27746	138	26	necessary	necessary	ADJ
ajst-27746	138	27	to	to	PART
ajst-27746	138	28	ensure	ensure	VERB
ajst-27746	138	29	that	that	SCONJ
ajst-27746	138	30	the	the	DET
ajst-27746	138	31	minimum	minimum	ADJ
ajst-27746	138	32	distance	distance	NOUN
ajst-27746	138	33	between	between	ADP
ajst-27746	138	34	the	the	DET
ajst-27746	138	35	adjacent	adjacent	ADJ
ajst-27746	138	36	board	board	NOUN
ajst-27746	138	37	and	and	CCONJ
ajst-27746	138	38	meet	meet	VERB
ajst-27746	138	39	:	:	PUNCT
ajst-27746	138	40			NOUN
ajst-27746	138	41			SYM
ajst-27746	138	42			NOUN
ajst-27746	138	43	2	2	NOUN
ajst-27746	138	44	22	22	NUM
ajst-27746	138	45	1	1	NUM
ajst-27746	138	46	1	1	NUM
ajst-27746	138	47	mini	mini	NOUN
ajst-27746	139	1	i	i	PRON
ajst-27746	139	2	i	i	PRON
ajst-27746	140	1	i	i	PRON
ajst-27746	140	2	ir	ir	VERB
ajst-27746	140	3	r	r	NOUN
ajst-27746	140	4	r	r	NOUN
ajst-27746	140	5	d	d	NOUN
ajst-27746	140	6			PROPN
ajst-27746	140	7			PROPN
ajst-27746	140	8			PUNCT
ajst-27746	140	9			PROPN
ajst-27746	140	10			NUM
ajst-27746	140	11	(	(	PUNCT
ajst-27746	140	12	24	24	NUM
ajst-27746	140	13	)	)	PUNCT
ajst-27746	140	14	distance	distance	NOUN
ajst-27746	140	15	constraint	constraint	NOUN
ajst-27746	140	16	between	between	ADP
ajst-27746	140	17	boards	board	NOUN
ajst-27746	140	18	:	:	PUNCT
ajst-27746	140	19	the	the	DET
ajst-27746	140	20	distance	distance	NOUN
ajst-27746	140	21	between	between	ADP
ajst-27746	140	22	adjacent	adjacent	ADJ
ajst-27746	140	23	boards	board	NOUN
ajst-27746	140	24	can	can	AUX
ajst-27746	140	25	not	not	PART
ajst-27746	140	26	be	be	AUX
ajst-27746	140	27	lower	low	ADJ
ajst-27746	140	28	than	than	ADP
ajst-27746	140	29	a	a	DET
ajst-27746	140	30	threshold	threshold	NOUN
ajst-27746	140	31	value	value	NOUN
ajst-27746	140	32	𝑑	𝑑	NOUN
ajst-27746	140	33	,	,	PUNCT
ajst-27746	140	34	which	which	PRON
ajst-27746	140	35	is	be	AUX
ajst-27746	140	36	also	also	ADV
ajst-27746	140	37	a	a	DET
ajst-27746	140	38	nonlinear	nonlinear	ADJ
ajst-27746	140	39	geometric	geometric	ADJ
ajst-27746	140	40	constraint	constraint	NOUN
ajst-27746	140	41	.	.	PUNCT
ajst-27746	141	1	due	due	ADP
ajst-27746	141	2	to	to	ADP
ajst-27746	141	3	the	the	DET
ajst-27746	141	4	above	above	ADJ
ajst-27746	141	5	constraints	constraint	NOUN
ajst-27746	141	6	,	,	PUNCT
ajst-27746	141	7	coupled	couple	VERB
ajst-27746	141	8	with	with	ADP
ajst-27746	141	9	the	the	DET
ajst-27746	141	10	nonlinear	nonlinear	ADJ
ajst-27746	141	11	geometric	geometric	ADJ
ajst-27746	141	12	properties	property	NOUN
ajst-27746	141	13	of	of	ADP
ajst-27746	141	14	the	the	DET
ajst-27746	141	15	helix	helix	NOUN
ajst-27746	142	1	𝑟	𝑟	NOUN
ajst-27746	142	2	𝜃	𝜃	X
ajst-27746	142	3	𝑎	𝑎	X
ajst-27746	142	4	𝑏𝜃	𝑏𝜃	NOUN
ajst-27746	142	5	:	:	PUNCT
ajst-27746	142	6	the	the	DET
ajst-27746	142	7	polar	polar	ADJ
ajst-27746	142	8	coordinate	coordinate	NOUN
ajst-27746	142	9	equation	equation	NOUN
ajst-27746	142	10	of	of	ADP
ajst-27746	142	11	the	the	DET
ajst-27746	142	12	helix	helix	NOUN
ajst-27746	142	13	is	be	AUX
ajst-27746	142	14	nonlinear	nonlinear	ADJ
ajst-27746	142	15	.	.	PUNCT
ajst-27746	143	1	we	we	PRON
ajst-27746	143	2	can	can	AUX
ajst-27746	143	3	formalize	formalize	VERB
ajst-27746	143	4	the	the	DET
ajst-27746	143	5	problem	problem	NOUN
ajst-27746	143	6	as	as	ADP
ajst-27746	143	7	the	the	DET
ajst-27746	143	8	following	follow	VERB
ajst-27746	143	9	non	non	ADJ
ajst-27746	143	10	-	-	ADJ
ajst-27746	143	11	convex	convex	ADJ
ajst-27746	143	12	optimization	optimization	NOUN
ajst-27746	143	13	problem	problem	NOUN
ajst-27746	143	14	,	,	PUNCT
ajst-27746	143	15	by	by	ADP
ajst-27746	143	16	minimizing	minimize	VERB
ajst-27746	143	17	the	the	DET
ajst-27746	143	18	travel	travel	NOUN
ajst-27746	143	19	distance	distance	NOUN
ajst-27746	143	20	or	or	CCONJ
ajst-27746	143	21	travel	travel	NOUN
ajst-27746	143	22	time	time	NOUN
ajst-27746	143	23	of	of	ADP
ajst-27746	143	24	the	the	DET
ajst-27746	143	25	faucet	faucet	NOUN
ajst-27746	143	26	,	,	PUNCT
ajst-27746	143	27	ensuring	ensure	VERB
ajst-27746	143	28	that	that	SCONJ
ajst-27746	143	29	the	the	DET
ajst-27746	143	30	faucet	faucet	NOUN
ajst-27746	143	31	enters	enter	VERB
ajst-27746	143	32	the	the	DET
ajst-27746	143	33	turning	turn	VERB
ajst-27746	143	34	space	space	NOUN
ajst-27746	143	35	with	with	ADP
ajst-27746	143	36	the	the	DET
ajst-27746	143	37	optimal	optimal	ADJ
ajst-27746	143	38	path	path	NOUN
ajst-27746	143	39	with	with	ADP
ajst-27746	143	40	the	the	DET
ajst-27746	143	41	smallest	small	ADJ
ajst-27746	143	42	pitch	pitch	NOUN
ajst-27746	143	43	.	.	PUNCT
ajst-27746	144	1	the	the	DET
ajst-27746	144	2	objective	objective	ADJ
ajst-27746	144	3	function	function	NOUN
ajst-27746	144	4	is	be	AUX
ajst-27746	144	5	as	as	SCONJ
ajst-27746	144	6	follows	follow	VERB
ajst-27746	144	7	:	:	PUNCT
ajst-27746	144	8			NOUN
ajst-27746	145	1			SYM
ajst-27746	145	2			NOUN
ajst-27746	145	3			SYM
ajst-27746	145	4			NOUN
ajst-27746	145	5			PROPN
ajst-27746	145	6	end	end	NOUN
ajst-27746	145	7	end	end	NOUN
ajst-27746	145	8	turn	turn	NOUN
ajst-27746	145	9	2	2	NUM
ajst-27746	145	10	22	22	NUM
ajst-27746	145	11	1	1	NUM
ajst-27746	145	12	1	1	NUM
ajst-27746	145	13	min	min	NOUN
ajst-27746	145	14	2	2	NUM
ajst-27746	145	15	hade	hade	NOUN
ajst-27746	145	16	max	max	PROPN
ajst-27746	145	17	min	min	PROPN
ajst-27746	145	18	,	,	PUNCT
ajst-27746	145	19	,	,	PUNCT
ajst-27746	145	20	b	b	X
ajst-27746	146	1	i	i	PRON
ajst-27746	146	2	i	i	PRON
ajst-27746	147	1	i	i	PRON
ajst-27746	147	2	i	i	INTJ
ajst-27746	148	1	i	i	VERB
ajst-27746	148	2	c	c	VERB
ajst-27746	149	1	b	b	NOUN
ajst-27746	149	2	r	r	NOUN
ajst-27746	149	3	a	a	DET
ajst-27746	149	4	b	b	NOUN
ajst-27746	149	5	r	r	NOUN
ajst-27746	149	6	r	r	NOUN
ajst-27746	149	7	r	r	NOUN
ajst-27746	149	8	r	r	NOUN
ajst-27746	149	9	d	d	NOUN
ajst-27746	149	10	i	i	PRON
ajst-27746	149	11	v	v	VERB
ajst-27746	149	12	a	a	DET
ajst-27746	149	13	a	a	DET
ajst-27746	149	14	a	a	DET
ajst-27746	149	15	b	b	NOUN
ajst-27746	149	16			X
ajst-27746	149	17			X
ajst-27746	149	18			PROPN
ajst-27746	149	19			PROPN
ajst-27746	149	20			PROPN
ajst-27746	150	1			PROPN
ajst-27746	150	2			VERB
ajst-27746	150	3			ADP
ajst-27746	150	4			X
ajst-27746	150	5			PROPN
ajst-27746	150	6			PUNCT
ajst-27746	150	7			NOUN
ajst-27746	150	8			NUM
ajst-27746	150	9			NUM
ajst-27746	150	10			NOUN
ajst-27746	150	11			VERB
ajst-27746	150	12			PROPN
ajst-27746	150	13			NUM
ajst-27746	150	14			NOUN
ajst-27746	150	15			NUM
ajst-27746	150	16			NUM
ajst-27746	150	17			NOUN
ajst-27746	150	18			NOUN
ajst-27746	151	1			ADV
ajst-27746	151	2	(	(	PUNCT
ajst-27746	151	3	25	25	NUM
ajst-27746	151	4	)	)	PUNCT
ajst-27746	151	5	according	accord	VERB
ajst-27746	151	6	to	to	ADP
ajst-27746	151	7	the	the	DET
ajst-27746	151	8	above	above	ADJ
ajst-27746	151	9	objective	objective	ADJ
ajst-27746	151	10	function	function	NOUN
ajst-27746	151	11	,	,	PUNCT
ajst-27746	151	12	the	the	DET
ajst-27746	151	13	following	follow	VERB
ajst-27746	151	14	objective	objective	ADJ
ajst-27746	151	15	function	function	NOUN
ajst-27746	151	16	with	with	ADP
ajst-27746	151	17	constraints	constraint	NOUN
ajst-27746	151	18	can	can	AUX
ajst-27746	151	19	be	be	AUX
ajst-27746	151	20	obtained	obtain	VERB
ajst-27746	151	21	:	:	PUNCT
ajst-27746	151	22	end	end	NOUN
ajst-27746	151	23	22	22	NUM
ajst-27746	151	24	20	20	NUM
ajst-27746	151	25	min	min	NOUN
ajst-27746	151	26	b	b	PROPN
ajst-27746	152	1	d	d	PROPN
ajst-27746	152	2	b	b	X
ajst-27746	152	3	dt	dt	X
ajst-27746	152	4	dt	dt	X
ajst-27746	152	5			X
ajst-27746	152	6			ADJ
ajst-27746	152	7			NOUN
ajst-27746	152	8			PROPN
ajst-27746	152	9			PROPN
ajst-27746	152	10			PROPN
ajst-27746	152	11			PROPN
ajst-27746	153	1			PROPN
ajst-27746	153	2			NOUN
ajst-27746	153	3			PUNCT
ajst-27746	153	4	(	(	PUNCT
ajst-27746	153	5	26	26	NUM
ajst-27746	153	6	)	)	PUNCT
ajst-27746	153	7	where	where	SCONJ
ajst-27746	153	8	,	,	PUNCT
ajst-27746	153	9	𝜆	𝜆	PRON
ajst-27746	153	10	is	be	AUX
ajst-27746	153	11	the	the	DET
ajst-27746	153	12	smoothness	smoothness	ADJ
ajst-27746	153	13	regularization	regularization	NOUN
ajst-27746	153	14	parameter	parameter	NOUN
ajst-27746	153	15	.	.	PUNCT
ajst-27746	154	1	in	in	ADP
ajst-27746	154	2	non	non	ADJ
ajst-27746	154	3	-	-	ADJ
ajst-27746	154	4	convex	convex	ADJ
ajst-27746	154	5	optimization	optimization	NOUN
ajst-27746	154	6	problems	problem	NOUN
ajst-27746	154	7	,	,	PUNCT
ajst-27746	154	8	the	the	DET
ajst-27746	154	9	objective	objective	ADJ
ajst-27746	154	10	function	function	NOUN
ajst-27746	154	11	and	and	CCONJ
ajst-27746	154	12	constraints	constraint	NOUN
ajst-27746	154	13	often	often	ADV
ajst-27746	154	14	have	have	VERB
ajst-27746	154	15	multiple	multiple	ADJ
ajst-27746	154	16	local	local	ADJ
ajst-27746	154	17	optimal	optimal	ADJ
ajst-27746	154	18	solutions	solution	NOUN
ajst-27746	154	19	.	.	PUNCT
ajst-27746	155	1	4.2	4.2	NUM
ajst-27746	155	2	.	.	X
ajst-27746	156	1	u	u	X
ajst-27746	156	2	-	-	NOUN
ajst-27746	156	3	turn	turn	VERB
ajst-27746	156	4	path	path	NOUN
ajst-27746	156	5	optimization	optimization	NOUN
ajst-27746	156	6	in	in	ADP
ajst-27746	156	7	order	order	NOUN
ajst-27746	156	8	to	to	PART
ajst-27746	156	9	further	far	ADV
ajst-27746	156	10	optimize	optimize	VERB
ajst-27746	156	11	the	the	DET
ajst-27746	156	12	speed	speed	NOUN
ajst-27746	156	13	control	control	NOUN
ajst-27746	156	14	,	,	PUNCT
ajst-27746	156	15	the	the	DET
ajst-27746	156	16	deeponet	deeponet	ADJ
ajst-27746	156	17	neural	neural	ADJ
ajst-27746	156	18	network	network	NOUN
ajst-27746	156	19	model	model	NOUN
ajst-27746	156	20	is	be	AUX
ajst-27746	156	21	introduced	introduce	VERB
ajst-27746	156	22	to	to	PART
ajst-27746	156	23	analyze	analyze	VERB
ajst-27746	156	24	the	the	DET
ajst-27746	156	25	path	path	NOUN
ajst-27746	156	26	planning	planning	NOUN
ajst-27746	156	27	and	and	CCONJ
ajst-27746	156	28	speed	speed	NOUN
ajst-27746	156	29	control	control	NOUN
ajst-27746	156	30	[	[	X
ajst-27746	156	31	8	8	NUM
ajst-27746	156	32	]	]	PUNCT
ajst-27746	156	33	.	.	PUNCT
ajst-27746	157	1	through	through	ADP
ajst-27746	157	2	the	the	DET
ajst-27746	157	3	combination	combination	NOUN
ajst-27746	157	4	of	of	ADP
ajst-27746	157	5	branch	branch	NOUN
ajst-27746	157	6	and	and	CCONJ
ajst-27746	157	7	backbone	backbone	NOUN
ajst-27746	157	8	network	network	NOUN
ajst-27746	157	9	,	,	PUNCT
ajst-27746	157	10	deeponet	deeponet	NOUN
ajst-27746	157	11	can	can	AUX
ajst-27746	157	12	effectively	effectively	ADV
ajst-27746	157	13	predict	predict	VERB
ajst-27746	157	14	the	the	DET
ajst-27746	157	15	speed	speed	NOUN
ajst-27746	157	16	and	and	CCONJ
ajst-27746	157	17	position	position	NOUN
ajst-27746	157	18	changes	change	NOUN
ajst-27746	157	19	of	of	ADP
ajst-27746	157	20	the	the	DET
ajst-27746	157	21	dragon	dragon	NOUN
ajst-27746	157	22	head	head	NOUN
ajst-27746	157	23	,	,	PUNCT
ajst-27746	157	24	body	body	NOUN
ajst-27746	157	25	and	and	CCONJ
ajst-27746	157	26	tail	tail	NOUN
ajst-27746	157	27	at	at	ADP
ajst-27746	157	28	different	different	ADJ
ajst-27746	157	29	time	time	NOUN
ajst-27746	157	30	points	point	NOUN
ajst-27746	157	31	.	.	PUNCT
ajst-27746	158	1	under	under	ADP
ajst-27746	158	2	the	the	DET
ajst-27746	158	3	given	give	VERB
ajst-27746	158	4	initial	initial	ADJ
ajst-27746	158	5	conditions	condition	NOUN
ajst-27746	158	6	and	and	CCONJ
ajst-27746	158	7	physical	physical	ADJ
ajst-27746	158	8	constraints	constraint	NOUN
ajst-27746	158	9	,	,	PUNCT
ajst-27746	158	10	the	the	DET
ajst-27746	158	11	path	path	NOUN
ajst-27746	158	12	and	and	CCONJ
ajst-27746	158	13	speed	speed	NOUN
ajst-27746	158	14	were	be	AUX
ajst-27746	158	15	dynamically	dynamically	ADV
ajst-27746	158	16	optimized	optimize	VERB
ajst-27746	158	17	through	through	ADP
ajst-27746	158	18	the	the	DET
ajst-27746	158	19	neural	neural	ADJ
ajst-27746	158	20	network	network	NOUN
ajst-27746	158	21	.	.	PUNCT
ajst-27746	159	1	the	the	DET
ajst-27746	159	2	introduction	introduction	NOUN
ajst-27746	159	3	of	of	ADP
ajst-27746	159	4	neural	neural	ADJ
ajst-27746	159	5	network	network	NOUN
ajst-27746	159	6	not	not	PART
ajst-27746	159	7	only	only	ADV
ajst-27746	159	8	improves	improve	VERB
ajst-27746	159	9	the	the	DET
ajst-27746	159	10	computational	computational	ADJ
ajst-27746	159	11	efficiency	efficiency	NOUN
ajst-27746	159	12	,	,	PUNCT
ajst-27746	159	13	but	but	CCONJ
ajst-27746	159	14	also	also	ADV
ajst-27746	159	15	increases	increase	VERB
ajst-27746	159	16	the	the	DET
ajst-27746	159	17	adaptability	adaptability	NOUN
ajst-27746	159	18	of	of	ADP
ajst-27746	159	19	the	the	DET
ajst-27746	159	20	model	model	NOUN
ajst-27746	159	21	in	in	ADP
ajst-27746	159	22	complex	complex	ADJ
ajst-27746	159	23	performance	performance	NOUN
ajst-27746	159	24	situations	situation	NOUN
ajst-27746	159	25	.	.	PUNCT
ajst-27746	160	1	with	with	ADP
ajst-27746	160	2	the	the	DET
ajst-27746	160	3	given	give	VERB
ajst-27746	160	4	pitch	pitch	NOUN
ajst-27746	160	5	,	,	PUNCT
ajst-27746	160	6	we	we	PRON
ajst-27746	160	7	can	can	AUX
ajst-27746	160	8	determine	determine	VERB
ajst-27746	160	9	the	the	DET
ajst-27746	160	10	spiral	spiral	ADJ
ajst-27746	160	11	equation	equation	NOUN
ajst-27746	160	12	of	of	ADP
ajst-27746	160	13	the	the	DET
ajst-27746	160	14	disc	disc	NOUN
ajst-27746	160	15	entry	entry	NOUN
ajst-27746	160	16	spiral	spiral	NOUN
ajst-27746	160	17	:	:	PUNCT
ajst-27746	160	18			PROPN
ajst-27746	160	19			PROPN
ajst-27746	160	20	in	in	ADP
ajst-27746	160	21	initial	initial	ADJ
ajst-27746	160	22	2	2	NUM
ajst-27746	160	23	in	in	ADP
ajst-27746	160	24	p	p	NOUN
ajst-27746	160	25	r	r	NOUN
ajst-27746	160	26	t	t	NOUN
ajst-27746	160	27	r	r	NOUN
ajst-27746	160	28			X
ajst-27746	160	29			PROPN
ajst-27746	160	30			PROPN
ajst-27746	160	31			ADJ
ajst-27746	160	32			PROPN
ajst-27746	160	33	(	(	PUNCT
ajst-27746	160	34	27	27	NUM
ajst-27746	160	35	)	)	PUNCT
ajst-27746	160	36	where	where	SCONJ
ajst-27746	160	37	,	,	PUNCT
ajst-27746	160	38	𝑟	𝑟	PRON
ajst-27746	160	39	is	be	AUX
ajst-27746	160	40	the	the	DET
ajst-27746	160	41	initial	initial	ADJ
ajst-27746	160	42	radius	radius	NOUN
ajst-27746	160	43	.	.	PUNCT
ajst-27746	161	1	since	since	SCONJ
ajst-27746	161	2	the	the	DET
ajst-27746	161	3	disc	disc	NOUN
ajst-27746	161	4	out	out	ADP
ajst-27746	161	5	spiral	spiral	ADJ
ajst-27746	161	6	is	be	AUX
ajst-27746	161	7	symmetric	symmetric	ADJ
ajst-27746	161	8	with	with	ADP
ajst-27746	161	9	the	the	DET
ajst-27746	161	10	center	center	NOUN
ajst-27746	161	11	of	of	ADP
ajst-27746	161	12	the	the	DET
ajst-27746	161	13	disc	disc	NOUN
ajst-27746	161	14	in	in	ADP
ajst-27746	161	15	spiral	spiral	NOUN
ajst-27746	161	16	,	,	PUNCT
ajst-27746	161	17	the	the	DET
ajst-27746	161	18	two	two	NUM
ajst-27746	161	19	curves	curve	NOUN
ajst-27746	161	20	are	be	AUX
ajst-27746	161	21	similar	similar	ADJ
ajst-27746	161	22	in	in	ADP
ajst-27746	161	23	form	form	NOUN
ajst-27746	161	24	,	,	PUNCT
ajst-27746	161	25	and	and	CCONJ
ajst-27746	161	26	we	we	PRON
ajst-27746	161	27	can	can	AUX
ajst-27746	161	28	get	get	VERB
ajst-27746	161	29	:	:	PUNCT
ajst-27746	161	30			NOUN
ajst-27746	161	31			PROPN
ajst-27746	161	32	out	out	ADP
ajst-27746	161	33	out	out	ADV
ajst-27746	161	34	initial	initial	ADJ
ajst-27746	161	35	2	2	NUM
ajst-27746	161	36	p	p	NOUN
ajst-27746	161	37	r	r	NOUN
ajst-27746	161	38	t	t	NOUN
ajst-27746	161	39	r	r	NOUN
ajst-27746	161	40			X
ajst-27746	161	41			PROPN
ajst-27746	161	42			PROPN
ajst-27746	161	43			ADJ
ajst-27746	161	44			PROPN
ajst-27746	161	45			CCONJ
ajst-27746	161	46	(	(	PUNCT
ajst-27746	161	47	28	28	NUM
ajst-27746	161	48	)	)	PUNCT
ajst-27746	161	49	according	accord	VERB
ajst-27746	161	50	to	to	PART
ajst-27746	161	51	figure	figure	NOUN
ajst-27746	161	52	2	2	NUM
ajst-27746	161	53	,	,	PUNCT
ajst-27746	161	54	the	the	DET
ajst-27746	161	55	faucet	faucet	NOUN
ajst-27746	161	56	enters	enter	VERB
ajst-27746	161	57	the	the	DET
ajst-27746	161	58	u	u	NOUN
ajst-27746	161	59	-	-	NOUN
ajst-27746	161	60	turn	turn	NOUN
ajst-27746	161	61	path	path	NOUN
ajst-27746	161	62	from	from	ADP
ajst-27746	161	63	the	the	DET
ajst-27746	161	64	right	right	ADJ
ajst-27746	161	65	tangent	tangent	NOUN
ajst-27746	161	66	point	point	NOUN
ajst-27746	161	67	,	,	PUNCT
ajst-27746	161	68	𝑟	𝑟	NOUN
ajst-27746	161	69	corresponding	correspond	VERB
ajst-27746	161	70	to	to	ADP
ajst-27746	161	71	the	the	DET
ajst-27746	161	72	arc	arc	NOUN
ajst-27746	161	73	radius	radius	NOUN
ajst-27746	161	74	of	of	ADP
ajst-27746	161	75	the	the	DET
ajst-27746	161	76	entering	enter	VERB
ajst-27746	161	77	part	part	NOUN
ajst-27746	161	78	and	and	CCONJ
ajst-27746	161	79	𝑟	𝑟	NOUN
ajst-27746	161	80	the	the	DET
ajst-27746	161	81	arc	arc	NOUN
ajst-27746	161	82	radius	radius	NOUN
ajst-27746	161	83	of	of	ADP
ajst-27746	161	84	the	the	DET
ajst-27746	161	85	leaving	leave	VERB
ajst-27746	161	86	part	part	NOUN
ajst-27746	161	87	,	,	PUNCT
ajst-27746	161	88	and	and	CCONJ
ajst-27746	161	89	the	the	DET
ajst-27746	161	90	red	red	ADJ
ajst-27746	161	91	line	line	NOUN
ajst-27746	161	92	is	be	AUX
ajst-27746	161	93	the	the	DET
ajst-27746	161	94	u	u	NOUN
ajst-27746	161	95	-	-	NOUN
ajst-27746	161	96	turn	turn	NOUN
ajst-27746	161	97	path	path	NOUN
ajst-27746	161	98	.	.	PUNCT
ajst-27746	162	1	according	accord	VERB
ajst-27746	162	2	to	to	ADP
ajst-27746	162	3	the	the	DET
ajst-27746	162	4	analysis	analysis	NOUN
ajst-27746	162	5	of	of	ADP
ajst-27746	162	6	known	known	ADJ
ajst-27746	162	7	conditions	condition	NOUN
ajst-27746	162	8	,	,	PUNCT
ajst-27746	162	9	since	since	SCONJ
ajst-27746	162	10	the	the	DET
ajst-27746	162	11	points	point	NOUN
ajst-27746	162	12	of	of	ADP
ajst-27746	162	13	entry	entry	NOUN
ajst-27746	162	14	and	and	CCONJ
ajst-27746	162	15	departure	departure	NOUN
ajst-27746	162	16	are	be	AUX
ajst-27746	162	17	uniquely	uniquely	ADV
ajst-27746	162	18	determined	determined	ADJ
ajst-27746	162	19	and	and	CCONJ
ajst-27746	162	20	the	the	DET
ajst-27746	162	21	centers	center	NOUN
ajst-27746	162	22	of	of	ADP
ajst-27746	162	23	the	the	DET
ajst-27746	162	24	two	two	NUM
ajst-27746	162	25	points	point	NOUN
ajst-27746	162	26	are	be	AUX
ajst-27746	162	27	symmetric	symmetric	ADJ
ajst-27746	162	28	,	,	PUNCT
ajst-27746	162	29	we	we	PRON
ajst-27746	162	30	connect	connect	VERB
ajst-27746	162	31	the	the	DET
ajst-27746	162	32	two	two	NUM
ajst-27746	162	33	points	point	NOUN
ajst-27746	162	34	,	,	PUNCT
ajst-27746	162	35	and	and	CCONJ
ajst-27746	162	36	the	the	DET
ajst-27746	162	37	length	length	NOUN
ajst-27746	162	38	of	of	ADP
ajst-27746	162	39	the	the	DET
ajst-27746	162	40	two	two	NUM
ajst-27746	162	41	points	point	NOUN
ajst-27746	162	42	𝐷	𝐷	NOUN
ajst-27746	162	43	is	be	AUX
ajst-27746	162	44	the	the	DET
ajst-27746	162	45	diameter	diameter	NOUN
ajst-27746	162	46	of	of	ADP
ajst-27746	162	47	the	the	DET
ajst-27746	162	48	u	u	NOUN
ajst-27746	162	49	-	-	NOUN
ajst-27746	162	50	turn	turn	NOUN
ajst-27746	162	51	area	area	NOUN
ajst-27746	162	52	.	.	PUNCT
ajst-27746	163	1	we	we	PRON
ajst-27746	163	2	can	can	AUX
ajst-27746	163	3	get	get	VERB
ajst-27746	163	4	the	the	DET
ajst-27746	163	5	following	follow	VERB
ajst-27746	163	6	relations	relation	NOUN
ajst-27746	163	7	𝐷	𝐷	PROPN
ajst-27746	163	8	⋅	⋅	PROPN
ajst-27746	163	9	cos	cos	PROPN
ajst-27746	163	10	𝛼	𝛼	NOUN
ajst-27746	163	11	𝑟	𝑟	NOUN
ajst-27746	163	12	𝑟	𝑟	ADP
ajst-27746	163	13	𝑟	𝑟	X
ajst-27746	163	14	𝑟	𝑟	X
ajst-27746	163	15	cos	cos	PROPN
ajst-27746	163	16	2𝛼.	2𝛼.	NUM
ajst-27746	163	17	according	accord	VERB
ajst-27746	163	18	to	to	ADP
ajst-27746	163	19	the	the	DET
ajst-27746	163	20	arc	arc	NOUN
ajst-27746	163	21	length	length	NOUN
ajst-27746	163	22	formula	formula	NOUN
ajst-27746	163	23	,	,	PUNCT
ajst-27746	163	24	the	the	DET
ajst-27746	163	25	total	total	ADJ
ajst-27746	163	26	length	length	NOUN
ajst-27746	163	27	of	of	ADP
ajst-27746	163	28	the	the	DET
ajst-27746	163	29	turn	turn	NOUN
ajst-27746	163	30	-	-	PUNCT
ajst-27746	163	31	around	around	ADP
ajst-27746	163	32	path	path	NOUN
ajst-27746	163	33	is	be	AUX
ajst-27746	163	34	𝑆turn	𝑆turn	PROPN
ajst-27746	163	35	𝑟	𝑟	NOUN
ajst-27746	163	36	𝑟	𝑟	X
ajst-27746	163	37	⋅	⋅	PROPN
ajst-27746	163	38	𝜋	𝜋	PRON
ajst-27746	163	39	2𝛼	2𝛼	PROPN
ajst-27746	163	40	.	.	PUNCT
ajst-27746	164	1	figure	figure	VERB
ajst-27746	164	2	3	3	NUM
ajst-27746	164	3	.	.	PUNCT
ajst-27746	164	4	schematic	schematic	ADJ
ajst-27746	164	5	diagram	diagram	NOUN
ajst-27746	164	6	of	of	ADP
ajst-27746	164	7	u	u	NOUN
ajst-27746	164	8	-	-	NOUN
ajst-27746	164	9	turn	turn	NOUN
ajst-27746	164	10	path	path	NOUN
ajst-27746	164	11	as	as	SCONJ
ajst-27746	164	12	shown	show	VERB
ajst-27746	164	13	in	in	ADP
ajst-27746	164	14	figure	figure	NOUN
ajst-27746	164	15	3	3	NUM
ajst-27746	164	16	,	,	PUNCT
ajst-27746	164	17	the	the	DET
ajst-27746	164	18	traditional	traditional	ADJ
ajst-27746	164	19	method	method	NOUN
ajst-27746	164	20	needs	need	VERB
ajst-27746	164	21	to	to	PART
ajst-27746	164	22	calculate	calculate	VERB
ajst-27746	164	23	the	the	DET
ajst-27746	164	24	turn	turn	VERB
ajst-27746	164	25	-	-	PUNCT
ajst-27746	164	26	around	around	ADP
ajst-27746	164	27	path	path	NOUN
ajst-27746	164	28	and	and	CCONJ
ajst-27746	164	29	speed	speed	NOUN
ajst-27746	164	30	change	change	NOUN
ajst-27746	164	31	of	of	ADP
ajst-27746	164	32	the	the	DET
ajst-27746	164	33	dragon	dragon	NOUN
ajst-27746	164	34	dance	dance	NOUN
ajst-27746	164	35	team	team	NOUN
ajst-27746	164	36	through	through	ADP
ajst-27746	164	37	complex	complex	ADJ
ajst-27746	164	38	geometric	geometric	ADJ
ajst-27746	164	39	analysis	analysis	NOUN
ajst-27746	164	40	,	,	PUNCT
ajst-27746	164	41	differential	differential	ADJ
ajst-27746	164	42	equation	equation	NOUN
ajst-27746	164	43	solving	solving	NOUN
ajst-27746	164	44	and	and	CCONJ
ajst-27746	164	45	other	other	ADJ
ajst-27746	164	46	methods	method	NOUN
ajst-27746	164	47	.	.	PUNCT
ajst-27746	165	1	in	in	ADP
ajst-27746	165	2	this	this	DET
ajst-27746	165	3	chapter	chapter	NOUN
ajst-27746	165	4	,	,	PUNCT
ajst-27746	165	5	the	the	DET
ajst-27746	165	6	tangential	tangential	ADJ
ajst-27746	165	7	conditions	condition	NOUN
ajst-27746	165	8	of	of	ADP
ajst-27746	165	9	spirals	spiral	NOUN
ajst-27746	165	10	,	,	PUNCT
ajst-27746	165	11	arcs	arc	NOUN
ajst-27746	165	12	,	,	PUNCT
ajst-27746	165	13	velocity	velocity	NOUN
ajst-27746	165	14	curves	curve	NOUN
ajst-27746	165	15	,	,	PUNCT
ajst-27746	165	16	etc	etc	X
ajst-27746	165	17	.	.	X
ajst-27746	165	18	,	,	PUNCT
ajst-27746	165	19	involve	involve	VERB
ajst-27746	165	20	a	a	DET
ajst-27746	165	21	variety	variety	NOUN
ajst-27746	165	22	of	of	ADP
ajst-27746	165	23	geometric	geometric	ADJ
ajst-27746	165	24	and	and	CCONJ
ajst-27746	165	25	physical	physical	ADJ
ajst-27746	165	26	laws	law	NOUN
ajst-27746	165	27	,	,	PUNCT
ajst-27746	165	28	which	which	PRON
ajst-27746	165	29	can	can	AUX
ajst-27746	165	30	make	make	VERB
ajst-27746	165	31	the	the	DET
ajst-27746	165	32	analytical	analytical	ADJ
ajst-27746	165	33	solution	solution	NOUN
ajst-27746	165	34	process	process	NOUN
ajst-27746	165	35	very	very	ADV
ajst-27746	165	36	tedious	tedious	ADJ
ajst-27746	165	37	.	.	PUNCT
ajst-27746	166	1	deepone	deepone	NOUN
ajst-27746	166	2	can	can	AUX
ajst-27746	166	3	map	map	VERB
ajst-27746	166	4	these	these	DET
ajst-27746	166	5	complex	complex	ADJ
ajst-27746	166	6	relationships	relationship	NOUN
ajst-27746	166	7	to	to	ADP
ajst-27746	166	8	the	the	DET
ajst-27746	166	9	process	process	NOUN
ajst-27746	166	10	of	of	ADP
ajst-27746	166	11	learning	learn	VERB
ajst-27746	166	12	by	by	ADP
ajst-27746	166	13	the	the	DET
ajst-27746	166	14	neural	neural	ADJ
ajst-27746	166	15	network	network	NOUN
ajst-27746	166	16	,	,	PUNCT
ajst-27746	166	17	which	which	PRON
ajst-27746	166	18	learns	learn	VERB
ajst-27746	166	19	directly	directly	ADV
ajst-27746	166	20	from	from	ADP
ajst-27746	166	21	the	the	DET
ajst-27746	166	22	input	input	NOUN
ajst-27746	166	23	data	datum	NOUN
ajst-27746	166	24	(	(	PUNCT
ajst-27746	166	25	such	such	ADJ
ajst-27746	166	26	as	as	ADP
ajst-27746	166	27	parameters	parameter	NOUN
ajst-27746	166	28	such	such	ADJ
ajst-27746	166	29	as	as	ADP
ajst-27746	166	30	pitch	pitch	NOUN
ajst-27746	166	31	,	,	PUNCT
ajst-27746	166	32	curvature	curvature	NOUN
ajst-27746	166	33	,	,	PUNCT
ajst-27746	166	34	velocity	velocity	NOUN
ajst-27746	166	35	,	,	PUNCT
ajst-27746	166	36	time	time	NOUN
ajst-27746	166	37	)	)	PUNCT
ajst-27746	166	38	to	to	ADP
ajst-27746	166	39	the	the	DET
ajst-27746	166	40	output	output	NOUN
ajst-27746	166	41	(	(	PUNCT
ajst-27746	166	42	position	position	NOUN
ajst-27746	166	43	and	and	CCONJ
ajst-27746	166	44	velocity	velocity	NOUN
ajst-27746	166	45	)	)	PUNCT
ajst-27746	166	46	,	,	PUNCT
ajst-27746	166	47	avoiding	avoid	VERB
ajst-27746	166	48	the	the	DET
ajst-27746	166	49	steps	step	NOUN
ajst-27746	166	50	of	of	ADP
ajst-27746	166	51	manually	manually	ADV
ajst-27746	166	52	solving	solve	VERB
ajst-27746	166	53	complex	complex	ADJ
ajst-27746	166	54	equations	equation	NOUN
ajst-27746	166	55	.	.	PUNCT
ajst-27746	167	1	deeponet	deeponet	NOUN
ajst-27746	167	2	is	be	AUX
ajst-27746	167	3	a	a	DET
ajst-27746	167	4	network	network	NOUN
ajst-27746	167	5	structure	structure	NOUN
ajst-27746	167	6	for	for	ADP
ajst-27746	167	7	learning	learn	VERB
ajst-27746	167	8	operators	operator	NOUN
ajst-27746	167	9	,	,	PUNCT
ajst-27746	167	10	suitable	suitable	ADJ
ajst-27746	167	11	for	for	ADP
ajst-27746	167	12	mapping	mapping	NOUN
ajst-27746	167	13	input	input	NOUN
ajst-27746	167	14	functions	function	NOUN
ajst-27746	167	15	to	to	ADP
ajst-27746	167	16	output	output	NOUN
ajst-27746	167	17	functions	function	NOUN
ajst-27746	167	18	.	.	PUNCT
ajst-27746	168	1	we	we	PRON
ajst-27746	168	2	hope	hope	VERB
ajst-27746	168	3	to	to	PART
ajst-27746	168	4	learn	learn	VERB
ajst-27746	168	5	the	the	DET
ajst-27746	168	6	movement	movement	NOUN
ajst-27746	168	7	of	of	ADP
ajst-27746	168	8	each	each	DET
ajst-27746	168	9	node	node	NOUN
ajst-27746	168	10	of	of	ADP
ajst-27746	168	11	the	the	DET
ajst-27746	168	12	dragon	dragon	NOUN
ajst-27746	168	13	dance	dance	NOUN
ajst-27746	168	14	team	team	NOUN
ajst-27746	168	15	through	through	ADP
ajst-27746	168	16	deeponet	deeponet	NOUN
ajst-27746	168	17	,	,	PUNCT
ajst-27746	168	18	especially	especially	ADV
ajst-27746	168	19	in	in	ADP
ajst-27746	168	20	the	the	DET
ajst-27746	168	21	process	process	NOUN
ajst-27746	168	22	of	of	ADP
ajst-27746	168	23	disc	disc	NOUN
ajst-27746	168	24	entry	entry	NOUN
ajst-27746	168	25	,	,	PUNCT
ajst-27746	168	26	turn	turn	VERB
ajst-27746	168	27	around	around	ADV
ajst-27746	168	28	and	and	CCONJ
ajst-27746	168	29	disc	disc	VERB
ajst-27746	168	30	out	out	ADP
ajst-27746	168	31	,	,	PUNCT
ajst-27746	168	32	and	and	CCONJ
ajst-27746	168	33	calculate	calculate	VERB
ajst-27746	168	34	the	the	DET
ajst-27746	168	35	position	position	NOUN
ajst-27746	168	36	and	and	CCONJ
ajst-27746	168	37	speed	speed	NOUN
ajst-27746	168	38	of	of	ADP
ajst-27746	168	39	the	the	DET
ajst-27746	168	40	dragon	dragon	NOUN
ajst-27746	168	41	head	head	NOUN
ajst-27746	168	42	,	,	PUNCT
ajst-27746	168	43	body	body	NOUN
ajst-27746	168	44	and	and	CCONJ
ajst-27746	168	45	tail	tail	NOUN
ajst-27746	168	46	.	.	PUNCT
ajst-27746	169	1	deeponet	deeponet	NOUN
ajst-27746	169	2	consists	consist	VERB
ajst-27746	169	3	of	of	ADP
ajst-27746	169	4	a	a	DET
ajst-27746	169	5	two	two	NUM
ajst-27746	169	6	-	-	PUNCT
ajst-27746	169	7	part	part	NOUN
ajst-27746	169	8	network	network	NOUN
ajst-27746	169	9	:	:	PUNCT
ajst-27746	169	10	307	307	NUM
ajst-27746	169	11	•	•	NOUN
ajst-27746	169	12	branch	branch	NOUN
ajst-27746	169	13	net	net	NOUN
ajst-27746	169	14	(	(	PUNCT
ajst-27746	169	15	branch	branch	NOUN
ajst-27746	169	16	network	network	NOUN
ajst-27746	169	17	)	)	PUNCT
ajst-27746	169	18	:	:	PUNCT
ajst-27746	169	19	for	for	ADP
ajst-27746	169	20	processing	processing	NOUN
ajst-27746	169	21	inputs	input	NOUN
ajst-27746	169	22	(	(	PUNCT
ajst-27746	169	23	such	such	ADJ
ajst-27746	169	24	as	as	ADP
ajst-27746	169	25	initial	initial	ADJ
ajst-27746	169	26	conditions	condition	NOUN
ajst-27746	169	27	,	,	PUNCT
ajst-27746	169	28	system	system	NOUN
ajst-27746	169	29	parameters	parameter	NOUN
ajst-27746	169	30	,	,	PUNCT
ajst-27746	169	31	etc	etc	X
ajst-27746	169	32	.	.	X
ajst-27746	169	33	)	)	PUNCT
ajst-27746	169	34	.	.	PUNCT
ajst-27746	170	1	•	•	NUM
ajst-27746	170	2	trunk	trunk	NOUN
ajst-27746	170	3	net	net	NOUN
ajst-27746	170	4	(	(	PUNCT
ajst-27746	170	5	trunk	trunk	NOUN
ajst-27746	170	6	network	network	NOUN
ajst-27746	170	7	)	)	PUNCT
ajst-27746	170	8	:	:	PUNCT
ajst-27746	170	9	used	use	VERB
ajst-27746	170	10	to	to	PART
ajst-27746	170	11	handle	handle	VERB
ajst-27746	170	12	solutions	solution	NOUN
ajst-27746	170	13	at	at	ADP
ajst-27746	170	14	predicted	predict	VERB
ajst-27746	170	15	points	point	NOUN
ajst-27746	170	16	in	in	ADP
ajst-27746	170	17	time	time	NOUN
ajst-27746	170	18	and	and	CCONJ
ajst-27746	170	19	space	space	NOUN
ajst-27746	170	20	.	.	PUNCT
ajst-27746	171	1	define	define	VERB
ajst-27746	171	2	the	the	DET
ajst-27746	171	3	inputs	input	NOUN
ajst-27746	171	4	as	as	ADP
ajst-27746	171	5	the	the	DET
ajst-27746	171	6	geometric	geometric	ADJ
ajst-27746	171	7	parameters	parameter	NOUN
ajst-27746	171	8	of	of	ADP
ajst-27746	171	9	the	the	DET
ajst-27746	171	10	dragon	dragon	NOUN
ajst-27746	171	11	dance	dance	NOUN
ajst-27746	171	12	team	team	NOUN
ajst-27746	171	13	and	and	CCONJ
ajst-27746	171	14	time	time	NOUN
ajst-27746	171	15	,	,	PUNCT
ajst-27746	171	16	and	and	CCONJ
ajst-27746	171	17	the	the	DET
ajst-27746	171	18	outputs	output	NOUN
ajst-27746	171	19	as	as	ADP
ajst-27746	171	20	the	the	DET
ajst-27746	171	21	position	position	NOUN
ajst-27746	171	22	information	information	NOUN
ajst-27746	171	23	and	and	CCONJ
ajst-27746	171	24	velocity	velocity	NOUN
ajst-27746	171	25	information	information	NOUN
ajst-27746	171	26	of	of	ADP
ajst-27746	171	27	the	the	DET
ajst-27746	171	28	front	front	ADJ
ajst-27746	171	29	and	and	CCONJ
ajst-27746	171	30	back	back	ADJ
ajst-27746	171	31	handles	handle	NOUN
ajst-27746	171	32	at	at	ADP
ajst-27746	171	33	these	these	DET
ajst-27746	171	34	points	point	NOUN
ajst-27746	171	35	in	in	ADP
ajst-27746	171	36	time	time	NOUN
ajst-27746	171	37	.	.	PUNCT
ajst-27746	172	1	the	the	DET
ajst-27746	172	2	modeling	modeling	NOUN
ajst-27746	172	3	is	be	AUX
ajst-27746	172	4	based	base	VERB
ajst-27746	172	5	on	on	ADP
ajst-27746	172	6	the	the	DET
ajst-27746	172	7	wave	wave	NOUN
ajst-27746	172	8	equation	equation	NOUN
ajst-27746	172	9	:	:	PUNCT
ajst-27746	172	10	2	2	NUM
ajst-27746	172	11	2	2	NUM
ajst-27746	172	12	2	2	NUM
ajst-27746	172	13	2	2	NUM
ajst-27746	172	14	2	2	NUM
ajst-27746	172	15	u	u	NOUN
ajst-27746	172	16	u	u	NOUN
ajst-27746	172	17	c	c	PROPN
ajst-27746	172	18	t	t	PROPN
ajst-27746	172	19	x	x	SYM
ajst-27746	172	20			ADJ
ajst-27746	172	21			ADJ
ajst-27746	172	22			PROPN
ajst-27746	172	23			ADJ
ajst-27746	172	24			PROPN
ajst-27746	172	25	(	(	PUNCT
ajst-27746	172	26	29	29	NUM
ajst-27746	172	27	)	)	PUNCT
ajst-27746	172	28	by	by	ADP
ajst-27746	172	29	introducing	introduce	VERB
ajst-27746	172	30	deeponet	deeponet	NOUN
ajst-27746	172	31	deep	deep	ADJ
ajst-27746	172	32	learning	learning	NOUN
ajst-27746	172	33	model	model	NOUN
ajst-27746	172	34	,	,	PUNCT
ajst-27746	172	35	the	the	DET
ajst-27746	172	36	computational	computational	ADJ
ajst-27746	172	37	efficiency	efficiency	NOUN
ajst-27746	172	38	and	and	CCONJ
ajst-27746	172	39	path	path	NOUN
ajst-27746	172	40	planning	planning	NOUN
ajst-27746	172	41	accuracy	accuracy	NOUN
ajst-27746	172	42	of	of	ADP
ajst-27746	172	43	the	the	DET
ajst-27746	172	44	model	model	NOUN
ajst-27746	172	45	are	be	AUX
ajst-27746	172	46	improved	improve	VERB
ajst-27746	172	47	.	.	PUNCT
ajst-27746	173	1	deeponet	deeponet	NOUN
ajst-27746	173	2	is	be	AUX
ajst-27746	173	3	able	able	ADJ
ajst-27746	173	4	to	to	PART
ajst-27746	173	5	learn	learn	VERB
ajst-27746	173	6	complex	complex	ADJ
ajst-27746	173	7	nonlinear	nonlinear	ADJ
ajst-27746	173	8	relationships	relationship	NOUN
ajst-27746	173	9	,	,	PUNCT
ajst-27746	173	10	and	and	CCONJ
ajst-27746	173	11	combined	combine	VERB
ajst-27746	173	12	with	with	ADP
ajst-27746	173	13	path	path	NOUN
ajst-27746	173	14	optimization	optimization	NOUN
ajst-27746	173	15	algorithms	algorithm	NOUN
ajst-27746	173	16	,	,	PUNCT
ajst-27746	173	17	ensure	ensure	VERB
ajst-27746	173	18	smooth	smooth	ADJ
ajst-27746	173	19	progress	progress	NOUN
ajst-27746	173	20	and	and	CCONJ
ajst-27746	173	21	speed	speed	NOUN
ajst-27746	173	22	expectations	expectation	NOUN
ajst-27746	173	23	of	of	ADP
ajst-27746	173	24	the	the	DET
ajst-27746	173	25	dragon	dragon	NOUN
ajst-27746	173	26	dance	dance	NOUN
ajst-27746	173	27	team	team	NOUN
ajst-27746	173	28	under	under	ADP
ajst-27746	173	29	different	different	ADJ
ajst-27746	173	30	space	space	NOUN
ajst-27746	173	31	and	and	CCONJ
ajst-27746	173	32	time	time	NOUN
ajst-27746	173	33	conditions	condition	NOUN
ajst-27746	173	34	.	.	PUNCT
ajst-27746	174	1	5	5	X
ajst-27746	174	2	.	.	X
ajst-27746	174	3	conclusions	conclusion	NOUN
ajst-27746	174	4	aiming	aim	VERB
ajst-27746	174	5	at	at	ADP
ajst-27746	174	6	the	the	DET
ajst-27746	174	7	problem	problem	NOUN
ajst-27746	174	8	of	of	ADP
ajst-27746	174	9	path	path	NOUN
ajst-27746	174	10	and	and	CCONJ
ajst-27746	174	11	speed	speed	NOUN
ajst-27746	174	12	control	control	NOUN
ajst-27746	174	13	in	in	ADP
ajst-27746	174	14	traditional	traditional	ADJ
ajst-27746	174	15	folk	folk	NOUN
ajst-27746	174	16	performance	performance	NOUN
ajst-27746	174	17	,	,	PUNCT
ajst-27746	174	18	this	this	DET
ajst-27746	174	19	paper	paper	NOUN
ajst-27746	174	20	proposes	propose	VERB
ajst-27746	174	21	a	a	DET
ajst-27746	174	22	set	set	NOUN
ajst-27746	174	23	of	of	ADP
ajst-27746	174	24	solutions	solution	NOUN
ajst-27746	174	25	based	base	VERB
ajst-27746	174	26	on	on	ADP
ajst-27746	174	27	mathematical	mathematical	ADJ
ajst-27746	174	28	modeling	modeling	NOUN
ajst-27746	174	29	,	,	PUNCT
ajst-27746	174	30	numerical	numerical	ADJ
ajst-27746	174	31	optimization	optimization	NOUN
ajst-27746	174	32	and	and	CCONJ
ajst-27746	174	33	deep	deep	ADJ
ajst-27746	174	34	learning	learning	NOUN
ajst-27746	174	35	model	model	NOUN
ajst-27746	174	36	.	.	PUNCT
ajst-27746	175	1	by	by	ADP
ajst-27746	175	2	accurately	accurately	ADV
ajst-27746	175	3	describing	describe	VERB
ajst-27746	175	4	the	the	DET
ajst-27746	175	5	movement	movement	NOUN
ajst-27746	175	6	mode	mode	NOUN
ajst-27746	175	7	of	of	ADP
ajst-27746	175	8	the	the	DET
ajst-27746	175	9	performing	perform	VERB
ajst-27746	175	10	team	team	NOUN
ajst-27746	175	11	,	,	PUNCT
ajst-27746	175	12	combined	combine	VERB
ajst-27746	175	13	with	with	ADP
ajst-27746	175	14	pde	pde	NOUN
ajst-27746	175	15	constraint	constraint	NOUN
ajst-27746	175	16	and	and	CCONJ
ajst-27746	175	17	optimization	optimization	NOUN
ajst-27746	175	18	algorithm	algorithm	NOUN
ajst-27746	175	19	,	,	PUNCT
ajst-27746	175	20	we	we	PRON
ajst-27746	175	21	realized	realize	VERB
ajst-27746	175	22	the	the	DET
ajst-27746	175	23	fine	fine	ADJ
ajst-27746	175	24	adjustment	adjustment	NOUN
ajst-27746	175	25	of	of	ADP
ajst-27746	175	26	the	the	DET
ajst-27746	175	27	path	path	NOUN
ajst-27746	175	28	and	and	CCONJ
ajst-27746	175	29	speed	speed	NOUN
ajst-27746	175	30	.	.	PUNCT
ajst-27746	176	1	the	the	DET
ajst-27746	176	2	research	research	NOUN
ajst-27746	176	3	results	result	NOUN
ajst-27746	176	4	show	show	VERB
ajst-27746	176	5	that	that	SCONJ
ajst-27746	176	6	this	this	DET
ajst-27746	176	7	scheme	scheme	NOUN
ajst-27746	176	8	can	can	AUX
ajst-27746	176	9	significantly	significantly	ADV
ajst-27746	176	10	improve	improve	VERB
ajst-27746	176	11	the	the	DET
ajst-27746	176	12	performance	performance	NOUN
ajst-27746	176	13	's	's	PART
ajst-27746	176	14	appreciation	appreciation	NOUN
ajst-27746	176	15	and	and	CCONJ
ajst-27746	176	16	execution	execution	NOUN
ajst-27746	176	17	accuracy	accuracy	NOUN
ajst-27746	176	18	,	,	PUNCT
ajst-27746	176	19	while	while	SCONJ
ajst-27746	176	20	ensuring	ensure	VERB
ajst-27746	176	21	the	the	DET
ajst-27746	176	22	smoothness	smoothness	NOUN
ajst-27746	176	23	of	of	ADP
ajst-27746	176	24	the	the	DET
ajst-27746	176	25	movement	movement	NOUN
ajst-27746	176	26	and	and	CCONJ
ajst-27746	176	27	the	the	DET
ajst-27746	176	28	rationality	rationality	NOUN
ajst-27746	176	29	of	of	ADP
ajst-27746	176	30	the	the	DET
ajst-27746	176	31	speed	speed	NOUN
ajst-27746	176	32	.	.	PUNCT
ajst-27746	177	1	in	in	ADP
ajst-27746	177	2	addition	addition	NOUN
ajst-27746	177	3	,	,	PUNCT
ajst-27746	177	4	we	we	PRON
ajst-27746	177	5	also	also	ADV
ajst-27746	177	6	verified	verify	VERB
ajst-27746	177	7	the	the	DET
ajst-27746	177	8	robustness	robustness	NOUN
ajst-27746	177	9	of	of	ADP
ajst-27746	177	10	the	the	DET
ajst-27746	177	11	model	model	NOUN
ajst-27746	177	12	through	through	ADP
ajst-27746	177	13	sensitivity	sensitivity	NOUN
ajst-27746	177	14	analysis	analysis	NOUN
ajst-27746	177	15	,	,	PUNCT
ajst-27746	177	16	and	and	CCONJ
ajst-27746	177	17	further	far	ADV
ajst-27746	177	18	improved	improve	VERB
ajst-27746	177	19	the	the	DET
ajst-27746	177	20	precision	precision	NOUN
ajst-27746	177	21	and	and	CCONJ
ajst-27746	177	22	efficiency	efficiency	NOUN
ajst-27746	177	23	of	of	ADP
ajst-27746	177	24	path	path	NOUN
ajst-27746	177	25	planning	planning	NOUN
ajst-27746	177	26	by	by	ADP
ajst-27746	177	27	introducing	introduce	VERB
ajst-27746	177	28	deeponet	deeponet	NOUN
ajst-27746	177	29	deep	deep	ADJ
ajst-27746	177	30	learning	learning	NOUN
ajst-27746	177	31	model	model	NOUN
ajst-27746	177	32	.	.	PUNCT
ajst-27746	178	1	references	reference	NOUN
ajst-27746	178	2	[	[	X
ajst-27746	178	3	1	1	NUM
ajst-27746	178	4	]	]	PUNCT
ajst-27746	178	5	jiayi	jiayi	NOUN
ajst-27746	178	6	l	l	NOUN
ajst-27746	178	7	,	,	PUNCT
ajst-27746	178	8	bin	bin	PROPN
ajst-27746	178	9	z	z	PROPN
ajst-27746	178	10	,	,	PUNCT
ajst-27746	178	11	fang	fang	X
ajst-27746	178	12	x	x	PUNCT
ajst-27746	178	13	.dynamic	.dynamic	PUNCT
ajst-27746	178	14	path	path	NOUN
ajst-27746	178	15	planning	planning	NOUN
ajst-27746	178	16	of	of	ADP
ajst-27746	178	17	intelligent	intelligent	ADJ
ajst-27746	178	18	robot	robot	NOUN
ajst-27746	178	19	in	in	ADP
ajst-27746	178	20	power	power	NOUN
ajst-27746	178	21	equipment	equipment	NOUN
ajst-27746	178	22	maintenance	maintenance	NOUN
ajst-27746	178	23	environment[j].energy	environment[j].energy	PROPN
ajst-27746	178	24	reports,2023,9(s8):784	reports,2023,9(s8):784	PROPN
ajst-27746	178	25	-	-	SYM
ajst-27746	178	26	791	791	NUM
ajst-27746	178	27	.	.	PUNCT
ajst-27746	179	1	[	[	X
ajst-27746	179	2	2	2	X
ajst-27746	179	3	]	]	PUNCT
ajst-27746	179	4	georgios	georgios	PROPN
ajst-27746	179	5	k	k	PROPN
ajst-27746	179	6	,	,	PUNCT
ajst-27746	179	7	n.	n.	PROPN
ajst-27746	179	8	e	e	PROPN
ajst-27746	179	9	k	k	PROPN
ajst-27746	179	10	,	,	PUNCT
ajst-27746	179	11	fotios	fotio	NOUN
ajst-27746	179	12	t	t	X
ajst-27746	179	13	.discrete	.discrete	PUNCT
ajst-27746	179	14	empirical	empirical	ADJ
ajst-27746	179	15	interpolation	interpolation	NOUN
ajst-27746	179	16	and	and	CCONJ
ajst-27746	179	17	unfitted	unfitted	ADJ
ajst-27746	179	18	mesh	mesh	NOUN
ajst-27746	179	19	fems	fem	NOUN
ajst-27746	179	20	:	:	PUNCT
ajst-27746	179	21	application	application	NOUN
ajst-27746	179	22	in	in	ADP
ajst-27746	179	23	pde	pde	NOUN
ajst-27746	179	24	-	-	PUNCT
ajst-27746	179	25	constrained	constrain	VERB
ajst-27746	179	26	optimization[j].optimization,2023,72(6):1609	optimization[j].optimization,2023,72(6):1609	NOUN
ajst-27746	179	27	-	-	PUNCT
ajst-27746	179	28	1642	1642	NUM
ajst-27746	179	29	.	.	PUNCT
ajst-27746	180	1	[	[	X
ajst-27746	180	2	3	3	X
ajst-27746	180	3	]	]	X
ajst-27746	180	4	zamani	zamani	PROPN
ajst-27746	180	5	m	m	PROPN
ajst-27746	180	6	,	,	PUNCT
ajst-27746	180	7	abbaszadehpeivasti	abbaszadehpeivasti	NOUN
ajst-27746	180	8	h	h	NOUN
ajst-27746	180	9	,	,	PUNCT
ajst-27746	180	10	klerk	klerk	NOUN
ajst-27746	180	11	d	d	PROPN
ajst-27746	180	12	e	e	PROPN
ajst-27746	180	13	.the	.the	DET
ajst-27746	180	14	exact	exact	ADJ
ajst-27746	180	15	worstcase	worstcase	NOUN
ajst-27746	180	16	convergence	convergence	NOUN
ajst-27746	180	17	rate	rate	NOUN
ajst-27746	180	18	of	of	ADP
ajst-27746	180	19	the	the	DET
ajst-27746	180	20	alternating	alternate	VERB
ajst-27746	180	21	direction	direction	NOUN
ajst-27746	180	22	method	method	NOUN
ajst-27746	180	23	of	of	ADP
ajst-27746	180	24	multipliers[j].mathematical	multipliers[j].mathematical	ADJ
ajst-27746	180	25	programming,2023,208(1	programming,2023,208(1	NOUN
ajst-27746	180	26	-	-	PUNCT
ajst-27746	180	27	2):243276	2):243276	NUM
ajst-27746	180	28	.	.	PUNCT
ajst-27746	181	1	[	[	X
ajst-27746	181	2	4	4	X
ajst-27746	181	3	]	]	X
ajst-27746	181	4	christian	christian	PROPN
ajst-27746	181	5	m	m	NOUN
ajst-27746	181	6	,	,	PUNCT
ajst-27746	181	7	shiqi	shiqi	PROPN
ajst-27746	181	8	z	z	PROPN
ajst-27746	181	9	,	,	PUNCT
ajst-27746	181	10	guang	guang	PROPN
ajst-27746	181	11	l	l	PROPN
ajst-27746	181	12	,	,	PUNCT
ajst-27746	181	13	et	et	NOUN
ajst-27746	181	14	al.deeponet	al.deeponet	NOUN
ajst-27746	181	15	-	-	PUNCT
ajst-27746	181	16	grid	grid	NOUN
ajst-27746	181	17	-	-	PUNCT
ajst-27746	181	18	uq	uq	NOUN
ajst-27746	181	19	:	:	PUNCT
ajst-27746	181	20	a	a	DET
ajst-27746	181	21	trustworthy	trustworthy	ADJ
ajst-27746	181	22	deep	deep	ADJ
ajst-27746	181	23	operator	operator	NOUN
ajst-27746	181	24	framework	framework	NOUN
ajst-27746	181	25	for	for	ADP
ajst-27746	181	26	predicting	predict	VERB
ajst-27746	181	27	the	the	DET
ajst-27746	181	28	power	power	NOUN
ajst-27746	181	29	grid	grid	NOUN
ajst-27746	181	30	’s	’s	PART
ajst-27746	181	31	post	post	ADJ
ajst-27746	181	32	-	-	ADJ
ajst-27746	181	33	fault	fault	ADJ
ajst-27746	181	34	trajectories[j].neurocomputing,2023,535166182	trajectories[j].neurocomputing,2023,535166182	NOUN
ajst-27746	181	35	.	.	PUNCT
ajst-27746	182	1	[	[	X
ajst-27746	182	2	5	5	NUM
ajst-27746	182	3	]	]	PUNCT
ajst-27746	182	4	hajer	hajer	NOUN
ajst-27746	182	5	t	t	NOUN
ajst-27746	182	6	,	,	PUNCT
ajst-27746	182	7	imene	imene	PROPN
ajst-27746	182	8	s	s	PROPN
ajst-27746	182	9	b	b	PROPN
ajst-27746	182	10	,	,	PUNCT
ajst-27746	182	11	mohamed	mohamed	PROPN
ajst-27746	182	12	h	h	PROPN
ajst-27746	182	13	.on	.on	PUNCT
ajst-27746	183	1	the	the	DET
ajst-27746	183	2	helix	helix	ADJ
ajst-27746	183	3	equation	equation	NOUN
ajst-27746	183	4	[	[	X
ajst-27746	183	5	j	j	X
ajst-27746	183	6	]	]	X
ajst-27746	183	7	.	.	PUNCT
ajst-27746	184	1	esaim	esaim	NOUN
ajst-27746	184	2	:	:	PUNCT
ajst-27746	184	3	proceedings	proceeding	NOUN
ajst-27746	184	4	and	and	CCONJ
ajst-27746	184	5	surveys,2012,36197	surveys,2012,36197	NOUN
ajst-27746	184	6	-	-	PUNCT
ajst-27746	184	7	208	208	NUM
ajst-27746	184	8	.	.	PUNCT
ajst-27746	185	1	[	[	X
ajst-27746	185	2	6	6	NUM
ajst-27746	185	3	]	]	X
ajst-27746	185	4	kaltenbacher	kaltenbacher	PROPN
ajst-27746	185	5	b	b	PROPN
ajst-27746	185	6	,	,	PUNCT
ajst-27746	185	7	lehner	lehner	PROPN
ajst-27746	185	8	p	p	PROPN
ajst-27746	185	9	.a	.a	PROPN
ajst-27746	186	1	first	first	ADJ
ajst-27746	186	2	order	order	NOUN
ajst-27746	186	3	in	in	ADP
ajst-27746	186	4	time	time	NOUN
ajst-27746	186	5	wave	wave	NOUN
ajst-27746	186	6	equation	equation	NOUN
ajst-27746	186	7	modeling	model	VERB
ajst-27746	186	8	nonlinear	nonlinear	ADJ
ajst-27746	186	9	acoustics[j].journal	acoustics[j].journal	ADJ
ajst-27746	186	10	of	of	ADP
ajst-27746	186	11	mathematical	mathematical	ADJ
ajst-27746	186	12	analysis	analysis	NOUN
ajst-27746	186	13	and	and	CCONJ
ajst-27746	186	14	applications,2025,543(2p2):128933	applications,2025,543(2p2):128933	NOUN
ajst-27746	186	15	-	-	PUNCT
ajst-27746	186	16	128933	128933	NUM
ajst-27746	186	17	.	.	PUNCT
ajst-27746	187	1	[	[	X
ajst-27746	187	2	7	7	X
ajst-27746	187	3	]	]	X
ajst-27746	187	4	oleg	oleg	PROPN
ajst-27746	187	5	d	d	PROPN
ajst-27746	187	6	,	,	PUNCT
ajst-27746	187	7	thi	thi	PROPN
ajst-27746	187	8	d	d	X
ajst-27746	187	9	o	o	PROPN
ajst-27746	187	10	,	,	PUNCT
ajst-27746	187	11	manh	manh	PROPN
ajst-27746	187	12	n	n	PROPN
ajst-27746	187	13	t	t	PROPN
ajst-27746	187	14	.improved	.improved	PUNCT
ajst-27746	187	15	stencil	stencil	PROPN
ajst-27746	187	16	selection	selection	NOUN
ajst-27746	187	17	for	for	ADP
ajst-27746	187	18	meshless	meshless	ADJ
ajst-27746	187	19	finite	finite	ADJ
ajst-27746	187	20	difference	difference	NOUN
ajst-27746	187	21	methods	method	NOUN
ajst-27746	187	22	in	in	ADP
ajst-27746	187	23	3d[j].journal	3d[j].journal	NUM
ajst-27746	187	24	of	of	ADP
ajst-27746	187	25	computational	computational	ADJ
ajst-27746	187	26	and	and	CCONJ
ajst-27746	187	27	applied	applied	ADJ
ajst-27746	187	28	mathematics,2023,425	mathematics,2023,425	NOUN
ajst-27746	187	29	.	.	PUNCT
ajst-27746	188	1	[	[	X
ajst-27746	188	2	8	8	NUM
ajst-27746	188	3	]	]	X
ajst-27746	188	4	junyan	junyan	PROPN
ajst-27746	188	5	h	h	PROPN
ajst-27746	188	6	,	,	PUNCT
ajst-27746	188	7	shashank	shashank	PROPN
ajst-27746	188	8	k	k	PROPN
ajst-27746	188	9	,	,	PUNCT
ajst-27746	188	10	jaewan	jaewan	PROPN
ajst-27746	188	11	p	p	PROPN
ajst-27746	188	12	,	,	PUNCT
ajst-27746	188	13	et	et	PROPN
ajst-27746	188	14	al.sequential	al.sequential	ADJ
ajst-27746	188	15	deep	deep	ADJ
ajst-27746	188	16	operator	operator	NOUN
ajst-27746	188	17	networks	network	NOUN
ajst-27746	188	18	(	(	PUNCT
ajst-27746	188	19	s	s	NOUN
ajst-27746	188	20	-	-	NOUN
ajst-27746	188	21	deeponet	deeponet	NOUN
ajst-27746	188	22	)	)	PUNCT
ajst-27746	188	23	for	for	ADP
ajst-27746	188	24	predicting	predict	VERB
ajst-27746	188	25	full	full	ADJ
ajst-27746	188	26	-	-	PUNCT
ajst-27746	188	27	field	field	NOUN
ajst-27746	188	28	solutions	solution	NOUN
ajst-27746	188	29	under	under	ADP
ajst-27746	188	30	time	time	NOUN
ajst-27746	188	31	-	-	PUNCT
ajst-27746	188	32	dependent	dependent	ADJ
ajst-27746	188	33	loads	load	NOUN
ajst-27746	189	1	[	[	X
ajst-27746	189	2	j	j	X
ajst-27746	189	3	]	]	X
ajst-27746	189	4	.	.	PUNCT
ajst-27746	190	1	engineering	engineering	NOUN
ajst-27746	190	2	applications	application	NOUN
ajst-27746	190	3	of	of	ADP
ajst-27746	190	4	artificial	artificial	ADJ
ajst-27746	190	5	intelligence,2024,127(pa	intelligence,2024,127(pa	NOUN
ajst-27746	190	6	):	):	PUNCT