id	sid	tid	token	lemma	pos
ejpam-2252	1	1	compile	compile	NOUN
ejpam-2252	1	2	/	/	SYM
ejpam-2252	1	3	output.dvi	output.dvi	NOUN
ejpam-2252	1	4	european	european	ADJ
ejpam-2252	1	5	journal	journal	NOUN
ejpam-2252	1	6	of	of	ADP
ejpam-2252	1	7	pure	pure	ADJ
ejpam-2252	1	8	and	and	CCONJ
ejpam-2252	1	9	applied	apply	VERB
ejpam-2252	1	10	mathematics	mathematic	NOUN
ejpam-2252	1	11	vol	vol	NOUN
ejpam-2252	1	12	.	.	PUNCT
ejpam-2252	2	1	7	7	NUM
ejpam-2252	2	2	,	,	PUNCT
ejpam-2252	2	3	no	no	INTJ
ejpam-2252	2	4	.	.	NOUN
ejpam-2252	2	5	3	3	NUM
ejpam-2252	2	6	,	,	PUNCT
ejpam-2252	2	7	2014	2014	NUM
ejpam-2252	2	8	,	,	PUNCT
ejpam-2252	2	9	335	335	NUM
ejpam-2252	2	10	-	-	SYM
ejpam-2252	2	11	342	342	NUM
ejpam-2252	2	12	issn	issn	PROPN
ejpam-2252	2	13	1307	1307	NUM
ejpam-2252	2	14	-	-	SYM
ejpam-2252	2	15	5543	5543	NUM
ejpam-2252	2	16	–	–	PUNCT
ejpam-2252	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-2252	2	18	one	one	NUM
ejpam-2252	2	19	-	-	PUNCT
ejpam-2252	2	20	parameter	parameter	NOUN
ejpam-2252	2	21	planar	planar	ADJ
ejpam-2252	2	22	motions	motion	NOUN
ejpam-2252	2	23	in	in	ADP
ejpam-2252	2	24	affine	affine	ADJ
ejpam-2252	2	25	cayley	cayley	ADJ
ejpam-2252	2	26	-	-	PUNCT
ejpam-2252	2	27	klein	klein	NOUN
ejpam-2252	2	28	planes	planes	PROPN
ejpam-2252	2	29	n.	n.	PROPN
ejpam-2252	2	30	(	(	PUNCT
ejpam-2252	2	31	bayrak	bayrak	PROPN
ejpam-2252	2	32	)	)	PUNCT
ejpam-2252	2	33	gürses∗	gürses∗	PROPN
ejpam-2252	2	34	,	,	PUNCT
ejpam-2252	2	35	s.	s.	PROPN
ejpam-2252	2	36	yüce	yüce	PROPN
ejpam-2252	2	37	department	department	PROPN
ejpam-2252	2	38	of	of	ADP
ejpam-2252	2	39	mathematics	mathematic	NOUN
ejpam-2252	2	40	,	,	PUNCT
ejpam-2252	2	41	faculty	faculty	NOUN
ejpam-2252	2	42	of	of	ADP
ejpam-2252	2	43	arts	art	NOUN
ejpam-2252	2	44	and	and	CCONJ
ejpam-2252	2	45	sciences	science	NOUN
ejpam-2252	2	46	,	,	PUNCT
ejpam-2252	2	47	yıldız	yıldız	PROPN
ejpam-2252	2	48	technical	technical	PROPN
ejpam-2252	2	49	university	university	PROPN
ejpam-2252	2	50	,	,	PUNCT
ejpam-2252	2	51	istanbul	istanbul	PROPN
ejpam-2252	2	52	,	,	PUNCT
ejpam-2252	2	53	turkey	turkey	PROPN
ejpam-2252	2	54	abstract	abstract	NOUN
ejpam-2252	2	55	.	.	PUNCT
ejpam-2252	3	1	in	in	ADP
ejpam-2252	3	2	1956	1956	NUM
ejpam-2252	3	3	,	,	PUNCT
ejpam-2252	3	4	w.	w.	PROPN
ejpam-2252	3	5	blaschke	blaschke	PROPN
ejpam-2252	3	6	and	and	CCONJ
ejpam-2252	3	7	h.r	h.r	PROPN
ejpam-2252	3	8	.	.	PROPN
ejpam-2252	3	9	müller	müller	PROPN
ejpam-2252	3	10	introduced	introduce	VERB
ejpam-2252	3	11	the	the	DET
ejpam-2252	3	12	one	one	NUM
ejpam-2252	3	13	-	-	PUNCT
ejpam-2252	3	14	parameter	parameter	NOUN
ejpam-2252	3	15	planar	planar	ADJ
ejpam-2252	3	16	motions	motion	NOUN
ejpam-2252	3	17	and	and	CCONJ
ejpam-2252	3	18	obtained	obtain	VERB
ejpam-2252	3	19	the	the	DET
ejpam-2252	3	20	relation	relation	NOUN
ejpam-2252	3	21	between	between	ADP
ejpam-2252	3	22	absolute	absolute	ADJ
ejpam-2252	3	23	,	,	PUNCT
ejpam-2252	3	24	relative	relative	ADJ
ejpam-2252	3	25	,	,	PUNCT
ejpam-2252	3	26	sliding	slide	VERB
ejpam-2252	3	27	velocities	velocity	NOUN
ejpam-2252	3	28	and	and	CCONJ
ejpam-2252	3	29	accelerations	acceleration	NOUN
ejpam-2252	3	30	in	in	ADP
ejpam-2252	3	31	the	the	DET
ejpam-2252	3	32	euclidean	euclidean	ADJ
ejpam-2252	3	33	plane	plane	NOUN
ejpam-2252	3	34	e2	e2	NOUN
ejpam-2252	4	1	[	[	X
ejpam-2252	4	2	3	3	NUM
ejpam-2252	4	3	]	]	PUNCT
ejpam-2252	4	4	.	.	PUNCT
ejpam-2252	4	5	a.	a.	NOUN
ejpam-2252	4	6	a.	a.	NOUN
ejpam-2252	4	7	ergin	ergin	NOUN
ejpam-2252	5	1	[	[	X
ejpam-2252	5	2	4	4	X
ejpam-2252	5	3	]	]	PUNCT
ejpam-2252	5	4	considering	consider	VERB
ejpam-2252	5	5	the	the	DET
ejpam-2252	5	6	lorentzian	lorentzian	ADJ
ejpam-2252	5	7	plane	plane	NOUN
ejpam-2252	5	8	l2	l2	NOUN
ejpam-2252	5	9	,	,	PUNCT
ejpam-2252	5	10	instead	instead	ADV
ejpam-2252	5	11	of	of	ADP
ejpam-2252	5	12	the	the	DET
ejpam-2252	5	13	euclidean	euclidean	ADJ
ejpam-2252	5	14	plane	plane	NOUN
ejpam-2252	5	15	e2	e2	PROPN
ejpam-2252	5	16	,	,	PUNCT
ejpam-2252	5	17	introduced	introduce	VERB
ejpam-2252	5	18	the	the	DET
ejpam-2252	5	19	one	one	NUM
ejpam-2252	5	20	-	-	PUNCT
ejpam-2252	5	21	parameter	parameter	NOUN
ejpam-2252	5	22	planar	planar	ADJ
ejpam-2252	5	23	motions	motion	NOUN
ejpam-2252	5	24	in	in	ADP
ejpam-2252	5	25	the	the	DET
ejpam-2252	5	26	lorentzian	lorentzian	ADJ
ejpam-2252	5	27	plane	plane	NOUN
ejpam-2252	5	28	l2	l2	NOUN
ejpam-2252	5	29	and	and	CCONJ
ejpam-2252	5	30	also	also	ADV
ejpam-2252	5	31	gave	give	VERB
ejpam-2252	5	32	the	the	DET
ejpam-2252	5	33	relations	relation	NOUN
ejpam-2252	5	34	between	between	ADP
ejpam-2252	5	35	the	the	DET
ejpam-2252	5	36	velocities	velocity	NOUN
ejpam-2252	5	37	and	and	CCONJ
ejpam-2252	5	38	accelerations	acceleration	NOUN
ejpam-2252	5	39	in	in	ADP
ejpam-2252	5	40	1991	1991	NUM
ejpam-2252	5	41	.	.	PUNCT
ejpam-2252	6	1	in	in	ADP
ejpam-2252	6	2	addition	addition	NOUN
ejpam-2252	6	3	to	to	ADP
ejpam-2252	6	4	this	this	PRON
ejpam-2252	6	5	,	,	PUNCT
ejpam-2252	6	6	in	in	ADP
ejpam-2252	6	7	2013	2013	NUM
ejpam-2252	6	8	,	,	PUNCT
ejpam-2252	6	9	m.	m.	NOUN
ejpam-2252	6	10	akar	akar	PROPN
ejpam-2252	6	11	and	and	CCONJ
ejpam-2252	6	12	s.	s.	PROPN
ejpam-2252	6	13	yüce	yüce	PROPN
ejpam-2252	7	1	[	[	X
ejpam-2252	7	2	1	1	X
ejpam-2252	7	3	]	]	PUNCT
ejpam-2252	7	4	introduced	introduce	VERB
ejpam-2252	7	5	the	the	DET
ejpam-2252	7	6	one	one	NUM
ejpam-2252	7	7	-	-	PUNCT
ejpam-2252	7	8	parameter	parameter	NOUN
ejpam-2252	7	9	motions	motion	NOUN
ejpam-2252	7	10	in	in	ADP
ejpam-2252	7	11	the	the	DET
ejpam-2252	7	12	galilean	galilean	PROPN
ejpam-2252	7	13	plane	plane	NOUN
ejpam-2252	7	14	g2	g2	PROPN
ejpam-2252	7	15	and	and	CCONJ
ejpam-2252	7	16	gave	give	VERB
ejpam-2252	7	17	same	same	ADJ
ejpam-2252	7	18	concepts	concept	NOUN
ejpam-2252	7	19	stated	state	VERB
ejpam-2252	7	20	above	above	ADV
ejpam-2252	7	21	.	.	PUNCT
ejpam-2252	8	1	in	in	ADP
ejpam-2252	8	2	this	this	DET
ejpam-2252	8	3	paper	paper	NOUN
ejpam-2252	8	4	,	,	PUNCT
ejpam-2252	8	5	we	we	PRON
ejpam-2252	8	6	will	will	AUX
ejpam-2252	8	7	introduce	introduce	VERB
ejpam-2252	8	8	one	one	NUM
ejpam-2252	8	9	parameter	parameter	NOUN
ejpam-2252	8	10	planar	planar	ADJ
ejpam-2252	8	11	motions	motion	NOUN
ejpam-2252	8	12	in	in	ADP
ejpam-2252	8	13	affine	affine	ADJ
ejpam-2252	8	14	cayley	cayley	PROPN
ejpam-2252	8	15	-	-	PUNCT
ejpam-2252	8	16	klein	klein	PROPN
ejpam-2252	8	17	(	(	PUNCT
ejpam-2252	8	18	ck	ck	PROPN
ejpam-2252	8	19	)	)	PUNCT
ejpam-2252	8	20	planes	plane	NOUN
ejpam-2252	8	21	pε	pε	NOUN
ejpam-2252	8	22	and	and	CCONJ
ejpam-2252	8	23	we	we	PRON
ejpam-2252	8	24	will	will	AUX
ejpam-2252	8	25	discuss	discuss	VERB
ejpam-2252	8	26	the	the	DET
ejpam-2252	8	27	relations	relation	NOUN
ejpam-2252	8	28	between	between	ADP
ejpam-2252	8	29	absolute	absolute	ADJ
ejpam-2252	8	30	,	,	PUNCT
ejpam-2252	8	31	relative	relative	ADJ
ejpam-2252	8	32	,	,	PUNCT
ejpam-2252	8	33	sliding	slide	VERB
ejpam-2252	8	34	velocities	velocity	NOUN
ejpam-2252	8	35	and	and	CCONJ
ejpam-2252	8	36	accelerations	acceleration	NOUN
ejpam-2252	8	37	.	.	PUNCT
ejpam-2252	9	1	2010	2010	NUM
ejpam-2252	9	2	mathematics	mathematic	NOUN
ejpam-2252	9	3	subject	subject	NOUN
ejpam-2252	9	4	classifications	classification	NOUN
ejpam-2252	9	5	:	:	PUNCT
ejpam-2252	9	6	53a17	53a17	NUM
ejpam-2252	9	7	,	,	PUNCT
ejpam-2252	9	8	53a35	53a35	NUM
ejpam-2252	9	9	,	,	PUNCT
ejpam-2252	9	10	53a40	53a40	NUM
ejpam-2252	9	11	.	.	PUNCT
ejpam-2252	10	1	key	key	ADJ
ejpam-2252	10	2	words	word	NOUN
ejpam-2252	10	3	and	and	CCONJ
ejpam-2252	10	4	phrases	phrase	NOUN
ejpam-2252	10	5	:	:	PUNCT
ejpam-2252	10	6	cayley	cayley	ADJ
ejpam-2252	10	7	-	-	PUNCT
ejpam-2252	10	8	klein	klein	NOUN
ejpam-2252	10	9	planes	plane	NOUN
ejpam-2252	10	10	,	,	PUNCT
ejpam-2252	10	11	one	one	NUM
ejpam-2252	10	12	-	-	PUNCT
ejpam-2252	10	13	parameter	parameter	NOUN
ejpam-2252	10	14	planar	planar	ADJ
ejpam-2252	10	15	motion	motion	NOUN
ejpam-2252	10	16	,	,	PUNCT
ejpam-2252	10	17	kinematics	kinematic	NOUN
ejpam-2252	10	18	1	1	NUM
ejpam-2252	10	19	.	.	PUNCT
ejpam-2252	10	20	introduction	introduction	NOUN
ejpam-2252	10	21	the	the	DET
ejpam-2252	10	22	geometrical	geometrical	ADJ
ejpam-2252	10	23	systems	system	NOUN
ejpam-2252	10	24	have	have	VERB
ejpam-2252	10	25	a	a	DET
ejpam-2252	10	26	significant	significant	ADJ
ejpam-2252	10	27	role	role	NOUN
ejpam-2252	10	28	in	in	ADP
ejpam-2252	10	29	plane	plane	NOUN
ejpam-2252	10	30	geometries	geometry	NOUN
ejpam-2252	10	31	.	.	PUNCT
ejpam-2252	11	1	cayley	cayley	PROPN
ejpam-2252	11	2	-	-	PUNCT
ejpam-2252	11	3	klein	klein	PROPN
ejpam-2252	11	4	(	(	PUNCT
ejpam-2252	11	5	ck	ck	NOUN
ejpam-2252	11	6	)	)	PUNCT
ejpam-2252	11	7	geometries	geometry	NOUN
ejpam-2252	11	8	,	,	PUNCT
ejpam-2252	11	9	first	first	ADV
ejpam-2252	11	10	introduced	introduce	VERB
ejpam-2252	11	11	by	by	ADP
ejpam-2252	11	12	klein	klein	PROPN
ejpam-2252	11	13	in	in	ADP
ejpam-2252	11	14	1871	1871	NUM
ejpam-2252	11	15	and	and	CCONJ
ejpam-2252	11	16	cayley	cayley	ADJ
ejpam-2252	11	17	,	,	PUNCT
ejpam-2252	11	18	are	be	AUX
ejpam-2252	11	19	number	number	NOUN
ejpam-2252	11	20	of	of	ADP
ejpam-2252	11	21	geometries	geometry	NOUN
ejpam-2252	11	22	including	include	VERB
ejpam-2252	11	23	euclidean	euclidean	PROPN
ejpam-2252	11	24	,	,	PUNCT
ejpam-2252	11	25	galilean	galilean	PROPN
ejpam-2252	11	26	,	,	PUNCT
ejpam-2252	11	27	minkowskian	minkowskian	NOUN
ejpam-2252	11	28	and	and	CCONJ
ejpam-2252	11	29	bolyai	bolyai	NOUN
ejpam-2252	11	30	-	-	PUNCT
ejpam-2252	11	31	lobachevsikan	lobachevsikan	NOUN
ejpam-2252	11	32	[	[	X
ejpam-2252	11	33	8	8	NUM
ejpam-2252	11	34	,	,	PUNCT
ejpam-2252	11	35	9	9	NUM
ejpam-2252	11	36	]	]	PUNCT
ejpam-2252	11	37	.	.	PUNCT
ejpam-2252	12	1	following	follow	VERB
ejpam-2252	12	2	cayley	cayley	NOUN
ejpam-2252	12	3	and	and	CCONJ
ejpam-2252	12	4	klein	klein	PROPN
ejpam-2252	12	5	,	,	PUNCT
ejpam-2252	12	6	yaglom	yaglom	NOUN
ejpam-2252	12	7	distinguished	distinguish	VERB
ejpam-2252	12	8	these	these	DET
ejpam-2252	12	9	geometries	geometry	NOUN
ejpam-2252	12	10	with	with	ADP
ejpam-2252	12	11	choosing	choose	VERB
ejpam-2252	12	12	one	one	NUM
ejpam-2252	12	13	of	of	ADP
ejpam-2252	12	14	three	three	NUM
ejpam-2252	12	15	ways	way	NOUN
ejpam-2252	12	16	of	of	ADP
ejpam-2252	12	17	measuring	measure	VERB
ejpam-2252	12	18	length	length	NOUN
ejpam-2252	12	19	(	(	PUNCT
ejpam-2252	12	20	parabolic	parabolic	ADJ
ejpam-2252	12	21	,	,	PUNCT
ejpam-2252	12	22	elliptic	elliptic	ADJ
ejpam-2252	12	23	,	,	PUNCT
ejpam-2252	12	24	or	or	CCONJ
ejpam-2252	12	25	hyperbolic	hyperbolic	ADJ
ejpam-2252	12	26	)	)	PUNCT
ejpam-2252	12	27	between	between	ADP
ejpam-2252	12	28	two	two	NUM
ejpam-2252	12	29	points	point	NOUN
ejpam-2252	12	30	on	on	ADP
ejpam-2252	12	31	a	a	DET
ejpam-2252	12	32	line	line	NOUN
ejpam-2252	12	33	and	and	CCONJ
ejpam-2252	12	34	one	one	NUM
ejpam-2252	12	35	of	of	ADP
ejpam-2252	12	36	the	the	DET
ejpam-2252	12	37	three	three	NUM
ejpam-2252	12	38	ways	way	NOUN
ejpam-2252	12	39	of	of	ADP
ejpam-2252	12	40	measuring	measure	VERB
ejpam-2252	12	41	angles	angle	NOUN
ejpam-2252	12	42	between	between	ADP
ejpam-2252	12	43	two	two	NUM
ejpam-2252	12	44	lines	line	NOUN
ejpam-2252	12	45	(	(	PUNCT
ejpam-2252	12	46	parabolic	parabolic	ADJ
ejpam-2252	12	47	,	,	PUNCT
ejpam-2252	12	48	elliptic	elliptic	ADJ
ejpam-2252	12	49	,	,	PUNCT
ejpam-2252	12	50	or	or	CCONJ
ejpam-2252	12	51	hyperbolic	hyperbolic	ADJ
ejpam-2252	12	52	)	)	PUNCT
ejpam-2252	13	1	[	[	X
ejpam-2252	13	2	14	14	NUM
ejpam-2252	13	3	]	]	PUNCT
ejpam-2252	13	4	.	.	PUNCT
ejpam-2252	14	1	this	this	PRON
ejpam-2252	14	2	gives	give	VERB
ejpam-2252	14	3	nine	nine	NUM
ejpam-2252	14	4	ways	way	NOUN
ejpam-2252	14	5	of	of	ADP
ejpam-2252	14	6	measuring	measure	VERB
ejpam-2252	14	7	lengths	length	NOUN
ejpam-2252	14	8	and	and	CCONJ
ejpam-2252	14	9	angles	angle	NOUN
ejpam-2252	14	10	and	and	CCONJ
ejpam-2252	14	11	thus	thus	ADV
ejpam-2252	14	12	the	the	DET
ejpam-2252	14	13	nine	nine	NUM
ejpam-2252	14	14	plane	plane	NOUN
ejpam-2252	14	15	geometries	geometry	NOUN
ejpam-2252	14	16	listed	list	VERB
ejpam-2252	14	17	in	in	ADP
ejpam-2252	14	18	table	table	NOUN
ejpam-2252	14	19	1	1	NUM
ejpam-2252	14	20	.	.	PUNCT
ejpam-2252	15	1	a	a	DET
ejpam-2252	15	2	great	great	ADJ
ejpam-2252	15	3	deal	deal	NOUN
ejpam-2252	15	4	of	of	ADP
ejpam-2252	15	5	studies	study	NOUN
ejpam-2252	15	6	are	be	AUX
ejpam-2252	15	7	conducted	conduct	VERB
ejpam-2252	15	8	in	in	ADP
ejpam-2252	15	9	ck	ck	NOUN
ejpam-2252	15	10	-	-	PUNCT
ejpam-2252	15	11	planes	plane	NOUN
ejpam-2252	15	12	[	[	X
ejpam-2252	15	13	5–7	5–7	NOUN
ejpam-2252	15	14	,	,	PUNCT
ejpam-2252	15	15	10–13	10–13	NUM
ejpam-2252	15	16	]	]	PUNCT
ejpam-2252	15	17	.	.	PUNCT
ejpam-2252	16	1	there	there	PRON
ejpam-2252	16	2	is	be	VERB
ejpam-2252	16	3	a	a	DET
ejpam-2252	16	4	known	know	VERB
ejpam-2252	16	5	(	(	PUNCT
ejpam-2252	16	6	but	but	CCONJ
ejpam-2252	16	7	not	not	PART
ejpam-2252	16	8	well	well	ADV
ejpam-2252	16	9	-	-	PUNCT
ejpam-2252	16	10	known	know	VERB
ejpam-2252	16	11	)	)	PUNCT
ejpam-2252	16	12	relationship	relationship	NOUN
ejpam-2252	16	13	between	between	ADP
ejpam-2252	16	14	the	the	DET
ejpam-2252	16	15	plane	plane	NOUN
ejpam-2252	16	16	geometries	geometry	NOUN
ejpam-2252	16	17	which	which	PRON
ejpam-2252	16	18	have	have	VERB
ejpam-2252	16	19	parabolic	parabolic	ADJ
ejpam-2252	16	20	measure	measure	NOUN
ejpam-2252	16	21	of	of	ADP
ejpam-2252	16	22	distance	distance	NOUN
ejpam-2252	16	23	:	:	PUNCT
ejpam-2252	16	24	euclidean	euclidean	ADJ
ejpam-2252	16	25	,	,	PUNCT
ejpam-2252	16	26	galilean	galilean	PROPN
ejpam-2252	16	27	and	and	CCONJ
ejpam-2252	16	28	minkowskian	minkowskian	PROPN
ejpam-2252	16	29	(	(	PUNCT
ejpam-2252	16	30	lorentz	lorentz	PROPN
ejpam-2252	16	31	)	)	PUNCT
ejpam-2252	16	32	geometries	geometry	NOUN
ejpam-2252	16	33	.	.	PUNCT
ejpam-2252	17	1	they	they	PRON
ejpam-2252	17	2	are	be	AUX
ejpam-2252	17	3	called	call	VERB
ejpam-2252	17	4	affine	affine	ADJ
ejpam-2252	17	5	ck	ck	ADJ
ejpam-2252	17	6	-	-	PUNCT
ejpam-2252	17	7	plane	plane	NOUN
ejpam-2252	17	8	geometries	geometry	NOUN
ejpam-2252	17	9	[	[	X
ejpam-2252	17	10	14	14	NUM
ejpam-2252	17	11	]	]	PUNCT
ejpam-2252	17	12	.	.	PUNCT
ejpam-2252	18	1	∗corresponding	∗corresponde	VERB
ejpam-2252	18	2	author	author	NOUN
ejpam-2252	18	3	.	.	PUNCT
ejpam-2252	19	1	email	email	NOUN
ejpam-2252	19	2	addresses	address	NOUN
ejpam-2252	19	3	:	:	PUNCT
ejpam-2252	19	4	nbayrak@yildiz.edu.tr	nbayrak@yildiz.edu.tr	INTJ
ejpam-2252	19	5	(	(	PUNCT
ejpam-2252	19	6	n.	n.	NOUN
ejpam-2252	19	7	gürses	gürse	NOUN
ejpam-2252	19	8	)	)	PUNCT
ejpam-2252	19	9	,	,	PUNCT
ejpam-2252	19	10	sayuce@yildiz.edu.tr	sayuce@yildiz.edu.tr	PROPN
ejpam-2252	19	11	(	(	PUNCT
ejpam-2252	19	12	s.	s.	PROPN
ejpam-2252	19	13	yüce	yüce	PROPN
ejpam-2252	19	14	)	)	PUNCT
ejpam-2252	19	15	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2252	20	1	335	335	NUM
ejpam-2252	21	1	c	c	X
ejpam-2252	21	2	©	©	NOUN
ejpam-2252	21	3	2014	2014	NUM
ejpam-2252	21	4	ejpam	ejpam	NOUN
ejpam-2252	21	5	all	all	DET
ejpam-2252	21	6	rights	right	NOUN
ejpam-2252	21	7	reserved	reserve	VERB
ejpam-2252	21	8	.	.	PUNCT
ejpam-2252	22	1	n.	n.	NOUN
ejpam-2252	22	2	gürses	gürse	NOUN
ejpam-2252	22	3	,	,	PUNCT
ejpam-2252	22	4	s.	s.	PROPN
ejpam-2252	22	5	yüce	yüce	PROPN
ejpam-2252	22	6	/	/	SYM
ejpam-2252	22	7	eur	eur	PROPN
ejpam-2252	22	8	.	.	PUNCT
ejpam-2252	23	1	j.	j.	PROPN
ejpam-2252	23	2	pure	pure	PROPN
ejpam-2252	23	3	appl	appl	PROPN
ejpam-2252	23	4	.	.	PROPN
ejpam-2252	23	5	math	math	PROPN
ejpam-2252	23	6	,	,	PUNCT
ejpam-2252	23	7	7	7	NUM
ejpam-2252	23	8	(	(	PUNCT
ejpam-2252	23	9	2014	2014	NUM
ejpam-2252	23	10	)	)	PUNCT
ejpam-2252	23	11	,	,	PUNCT
ejpam-2252	23	12	335	335	NUM
ejpam-2252	23	13	-	-	SYM
ejpam-2252	23	14	342	342	NUM
ejpam-2252	23	15	336	336	NUM
ejpam-2252	23	16	table	table	NOUN
ejpam-2252	23	17	1	1	NUM
ejpam-2252	23	18	:	:	SYM
ejpam-2252	23	19	nine	nine	NUM
ejpam-2252	23	20	ck	ck	NOUN
ejpam-2252	23	21	-	-	PUNCT
ejpam-2252	23	22	geometries	geometry	NOUN
ejpam-2252	23	23	in	in	ADP
ejpam-2252	23	24	the	the	DET
ejpam-2252	23	25	plane	plane	NOUN
ejpam-2252	23	26	measure	measure	NOUN
ejpam-2252	23	27	of	of	ADP
ejpam-2252	23	28	length	length	NOUN
ejpam-2252	23	29	between	between	ADP
ejpam-2252	23	30	two	two	NUM
ejpam-2252	23	31	points	point	NOUN
ejpam-2252	23	32	elliptic	elliptic	ADJ
ejpam-2252	23	33	parabolic	parabolic	PROPN
ejpam-2252	23	34	hyperbolic	hyperbolic	ADJ
ejpam-2252	23	35	elliptic	elliptic	ADJ
ejpam-2252	23	36	elliptic	elliptic	ADJ
ejpam-2252	23	37	euclidean	euclidean	ADJ
ejpam-2252	23	38	hyperbolic	hyperbolic	ADJ
ejpam-2252	23	39	geometry	geometry	NOUN
ejpam-2252	23	40	geometry	geometry	NOUN
ejpam-2252	23	41	geometry	geometry	NOUN
ejpam-2252	23	42	measure	measure	NOUN
ejpam-2252	23	43	of	of	ADP
ejpam-2252	23	44	angles	angle	NOUN
ejpam-2252	23	45	parabolic	parabolic	NOUN
ejpam-2252	23	46	co	co	NOUN
ejpam-2252	23	47	-	-	ADJ
ejpam-2252	23	48	euclidean	euclidean	ADJ
ejpam-2252	23	49	galilean	galilean	PROPN
ejpam-2252	23	50	co	co	NOUN
ejpam-2252	23	51	-	-	NOUN
ejpam-2252	23	52	minkowskian	minkowskian	NOUN
ejpam-2252	23	53	between	between	ADP
ejpam-2252	23	54	two	two	NUM
ejpam-2252	23	55	lines	line	NOUN
ejpam-2252	23	56	(	(	PUNCT
ejpam-2252	23	57	euclidean	euclidean	ADJ
ejpam-2252	23	58	)	)	PUNCT
ejpam-2252	23	59	geometry	geometry	NOUN
ejpam-2252	23	60	geometry	geometry	NOUN
ejpam-2252	23	61	geometry	geometry	NOUN
ejpam-2252	23	62	(	(	PUNCT
ejpam-2252	23	63	anti	anti	ADJ
ejpam-2252	23	64	-	-	ADJ
ejpam-2252	23	65	newton	newton	PROPN
ejpam-2252	23	66	hooke	hooke	PROPN
ejpam-2252	23	67	)	)	PUNCT
ejpam-2252	23	68	(	(	PUNCT
ejpam-2252	23	69	newton	newton	PROPN
ejpam-2252	23	70	-	-	PUNCT
ejpam-2252	23	71	hooke	hooke	PROPN
ejpam-2252	23	72	)	)	PUNCT
ejpam-2252	23	73	hyperbolic	hyperbolic	ADJ
ejpam-2252	23	74	co	co	NOUN
ejpam-2252	23	75	-	-	ADJ
ejpam-2252	23	76	hyperbolic	hyperbolic	ADJ
ejpam-2252	23	77	minkowskian	minkowskian	NOUN
ejpam-2252	23	78	doubly	doubly	ADV
ejpam-2252	23	79	-	-	PUNCT
ejpam-2252	23	80	hyperbolic	hyperbolic	ADJ
ejpam-2252	23	81	geometry	geometry	NOUN
ejpam-2252	23	82	geometry	geometry	NOUN
ejpam-2252	23	83	geometry	geometry	NOUN
ejpam-2252	23	84	(	(	PUNCT
ejpam-2252	23	85	anti	anti	ADJ
ejpam-2252	23	86	-	-	ADJ
ejpam-2252	23	87	de	de	ADJ
ejpam-2252	23	88	-	-	NOUN
ejpam-2252	23	89	sitter	sitter	NOUN
ejpam-2252	23	90	)	)	PUNCT
ejpam-2252	23	91	(	(	PUNCT
ejpam-2252	23	92	de	de	NOUN
ejpam-2252	23	93	-	-	NOUN
ejpam-2252	23	94	sitter	sitter	NOUN
ejpam-2252	23	95	)	)	PUNCT
ejpam-2252	23	96	in	in	ADP
ejpam-2252	23	97	kinematics	kinematic	NOUN
ejpam-2252	23	98	,	,	PUNCT
ejpam-2252	23	99	the	the	DET
ejpam-2252	23	100	one	one	NUM
ejpam-2252	23	101	-	-	PUNCT
ejpam-2252	23	102	parameter	parameter	NOUN
ejpam-2252	23	103	planar	planar	ADJ
ejpam-2252	23	104	motions	motion	NOUN
ejpam-2252	23	105	introduced	introduce	VERB
ejpam-2252	23	106	by	by	ADP
ejpam-2252	23	107	w.	w.	PROPN
ejpam-2252	23	108	blaschke	blaschke	PROPN
ejpam-2252	23	109	and	and	CCONJ
ejpam-2252	23	110	h.r	h.r	PROPN
ejpam-2252	23	111	.	.	PROPN
ejpam-2252	23	112	müller	müller	PROPN
ejpam-2252	23	113	and	and	CCONJ
ejpam-2252	23	114	the	the	DET
ejpam-2252	23	115	relation	relation	NOUN
ejpam-2252	23	116	between	between	ADP
ejpam-2252	23	117	absolute	absolute	ADJ
ejpam-2252	23	118	,	,	PUNCT
ejpam-2252	23	119	relative	relative	ADJ
ejpam-2252	23	120	and	and	CCONJ
ejpam-2252	23	121	sliding	slide	VERB
ejpam-2252	23	122	velocities	velocity	NOUN
ejpam-2252	23	123	(	(	PUNCT
ejpam-2252	23	124	accelerations	acceleration	NOUN
ejpam-2252	23	125	)	)	PUNCT
ejpam-2252	23	126	are	be	AUX
ejpam-2252	23	127	examined	examine	VERB
ejpam-2252	23	128	on	on	ADP
ejpam-2252	23	129	the	the	DET
ejpam-2252	23	130	euclidean	euclidean	ADJ
ejpam-2252	23	131	plane	plane	NOUN
ejpam-2252	23	132	e2	e2	NOUN
ejpam-2252	23	133	[	[	X
ejpam-2252	23	134	3	3	NUM
ejpam-2252	23	135	]	]	PUNCT
ejpam-2252	23	136	.	.	PUNCT
ejpam-2252	24	1	then	then	ADV
ejpam-2252	24	2	,	,	PUNCT
ejpam-2252	24	3	the	the	DET
ejpam-2252	24	4	one	one	NUM
ejpam-2252	24	5	-	-	PUNCT
ejpam-2252	24	6	parameter	parameter	NOUN
ejpam-2252	24	7	planar	planar	ADJ
ejpam-2252	24	8	motions	motion	NOUN
ejpam-2252	24	9	on	on	ADP
ejpam-2252	24	10	the	the	DET
ejpam-2252	24	11	lorentzian	lorentzian	ADJ
ejpam-2252	24	12	(	(	PUNCT
ejpam-2252	24	13	minkowskian	minkowskian	ADJ
ejpam-2252	24	14	)	)	PUNCT
ejpam-2252	24	15	plane	plane	NOUN
ejpam-2252	24	16	l2	l2	NOUN
ejpam-2252	24	17	were	be	AUX
ejpam-2252	24	18	given	give	VERB
ejpam-2252	24	19	by	by	ADP
ejpam-2252	24	20	[	[	X
ejpam-2252	24	21	4	4	NUM
ejpam-2252	24	22	]	]	PUNCT
ejpam-2252	24	23	.	.	PUNCT
ejpam-2252	25	1	in	in	ADP
ejpam-2252	25	2	addition	addition	NOUN
ejpam-2252	25	3	to	to	ADP
ejpam-2252	25	4	this	this	PRON
ejpam-2252	25	5	,	,	PUNCT
ejpam-2252	25	6	same	same	ADJ
ejpam-2252	25	7	concept	concept	NOUN
ejpam-2252	25	8	are	be	AUX
ejpam-2252	25	9	investigated	investigate	VERB
ejpam-2252	25	10	on	on	ADP
ejpam-2252	25	11	the	the	DET
ejpam-2252	25	12	galilean	galilean	PROPN
ejpam-2252	25	13	plane	plane	NOUN
ejpam-2252	25	14	g2	g2	PROPN
ejpam-2252	25	15	by	by	ADP
ejpam-2252	25	16	[	[	X
ejpam-2252	25	17	1	1	NUM
ejpam-2252	25	18	]	]	PUNCT
ejpam-2252	25	19	and	and	CCONJ
ejpam-2252	25	20	[	[	X
ejpam-2252	25	21	2	2	NUM
ejpam-2252	25	22	]	]	PUNCT
ejpam-2252	25	23	.	.	PUNCT
ejpam-2252	26	1	in	in	ADP
ejpam-2252	26	2	this	this	DET
ejpam-2252	26	3	paper	paper	NOUN
ejpam-2252	26	4	,	,	PUNCT
ejpam-2252	26	5	we	we	PRON
ejpam-2252	26	6	will	will	AUX
ejpam-2252	26	7	introduce	introduce	VERB
ejpam-2252	26	8	and	and	CCONJ
ejpam-2252	26	9	focus	focus	VERB
ejpam-2252	26	10	on	on	ADP
ejpam-2252	26	11	one	one	NUM
ejpam-2252	26	12	parameter	parameter	NOUN
ejpam-2252	26	13	planar	planar	ADJ
ejpam-2252	26	14	motions	motion	NOUN
ejpam-2252	26	15	in	in	ADP
ejpam-2252	26	16	affine	affine	NOUN
ejpam-2252	26	17	ckplanes	ckplane	NOUN
ejpam-2252	26	18	with	with	ADP
ejpam-2252	26	19	generalizing	generalize	VERB
ejpam-2252	26	20	the	the	DET
ejpam-2252	26	21	notations	notation	NOUN
ejpam-2252	26	22	introduced	introduce	VERB
ejpam-2252	26	23	by	by	ADP
ejpam-2252	26	24	above	above	ADP
ejpam-2252	26	25	scientists	scientist	NOUN
ejpam-2252	26	26	.	.	PUNCT
ejpam-2252	27	1	also	also	ADV
ejpam-2252	27	2	,	,	PUNCT
ejpam-2252	27	3	we	we	PRON
ejpam-2252	27	4	will	will	AUX
ejpam-2252	27	5	discuss	discuss	VERB
ejpam-2252	27	6	the	the	DET
ejpam-2252	27	7	relations	relation	NOUN
ejpam-2252	27	8	between	between	ADP
ejpam-2252	27	9	absolute	absolute	ADJ
ejpam-2252	27	10	,	,	PUNCT
ejpam-2252	27	11	relative	relative	ADJ
ejpam-2252	27	12	and	and	CCONJ
ejpam-2252	27	13	sliding	slide	VERB
ejpam-2252	27	14	velocities	velocity	NOUN
ejpam-2252	27	15	(	(	PUNCT
ejpam-2252	27	16	accelerations	acceleration	NOUN
ejpam-2252	27	17	)	)	PUNCT
ejpam-2252	27	18	.	.	PUNCT
ejpam-2252	28	1	2	2	X
ejpam-2252	28	2	.	.	X
ejpam-2252	28	3	basic	basic	ADJ
ejpam-2252	28	4	notations	notation	NOUN
ejpam-2252	28	5	of	of	ADP
ejpam-2252	28	6	affine	affine	NOUN
ejpam-2252	28	7	ck	ck	NOUN
ejpam-2252	28	8	-	-	PUNCT
ejpam-2252	28	9	planes	plane	NOUN
ejpam-2252	28	10	in	in	ADP
ejpam-2252	28	11	this	this	DET
ejpam-2252	28	12	section	section	NOUN
ejpam-2252	28	13	,	,	PUNCT
ejpam-2252	28	14	we	we	PRON
ejpam-2252	28	15	will	will	AUX
ejpam-2252	28	16	investigate	investigate	VERB
ejpam-2252	28	17	the	the	DET
ejpam-2252	28	18	basic	basic	ADJ
ejpam-2252	28	19	notations	notation	NOUN
ejpam-2252	28	20	of	of	ADP
ejpam-2252	28	21	affine	affine	NOUN
ejpam-2252	28	22	ck	ck	NOUN
ejpam-2252	28	23	-	-	PUNCT
ejpam-2252	28	24	planes	plane	NOUN
ejpam-2252	28	25	[	[	X
ejpam-2252	28	26	6	6	NUM
ejpam-2252	28	27	,	,	PUNCT
ejpam-2252	28	28	14	14	NUM
ejpam-2252	28	29	]	]	PUNCT
ejpam-2252	28	30	.	.	PUNCT
ejpam-2252	29	1	these	these	DET
ejpam-2252	29	2	planes	plane	NOUN
ejpam-2252	29	3	are	be	AUX
ejpam-2252	29	4	denoted	denote	VERB
ejpam-2252	29	5	by	by	ADP
ejpam-2252	29	6	pε	pε	PROPN
ejpam-2252	29	7	.	.	PUNCT
ejpam-2252	30	1	let	let	VERB
ejpam-2252	30	2	us	we	PRON
ejpam-2252	30	3	consider	consider	VERB
ejpam-2252	30	4	r2	r2	PROPN
ejpam-2252	30	5	with	with	ADP
ejpam-2252	30	6	the	the	DET
ejpam-2252	30	7	bilinear	bilinear	NOUN
ejpam-2252	30	8	form	form	NOUN
ejpam-2252	30	9	〈	〈	PROPN
ejpam-2252	30	10	x	x	NOUN
ejpam-2252	30	11	,	,	PUNCT
ejpam-2252	30	12	y〉ε	y〉ε	ADJ
ejpam-2252	31	1	=	=	SYM
ejpam-2252	31	2	x1	x1	NUM
ejpam-2252	31	3	y1	y1	NOUN
ejpam-2252	31	4	+	+	CCONJ
ejpam-2252	31	5	εx2	εx2	PROPN
ejpam-2252	31	6	y2	y2	PROPN
ejpam-2252	31	7	where	where	SCONJ
ejpam-2252	31	8	ε	ε	PROPN
ejpam-2252	31	9	may	may	AUX
ejpam-2252	31	10	be	be	AUX
ejpam-2252	31	11	1,0	1,0	NUM
ejpam-2252	31	12	or	or	CCONJ
ejpam-2252	31	13	−1	−1	NOUN
ejpam-2252	31	14	and	and	CCONJ
ejpam-2252	31	15	x	x	SYM
ejpam-2252	31	16	=	=	SYM
ejpam-2252	31	17	(	(	PUNCT
ejpam-2252	31	18	x1	x1	PROPN
ejpam-2252	31	19	,	,	PUNCT
ejpam-2252	31	20	x2	x2	PROPN
ejpam-2252	31	21	)	)	PUNCT
ejpam-2252	31	22	,	,	PUNCT
ejpam-2252	31	23	y	y	PROPN
ejpam-2252	31	24	=	=	SYM
ejpam-2252	31	25	(	(	PUNCT
ejpam-2252	31	26	y1	y1	INTJ
ejpam-2252	31	27	,	,	PUNCT
ejpam-2252	31	28	y2	y2	PROPN
ejpam-2252	31	29	)	)	PUNCT
ejpam-2252	31	30	.	.	PUNCT
ejpam-2252	32	1	the	the	DET
ejpam-2252	32	2	matrix	matrix	NOUN
ejpam-2252	32	3	of	of	ADP
ejpam-2252	32	4	this	this	DET
ejpam-2252	32	5	bilinear	bilinear	NOUN
ejpam-2252	32	6	form	form	NOUN
ejpam-2252	32	7	is	be	AUX
ejpam-2252	32	8	given	give	VERB
ejpam-2252	32	9	as	as	ADP
ejpam-2252	32	10	below	below	ADV
ejpam-2252	32	11	:	:	PUNCT
ejpam-2252	32	12	b	b	X
ejpam-2252	32	13	=	=	SYM
ejpam-2252	32	14	�	�	PROPN
ejpam-2252	32	15	1	1	NUM
ejpam-2252	32	16	0	0	NUM
ejpam-2252	32	17	0	0	NUM
ejpam-2252	32	18	ε	ε	PROPN
ejpam-2252	32	19	�	�	PROPN
ejpam-2252	32	20	.	.	PUNCT
ejpam-2252	33	1	for	for	ADP
ejpam-2252	33	2	all	all	DET
ejpam-2252	33	3	x	x	PUNCT
ejpam-2252	33	4	and	and	CCONJ
ejpam-2252	33	5	y	y	PROPN
ejpam-2252	33	6	in	in	ADP
ejpam-2252	33	7	pε	pε	NOUN
ejpam-2252	33	8	we	we	PRON
ejpam-2252	33	9	can	can	AUX
ejpam-2252	33	10	write	write	VERB
ejpam-2252	33	11	〈	〈	PROPN
ejpam-2252	33	12	x	x	PROPN
ejpam-2252	33	13	,	,	PUNCT
ejpam-2252	33	14	y	y	NOUN
ejpam-2252	33	15	〉	〉	NOUN
ejpam-2252	33	16	=	=	SYM
ejpam-2252	33	17	xt	xt	X
ejpam-2252	33	18	by	by	ADP
ejpam-2252	33	19	.	.	PUNCT
ejpam-2252	34	1	for	for	ADP
ejpam-2252	34	2	ε	ε	PROPN
ejpam-2252	34	3	=	=	SYM
ejpam-2252	34	4	1	1	NUM
ejpam-2252	34	5	we	we	PRON
ejpam-2252	34	6	have	have	VERB
ejpam-2252	34	7	euclidean	euclidean	ADJ
ejpam-2252	34	8	plane	plane	NOUN
ejpam-2252	34	9	e2	e2	PROPN
ejpam-2252	34	10	,	,	PUNCT
ejpam-2252	34	11	for	for	ADP
ejpam-2252	34	12	ε=	ε=	NOUN
ejpam-2252	34	13	0	0	NUM
ejpam-2252	35	1	we	we	PRON
ejpam-2252	35	2	have	have	VERB
ejpam-2252	35	3	galilean	galilean	PROPN
ejpam-2252	35	4	plane	plane	NOUN
ejpam-2252	35	5	g2	g2	PROPN
ejpam-2252	35	6	and	and	CCONJ
ejpam-2252	35	7	for	for	ADP
ejpam-2252	35	8	ε=	ε=	ADJ
ejpam-2252	35	9	−1	−1	NOUN
ejpam-2252	35	10	we	we	PRON
ejpam-2252	35	11	have	have	VERB
ejpam-2252	35	12	lorentzian	lorentzian	ADJ
ejpam-2252	35	13	plane	plane	NOUN
ejpam-2252	35	14	l2	l2	NOUN
ejpam-2252	35	15	.	.	PUNCT
ejpam-2252	36	1	if	if	SCONJ
ejpam-2252	36	2	〈	〈	PROPN
ejpam-2252	36	3	x	x	X
ejpam-2252	36	4	,	,	PUNCT
ejpam-2252	36	5	y〉ε	y〉ε	ADJ
ejpam-2252	36	6	=	=	SYM
ejpam-2252	36	7	0	0	NUM
ejpam-2252	36	8	,	,	PUNCT
ejpam-2252	36	9	then	then	ADV
ejpam-2252	36	10	the	the	DET
ejpam-2252	36	11	vectors	vector	NOUN
ejpam-2252	36	12	x	x	PUNCT
ejpam-2252	36	13	and	and	CCONJ
ejpam-2252	36	14	y	y	PROPN
ejpam-2252	36	15	in	in	ADP
ejpam-2252	36	16	pε	pε	PROPN
ejpam-2252	36	17	are	be	AUX
ejpam-2252	36	18	orthogonal	orthogonal	ADJ
ejpam-2252	36	19	.	.	PUNCT
ejpam-2252	37	1	self	self	NOUN
ejpam-2252	37	2	-	-	PUNCT
ejpam-2252	37	3	orthogonal	orthogonal	ADJ
ejpam-2252	37	4	vectors	vector	NOUN
ejpam-2252	37	5	are	be	AUX
ejpam-2252	37	6	called	call	VERB
ejpam-2252	37	7	isotropic	isotropic	NOUN
ejpam-2252	37	8	.	.	PUNCT
ejpam-2252	38	1	n.	n.	NOUN
ejpam-2252	38	2	gürses	gürse	NOUN
ejpam-2252	38	3	,	,	PUNCT
ejpam-2252	38	4	s.	s.	PROPN
ejpam-2252	38	5	yüce	yüce	PROPN
ejpam-2252	38	6	/	/	SYM
ejpam-2252	38	7	eur	eur	PROPN
ejpam-2252	38	8	.	.	PUNCT
ejpam-2252	39	1	j.	j.	PROPN
ejpam-2252	39	2	pure	pure	PROPN
ejpam-2252	39	3	appl	appl	PROPN
ejpam-2252	39	4	.	.	PROPN
ejpam-2252	39	5	math	math	PROPN
ejpam-2252	39	6	,	,	PUNCT
ejpam-2252	39	7	7	7	NUM
ejpam-2252	39	8	(	(	PUNCT
ejpam-2252	39	9	2014	2014	NUM
ejpam-2252	39	10	)	)	PUNCT
ejpam-2252	39	11	,	,	PUNCT
ejpam-2252	39	12	335	335	NUM
ejpam-2252	39	13	-	-	SYM
ejpam-2252	39	14	342	342	NUM
ejpam-2252	39	15	337	337	NUM
ejpam-2252	39	16	the	the	DET
ejpam-2252	39	17	norm	norm	NOUN
ejpam-2252	39	18	of	of	ADP
ejpam-2252	39	19	the	the	DET
ejpam-2252	39	20	vector	vector	NOUN
ejpam-2252	39	21	x=	x=	PUNCT
ejpam-2252	40	1	(	(	PUNCT
ejpam-2252	40	2	x1	x1	PROPN
ejpam-2252	40	3	,	,	PUNCT
ejpam-2252	40	4	x2	x2	PROPN
ejpam-2252	40	5	)	)	PUNCT
ejpam-2252	40	6	in	in	ADP
ejpam-2252	40	7	pε	pε	PROPN
ejpam-2252	40	8	is	be	AUX
ejpam-2252	40	9	defined	define	VERB
ejpam-2252	40	10	by	by	ADP
ejpam-2252	40	11	‖x‖ε	‖x‖ε	NOUN
ejpam-2252	40	12	=	=	SYM
ejpam-2252	40	13	ç	ç	X
ejpam-2252	40	14	�	�	PROPN
ejpam-2252	40	15	�	�	PROPN
ejpam-2252	40	16	〈	〈	PROPN
ejpam-2252	40	17	x	x	PROPN
ejpam-2252	40	18	,	,	PUNCT
ejpam-2252	40	19	x〉ε	x〉ε	PROPN
ejpam-2252	40	20	�	�	PROPN
ejpam-2252	40	21	�	�	PROPN
ejpam-2252	40	22	=	=	SYM
ejpam-2252	40	23	ç	ç	SYM
ejpam-2252	40	24	�	�	PROPN
ejpam-2252	40	25	�	�	PROPN
ejpam-2252	40	26	x2	x2	PROPN
ejpam-2252	40	27	1	1	NUM
ejpam-2252	40	28	+	+	CCONJ
ejpam-2252	40	29	εx2	εx2	PROPN
ejpam-2252	40	30	2	2	NUM
ejpam-2252	40	31	�	�	PROPN
ejpam-2252	40	32	�	�	PROPN
ejpam-2252	40	33	.	.	PUNCT
ejpam-2252	41	1	the	the	DET
ejpam-2252	41	2	vector	vector	NOUN
ejpam-2252	41	3	system	system	NOUN
ejpam-2252	41	4	�	�	PROPN
ejpam-2252	41	5	c1	c1	PROPN
ejpam-2252	41	6	=	=	PUNCT
ejpam-2252	41	7	(	(	PUNCT
ejpam-2252	41	8	1,0	1,0	NUM
ejpam-2252	41	9	)	)	PUNCT
ejpam-2252	41	10	,	,	PUNCT
ejpam-2252	41	11	c2	c2	PROPN
ejpam-2252	41	12	=	=	SYM
ejpam-2252	41	13	(	(	PUNCT
ejpam-2252	41	14	0,1	0,1	NUM
ejpam-2252	41	15	)	)	PUNCT
ejpam-2252	41	16	is	be	AUX
ejpam-2252	41	17	orthonormal	orthonormal	ADJ
ejpam-2252	41	18	basis	basis	NOUN
ejpam-2252	41	19	for	for	ADP
ejpam-2252	41	20	pε	pε	NOUN
ejpam-2252	41	21	.	.	PUNCT
ejpam-2252	42	1	the	the	DET
ejpam-2252	42	2	distance	distance	NOUN
ejpam-2252	42	3	between	between	ADP
ejpam-2252	42	4	two	two	NUM
ejpam-2252	42	5	points	point	NOUN
ejpam-2252	42	6	a=	a=	PROPN
ejpam-2252	42	7	�	�	PROPN
ejpam-2252	43	1	x1	x1	PROPN
ejpam-2252	43	2	,	,	PUNCT
ejpam-2252	43	3	x2	x2	PROPN
ejpam-2252	43	4	�	�	PROPN
ejpam-2252	43	5	and	and	CCONJ
ejpam-2252	43	6	b	b	PROPN
ejpam-2252	43	7	=	=	SYM
ejpam-2252	43	8	�	�	PROPN
ejpam-2252	43	9	y1	y1	PROPN
ejpam-2252	43	10	,	,	PUNCT
ejpam-2252	43	11	y2	y2	PROPN
ejpam-2252	43	12	�	�	PROPN
ejpam-2252	43	13	is	be	AUX
ejpam-2252	43	14	defined	define	VERB
ejpam-2252	43	15	by	by	ADP
ejpam-2252	43	16	‖ab‖=	‖ab‖=	PROPN
ejpam-2252	43	17	ç	ç	SYM
ejpam-2252	43	18	�	�	PROPN
ejpam-2252	43	19	�	�	PROPN
ejpam-2252	43	20	〈	〈	PROPN
ejpam-2252	43	21	ab	ab	PROPN
ejpam-2252	43	22	,	,	PUNCT
ejpam-2252	43	23	ab〉ε	ab〉ε	PROPN
ejpam-2252	43	24	�	�	PROPN
ejpam-2252	43	25	�	�	PROPN
ejpam-2252	43	26	=	=	SYM
ejpam-2252	43	27	dab	dab	PROPN
ejpam-2252	43	28	=	=	SYM
ejpam-2252	43	29	s	s	PART
ejpam-2252	43	30	�	�	PROPN
ejpam-2252	43	31	�	�	PROPN
ejpam-2252	43	32	�	�	PROPN
ejpam-2252	43	33	�	�	PROPN
ejpam-2252	43	34	y1	y1	PROPN
ejpam-2252	43	35	−	−	PROPN
ejpam-2252	43	36	x1	x1	PROPN
ejpam-2252	44	1	�	�	PROPN
ejpam-2252	44	2	2	2	NUM
ejpam-2252	44	3	+	+	CCONJ
ejpam-2252	44	4	ε	ε	PROPN
ejpam-2252	44	5	�	�	PROPN
ejpam-2252	44	6	y2	y2	PROPN
ejpam-2252	44	7	−	−	PROPN
ejpam-2252	44	8	x2	x2	PROPN
ejpam-2252	44	9	�	�	PROPN
ejpam-2252	44	10	2	2	NUM
ejpam-2252	44	11	�	�	PROPN
ejpam-2252	44	12	�	�	PROPN
ejpam-2252	44	13	�	�	PROPN
ejpam-2252	44	14	.	.	PUNCT
ejpam-2252	45	1	for	for	ADP
ejpam-2252	45	2	ε=	ε=	ADJ
ejpam-2252	45	3	1	1	NUM
ejpam-2252	45	4	only	only	ADV
ejpam-2252	45	5	the	the	DET
ejpam-2252	45	6	zero	zero	NUM
ejpam-2252	45	7	vector	vector	NOUN
ejpam-2252	45	8	,	,	PUNCT
ejpam-2252	45	9	for	for	ADP
ejpam-2252	45	10	ε=	ε=	ADJ
ejpam-2252	45	11	0	0	NUM
ejpam-2252	45	12	zero	zero	NUM
ejpam-2252	45	13	vectors	vector	NOUN
ejpam-2252	45	14	and	and	CCONJ
ejpam-2252	45	15	vertical	vertical	ADJ
ejpam-2252	45	16	vectors	vector	NOUN
ejpam-2252	45	17	are	be	AUX
ejpam-2252	45	18	isotropic	isotropic	ADJ
ejpam-2252	45	19	and	and	CCONJ
ejpam-2252	45	20	for	for	ADP
ejpam-2252	45	21	ε=	ε=	ADJ
ejpam-2252	45	22	−1	−1	NOUN
ejpam-2252	45	23	zero	zero	NUM
ejpam-2252	45	24	vectors	vector	NOUN
ejpam-2252	45	25	and	and	CCONJ
ejpam-2252	45	26	vectors	vector	NOUN
ejpam-2252	45	27	parallel	parallel	ADJ
ejpam-2252	45	28	to	to	ADP
ejpam-2252	45	29	(	(	PUNCT
ejpam-2252	45	30	±1,1	±1,1	ADV
ejpam-2252	45	31	)	)	PUNCT
ejpam-2252	45	32	are	be	AUX
ejpam-2252	45	33	isotropic	isotropic	ADJ
ejpam-2252	45	34	[	[	X
ejpam-2252	45	35	6	6	NUM
ejpam-2252	45	36	]	]	PUNCT
ejpam-2252	45	37	.	.	PUNCT
ejpam-2252	46	1	a	a	DET
ejpam-2252	46	2	circle	circle	NOUN
ejpam-2252	46	3	is	be	AUX
ejpam-2252	46	4	the	the	DET
ejpam-2252	46	5	locus	locus	NOUN
ejpam-2252	46	6	of	of	ADP
ejpam-2252	46	7	points	point	NOUN
ejpam-2252	46	8	equidistant	equidistant	ADJ
ejpam-2252	46	9	from	from	ADP
ejpam-2252	46	10	a	a	DET
ejpam-2252	46	11	given	give	VERB
ejpam-2252	46	12	fixed	fix	VERB
ejpam-2252	46	13	point	point	NOUN
ejpam-2252	46	14	,	,	PUNCT
ejpam-2252	46	15	the	the	DET
ejpam-2252	46	16	center	center	NOUN
ejpam-2252	46	17	of	of	ADP
ejpam-2252	46	18	the	the	DET
ejpam-2252	46	19	circle	circle	NOUN
ejpam-2252	46	20	.	.	PUNCT
ejpam-2252	47	1	the	the	DET
ejpam-2252	47	2	unit	unit	NOUN
ejpam-2252	47	3	circle	circle	NOUN
ejpam-2252	47	4	in	in	ADP
ejpam-2252	47	5	pε	pε	PROPN
ejpam-2252	47	6	is	be	AUX
ejpam-2252	47	7	the	the	DET
ejpam-2252	47	8	set	set	NOUN
ejpam-2252	47	9	of	of	ADP
ejpam-2252	47	10	points	point	NOUN
ejpam-2252	47	11	with	with	ADP
ejpam-2252	47	12	‖p‖	‖p‖	PROPN
ejpam-2252	47	13	=	=	SYM
ejpam-2252	47	14	1	1	PROPN
ejpam-2252	47	15	,	,	PUNCT
ejpam-2252	47	16	for	for	ADP
ejpam-2252	47	17	all	all	DET
ejpam-2252	47	18	p	p	PROPN
ejpam-2252	47	19	∈	∈	PROPN
ejpam-2252	47	20	pε	pε	NOUN
ejpam-2252	47	21	.	.	PUNCT
ejpam-2252	48	1	the	the	DET
ejpam-2252	48	2	equation	equation	NOUN
ejpam-2252	48	3	of	of	ADP
ejpam-2252	48	4	the	the	DET
ejpam-2252	48	5	unit	unit	NOUN
ejpam-2252	48	6	circle	circle	NOUN
ejpam-2252	48	7	in	in	ADP
ejpam-2252	48	8	pε	pε	PROPN
ejpam-2252	48	9	is	be	AUX
ejpam-2252	48	10	x2	x2	PROPN
ejpam-2252	48	11	+	+	NUM
ejpam-2252	48	12	εy2	εy2	NOUN
ejpam-2252	48	13	=	=	PUNCT
ejpam-2252	48	14	±1	±1	VERB
ejpam-2252	48	15	.	.	PUNCT
ejpam-2252	49	1	they	they	PRON
ejpam-2252	49	2	are	be	AUX
ejpam-2252	49	3	shown	show	VERB
ejpam-2252	49	4	in	in	ADP
ejpam-2252	49	5	the	the	DET
ejpam-2252	49	6	figure	figure	NOUN
ejpam-2252	49	7	1	1	NUM
ejpam-2252	49	8	.	.	PUNCT
ejpam-2252	49	9	figure	figure	NOUN
ejpam-2252	49	10	1	1	NUM
ejpam-2252	49	11	:	:	PUNCT
ejpam-2252	49	12	unit	unit	NOUN
ejpam-2252	49	13	circles	circle	NOUN
ejpam-2252	49	14	in	in	ADP
ejpam-2252	49	15	pε	pε	PROPN
ejpam-2252	49	16	the	the	DET
ejpam-2252	49	17	linear	linear	PROPN
ejpam-2252	49	18	transformation	transformation	NOUN
ejpam-2252	49	19	j	j	PROPN
ejpam-2252	49	20	:	:	PUNCT
ejpam-2252	49	21	pε→	pε→	ADJ
ejpam-2252	49	22	pε	pε	VERB
ejpam-2252	49	23	with	with	ADP
ejpam-2252	49	24	matrix	matrix	NOUN
ejpam-2252	49	25	,	,	PUNCT
ejpam-2252	49	26	also	also	ADV
ejpam-2252	49	27	denoted	denote	VERB
ejpam-2252	49	28	by	by	ADP
ejpam-2252	49	29	j	j	PROPN
ejpam-2252	49	30	and	and	CCONJ
ejpam-2252	49	31	given	give	VERB
ejpam-2252	49	32	as	as	ADP
ejpam-2252	49	33	below	below	ADV
ejpam-2252	49	34	:	:	PUNCT
ejpam-2252	49	35	j	j	PROPN
ejpam-2252	49	36	=	=	SYM
ejpam-2252	49	37	�	�	PROPN
ejpam-2252	49	38	0	0	NUM
ejpam-2252	49	39	−ε	−ε	PROPN
ejpam-2252	49	40	1	1	NUM
ejpam-2252	49	41	0	0	NUM
ejpam-2252	49	42	�	�	PROPN
ejpam-2252	49	43	.	.	PUNCT
ejpam-2252	50	1	this	this	DET
ejpam-2252	50	2	linear	linear	ADJ
ejpam-2252	50	3	transformation	transformation	NOUN
ejpam-2252	50	4	converts	convert	VERB
ejpam-2252	50	5	any	any	DET
ejpam-2252	50	6	vector	vector	NOUN
ejpam-2252	50	7	x	x	PUNCT
ejpam-2252	50	8	to	to	ADP
ejpam-2252	50	9	an	an	DET
ejpam-2252	50	10	orthogonal	orthogonal	ADJ
ejpam-2252	50	11	vector	vector	NOUN
ejpam-2252	50	12	jx	jx	PROPN
ejpam-2252	50	13	.	.	PUNCT
ejpam-2252	51	1	if	if	SCONJ
ejpam-2252	51	2	x	x	PRON
ejpam-2252	51	3	is	be	AUX
ejpam-2252	51	4	a	a	DET
ejpam-2252	51	5	nonisotropic	nonisotropic	ADJ
ejpam-2252	51	6	and	and	CCONJ
ejpam-2252	51	7	y	y	PROPN
ejpam-2252	51	8	is	be	AUX
ejpam-2252	51	9	orthogonal	orthogonal	ADJ
ejpam-2252	51	10	to	to	ADP
ejpam-2252	51	11	x	x	PRON
ejpam-2252	51	12	,	,	PUNCT
ejpam-2252	51	13	then	then	ADV
ejpam-2252	51	14	it	it	PRON
ejpam-2252	51	15	is	be	AUX
ejpam-2252	51	16	written	write	VERB
ejpam-2252	51	17	such	such	ADJ
ejpam-2252	51	18	that	that	SCONJ
ejpam-2252	51	19	y	y	PROPN
ejpam-2252	51	20	=	=	PUNCT
ejpam-2252	51	21	kjx	kjx	PROPN
ejpam-2252	51	22	for	for	ADP
ejpam-2252	51	23	some	some	DET
ejpam-2252	51	24	real	real	ADJ
ejpam-2252	51	25	number	number	NOUN
ejpam-2252	51	26	k	k	PROPN
ejpam-2252	52	1	[	[	X
ejpam-2252	52	2	6	6	NUM
ejpam-2252	52	3	]	]	PUNCT
ejpam-2252	52	4	.	.	PUNCT
ejpam-2252	53	1	it	it	PRON
ejpam-2252	53	2	is	be	AUX
ejpam-2252	53	3	not	not	PART
ejpam-2252	53	4	difficult	difficult	ADJ
ejpam-2252	53	5	to	to	PART
ejpam-2252	53	6	verify	verify	VERB
ejpam-2252	53	7	directly	directly	ADV
ejpam-2252	53	8	from	from	ADP
ejpam-2252	53	9	the	the	DET
ejpam-2252	53	10	definition	definition	NOUN
ejpam-2252	53	11	of	of	ADP
ejpam-2252	53	12	the	the	DET
ejpam-2252	53	13	matrix	matrix	NOUN
ejpam-2252	53	14	exponential	exponential	NOUN
ejpam-2252	53	15	as	as	ADP
ejpam-2252	53	16	ejϕ	ejϕ	NOUN
ejpam-2252	53	17	=	=	SYM
ejpam-2252	53	18	∑∞	∑∞	NOUN
ejpam-2252	53	19	n=0	n=0	X
ejpam-2252	53	20	(	(	PUNCT
ejpam-2252	53	21	jϕ)n	jϕ)n	PROPN
ejpam-2252	53	22	n	n	CCONJ
ejpam-2252	53	23	!	!	PUNCT
ejpam-2252	54	1	that	that	DET
ejpam-2252	54	2	ejϕ	ejϕ	PROPN
ejpam-2252	54	3	=	=	PUNCT
ejpam-2252	54	4	cos	cos	ADP
ejpam-2252	54	5	εϕ	εϕ	PROPN
ejpam-2252	54	6	+	+	NUM
ejpam-2252	54	7	j	j	PROPN
ejpam-2252	54	8	sin	sin	NOUN
ejpam-2252	54	9	εϕ	εϕ	NOUN
ejpam-2252	54	10	=	=	SYM
ejpam-2252	54	11	�	�	PROPN
ejpam-2252	54	12	cos	cos	PROPN
ejpam-2252	54	13	εϕ	εϕ	PROPN
ejpam-2252	54	14	−ε	−ε	PROPN
ejpam-2252	54	15	sin	sin	NOUN
ejpam-2252	54	16	εϕ	εϕ	NOUN
ejpam-2252	54	17	sin	sin	NOUN
ejpam-2252	54	18	εϕ	εϕ	NOUN
ejpam-2252	54	19	cosεϕ	cosεϕ	PROPN
ejpam-2252	54	20	�	�	PROPN
ejpam-2252	54	21	n.	n.	PROPN
ejpam-2252	54	22	gürses	gürse	NOUN
ejpam-2252	54	23	,	,	PUNCT
ejpam-2252	54	24	s.	s.	PROPN
ejpam-2252	54	25	yüce	yüce	PROPN
ejpam-2252	54	26	/	/	SYM
ejpam-2252	54	27	eur	eur	PROPN
ejpam-2252	54	28	.	.	PUNCT
ejpam-2252	55	1	j.	j.	PROPN
ejpam-2252	55	2	pure	pure	PROPN
ejpam-2252	55	3	appl	appl	PROPN
ejpam-2252	55	4	.	.	PROPN
ejpam-2252	55	5	math	math	PROPN
ejpam-2252	55	6	,	,	PUNCT
ejpam-2252	55	7	7	7	NUM
ejpam-2252	55	8	(	(	PUNCT
ejpam-2252	55	9	2014	2014	NUM
ejpam-2252	55	10	)	)	PUNCT
ejpam-2252	55	11	,	,	PUNCT
ejpam-2252	55	12	335	335	NUM
ejpam-2252	55	13	-	-	SYM
ejpam-2252	55	14	342	342	NUM
ejpam-2252	55	15	338	338	NUM
ejpam-2252	55	16	where	where	SCONJ
ejpam-2252	55	17	cos	cos	ADP
ejpam-2252	55	18	εϕ	εϕ	NOUN
ejpam-2252	55	19	=	=	SYM
ejpam-2252	55	20	∞	∞	PROPN
ejpam-2252	55	21	∑	∑	PROPN
ejpam-2252	55	22	n=0	n=0	NUM
ejpam-2252	55	23	(	(	PUNCT
ejpam-2252	55	24	−εn)ϕ2n	−εn)ϕ2n	PROPN
ejpam-2252	55	25	(	(	PUNCT
ejpam-2252	55	26	2n	2n	NUM
ejpam-2252	55	27	)	)	PUNCT
ejpam-2252	55	28	!	!	PUNCT
ejpam-2252	56	1	sin	sin	VERB
ejpam-2252	56	2	εϕ	εϕ	NOUN
ejpam-2252	56	3	=	=	SYM
ejpam-2252	56	4	∞	∞	PROPN
ejpam-2252	56	5	∑	∑	PROPN
ejpam-2252	56	6	n=0	n=0	NUM
ejpam-2252	56	7	(	(	PUNCT
ejpam-2252	56	8	−εn)ϕ2n+1	−εn)ϕ2n+1	PROPN
ejpam-2252	56	9	(	(	PUNCT
ejpam-2252	56	10	2n+1	2n+1	PROPN
ejpam-2252	56	11	)	)	PUNCT
ejpam-2252	56	12	!	!	PUNCT
ejpam-2252	56	13	.	.	PUNCT
ejpam-2252	57	1	for	for	ADP
ejpam-2252	57	2	ε	ε	PROPN
ejpam-2252	57	3	=	=	SYM
ejpam-2252	57	4	1	1	NUM
ejpam-2252	57	5	these	these	PRON
ejpam-2252	57	6	are	be	AUX
ejpam-2252	57	7	usual	usual	ADJ
ejpam-2252	57	8	cosine	cosine	NOUN
ejpam-2252	57	9	and	and	CCONJ
ejpam-2252	57	10	sine	sine	ADJ
ejpam-2252	57	11	functions	function	NOUN
ejpam-2252	57	12	,	,	PUNCT
ejpam-2252	57	13	for	for	ADP
ejpam-2252	57	14	ε	ε	PROPN
ejpam-2252	57	15	=	=	SYM
ejpam-2252	57	16	−1	−1	NOUN
ejpam-2252	57	17	they	they	PRON
ejpam-2252	57	18	are	be	AUX
ejpam-2252	57	19	hyperbolic	hyperbolic	ADJ
ejpam-2252	57	20	cosine	cosine	NOUN
ejpam-2252	57	21	and	and	CCONJ
ejpam-2252	57	22	sine	sine	ADJ
ejpam-2252	57	23	functions	function	NOUN
ejpam-2252	57	24	,	,	PUNCT
ejpam-2252	57	25	and	and	CCONJ
ejpam-2252	57	26	for	for	ADP
ejpam-2252	57	27	ε=	ε=	NOUN
ejpam-2252	57	28	0	0	NUM
ejpam-2252	58	1	they	they	PRON
ejpam-2252	58	2	are	be	AUX
ejpam-2252	58	3	just	just	ADV
ejpam-2252	58	4	cos	cos	ADP
ejpam-2252	58	5	0ϕ	0ϕ	NOUN
ejpam-2252	58	6	=	=	SYM
ejpam-2252	58	7	1	1	NUM
ejpam-2252	58	8	and	and	CCONJ
ejpam-2252	58	9	cos	cos	PROPN
ejpam-2252	58	10	0ϕ	0ϕ	PROPN
ejpam-2252	58	11	=	=	SYM
ejpam-2252	58	12	ϕ	ϕ	PROPN
ejpam-2252	58	13	for	for	ADP
ejpam-2252	58	14	all	all	DET
ejpam-2252	58	15	ϕ.	ϕ.	NOUN
ejpam-2252	58	16	in	in	ADP
ejpam-2252	58	17	all	all	DET
ejpam-2252	58	18	cases	case	NOUN
ejpam-2252	58	19	,	,	PUNCT
ejpam-2252	58	20	we	we	PRON
ejpam-2252	58	21	obtain	obtain	VERB
ejpam-2252	58	22	cos2	cos2	NOUN
ejpam-2252	58	23	εϕ	εϕ	NOUN
ejpam-2252	58	24	+	+	CCONJ
ejpam-2252	58	25	ε	ε	PROPN
ejpam-2252	58	26	sin2	sin2	NOUN
ejpam-2252	58	27	εϕ	εϕ	NOUN
ejpam-2252	58	28	=	=	SYM
ejpam-2252	58	29	1	1	NUM
ejpam-2252	58	30	and	and	CCONJ
ejpam-2252	58	31	∂ϕ	∂ϕ	PROPN
ejpam-2252	59	1	cos	cos	PROPN
ejpam-2252	59	2	εϕ	εϕ	PROPN
ejpam-2252	59	3	=	=	SYM
ejpam-2252	59	4	−ε	−ε	PROPN
ejpam-2252	59	5	sin	sin	NOUN
ejpam-2252	59	6	εϕ,∂ϕ	εϕ,∂ϕ	ADV
ejpam-2252	59	7	sin	sin	VERB
ejpam-2252	59	8	εϕ	εϕ	NOUN
ejpam-2252	59	9	=	=	PUNCT
ejpam-2252	59	10	cos	cos	X
ejpam-2252	59	11	εϕ.	εϕ.	X
ejpam-2252	59	12	by	by	ADP
ejpam-2252	59	13	equating	equate	VERB
ejpam-2252	59	14	corresponding	corresponding	ADJ
ejpam-2252	59	15	entries	entry	NOUN
ejpam-2252	59	16	of	of	ADP
ejpam-2252	59	17	the	the	DET
ejpam-2252	59	18	matrix	matrix	NOUN
ejpam-2252	59	19	equation	equation	NOUN
ejpam-2252	59	20	ej(ϕ+θ	ej(ϕ+θ	NOUN
ejpam-2252	59	21	)	)	PUNCT
ejpam-2252	60	1	=	=	PUNCT
ejpam-2252	60	2	ejϕejθ	ejϕejθ	PROPN
ejpam-2252	60	3	,	,	PUNCT
ejpam-2252	60	4	we	we	PRON
ejpam-2252	60	5	can	can	AUX
ejpam-2252	60	6	find	find	VERB
ejpam-2252	60	7	the	the	DET
ejpam-2252	60	8	sum	sum	NOUN
ejpam-2252	60	9	formulae	formulae	NOUN
ejpam-2252	60	10	[	[	X
ejpam-2252	60	11	14	14	NUM
ejpam-2252	60	12	]	]	PUNCT
ejpam-2252	60	13	as	as	SCONJ
ejpam-2252	60	14	follows	follow	VERB
ejpam-2252	60	15	:	:	PUNCT
ejpam-2252	60	16	cos	cos	PROPN
ejpam-2252	60	17	ε(ϕ	ε(ϕ	PROPN
ejpam-2252	60	18	+	+	PROPN
ejpam-2252	60	19	θ	θ	NOUN
ejpam-2252	60	20	)	)	PUNCT
ejpam-2252	61	1	=	=	PUNCT
ejpam-2252	61	2	cos	cos	ADP
ejpam-2252	61	3	εϕ	εϕ	PROPN
ejpam-2252	61	4	cos	cos	PROPN
ejpam-2252	61	5	εθ	εθ	PROPN
ejpam-2252	61	6	−	−	PROPN
ejpam-2252	61	7	ε	ε	PROPN
ejpam-2252	61	8	sin	sin	VERB
ejpam-2252	61	9	εϕ	εϕ	NOUN
ejpam-2252	61	10	sin	sin	NOUN
ejpam-2252	61	11	εθ	εθ	AUX
ejpam-2252	61	12	sin	sin	VERB
ejpam-2252	61	13	ε(ϕ	ε(ϕ	PROPN
ejpam-2252	61	14	+	+	NUM
ejpam-2252	61	15	θ	θ	NOUN
ejpam-2252	61	16	)	)	PUNCT
ejpam-2252	62	1	=	=	PRON
ejpam-2252	62	2	sin	sin	VERB
ejpam-2252	62	3	εϕ	εϕ	NOUN
ejpam-2252	62	4	cos	cos	PROPN
ejpam-2252	62	5	εθ	εθ	PROPN
ejpam-2252	62	6	+	+	CCONJ
ejpam-2252	62	7	cos	cos	ADP
ejpam-2252	62	8	εϕ	εϕ	NOUN
ejpam-2252	62	9	sin	sin	VERB
ejpam-2252	62	10	εθ	εθ	NOUN
ejpam-2252	62	11	.	.	PUNCT
ejpam-2252	63	1	3	3	X
ejpam-2252	63	2	.	.	X
ejpam-2252	63	3	one	one	NUM
ejpam-2252	63	4	-	-	PUNCT
ejpam-2252	63	5	parameter	parameter	NOUN
ejpam-2252	63	6	planar	planar	ADJ
ejpam-2252	63	7	motions	motion	NOUN
ejpam-2252	63	8	in	in	ADP
ejpam-2252	63	9	affine	affine	NOUN
ejpam-2252	63	10	ck	ck	PROPN
ejpam-2252	63	11	-	-	PUNCT
ejpam-2252	63	12	planes	plane	NOUN
ejpam-2252	63	13	3.1	3.1	NUM
ejpam-2252	63	14	.	.	PUNCT
ejpam-2252	64	1	derivative	derivative	ADJ
ejpam-2252	64	2	formulae	formulae	NOUN
ejpam-2252	64	3	,	,	PUNCT
ejpam-2252	64	4	velocities	velocity	NOUN
ejpam-2252	64	5	and	and	CCONJ
ejpam-2252	64	6	pole	pole	NOUN
ejpam-2252	64	7	point	point	NOUN
ejpam-2252	64	8	notation	notation	NOUN
ejpam-2252	64	9	in	in	ADP
ejpam-2252	64	10	this	this	DET
ejpam-2252	64	11	section	section	NOUN
ejpam-2252	64	12	,	,	PUNCT
ejpam-2252	64	13	we	we	PRON
ejpam-2252	64	14	stated	state	VERB
ejpam-2252	64	15	that	that	SCONJ
ejpam-2252	64	16	the	the	DET
ejpam-2252	64	17	one	one	NUM
ejpam-2252	64	18	-	-	PUNCT
ejpam-2252	64	19	parameter	parameter	NOUN
ejpam-2252	64	20	planar	planar	ADJ
ejpam-2252	64	21	motions	motion	NOUN
ejpam-2252	64	22	in	in	ADP
ejpam-2252	64	23	affine	affine	NOUN
ejpam-2252	64	24	ck	ck	NOUN
ejpam-2252	64	25	-	-	PUNCT
ejpam-2252	64	26	planes	plane	NOUN
ejpam-2252	64	27	is	be	AUX
ejpam-2252	64	28	an	an	DET
ejpam-2252	64	29	extension	extension	NOUN
ejpam-2252	64	30	of	of	ADP
ejpam-2252	64	31	the	the	DET
ejpam-2252	64	32	one	one	NUM
ejpam-2252	64	33	-	-	PUNCT
ejpam-2252	64	34	parameter	parameter	NOUN
ejpam-2252	64	35	planar	planar	ADJ
ejpam-2252	64	36	motions	motion	NOUN
ejpam-2252	64	37	in	in	ADP
ejpam-2252	64	38	the	the	DET
ejpam-2252	64	39	euclidean	euclidean	ADJ
ejpam-2252	64	40	plane	plane	NOUN
ejpam-2252	64	41	,	,	PUNCT
ejpam-2252	64	42	lorentzian	lorentzian	ADJ
ejpam-2252	64	43	plane	plane	NOUN
ejpam-2252	64	44	,	,	PUNCT
ejpam-2252	64	45	and	and	CCONJ
ejpam-2252	64	46	galilean	galilean	PROPN
ejpam-2252	64	47	plane	plane	NOUN
ejpam-2252	64	48	,	,	PUNCT
ejpam-2252	64	49	respectively	respectively	ADV
ejpam-2252	64	50	given	give	VERB
ejpam-2252	64	51	[	[	X
ejpam-2252	64	52	3	3	NUM
ejpam-2252	64	53	]	]	PUNCT
ejpam-2252	64	54	,	,	PUNCT
ejpam-2252	65	1	[	[	X
ejpam-2252	65	2	4	4	X
ejpam-2252	65	3	]	]	PUNCT
ejpam-2252	65	4	and	and	CCONJ
ejpam-2252	65	5	[	[	X
ejpam-2252	65	6	1	1	NUM
ejpam-2252	65	7	]	]	PUNCT
ejpam-2252	65	8	.	.	PUNCT
ejpam-2252	66	1	we	we	PRON
ejpam-2252	66	2	will	will	AUX
ejpam-2252	66	3	define	define	VERB
ejpam-2252	66	4	the	the	DET
ejpam-2252	66	5	one	one	NUM
ejpam-2252	66	6	-	-	PUNCT
ejpam-2252	66	7	parameter	parameter	NOUN
ejpam-2252	66	8	planar	planar	ADJ
ejpam-2252	66	9	motions	motion	NOUN
ejpam-2252	66	10	in	in	ADP
ejpam-2252	66	11	affine	affine	NOUN
ejpam-2252	66	12	ck	ck	NOUN
ejpam-2252	66	13	-	-	PUNCT
ejpam-2252	66	14	planes	plane	NOUN
ejpam-2252	66	15	and	and	CCONJ
ejpam-2252	66	16	we	we	PRON
ejpam-2252	66	17	will	will	AUX
ejpam-2252	66	18	obtain	obtain	VERB
ejpam-2252	66	19	the	the	DET
ejpam-2252	66	20	relations	relation	NOUN
ejpam-2252	66	21	between	between	ADP
ejpam-2252	66	22	velocities	velocity	NOUN
ejpam-2252	66	23	and	and	CCONJ
ejpam-2252	66	24	accelerations	acceleration	NOUN
ejpam-2252	66	25	of	of	ADP
ejpam-2252	66	26	a	a	DET
ejpam-2252	66	27	point	point	NOUN
ejpam-2252	66	28	under	under	ADP
ejpam-2252	66	29	these	these	DET
ejpam-2252	66	30	motions	motion	NOUN
ejpam-2252	66	31	.	.	PUNCT
ejpam-2252	67	1	let	let	VERB
ejpam-2252	67	2	pε	pε	NOUN
ejpam-2252	67	3	and	and	CCONJ
ejpam-2252	67	4	p′ε	p′ε	PROPN
ejpam-2252	67	5	be	be	AUX
ejpam-2252	67	6	moving	move	VERB
ejpam-2252	67	7	and	and	CCONJ
ejpam-2252	67	8	fixed	fix	VERB
ejpam-2252	67	9	affine	affine	NOUN
ejpam-2252	67	10	ck	ck	NOUN
ejpam-2252	67	11	-	-	PUNCT
ejpam-2252	67	12	planes	plane	NOUN
ejpam-2252	67	13	and	and	CCONJ
ejpam-2252	67	14	{	{	PUNCT
ejpam-2252	67	15	o;c1,c2	o;c1,c2	NOUN
ejpam-2252	67	16	}	}	PUNCT
ejpam-2252	67	17	and	and	CCONJ
ejpam-2252	67	18	{	{	PUNCT
ejpam-2252	67	19	o′;c′1,c′2	o′;c′1,c′2	NOUN
ejpam-2252	67	20	}	}	PUNCT
ejpam-2252	67	21	be	be	VERB
ejpam-2252	67	22	their	their	PRON
ejpam-2252	67	23	orthonormal	orthonormal	ADJ
ejpam-2252	67	24	coordinate	coordinate	NOUN
ejpam-2252	67	25	systems	system	NOUN
ejpam-2252	67	26	,	,	PUNCT
ejpam-2252	67	27	respectively	respectively	ADV
ejpam-2252	67	28	.	.	PUNCT
ejpam-2252	68	1	let	let	VERB
ejpam-2252	68	2	us	we	PRON
ejpam-2252	68	3	take	take	VERB
ejpam-2252	68	4	the	the	DET
ejpam-2252	68	5	vector	vector	NOUN
ejpam-2252	68	6	oo′	oo′	NOUN
ejpam-2252	68	7	=	=	SYM
ejpam-2252	68	8	u=	u=	NOUN
ejpam-2252	68	9	u1c1	u1c1	X
ejpam-2252	68	10	+	+	CCONJ
ejpam-2252	68	11	u2c2	u2c2	X
ejpam-2252	68	12	for	for	ADP
ejpam-2252	68	13	u1,u2	u1,u2	PROPN
ejpam-2252	68	14	∈	∈	PROPN
ejpam-2252	68	15	r.	r.	PROPN
ejpam-2252	68	16	(	(	PUNCT
ejpam-2252	68	17	1	1	X
ejpam-2252	68	18	)	)	PUNCT
ejpam-2252	68	19	let	let	VERB
ejpam-2252	68	20	us	we	PRON
ejpam-2252	68	21	define	define	VERB
ejpam-2252	68	22	a	a	DET
ejpam-2252	68	23	transformation	transformation	NOUN
ejpam-2252	68	24	as	as	SCONJ
ejpam-2252	68	25	given	give	VERB
ejpam-2252	68	26	below	below	ADV
ejpam-2252	68	27	:	:	PUNCT
ejpam-2252	68	28	x′	x′	PROPN
ejpam-2252	68	29	=	=	SYM
ejpam-2252	68	30	x−	x−	PROPN
ejpam-2252	68	31	u	u	PROPN
ejpam-2252	68	32	,	,	PUNCT
ejpam-2252	68	33	(	(	PUNCT
ejpam-2252	68	34	2	2	X
ejpam-2252	68	35	)	)	PUNCT
ejpam-2252	68	36	where	where	SCONJ
ejpam-2252	68	37	x	x	X
ejpam-2252	68	38	,	,	PUNCT
ejpam-2252	68	39	x′	x′	PROPN
ejpam-2252	68	40	are	be	AUX
ejpam-2252	68	41	coordinate	coordinate	ADJ
ejpam-2252	68	42	vectors	vector	NOUN
ejpam-2252	68	43	with	with	ADP
ejpam-2252	68	44	respect	respect	NOUN
ejpam-2252	68	45	to	to	ADP
ejpam-2252	68	46	the	the	DET
ejpam-2252	68	47	moving	move	VERB
ejpam-2252	68	48	and	and	CCONJ
ejpam-2252	68	49	fixed	fix	VERB
ejpam-2252	68	50	rectangular	rectangular	ADJ
ejpam-2252	68	51	coordinate	coordinate	NOUN
ejpam-2252	68	52	system	system	NOUN
ejpam-2252	68	53	of	of	ADP
ejpam-2252	68	54	a	a	DET
ejpam-2252	68	55	point	point	NOUN
ejpam-2252	68	56	x	x	X
ejpam-2252	68	57	=	=	SYM
ejpam-2252	68	58	(	(	PUNCT
ejpam-2252	68	59	x1	x1	PROPN
ejpam-2252	68	60	,	,	PUNCT
ejpam-2252	68	61	x2	x2	PROPN
ejpam-2252	68	62	)	)	PUNCT
ejpam-2252	68	63	∈	∈	PROPN
ejpam-2252	68	64	pε	pε	NOUN
ejpam-2252	68	65	,	,	PUNCT
ejpam-2252	68	66	respectively	respectively	ADV
ejpam-2252	68	67	.	.	PUNCT
ejpam-2252	69	1	by	by	ADP
ejpam-2252	69	2	the	the	DET
ejpam-2252	69	3	equation	equation	NOUN
ejpam-2252	69	4	(	(	PUNCT
ejpam-2252	69	5	2	2	NUM
ejpam-2252	69	6	)	)	PUNCT
ejpam-2252	69	7	,	,	PUNCT
ejpam-2252	69	8	one	one	NUM
ejpam-2252	69	9	-	-	PUNCT
ejpam-2252	69	10	parameter	parameter	NOUN
ejpam-2252	69	11	planar	planar	ADJ
ejpam-2252	69	12	motions	motion	NOUN
ejpam-2252	69	13	in	in	ADP
ejpam-2252	69	14	affine	affine	NOUN
ejpam-2252	69	15	ck	ck	NOUN
ejpam-2252	69	16	-	-	PUNCT
ejpam-2252	69	17	planes	plane	NOUN
ejpam-2252	69	18	are	be	AUX
ejpam-2252	69	19	defined	define	VERB
ejpam-2252	69	20	.	.	PUNCT
ejpam-2252	70	1	these	these	DET
ejpam-2252	70	2	motions	motion	NOUN
ejpam-2252	70	3	denoted	denote	VERB
ejpam-2252	70	4	by	by	ADP
ejpam-2252	70	5	pε	pε	PROPN
ejpam-2252	70	6	/	/	SYM
ejpam-2252	70	7	p	p	NOUN
ejpam-2252	70	8	′	′	NUM
ejpam-2252	70	9	ε	ε	PROPN
ejpam-2252	70	10	.	.	PUNCT
ejpam-2252	71	1	moreover	moreover	ADV
ejpam-2252	71	2	,	,	PUNCT
ejpam-2252	71	3	ϕ	ϕ	PROPN
ejpam-2252	71	4	,	,	PUNCT
ejpam-2252	71	5	the	the	DET
ejpam-2252	71	6	angle	angle	NOUN
ejpam-2252	71	7	between	between	ADP
ejpam-2252	71	8	the	the	DET
ejpam-2252	71	9	vectors	vector	NOUN
ejpam-2252	71	10	c1	c1	PROPN
ejpam-2252	71	11	and	and	CCONJ
ejpam-2252	71	12	c′1	c′1	PROPN
ejpam-2252	71	13	,	,	PUNCT
ejpam-2252	71	14	is	be	AUX
ejpam-2252	71	15	the	the	DET
ejpam-2252	71	16	rotation	rotation	NOUN
ejpam-2252	71	17	angle	angle	NOUN
ejpam-2252	71	18	of	of	ADP
ejpam-2252	71	19	the	the	DET
ejpam-2252	71	20	motions	motion	NOUN
ejpam-2252	71	21	pε	pε	PROPN
ejpam-2252	71	22	/	/	SYM
ejpam-2252	71	23	p	p	NOUN
ejpam-2252	71	24	′	′	NUM
ejpam-2252	71	25	ε	ε	PROPN
ejpam-2252	71	26	and	and	CCONJ
ejpam-2252	71	27	x	x	PROPN
ejpam-2252	71	28	,	,	PUNCT
ejpam-2252	71	29	x′	x′	PROPN
ejpam-2252	71	30	,	,	PUNCT
ejpam-2252	71	31	u	u	PRON
ejpam-2252	71	32	are	be	AUX
ejpam-2252	71	33	continuously	continuously	ADV
ejpam-2252	71	34	differentiable	differentiable	ADJ
ejpam-2252	71	35	functions	function	NOUN
ejpam-2252	71	36	of	of	ADP
ejpam-2252	71	37	a	a	DET
ejpam-2252	71	38	time	time	NOUN
ejpam-2252	71	39	parameter	parameter	NOUN
ejpam-2252	71	40	t	t	PROPN
ejpam-2252	71	41	∈	∈	PROPN
ejpam-2252	72	1	i	i	PRON
ejpam-2252	72	2	⊂	⊂	PROPN
ejpam-2252	72	3	r.	r.	PROPN
ejpam-2252	72	4	for	for	ADP
ejpam-2252	72	5	t	t	PROPN
ejpam-2252	72	6	=	=	SYM
ejpam-2252	72	7	0	0	PROPN
ejpam-2252	72	8	,	,	PUNCT
ejpam-2252	72	9	the	the	DET
ejpam-2252	72	10	coordinate	coordinate	NOUN
ejpam-2252	72	11	systems	system	NOUN
ejpam-2252	72	12	are	be	AUX
ejpam-2252	72	13	coincident	coincident	ADJ
ejpam-2252	72	14	.	.	PUNCT
ejpam-2252	73	1	by	by	ADP
ejpam-2252	73	2	taking	take	VERB
ejpam-2252	73	3	ϕ	ϕ	NOUN
ejpam-2252	73	4	=	=	PUNCT
ejpam-2252	73	5	ϕ(t	ϕ(t	NUM
ejpam-2252	73	6	)	)	PUNCT
ejpam-2252	73	7	,	,	PUNCT
ejpam-2252	73	8	we	we	PRON
ejpam-2252	73	9	can	can	AUX
ejpam-2252	73	10	write	write	VERB
ejpam-2252	73	11	�	�	PROPN
ejpam-2252	73	12	c1	c1	PROPN
ejpam-2252	73	13	=	=	PROPN
ejpam-2252	74	1	cos	cos	PROPN
ejpam-2252	74	2	εϕc′1	εϕc′1	PROPN
ejpam-2252	74	3	+	+	CCONJ
ejpam-2252	74	4	sin	sin	NOUN
ejpam-2252	74	5	εϕc′2	εϕc′2	PROPN
ejpam-2252	74	6	c2	c2	PROPN
ejpam-2252	74	7	=	=	PROPN
ejpam-2252	74	8	−ε	−ε	PROPN
ejpam-2252	74	9	sin	sin	NOUN
ejpam-2252	74	10	εϕc′1	εϕc′1	NOUN
ejpam-2252	74	11	+	+	X
ejpam-2252	74	12	cos	cos	ADP
ejpam-2252	74	13	εϕc′2	εϕc′2	NOUN
ejpam-2252	74	14	(	(	PUNCT
ejpam-2252	74	15	3	3	X
ejpam-2252	74	16	)	)	PUNCT
ejpam-2252	74	17	n.	n.	NOUN
ejpam-2252	74	18	gürses	gürse	NOUN
ejpam-2252	74	19	,	,	PUNCT
ejpam-2252	74	20	s.	s.	PROPN
ejpam-2252	74	21	yüce	yüce	PROPN
ejpam-2252	74	22	/	/	SYM
ejpam-2252	74	23	eur	eur	PROPN
ejpam-2252	74	24	.	.	PUNCT
ejpam-2252	75	1	j.	j.	PROPN
ejpam-2252	75	2	pure	pure	PROPN
ejpam-2252	75	3	appl	appl	PROPN
ejpam-2252	75	4	.	.	PROPN
ejpam-2252	75	5	math	math	PROPN
ejpam-2252	75	6	,	,	PUNCT
ejpam-2252	75	7	7	7	NUM
ejpam-2252	75	8	(	(	PUNCT
ejpam-2252	75	9	2014	2014	NUM
ejpam-2252	75	10	)	)	PUNCT
ejpam-2252	75	11	,	,	PUNCT
ejpam-2252	75	12	335	335	NUM
ejpam-2252	75	13	-	-	SYM
ejpam-2252	75	14	342	342	NUM
ejpam-2252	75	15	339	339	NUM
ejpam-2252	76	1	we	we	PRON
ejpam-2252	76	2	assume	assume	VERB
ejpam-2252	76	3	that	that	SCONJ
ejpam-2252	76	4	ϕ̇	ϕ̇	PROPN
ejpam-2252	76	5	(	(	PUNCT
ejpam-2252	76	6	t	t	NOUN
ejpam-2252	76	7	)	)	PUNCT
ejpam-2252	76	8	=	=	PUNCT
ejpam-2252	76	9	dϕ	dϕ	NOUN
ejpam-2252	76	10	d	d	X
ejpam-2252	76	11	t	t	PROPN
ejpam-2252	76	12	6=	6=	PROPN
ejpam-2252	76	13	0	0	NUM
ejpam-2252	76	14	,	,	PUNCT
ejpam-2252	76	15	and	and	CCONJ
ejpam-2252	76	16	ϕ̇	ϕ̇	PRON
ejpam-2252	76	17	(	(	PUNCT
ejpam-2252	76	18	t	t	NOUN
ejpam-2252	76	19	)	)	PUNCT
ejpam-2252	76	20	is	be	AUX
ejpam-2252	76	21	called	call	VERB
ejpam-2252	76	22	the	the	DET
ejpam-2252	76	23	angular	angular	ADJ
ejpam-2252	76	24	velocity	velocity	NOUN
ejpam-2252	76	25	of	of	ADP
ejpam-2252	76	26	the	the	DET
ejpam-2252	76	27	motions	motion	NOUN
ejpam-2252	76	28	pε	pε	PROPN
ejpam-2252	76	29	/	/	SYM
ejpam-2252	76	30	p	p	NOUN
ejpam-2252	77	1	′	′	NUM
ejpam-2252	77	2	ε	ε	PROPN
ejpam-2252	77	3	.	.	PUNCT
ejpam-2252	77	4	by	by	ADP
ejpam-2252	77	5	differentiating	differentiate	VERB
ejpam-2252	77	6	the	the	DET
ejpam-2252	77	7	equations	equation	NOUN
ejpam-2252	77	8	(	(	PUNCT
ejpam-2252	77	9	1	1	NUM
ejpam-2252	77	10	)	)	PUNCT
ejpam-2252	77	11	and	and	CCONJ
ejpam-2252	77	12	(	(	PUNCT
ejpam-2252	77	13	3	3	X
ejpam-2252	77	14	)	)	PUNCT
ejpam-2252	77	15	with	with	ADP
ejpam-2252	77	16	respect	respect	NOUN
ejpam-2252	77	17	to	to	ADP
ejpam-2252	77	18	t	t	PROPN
ejpam-2252	77	19	,	,	PUNCT
ejpam-2252	77	20	the	the	DET
ejpam-2252	77	21	derivative	derivative	ADJ
ejpam-2252	77	22	formulae	formulae	NOUN
ejpam-2252	77	23	of	of	ADP
ejpam-2252	77	24	the	the	DET
ejpam-2252	77	25	motions	motion	NOUN
ejpam-2252	77	26	pε	pε	PROPN
ejpam-2252	77	27	/	/	SYM
ejpam-2252	77	28	p	p	NOUN
ejpam-2252	77	29	′	′	NUM
ejpam-2252	77	30	ε	ε	PROPN
ejpam-2252	77	31	are	be	AUX
ejpam-2252	77	32	obtained	obtain	VERB
ejpam-2252	77	33	as	as	ADP
ejpam-2252	77	34	follows	follow	VERB
ejpam-2252	77	35	:	:	PUNCT
ejpam-2252	77	36			PROPN
ejpam-2252	77	37			PRON
ejpam-2252	77	38			NOUN
ejpam-2252	77	39	ċ1	ċ1	PROPN
ejpam-2252	77	40	=	=	SYM
ejpam-2252	78	1	ϕ̇c2	ϕ̇c2	PROPN
ejpam-2252	79	1	ċ2	ċ2	NOUN
ejpam-2252	79	2	=	=	SYM
ejpam-2252	79	3	−εϕ̇c1	−εϕ̇c1	NOUN
ejpam-2252	79	4	u̇	u̇	NOUN
ejpam-2252	80	1	=	=	PRON
ejpam-2252	80	2	(	(	PUNCT
ejpam-2252	80	3	u̇1	u̇1	INTJ
ejpam-2252	80	4	−	−	NOUN
ejpam-2252	80	5	εϕ̇u2)c1	εϕ̇u2)c1	NOUN
ejpam-2252	80	6	+	+	CCONJ
ejpam-2252	80	7	(	(	PUNCT
ejpam-2252	80	8	u̇2	u̇2	PROPN
ejpam-2252	80	9	+	+	NUM
ejpam-2252	80	10	ϕ̇u1)c2	ϕ̇u1)c2	PROPN
ejpam-2252	80	11	.	.	PUNCT
ejpam-2252	81	1	(	(	PUNCT
ejpam-2252	81	2	4	4	NUM
ejpam-2252	81	3	)	)	PUNCT
ejpam-2252	81	4	by	by	ADP
ejpam-2252	81	5	using	use	VERB
ejpam-2252	81	6	these	these	DET
ejpam-2252	81	7	derivative	derivative	ADJ
ejpam-2252	81	8	formulae	formulae	NOUN
ejpam-2252	81	9	,	,	PUNCT
ejpam-2252	81	10	we	we	PRON
ejpam-2252	81	11	will	will	AUX
ejpam-2252	81	12	define	define	VERB
ejpam-2252	81	13	velocities	velocity	NOUN
ejpam-2252	81	14	of	of	ADP
ejpam-2252	81	15	a	a	DET
ejpam-2252	81	16	point	point	NOUN
ejpam-2252	81	17	x	x	X
ejpam-2252	81	18	=	=	SYM
ejpam-2252	81	19	(	(	PUNCT
ejpam-2252	81	20	x1	x1	PROPN
ejpam-2252	81	21	,	,	PUNCT
ejpam-2252	81	22	x2	x2	PROPN
ejpam-2252	81	23	)	)	PUNCT
ejpam-2252	81	24	∈	∈	PROPN
ejpam-2252	81	25	pε	pε	NOUN
ejpam-2252	81	26	.	.	PUNCT
ejpam-2252	82	1	the	the	DET
ejpam-2252	82	2	velocity	velocity	NOUN
ejpam-2252	82	3	of	of	ADP
ejpam-2252	82	4	the	the	DET
ejpam-2252	82	5	point	point	NOUN
ejpam-2252	82	6	x	x	PUNCT
ejpam-2252	82	7	with	with	ADP
ejpam-2252	82	8	respect	respect	NOUN
ejpam-2252	82	9	to	to	ADP
ejpam-2252	82	10	pε	pε	PROPN
ejpam-2252	82	11	is	be	AUX
ejpam-2252	82	12	called	call	VERB
ejpam-2252	82	13	the	the	DET
ejpam-2252	82	14	relative	relative	ADJ
ejpam-2252	82	15	velocity	velocity	NOUN
ejpam-2252	82	16	denoted	denote	VERB
ejpam-2252	82	17	by	by	ADP
ejpam-2252	82	18	vr	vr	NOUN
ejpam-2252	82	19	and	and	CCONJ
ejpam-2252	82	20	it	it	PRON
ejpam-2252	82	21	is	be	AUX
ejpam-2252	82	22	defined	define	VERB
ejpam-2252	82	23	by	by	ADP
ejpam-2252	82	24	dx	dx	PROPN
ejpam-2252	82	25	d	d	PROPN
ejpam-2252	82	26	t	t	PROPN
ejpam-2252	82	27	=	=	SYM
ejpam-2252	82	28	ẋ	ẋ	PROPN
ejpam-2252	82	29	:	:	PUNCT
ejpam-2252	82	30	vr	vr	PROPN
ejpam-2252	82	31	=	=	SYM
ejpam-2252	82	32	ẋ1c1	ẋ1c1	PROPN
ejpam-2252	82	33	+	+	PROPN
ejpam-2252	82	34	ẋ2c2	ẋ2c2	PROPN
ejpam-2252	82	35	.	.	PUNCT
ejpam-2252	83	1	(	(	PUNCT
ejpam-2252	83	2	5	5	NUM
ejpam-2252	83	3	)	)	PUNCT
ejpam-2252	83	4	besides	besides	SCONJ
ejpam-2252	83	5	,	,	PUNCT
ejpam-2252	83	6	the	the	DET
ejpam-2252	83	7	absolute	absolute	ADJ
ejpam-2252	83	8	velocity	velocity	NOUN
ejpam-2252	83	9	of	of	ADP
ejpam-2252	83	10	the	the	DET
ejpam-2252	83	11	x	x	PUNCT
ejpam-2252	83	12	with	with	ADP
ejpam-2252	83	13	respect	respect	NOUN
ejpam-2252	83	14	to	to	ADP
ejpam-2252	83	15	pε	pε	PROPN
ejpam-2252	83	16	is	be	AUX
ejpam-2252	83	17	obtained	obtain	VERB
ejpam-2252	83	18	by	by	ADP
ejpam-2252	83	19	differentiating	differentiate	VERB
ejpam-2252	83	20	the	the	DET
ejpam-2252	83	21	equation	equation	NOUN
ejpam-2252	83	22	(	(	PUNCT
ejpam-2252	83	23	2	2	NUM
ejpam-2252	83	24	)	)	PUNCT
ejpam-2252	83	25	with	with	ADP
ejpam-2252	83	26	respect	respect	NOUN
ejpam-2252	83	27	to	to	ADP
ejpam-2252	83	28	t	t	NOUN
ejpam-2252	83	29	and	and	CCONJ
ejpam-2252	83	30	using	use	VERB
ejpam-2252	83	31	derivative	derivative	ADJ
ejpam-2252	83	32	formulae	formulae	NOUN
ejpam-2252	83	33	.	.	PUNCT
ejpam-2252	84	1	it	it	PRON
ejpam-2252	84	2	is	be	AUX
ejpam-2252	84	3	denoted	denote	VERB
ejpam-2252	84	4	by	by	ADP
ejpam-2252	84	5	va	va	PROPN
ejpam-2252	84	6	and	and	CCONJ
ejpam-2252	84	7	obtained	obtain	VERB
ejpam-2252	84	8	as	as	SCONJ
ejpam-2252	84	9	follows	follow	VERB
ejpam-2252	84	10	:	:	PUNCT
ejpam-2252	84	11	va	va	NOUN
ejpam-2252	84	12	=	=	PUNCT
ejpam-2252	84	13	dx′	dx′	PROPN
ejpam-2252	84	14	d	d	X
ejpam-2252	84	15	t	t	NOUN
ejpam-2252	84	16	=	=	SYM
ejpam-2252	84	17	{	{	PUNCT
ejpam-2252	84	18	−u̇1	−u̇1	X
ejpam-2252	85	1	+	+	CCONJ
ejpam-2252	85	2	εϕ̇(u2	εϕ̇(u2	ADV
ejpam-2252	85	3	−	−	PROPN
ejpam-2252	86	1	x2)}c1	x2)}c1	X
ejpam-2252	86	2	+	+	CCONJ
ejpam-2252	86	3	{	{	PUNCT
ejpam-2252	86	4	u̇2	u̇2	VERB
ejpam-2252	86	5	+	+	CCONJ
ejpam-2252	86	6	ϕ̇(−u1	ϕ̇(−u1	NOUN
ejpam-2252	87	1	+	+	CCONJ
ejpam-2252	88	1	x1)}c2	x1)}c2	PROPN
ejpam-2252	88	2	+	+	NOUN
ejpam-2252	88	3	vr	vr	PROPN
ejpam-2252	88	4	.	.	PUNCT
ejpam-2252	89	1	(	(	PUNCT
ejpam-2252	89	2	6	6	NUM
ejpam-2252	89	3	)	)	PUNCT
ejpam-2252	89	4	by	by	ADP
ejpam-2252	89	5	using	use	VERB
ejpam-2252	89	6	equation	equation	NOUN
ejpam-2252	89	7	(	(	PUNCT
ejpam-2252	89	8	6	6	NUM
ejpam-2252	89	9	)	)	PUNCT
ejpam-2252	89	10	,	,	PUNCT
ejpam-2252	89	11	we	we	PRON
ejpam-2252	89	12	get	get	VERB
ejpam-2252	89	13	the	the	DET
ejpam-2252	89	14	sliding	slide	VERB
ejpam-2252	89	15	velocity	velocity	NOUN
ejpam-2252	89	16	vector	vector	NOUN
ejpam-2252	89	17	as	as	ADP
ejpam-2252	89	18	below	below	ADV
ejpam-2252	89	19	:	:	PUNCT
ejpam-2252	89	20	v	v	NOUN
ejpam-2252	89	21	f	f	NOUN
ejpam-2252	89	22	=	=	PRON
ejpam-2252	89	23	{	{	PUNCT
ejpam-2252	89	24	−u̇1	−u̇1	X
ejpam-2252	89	25	+	+	CCONJ
ejpam-2252	89	26	εϕ̇(u2	εϕ̇(u2	ADV
ejpam-2252	89	27	−	−	PROPN
ejpam-2252	90	1	x2)}c1	x2)}c1	X
ejpam-2252	90	2	+	+	CCONJ
ejpam-2252	90	3	{	{	PUNCT
ejpam-2252	90	4	u̇2	u̇2	VERB
ejpam-2252	90	5	+	+	CCONJ
ejpam-2252	90	6	ϕ̇(−u1	ϕ̇(−u1	NOUN
ejpam-2252	91	1	+	+	CCONJ
ejpam-2252	91	2	x1)}c2	x1)}c2	PROPN
ejpam-2252	91	3	.	.	PUNCT
ejpam-2252	92	1	(	(	PUNCT
ejpam-2252	92	2	7	7	NUM
ejpam-2252	92	3	)	)	PUNCT
ejpam-2252	92	4	from	from	ADP
ejpam-2252	92	5	equations	equation	NOUN
ejpam-2252	92	6	(	(	PUNCT
ejpam-2252	92	7	5	5	NUM
ejpam-2252	92	8	)	)	PUNCT
ejpam-2252	92	9	,	,	PUNCT
ejpam-2252	92	10	(	(	PUNCT
ejpam-2252	92	11	6	6	NUM
ejpam-2252	92	12	)	)	PUNCT
ejpam-2252	92	13	,	,	PUNCT
ejpam-2252	92	14	and	and	CCONJ
ejpam-2252	92	15	(	(	PUNCT
ejpam-2252	92	16	7	7	NUM
ejpam-2252	92	17	)	)	PUNCT
ejpam-2252	92	18	,	,	PUNCT
ejpam-2252	92	19	the	the	DET
ejpam-2252	92	20	following	follow	VERB
ejpam-2252	92	21	theorem	theorem	NOUN
ejpam-2252	92	22	can	can	AUX
ejpam-2252	92	23	be	be	AUX
ejpam-2252	92	24	given	give	VERB
ejpam-2252	92	25	.	.	PUNCT
ejpam-2252	93	1	theorem	theorem	NOUN
ejpam-2252	93	2	1	1	NUM
ejpam-2252	93	3	.	.	PUNCT
ejpam-2252	94	1	let	let	VERB
ejpam-2252	94	2	x	x	PRON
ejpam-2252	94	3	be	be	AUX
ejpam-2252	94	4	a	a	DET
ejpam-2252	94	5	moving	move	VERB
ejpam-2252	94	6	point	point	NOUN
ejpam-2252	94	7	on	on	ADP
ejpam-2252	94	8	the	the	DET
ejpam-2252	94	9	plane	plane	NOUN
ejpam-2252	94	10	pε	pε	NOUN
ejpam-2252	94	11	and	and	CCONJ
ejpam-2252	94	12	vr	vr	PROPN
ejpam-2252	94	13	,	,	PUNCT
ejpam-2252	94	14	va	va	PROPN
ejpam-2252	94	15	and	and	CCONJ
ejpam-2252	94	16	v	v	NOUN
ejpam-2252	94	17	f	f	PROPN
ejpam-2252	94	18	be	be	AUX
ejpam-2252	94	19	the	the	DET
ejpam-2252	94	20	relative	relative	ADJ
ejpam-2252	94	21	,	,	PUNCT
ejpam-2252	94	22	absolute	absolute	ADJ
ejpam-2252	94	23	and	and	CCONJ
ejpam-2252	94	24	sliding	slide	VERB
ejpam-2252	94	25	velocities	velocity	NOUN
ejpam-2252	94	26	of	of	ADP
ejpam-2252	94	27	x	x	PUNCT
ejpam-2252	94	28	under	under	ADP
ejpam-2252	94	29	the	the	DET
ejpam-2252	94	30	one	one	NUM
ejpam-2252	94	31	-	-	PUNCT
ejpam-2252	94	32	parameter	parameter	NOUN
ejpam-2252	94	33	planar	planar	ADJ
ejpam-2252	94	34	motions	motion	NOUN
ejpam-2252	94	35	pε	pε	VERB
ejpam-2252	94	36	/	/	SYM
ejpam-2252	94	37	p	p	NOUN
ejpam-2252	94	38	′	′	NUM
ejpam-2252	94	39	ε	ε	PROPN
ejpam-2252	94	40	,	,	PUNCT
ejpam-2252	94	41	respectively	respectively	ADV
ejpam-2252	94	42	.	.	PUNCT
ejpam-2252	95	1	then	then	ADV
ejpam-2252	95	2	,	,	PUNCT
ejpam-2252	95	3	the	the	DET
ejpam-2252	95	4	relation	relation	NOUN
ejpam-2252	95	5	between	between	ADP
ejpam-2252	95	6	the	the	DET
ejpam-2252	95	7	velocities	velocity	NOUN
ejpam-2252	95	8	are	be	AUX
ejpam-2252	95	9	given	give	VERB
ejpam-2252	95	10	as	as	ADP
ejpam-2252	95	11	below	below	ADV
ejpam-2252	95	12	:	:	PUNCT
ejpam-2252	95	13	va	va	PROPN
ejpam-2252	95	14	=	=	PROPN
ejpam-2252	95	15	v	v	PROPN
ejpam-2252	95	16	f	f	PROPN
ejpam-2252	96	1	+	+	NOUN
ejpam-2252	96	2	vr	vr	PROPN
ejpam-2252	96	3	.	.	PUNCT
ejpam-2252	97	1	proof	proof	NOUN
ejpam-2252	97	2	.	.	PUNCT
ejpam-2252	98	1	the	the	DET
ejpam-2252	98	2	proof	proof	NOUN
ejpam-2252	98	3	is	be	AUX
ejpam-2252	98	4	obvious	obvious	ADJ
ejpam-2252	98	5	from	from	ADP
ejpam-2252	98	6	the	the	DET
ejpam-2252	98	7	calculations	calculation	NOUN
ejpam-2252	98	8	of	of	ADP
ejpam-2252	98	9	velocities	velocity	NOUN
ejpam-2252	98	10	given	give	VERB
ejpam-2252	98	11	in	in	ADP
ejpam-2252	98	12	the	the	DET
ejpam-2252	98	13	equations	equation	NOUN
ejpam-2252	98	14	(	(	PUNCT
ejpam-2252	98	15	5	5	NUM
ejpam-2252	98	16	)	)	PUNCT
ejpam-2252	98	17	,	,	PUNCT
ejpam-2252	98	18	(	(	PUNCT
ejpam-2252	98	19	6	6	NUM
ejpam-2252	98	20	)	)	PUNCT
ejpam-2252	98	21	,	,	PUNCT
ejpam-2252	98	22	and	and	CCONJ
ejpam-2252	98	23	(	(	PUNCT
ejpam-2252	98	24	7	7	NUM
ejpam-2252	98	25	)	)	PUNCT
ejpam-2252	98	26	.	.	PUNCT
ejpam-2252	99	1	now	now	ADV
ejpam-2252	99	2	,	,	PUNCT
ejpam-2252	99	3	we	we	PRON
ejpam-2252	99	4	will	will	AUX
ejpam-2252	99	5	investigate	investigate	VERB
ejpam-2252	99	6	the	the	DET
ejpam-2252	99	7	points	point	NOUN
ejpam-2252	99	8	that	that	PRON
ejpam-2252	99	9	does	do	AUX
ejpam-2252	99	10	not	not	PART
ejpam-2252	99	11	move	move	VERB
ejpam-2252	99	12	during	during	ADP
ejpam-2252	99	13	the	the	DET
ejpam-2252	99	14	motions	motion	NOUN
ejpam-2252	99	15	pε	pε	PROPN
ejpam-2252	99	16	/	/	SYM
ejpam-2252	99	17	p	p	NOUN
ejpam-2252	99	18	′	′	NUM
ejpam-2252	99	19	ε	ε	PROPN
ejpam-2252	99	20	and	and	CCONJ
ejpam-2252	99	21	the	the	DET
ejpam-2252	99	22	sliding	slide	VERB
ejpam-2252	99	23	velocity	velocity	NOUN
ejpam-2252	99	24	vector	vector	NOUN
ejpam-2252	99	25	v	v	X
ejpam-2252	99	26	f	f	PROPN
ejpam-2252	99	27	is	be	AUX
ejpam-2252	99	28	equal	equal	ADJ
ejpam-2252	99	29	to	to	ADP
ejpam-2252	99	30	zero	zero	NUM
ejpam-2252	99	31	for	for	ADP
ejpam-2252	99	32	every	every	DET
ejpam-2252	99	33	t	t	NOUN
ejpam-2252	99	34	∈	∈	PROPN
ejpam-2252	99	35	[	[	X
ejpam-2252	99	36	t0	t0	NOUN
ejpam-2252	99	37	,	,	PUNCT
ejpam-2252	99	38	t1	t1	PROPN
ejpam-2252	99	39	]	]	X
ejpam-2252	99	40	.	.	PUNCT
ejpam-2252	100	1	these	these	DET
ejpam-2252	100	2	points	point	NOUN
ejpam-2252	100	3	are	be	AUX
ejpam-2252	100	4	called	call	VERB
ejpam-2252	100	5	the	the	DET
ejpam-2252	100	6	pole	pole	NOUN
ejpam-2252	100	7	points	point	NOUN
ejpam-2252	100	8	or	or	CCONJ
ejpam-2252	100	9	the	the	DET
ejpam-2252	100	10	instantaneous	instantaneous	ADJ
ejpam-2252	100	11	rotation	rotation	NOUN
ejpam-2252	100	12	pole	pole	NOUN
ejpam-2252	100	13	centers	center	NOUN
ejpam-2252	100	14	.	.	PUNCT
ejpam-2252	101	1	if	if	SCONJ
ejpam-2252	101	2	we	we	PRON
ejpam-2252	101	3	use	use	VERB
ejpam-2252	101	4	the	the	DET
ejpam-2252	101	5	equation	equation	NOUN
ejpam-2252	101	6	(	(	PUNCT
ejpam-2252	101	7	8)	8)	NUM
ejpam-2252	101	8	for	for	ADP
ejpam-2252	101	9	a	a	DET
ejpam-2252	101	10	pole	pole	NOUN
ejpam-2252	101	11	point	point	NOUN
ejpam-2252	101	12	p	p	X
ejpam-2252	101	13	=	=	X
ejpam-2252	101	14	(	(	PUNCT
ejpam-2252	101	15	p1	p1	PROPN
ejpam-2252	101	16	,	,	PUNCT
ejpam-2252	101	17	p2	p2	NOUN
ejpam-2252	101	18	)	)	PUNCT
ejpam-2252	101	19	∈	∈	NOUN
ejpam-2252	101	20	pε	pε	NOUN
ejpam-2252	101	21	of	of	ADP
ejpam-2252	101	22	the	the	DET
ejpam-2252	101	23	motions	motion	NOUN
ejpam-2252	101	24	pε	pε	PROPN
ejpam-2252	101	25	/	/	SYM
ejpam-2252	101	26	p	p	NOUN
ejpam-2252	101	27	′	′	NUM
ejpam-2252	101	28	ε	ε	PROPN
ejpam-2252	101	29	,	,	PUNCT
ejpam-2252	101	30	we	we	PRON
ejpam-2252	101	31	have	have	VERB
ejpam-2252	101	32	�	�	PROPN
ejpam-2252	101	33	−u̇2	−u̇2	PROPN
ejpam-2252	101	34	+	+	CCONJ
ejpam-2252	101	35	ϕ̇(−u1	ϕ̇(−u1	X
ejpam-2252	102	1	+	+	CCONJ
ejpam-2252	102	2	x1	x1	X
ejpam-2252	102	3	)	)	PUNCT
ejpam-2252	102	4	=	=	SYM
ejpam-2252	102	5	0	0	NUM
ejpam-2252	102	6	−u̇1	−u̇1	PUNCT
ejpam-2252	103	1	+	+	CCONJ
ejpam-2252	103	2	εϕ̇(u2	εϕ̇(u2	X
ejpam-2252	103	3	−	−	PROPN
ejpam-2252	103	4	x2	x2	PROPN
ejpam-2252	103	5	)	)	PUNCT
ejpam-2252	103	6	=	=	SYM
ejpam-2252	103	7	0	0	PUNCT
ejpam-2252	103	8	(	(	PUNCT
ejpam-2252	103	9	8)	8)	NUM
ejpam-2252	103	10	n.	n.	NOUN
ejpam-2252	103	11	gürses	gürse	NOUN
ejpam-2252	103	12	,	,	PUNCT
ejpam-2252	103	13	s.	s.	PROPN
ejpam-2252	103	14	yüce	yüce	PROPN
ejpam-2252	103	15	/	/	SYM
ejpam-2252	103	16	eur	eur	PROPN
ejpam-2252	103	17	.	.	PUNCT
ejpam-2252	104	1	j.	j.	PROPN
ejpam-2252	104	2	pure	pure	PROPN
ejpam-2252	104	3	appl	appl	PROPN
ejpam-2252	104	4	.	.	PROPN
ejpam-2252	104	5	math	math	PROPN
ejpam-2252	104	6	,	,	PUNCT
ejpam-2252	104	7	7	7	NUM
ejpam-2252	104	8	(	(	PUNCT
ejpam-2252	104	9	2014	2014	NUM
ejpam-2252	104	10	)	)	PUNCT
ejpam-2252	104	11	,	,	PUNCT
ejpam-2252	104	12	335	335	NUM
ejpam-2252	104	13	-	-	SYM
ejpam-2252	104	14	342	342	NUM
ejpam-2252	104	15	340	340	NUM
ejpam-2252	104	16	so	so	ADV
ejpam-2252	104	17	,	,	PUNCT
ejpam-2252	104	18	we	we	PRON
ejpam-2252	104	19	obtain	obtain	VERB
ejpam-2252	104	20	the	the	DET
ejpam-2252	104	21	pole	pole	NOUN
ejpam-2252	104	22	point	point	NOUN
ejpam-2252	104	23	from	from	ADP
ejpam-2252	104	24	the	the	DET
ejpam-2252	104	25	solution	solution	NOUN
ejpam-2252	104	26	of	of	ADP
ejpam-2252	104	27	the	the	DET
ejpam-2252	104	28	system	system	NOUN
ejpam-2252	104	29	(	(	PUNCT
ejpam-2252	104	30	8)	8)	NUM
ejpam-2252	104	31	as	as	SCONJ
ejpam-2252	104	32	follows	follow	VERB
ejpam-2252	104	33	:	:	PUNCT
ejpam-2252	104	34	(	(	PUNCT
ejpam-2252	104	35	p1(t	p1(t	PROPN
ejpam-2252	104	36	)	)	PUNCT
ejpam-2252	104	37	=	=	SYM
ejpam-2252	104	38	x1(t	x1(t	PROPN
ejpam-2252	104	39	)	)	PUNCT
ejpam-2252	104	40	=	=	SYM
ejpam-2252	105	1	u1(t	u1(t	PROPN
ejpam-2252	105	2	)	)	PUNCT
ejpam-2252	105	3	+	+	CCONJ
ejpam-2252	105	4	u̇2(t	u̇2(t	NOUN
ejpam-2252	105	5	)	)	PUNCT
ejpam-2252	105	6	ϕ̇(t	ϕ̇(t	NOUN
ejpam-2252	105	7	)	)	PUNCT
ejpam-2252	105	8	εp2(t	εp2(t	NOUN
ejpam-2252	105	9	)	)	PUNCT
ejpam-2252	105	10	=	=	SYM
ejpam-2252	105	11	εx2(t	εx2(t	PROPN
ejpam-2252	105	12	)	)	PUNCT
ejpam-2252	105	13	=	=	PUNCT
ejpam-2252	105	14	εu2(t)−	εu2(t)−	PROPN
ejpam-2252	105	15	u̇1(t	u̇1(t	PROPN
ejpam-2252	105	16	)	)	PUNCT
ejpam-2252	105	17	ϕ̇(t	ϕ̇(t	PROPN
ejpam-2252	105	18	)	)	PUNCT
ejpam-2252	105	19	(	(	PUNCT
ejpam-2252	105	20	9	9	NUM
ejpam-2252	105	21	)	)	PUNCT
ejpam-2252	105	22	therefore	therefore	ADV
ejpam-2252	105	23	,	,	PUNCT
ejpam-2252	105	24	the	the	DET
ejpam-2252	105	25	point	point	NOUN
ejpam-2252	105	26	p	p	NOUN
ejpam-2252	105	27	is	be	AUX
ejpam-2252	105	28	instant	instant	ADJ
ejpam-2252	105	29	in	in	ADP
ejpam-2252	105	30	the	the	DET
ejpam-2252	105	31	plane	plane	NOUN
ejpam-2252	105	32	pε	pε	NOUN
ejpam-2252	105	33	.	.	PUNCT
ejpam-2252	106	1	let	let	VERB
ejpam-2252	106	2	us	we	PRON
ejpam-2252	106	3	rearrange	rearrange	VERB
ejpam-2252	106	4	the	the	DET
ejpam-2252	106	5	sliding	slide	VERB
ejpam-2252	106	6	velocity	velocity	NOUN
ejpam-2252	106	7	vector	vector	NOUN
ejpam-2252	106	8	(	(	PUNCT
ejpam-2252	106	9	7	7	NUM
ejpam-2252	106	10	)	)	PUNCT
ejpam-2252	106	11	by	by	ADP
ejpam-2252	106	12	using	use	VERB
ejpam-2252	106	13	the	the	DET
ejpam-2252	106	14	equation	equation	NOUN
ejpam-2252	106	15	(	(	PUNCT
ejpam-2252	106	16	9	9	NUM
ejpam-2252	106	17	):	):	PUNCT
ejpam-2252	106	18	v	v	NOUN
ejpam-2252	106	19	f	f	NOUN
ejpam-2252	106	20	=	=	SYM
ejpam-2252	106	21	{	{	PUNCT
ejpam-2252	106	22	−ε(x2	−ε(x2	PROPN
ejpam-2252	106	23	−	−	NOUN
ejpam-2252	107	1	p2)c1	p2)c1	NOUN
ejpam-2252	108	1	+	+	CCONJ
ejpam-2252	109	1	(	(	PUNCT
ejpam-2252	109	2	x1	x1	NUM
ejpam-2252	109	3	−	−	PROPN
ejpam-2252	109	4	p1)c2}ϕ̇.	p1)c2}ϕ̇.	PRON
ejpam-2252	109	5	(	(	PUNCT
ejpam-2252	109	6	10	10	NUM
ejpam-2252	109	7	)	)	PUNCT
ejpam-2252	109	8	with	with	ADP
ejpam-2252	109	9	reference	reference	NOUN
ejpam-2252	109	10	the	the	DET
ejpam-2252	109	11	above	above	ADJ
ejpam-2252	109	12	equation	equation	NOUN
ejpam-2252	109	13	,	,	PUNCT
ejpam-2252	109	14	we	we	PRON
ejpam-2252	109	15	can	can	AUX
ejpam-2252	109	16	give	give	VERB
ejpam-2252	109	17	the	the	DET
ejpam-2252	109	18	following	follow	VERB
ejpam-2252	109	19	corollaries	corollary	NOUN
ejpam-2252	109	20	:	:	PUNCT
ejpam-2252	109	21	corollary	corollary	ADJ
ejpam-2252	109	22	1	1	NUM
ejpam-2252	109	23	.	.	PUNCT
ejpam-2252	110	1	during	during	ADP
ejpam-2252	110	2	the	the	DET
ejpam-2252	110	3	one	one	NUM
ejpam-2252	110	4	-	-	PUNCT
ejpam-2252	110	5	parameter	parameter	NOUN
ejpam-2252	110	6	planar	planar	ADJ
ejpam-2252	110	7	motions	motion	NOUN
ejpam-2252	110	8	pε	pε	VERB
ejpam-2252	110	9	/	/	SYM
ejpam-2252	110	10	p	p	NOUN
ejpam-2252	110	11	′	′	NUM
ejpam-2252	110	12	ε	ε	PROPN
ejpam-2252	110	13	in	in	ADP
ejpam-2252	110	14	affine	affine	NOUN
ejpam-2252	110	15	ck	ck	NOUN
ejpam-2252	110	16	-	-	PUNCT
ejpam-2252	110	17	planes	plane	NOUN
ejpam-2252	110	18	,	,	PUNCT
ejpam-2252	110	19	the	the	DET
ejpam-2252	110	20	pole	pole	NOUN
ejpam-2252	110	21	ray	ray	NOUN
ejpam-2252	110	22	px	px	PROPN
ejpam-2252	110	23	and	and	CCONJ
ejpam-2252	110	24	the	the	DET
ejpam-2252	110	25	sliding	slide	VERB
ejpam-2252	110	26	velocity	velocity	NOUN
ejpam-2252	110	27	v	v	ADP
ejpam-2252	110	28	f	f	NOUN
ejpam-2252	110	29	are	be	AUX
ejpam-2252	110	30	perpendicular	perpendicular	ADJ
ejpam-2252	110	31	vectors	vector	NOUN
ejpam-2252	110	32	in	in	ADP
ejpam-2252	110	33	the	the	DET
ejpam-2252	110	34	sense	sense	NOUN
ejpam-2252	110	35	of	of	ADP
ejpam-2252	110	36	affine	affine	NOUN
ejpam-2252	110	37	ck	ck	NOUN
ejpam-2252	110	38	-	-	PUNCT
ejpam-2252	110	39	geometry	geometry	NOUN
ejpam-2252	110	40	,	,	PUNCT
ejpam-2252	110	41	i.e.	i.e.	X
ejpam-2252	110	42	,	,	PUNCT
ejpam-2252	110	43	〈	〈	PROPN
ejpam-2252	110	44	px	px	PROPN
ejpam-2252	110	45	,	,	PUNCT
ejpam-2252	110	46	v	v	NOUN
ejpam-2252	110	47	f	f	PROPN
ejpam-2252	110	48	〉	〉	NOUN
ejpam-2252	110	49	ε	ε	NOUN
ejpam-2252	110	50	=	=	SYM
ejpam-2252	110	51	0	0	PROPN
ejpam-2252	110	52	.	.	PUNCT
ejpam-2252	111	1	then	then	ADV
ejpam-2252	111	2	,	,	PUNCT
ejpam-2252	111	3	the	the	DET
ejpam-2252	111	4	focus	focus	NOUN
ejpam-2252	111	5	of	of	ADP
ejpam-2252	111	6	the	the	DET
ejpam-2252	111	7	point	point	NOUN
ejpam-2252	111	8	x	x	PUNCT
ejpam-2252	111	9	of	of	ADP
ejpam-2252	111	10	the	the	DET
ejpam-2252	111	11	motions	motion	NOUN
ejpam-2252	111	12	pε	pε	PROPN
ejpam-2252	111	13	/	/	SYM
ejpam-2252	111	14	p	p	NOUN
ejpam-2252	111	15	′	′	NUM
ejpam-2252	111	16	ε	ε	PROPN
ejpam-2252	111	17	is	be	AUX
ejpam-2252	111	18	an	an	DET
ejpam-2252	111	19	orbit	orbit	NOUN
ejpam-2252	111	20	that	that	PRON
ejpam-2252	111	21	its	its	PRON
ejpam-2252	111	22	normal	normal	ADJ
ejpam-2252	111	23	pass	pass	NOUN
ejpam-2252	111	24	through	through	ADP
ejpam-2252	111	25	the	the	DET
ejpam-2252	111	26	rotation	rotation	NOUN
ejpam-2252	111	27	pole	pole	NOUN
ejpam-2252	111	28	p.	p.	NOUN
ejpam-2252	111	29	corollary	corollary	NOUN
ejpam-2252	111	30	2	2	NUM
ejpam-2252	111	31	.	.	PUNCT
ejpam-2252	112	1	under	under	ADP
ejpam-2252	112	2	the	the	DET
ejpam-2252	112	3	motions	motion	NOUN
ejpam-2252	112	4	pε	pε	PROPN
ejpam-2252	112	5	/	/	SYM
ejpam-2252	112	6	p	p	NOUN
ejpam-2252	112	7	′	′	NUM
ejpam-2252	112	8	ε	ε	PROPN
ejpam-2252	112	9	,	,	PUNCT
ejpam-2252	112	10	the	the	DET
ejpam-2252	112	11	affine	affine	NOUN
ejpam-2252	112	12	ck	ck	NOUN
ejpam-2252	112	13	-	-	PUNCT
ejpam-2252	112	14	norm	norm	NOUN
ejpam-2252	112	15	of	of	ADP
ejpam-2252	112	16	the	the	DET
ejpam-2252	112	17	sliding	slide	VERB
ejpam-2252	112	18	velocity	velocity	NOUN
ejpam-2252	112	19	v	v	ADP
ejpam-2252	112	20	f	f	PROPN
ejpam-2252	112	21	is	be	AUX
ejpam-2252	112	22	written	write	VERB
ejpam-2252	112	23	below	below	ADP
ejpam-2252	112	24	:	:	PUNCT
ejpam-2252	112	25	v	v	X
ejpam-2252	112	26	f	f	X
ejpam-2252	112	27	ε	ε	PROPN
ejpam-2252	112	28	=	=	SYM
ejpam-2252	112	29	‖px‖ε	‖px‖ε	PROPN
ejpam-2252	112	30	�	�	PROPN
ejpam-2252	112	31	�	�	PROPN
ejpam-2252	112	32	ϕ̇	ϕ̇	PROPN
ejpam-2252	112	33	�	�	PROPN
ejpam-2252	112	34	�	�	PROPN
ejpam-2252	112	35	.	.	PUNCT
ejpam-2252	113	1	3.2	3.2	NUM
ejpam-2252	113	2	.	.	PUNCT
ejpam-2252	114	1	accelerations	acceleration	NOUN
ejpam-2252	114	2	and	and	CCONJ
ejpam-2252	114	3	acceleration	acceleration	NOUN
ejpam-2252	114	4	pole	pole	NOUN
ejpam-2252	114	5	point	point	NOUN
ejpam-2252	114	6	notation	notation	NOUN
ejpam-2252	114	7	in	in	ADP
ejpam-2252	114	8	this	this	DET
ejpam-2252	114	9	section	section	NOUN
ejpam-2252	114	10	,	,	PUNCT
ejpam-2252	114	11	we	we	PRON
ejpam-2252	114	12	will	will	AUX
ejpam-2252	114	13	define	define	VERB
ejpam-2252	114	14	relative	relative	ADJ
ejpam-2252	114	15	,	,	PUNCT
ejpam-2252	114	16	absolute	absolute	ADJ
ejpam-2252	114	17	,	,	PUNCT
ejpam-2252	114	18	sliding	sliding	ADJ
ejpam-2252	114	19	and	and	CCONJ
ejpam-2252	114	20	coriolis	coriolis	PROPN
ejpam-2252	114	21	acceleration	acceleration	NOUN
ejpam-2252	114	22	vectors	vector	NOUN
ejpam-2252	114	23	denoted	denote	VERB
ejpam-2252	114	24	by	by	ADP
ejpam-2252	114	25	br	br	PROPN
ejpam-2252	114	26	,	,	PUNCT
ejpam-2252	114	27	ba	ba	PROPN
ejpam-2252	114	28	,	,	PUNCT
ejpam-2252	114	29	bf	bf	NOUN
ejpam-2252	114	30	and	and	CCONJ
ejpam-2252	114	31	bc	bc	PROPN
ejpam-2252	114	32	,	,	PUNCT
ejpam-2252	114	33	respectively	respectively	ADV
ejpam-2252	114	34	,	,	PUNCT
ejpam-2252	114	35	during	during	ADP
ejpam-2252	114	36	the	the	DET
ejpam-2252	114	37	one	one	NUM
ejpam-2252	114	38	-	-	PUNCT
ejpam-2252	114	39	parameter	parameter	NOUN
ejpam-2252	114	40	planar	planar	ADJ
ejpam-2252	114	41	motions	motion	NOUN
ejpam-2252	114	42	pε	pε	VERB
ejpam-2252	114	43	/	/	SYM
ejpam-2252	114	44	p	p	NOUN
ejpam-2252	114	45	′	′	NUM
ejpam-2252	114	46	ε	ε	PROPN
ejpam-2252	114	47	in	in	ADP
ejpam-2252	114	48	affine	affine	NOUN
ejpam-2252	114	49	ck	ck	NOUN
ejpam-2252	114	50	-	-	PUNCT
ejpam-2252	114	51	planes	plane	NOUN
ejpam-2252	114	52	.	.	PUNCT
ejpam-2252	115	1	let	let	VERB
ejpam-2252	115	2	x	x	PRON
ejpam-2252	115	3	be	be	AUX
ejpam-2252	115	4	a	a	DET
ejpam-2252	115	5	moving	move	VERB
ejpam-2252	115	6	point	point	NOUN
ejpam-2252	115	7	in	in	ADP
ejpam-2252	115	8	pε	pε	NOUN
ejpam-2252	115	9	.	.	PUNCT
ejpam-2252	116	1	by	by	ADP
ejpam-2252	116	2	differentiating	differentiate	VERB
ejpam-2252	116	3	the	the	DET
ejpam-2252	116	4	relative	relative	ADJ
ejpam-2252	116	5	velocity	velocity	NOUN
ejpam-2252	116	6	vector	vector	NOUN
ejpam-2252	116	7	according	accord	VERB
ejpam-2252	116	8	to	to	ADP
ejpam-2252	116	9	t	t	PROPN
ejpam-2252	116	10	,	,	PUNCT
ejpam-2252	116	11	we	we	PRON
ejpam-2252	116	12	obtain	obtain	VERB
ejpam-2252	116	13	the	the	DET
ejpam-2252	116	14	relative	relative	ADJ
ejpam-2252	116	15	acceleration	acceleration	NOUN
ejpam-2252	116	16	br	br	NOUN
ejpam-2252	116	17	as	as	ADP
ejpam-2252	116	18	below	below	ADV
ejpam-2252	116	19	:	:	PUNCT
ejpam-2252	116	20	br	br	NOUN
ejpam-2252	116	21	=	=	SYM
ejpam-2252	116	22	v̇r	v̇r	PROPN
ejpam-2252	116	23	=	=	PUNCT
ejpam-2252	116	24	ẍ=	ẍ=	PROPN
ejpam-2252	116	25	ẍ1c1	ẍ1c1	PROPN
ejpam-2252	117	1	+	+	PUNCT
ejpam-2252	117	2	ẍ2c2	ẍ2c2	PROPN
ejpam-2252	117	3	.	.	PUNCT
ejpam-2252	118	1	(	(	PUNCT
ejpam-2252	118	2	11	11	NUM
ejpam-2252	118	3	)	)	PUNCT
ejpam-2252	118	4	the	the	DET
ejpam-2252	118	5	acceleration	acceleration	NOUN
ejpam-2252	118	6	of	of	ADP
ejpam-2252	118	7	the	the	DET
ejpam-2252	118	8	point	point	NOUN
ejpam-2252	118	9	x	x	PUNCT
ejpam-2252	118	10	with	with	ADP
ejpam-2252	118	11	respect	respect	NOUN
ejpam-2252	118	12	to	to	ADP
ejpam-2252	118	13	p′ε	p′ε	PROPN
ejpam-2252	118	14	is	be	AUX
ejpam-2252	118	15	known	know	VERB
ejpam-2252	118	16	as	as	ADP
ejpam-2252	118	17	the	the	DET
ejpam-2252	118	18	absolute	absolute	ADJ
ejpam-2252	118	19	acceleration	acceleration	NOUN
ejpam-2252	118	20	and	and	CCONJ
ejpam-2252	118	21	it	it	PRON
ejpam-2252	118	22	is	be	AUX
ejpam-2252	118	23	defined	define	VERB
ejpam-2252	118	24	by	by	ADP
ejpam-2252	118	25	ba	ba	PROPN
ejpam-2252	118	26	=	=	PUNCT
ejpam-2252	118	27	dva	dva	PROPN
ejpam-2252	119	1	d	d	NOUN
ejpam-2252	119	2	t	t	NOUN
ejpam-2252	119	3	=	=	SYM
ejpam-2252	119	4	v̇a	v̇a	PROPN
ejpam-2252	119	5	.	.	PUNCT
ejpam-2252	120	1	if	if	SCONJ
ejpam-2252	120	2	we	we	PRON
ejpam-2252	120	3	differentiate	differentiate	VERB
ejpam-2252	120	4	the	the	DET
ejpam-2252	120	5	equation	equation	NOUN
ejpam-2252	120	6	(	(	PUNCT
ejpam-2252	120	7	6	6	NUM
ejpam-2252	120	8	)	)	PUNCT
ejpam-2252	120	9	with	with	ADP
ejpam-2252	120	10	respect	respect	NOUN
ejpam-2252	120	11	to	to	ADP
ejpam-2252	120	12	t	t	NOUN
ejpam-2252	120	13	and	and	CCONJ
ejpam-2252	120	14	use	use	VERB
ejpam-2252	120	15	the	the	DET
ejpam-2252	120	16	equations	equation	NOUN
ejpam-2252	120	17	(	(	PUNCT
ejpam-2252	120	18	4	4	NUM
ejpam-2252	120	19	)	)	PUNCT
ejpam-2252	120	20	,	,	PUNCT
ejpam-2252	120	21	we	we	PRON
ejpam-2252	120	22	obtain	obtain	VERB
ejpam-2252	120	23	the	the	DET
ejpam-2252	120	24	absolute	absolute	ADJ
ejpam-2252	120	25	acceleration	acceleration	NOUN
ejpam-2252	120	26	as	as	ADP
ejpam-2252	120	27	below	below	ADV
ejpam-2252	120	28	:	:	PUNCT
ejpam-2252	120	29	ba	ba	PROPN
ejpam-2252	120	30	=	=	PROPN
ejpam-2252	120	31	ε	ε	PROPN
ejpam-2252	120	32	�	�	PROPN
ejpam-2252	120	33	ϕ̇	ϕ̇	NOUN
ejpam-2252	120	34	ṗ2	ṗ2	PROPN
ejpam-2252	120	35	−	−	NOUN
ejpam-2252	120	36	(	(	PUNCT
ejpam-2252	120	37	ϕ̇	ϕ̇	NOUN
ejpam-2252	120	38	)	)	PUNCT
ejpam-2252	120	39	2(x1	2(x1	NUM
ejpam-2252	120	40	−	−	NOUN
ejpam-2252	120	41	p1)−	p1)−	PROPN
ejpam-2252	120	42	ϕ̈(x2	ϕ̈(x2	PROPN
ejpam-2252	120	43	−	−	PROPN
ejpam-2252	120	44	p2	p2	PROPN
ejpam-2252	120	45	)	)	PUNCT
ejpam-2252	120	46	c1	c1	NOUN
ejpam-2252	120	47	+	+	CCONJ
ejpam-2252	120	48	�	�	PROPN
ejpam-2252	120	49	−ϕ̇	−ϕ̇	PROPN
ejpam-2252	120	50	ṗ1	ṗ1	PROPN
ejpam-2252	120	51	−	−	ADP
ejpam-2252	120	52	ε(ϕ̇	ε(ϕ̇	PROPN
ejpam-2252	120	53	)	)	PUNCT
ejpam-2252	120	54	2(x2	2(x2	NOUN
ejpam-2252	120	55	−	−	NOUN
ejpam-2252	120	56	p2	p2	NOUN
ejpam-2252	120	57	)	)	PUNCT
ejpam-2252	121	1	+	+	CCONJ
ejpam-2252	121	2	ϕ̈(x1	ϕ̈(x1	ADJ
ejpam-2252	121	3	−	−	PROPN
ejpam-2252	121	4	p1	p1	PROPN
ejpam-2252	121	5	)	)	PUNCT
ejpam-2252	121	6	c2	c2	PROPN
ejpam-2252	121	7	+	+	CCONJ
ejpam-2252	121	8	ẍ1c1	ẍ1c1	X
ejpam-2252	122	1	+	+	PUNCT
ejpam-2252	122	2	ẍ2c2	ẍ2c2	PROPN
ejpam-2252	123	1	+	+	CCONJ
ejpam-2252	123	2	2ϕ̇(−ε	2ϕ̇(−ε	NUM
ejpam-2252	123	3	ẋ2c1	ẋ2c1	PROPN
ejpam-2252	123	4	+	+	CCONJ
ejpam-2252	123	5	ẋ1c2	ẋ1c2	NUM
ejpam-2252	123	6	)	)	PUNCT
ejpam-2252	123	7	.	.	PUNCT
ejpam-2252	124	1	(	(	PUNCT
ejpam-2252	124	2	12	12	NUM
ejpam-2252	124	3	)	)	PUNCT
ejpam-2252	124	4	in	in	ADP
ejpam-2252	124	5	the	the	DET
ejpam-2252	124	6	equation	equation	NOUN
ejpam-2252	124	7	(	(	PUNCT
ejpam-2252	124	8	12	12	NUM
ejpam-2252	124	9	)	)	PUNCT
ejpam-2252	124	10	,	,	PUNCT
ejpam-2252	124	11	the	the	DET
ejpam-2252	124	12	expression	expression	NOUN
ejpam-2252	124	13	b	b	NOUN
ejpam-2252	124	14	f	f	PROPN
ejpam-2252	124	15	=	=	SYM
ejpam-2252	124	16	ε	ε	PROPN
ejpam-2252	124	17	�	�	PROPN
ejpam-2252	125	1	ϕ̇	ϕ̇	NOUN
ejpam-2252	125	2	ṗ2	ṗ2	PROPN
ejpam-2252	125	3	−	−	NOUN
ejpam-2252	125	4	(	(	PUNCT
ejpam-2252	125	5	ϕ̇	ϕ̇	NOUN
ejpam-2252	125	6	)	)	PUNCT
ejpam-2252	125	7	2(x1	2(x1	NUM
ejpam-2252	125	8	−	−	NOUN
ejpam-2252	125	9	p1)−	p1)−	PROPN
ejpam-2252	125	10	ϕ̈(x2	ϕ̈(x2	PROPN
ejpam-2252	125	11	−	−	PROPN
ejpam-2252	125	12	p2	p2	PROPN
ejpam-2252	125	13	)	)	PUNCT
ejpam-2252	125	14	c1	c1	NOUN
ejpam-2252	125	15	+	+	CCONJ
ejpam-2252	125	16	�	�	PROPN
ejpam-2252	125	17	−ϕ̇	−ϕ̇	PROPN
ejpam-2252	125	18	ṗ1	ṗ1	PROPN
ejpam-2252	125	19	−	−	ADP
ejpam-2252	125	20	ε(ϕ̇	ε(ϕ̇	PROPN
ejpam-2252	125	21	)	)	PUNCT
ejpam-2252	125	22	2(x2	2(x2	NOUN
ejpam-2252	125	23	−	−	NOUN
ejpam-2252	125	24	p2	p2	NOUN
ejpam-2252	125	25	)	)	PUNCT
ejpam-2252	126	1	+	+	CCONJ
ejpam-2252	126	2	ϕ̈(x1	ϕ̈(x1	ADJ
ejpam-2252	126	3	−	−	PROPN
ejpam-2252	126	4	p1	p1	PROPN
ejpam-2252	126	5	)	)	PUNCT
ejpam-2252	126	6	c2	c2	PROPN
ejpam-2252	126	7	(	(	PUNCT
ejpam-2252	126	8	13	13	NUM
ejpam-2252	126	9	)	)	PUNCT
ejpam-2252	126	10	is	be	AUX
ejpam-2252	126	11	called	call	VERB
ejpam-2252	126	12	the	the	DET
ejpam-2252	126	13	sliding	slide	VERB
ejpam-2252	126	14	acceleration	acceleration	NOUN
ejpam-2252	126	15	and	and	CCONJ
ejpam-2252	126	16	bc	bc	PROPN
ejpam-2252	126	17	=	=	SYM
ejpam-2252	126	18	2ϕ̇(−ε	2ϕ̇(−ε	NUM
ejpam-2252	127	1	ẋ2c1	ẋ2c1	PROPN
ejpam-2252	127	2	+	+	CCONJ
ejpam-2252	127	3	ẋ1c2	ẋ1c2	NUM
ejpam-2252	127	4	)	)	PUNCT
ejpam-2252	127	5	.	.	PUNCT
ejpam-2252	128	1	(	(	PUNCT
ejpam-2252	128	2	14	14	NUM
ejpam-2252	128	3	)	)	PUNCT
ejpam-2252	128	4	is	be	AUX
ejpam-2252	128	5	called	call	VERB
ejpam-2252	128	6	the	the	DET
ejpam-2252	128	7	coriolis	corioli	NOUN
ejpam-2252	128	8	acceleration	acceleration	NOUN
ejpam-2252	128	9	of	of	ADP
ejpam-2252	128	10	the	the	DET
ejpam-2252	128	11	one	one	NUM
ejpam-2252	128	12	-	-	PUNCT
ejpam-2252	128	13	parameter	parameter	NOUN
ejpam-2252	128	14	planar	planar	ADJ
ejpam-2252	128	15	motion	motion	NOUN
ejpam-2252	128	16	pε	pε	PROPN
ejpam-2252	128	17	/	/	SYM
ejpam-2252	128	18	p	p	NOUN
ejpam-2252	128	19	′	′	NUM
ejpam-2252	128	20	ε	ε	PROPN
ejpam-2252	128	21	.	.	PUNCT
ejpam-2252	129	1	consequently	consequently	ADV
ejpam-2252	129	2	,	,	PUNCT
ejpam-2252	129	3	we	we	PRON
ejpam-2252	129	4	can	can	AUX
ejpam-2252	129	5	give	give	VERB
ejpam-2252	129	6	the	the	DET
ejpam-2252	129	7	following	follow	VERB
ejpam-2252	129	8	theorem	theorem	NOUN
ejpam-2252	129	9	and	and	CCONJ
ejpam-2252	129	10	corollary	corollary	ADJ
ejpam-2252	129	11	with	with	ADP
ejpam-2252	129	12	using	use	VERB
ejpam-2252	129	13	the	the	DET
ejpam-2252	129	14	equations	equation	NOUN
ejpam-2252	129	15	(	(	PUNCT
ejpam-2252	129	16	11	11	NUM
ejpam-2252	129	17	)	)	PUNCT
ejpam-2252	129	18	,	,	PUNCT
ejpam-2252	129	19	(	(	PUNCT
ejpam-2252	129	20	12	12	NUM
ejpam-2252	129	21	)	)	PUNCT
ejpam-2252	129	22	,	,	PUNCT
ejpam-2252	129	23	(	(	PUNCT
ejpam-2252	129	24	13	13	NUM
ejpam-2252	129	25	)	)	PUNCT
ejpam-2252	129	26	,	,	PUNCT
ejpam-2252	129	27	and	and	CCONJ
ejpam-2252	129	28	(	(	PUNCT
ejpam-2252	129	29	14	14	NUM
ejpam-2252	129	30	)	)	PUNCT
ejpam-2252	129	31	.	.	PUNCT
ejpam-2252	130	1	references	reference	NOUN
ejpam-2252	130	2	341	341	NUM
ejpam-2252	130	3	theorem	theorem	NOUN
ejpam-2252	130	4	2	2	NUM
ejpam-2252	130	5	.	.	PUNCT
ejpam-2252	131	1	let	let	VERB
ejpam-2252	131	2	x	x	PRON
ejpam-2252	131	3	be	be	AUX
ejpam-2252	131	4	a	a	DET
ejpam-2252	131	5	moving	move	VERB
ejpam-2252	131	6	point	point	NOUN
ejpam-2252	131	7	on	on	ADP
ejpam-2252	131	8	the	the	DET
ejpam-2252	131	9	plane	plane	NOUN
ejpam-2252	131	10	pε	pε	NOUN
ejpam-2252	131	11	and	and	CCONJ
ejpam-2252	131	12	br	br	PROPN
ejpam-2252	131	13	,	,	PUNCT
ejpam-2252	131	14	ba	ba	PROPN
ejpam-2252	131	15	,	,	PUNCT
ejpam-2252	131	16	b	b	PROPN
ejpam-2252	131	17	f	f	PROPN
ejpam-2252	131	18	and	and	CCONJ
ejpam-2252	131	19	bc	bc	PROPN
ejpam-2252	131	20	be	be	AUX
ejpam-2252	131	21	the	the	DET
ejpam-2252	131	22	relative	relative	ADJ
ejpam-2252	131	23	,	,	PUNCT
ejpam-2252	131	24	absolute	absolute	ADJ
ejpam-2252	131	25	,	,	PUNCT
ejpam-2252	131	26	sliding	sliding	ADJ
ejpam-2252	131	27	and	and	CCONJ
ejpam-2252	131	28	coriolis	corioli	VERB
ejpam-2252	131	29	accelerations	acceleration	NOUN
ejpam-2252	131	30	of	of	ADP
ejpam-2252	131	31	x	x	PRON
ejpam-2252	131	32	,	,	PUNCT
ejpam-2252	131	33	respectively	respectively	ADV
ejpam-2252	131	34	.	.	PUNCT
ejpam-2252	132	1	then	then	ADV
ejpam-2252	132	2	,	,	PUNCT
ejpam-2252	132	3	the	the	DET
ejpam-2252	132	4	relation	relation	NOUN
ejpam-2252	132	5	between	between	ADP
ejpam-2252	132	6	the	the	DET
ejpam-2252	132	7	accelerations	acceleration	NOUN
ejpam-2252	132	8	under	under	ADP
ejpam-2252	132	9	the	the	DET
ejpam-2252	132	10	one	one	NUM
ejpam-2252	132	11	-	-	PUNCT
ejpam-2252	132	12	parameter	parameter	NOUN
ejpam-2252	132	13	planar	planar	ADJ
ejpam-2252	132	14	motions	motion	NOUN
ejpam-2252	132	15	pε	pε	VERB
ejpam-2252	132	16	/	/	SYM
ejpam-2252	132	17	p	p	NOUN
ejpam-2252	132	18	′	′	NUM
ejpam-2252	132	19	ε	ε	PROPN
ejpam-2252	132	20	are	be	AUX
ejpam-2252	132	21	given	give	VERB
ejpam-2252	132	22	as	as	ADP
ejpam-2252	132	23	below	below	ADV
ejpam-2252	132	24	:	:	PUNCT
ejpam-2252	132	25	ba	ba	PROPN
ejpam-2252	133	1	=	=	SYM
ejpam-2252	133	2	b	b	PROPN
ejpam-2252	133	3	f	f	PROPN
ejpam-2252	133	4	+	+	CCONJ
ejpam-2252	133	5	bc	bc	PROPN
ejpam-2252	133	6	+	+	CCONJ
ejpam-2252	133	7	br	br	NOUN
ejpam-2252	133	8	.	.	PUNCT
ejpam-2252	134	1	corollary	corollary	ADJ
ejpam-2252	134	2	3	3	NUM
ejpam-2252	134	3	.	.	PUNCT
ejpam-2252	135	1	during	during	ADP
ejpam-2252	135	2	the	the	DET
ejpam-2252	135	3	motions	motion	NOUN
ejpam-2252	135	4	pε	pε	PROPN
ejpam-2252	135	5	/	/	SYM
ejpam-2252	135	6	p	p	NOUN
ejpam-2252	135	7	′	′	NUM
ejpam-2252	135	8	ε	ε	PROPN
ejpam-2252	135	9	,	,	PUNCT
ejpam-2252	135	10	the	the	DET
ejpam-2252	135	11	coriolis	coriolis	PROPN
ejpam-2252	135	12	acceleration	acceleration	PROPN
ejpam-2252	135	13	vector	vector	PROPN
ejpam-2252	135	14	bc	bc	PROPN
ejpam-2252	135	15	and	and	CCONJ
ejpam-2252	135	16	the	the	DET
ejpam-2252	135	17	relative	relative	ADJ
ejpam-2252	135	18	velocity	velocity	NOUN
ejpam-2252	135	19	vector	vector	NOUN
ejpam-2252	135	20	vr	vr	PROPN
ejpam-2252	135	21	are	be	AUX
ejpam-2252	135	22	perpendicular	perpendicular	ADJ
ejpam-2252	135	23	to	to	ADP
ejpam-2252	135	24	each	each	DET
ejpam-2252	135	25	other	other	ADJ
ejpam-2252	135	26	in	in	ADP
ejpam-2252	135	27	the	the	DET
ejpam-2252	135	28	sense	sense	NOUN
ejpam-2252	135	29	of	of	ADP
ejpam-2252	135	30	affine	affine	NOUN
ejpam-2252	135	31	ck	ck	NOUN
ejpam-2252	135	32	-	-	PUNCT
ejpam-2252	135	33	geometry	geometry	NOUN
ejpam-2252	135	34	,	,	PUNCT
ejpam-2252	135	35	i.e.	i.e.	X
ejpam-2252	135	36	〈	〈	NOUN
ejpam-2252	135	37	vr	vr	NOUN
ejpam-2252	135	38	,	,	PUNCT
ejpam-2252	135	39	bc〉ε	bc〉ε	PROPN
ejpam-2252	135	40	=	=	SYM
ejpam-2252	135	41	0	0	X
ejpam-2252	135	42	.	.	PUNCT
ejpam-2252	136	1	during	during	ADP
ejpam-2252	136	2	the	the	DET
ejpam-2252	136	3	one	one	NUM
ejpam-2252	136	4	-	-	PUNCT
ejpam-2252	136	5	parameter	parameter	NOUN
ejpam-2252	136	6	planar	planar	ADJ
ejpam-2252	136	7	motions	motion	NOUN
ejpam-2252	136	8	pε	pε	VERB
ejpam-2252	136	9	/	/	SYM
ejpam-2252	136	10	p	p	NOUN
ejpam-2252	136	11	′	′	NUM
ejpam-2252	136	12	ε	ε	PROPN
ejpam-2252	136	13	,	,	PUNCT
ejpam-2252	136	14	the	the	DET
ejpam-2252	136	15	acceleration	acceleration	NOUN
ejpam-2252	136	16	pole	pole	NOUN
ejpam-2252	136	17	is	be	AUX
ejpam-2252	136	18	characterized	characterize	VERB
ejpam-2252	136	19	by	by	ADP
ejpam-2252	136	20	b	b	PROPN
ejpam-2252	136	21	f=	f=	NUM
ejpam-2252	136	22	0	0	NUM
ejpam-2252	136	23	.	.	PUNCT
ejpam-2252	137	1	then	then	ADV
ejpam-2252	137	2	,	,	PUNCT
ejpam-2252	137	3	if	if	SCONJ
ejpam-2252	137	4	we	we	PRON
ejpam-2252	137	5	take	take	VERB
ejpam-2252	137	6	the	the	DET
ejpam-2252	137	7	acceleration	acceleration	NOUN
ejpam-2252	137	8	pole	pole	NOUN
ejpam-2252	137	9	point	point	NOUN
ejpam-2252	137	10	q	q	NOUN
ejpam-2252	138	1	=	=	PUNCT
ejpam-2252	138	2	(	(	PUNCT
ejpam-2252	138	3	q1,q2	q1,q2	PROPN
ejpam-2252	138	4	)	)	PUNCT
ejpam-2252	138	5	∈	∈	PROPN
ejpam-2252	138	6	pε	pε	NOUN
ejpam-2252	138	7	of	of	ADP
ejpam-2252	138	8	the	the	DET
ejpam-2252	138	9	motions	motion	NOUN
ejpam-2252	138	10	pε	pε	PROPN
ejpam-2252	138	11	/	/	SYM
ejpam-2252	138	12	p	p	NOUN
ejpam-2252	138	13	′	′	NUM
ejpam-2252	138	14	ε	ε	PROPN
ejpam-2252	138	15	,	,	PUNCT
ejpam-2252	138	16	we	we	PRON
ejpam-2252	138	17	get	get	VERB
ejpam-2252	138	18	the	the	DET
ejpam-2252	138	19	following	follow	VERB
ejpam-2252	138	20	equation	equation	NOUN
ejpam-2252	138	21	system	system	NOUN
ejpam-2252	138	22	:	:	PUNCT
ejpam-2252	138	23	¨	¨	X
ejpam-2252	138	24	ε	ε	PROPN
ejpam-2252	138	25	�	�	PROPN
ejpam-2252	138	26	ϕ̇	ϕ̇	PRON
ejpam-2252	138	27	�	�	PROPN
ejpam-2252	138	28	2	2	NUM
ejpam-2252	138	29	�	�	PROPN
ejpam-2252	138	30	x1	x1	NUM
ejpam-2252	138	31	−	−	PROPN
ejpam-2252	138	32	p1	p1	PROPN
ejpam-2252	138	33	�	�	PROPN
ejpam-2252	138	34	+	+	CCONJ
ejpam-2252	138	35	εϕ̈	εϕ̈	PROPN
ejpam-2252	138	36	�	�	PROPN
ejpam-2252	138	37	x2	x2	CCONJ
ejpam-2252	138	38	−	−	PROPN
ejpam-2252	138	39	p2	p2	PROPN
ejpam-2252	138	40	�	�	PROPN
ejpam-2252	138	41	=	=	SYM
ejpam-2252	139	1	εϕ̇	εϕ̇	PROPN
ejpam-2252	139	2	ṗ2	ṗ2	PROPN
ejpam-2252	139	3	ϕ̈	ϕ̈	PROPN
ejpam-2252	139	4	�	�	PROPN
ejpam-2252	140	1	x1	x1	CCONJ
ejpam-2252	140	2	−	−	PROPN
ejpam-2252	140	3	p1	p1	PROPN
ejpam-2252	140	4	�	�	PROPN
ejpam-2252	140	5	−	−	ADP
ejpam-2252	140	6	ε	ε	PROPN
ejpam-2252	140	7	�	�	PROPN
ejpam-2252	140	8	ϕ̇	ϕ̇	PRON
ejpam-2252	140	9	�	�	PROPN
ejpam-2252	140	10	2	2	NUM
ejpam-2252	140	11	�	�	PROPN
ejpam-2252	140	12	x2	x2	CCONJ
ejpam-2252	140	13	−	−	PROPN
ejpam-2252	140	14	p2	p2	PROPN
ejpam-2252	140	15	�	�	PROPN
ejpam-2252	140	16	=	=	PUNCT
ejpam-2252	140	17	ṗ1ϕ̇	ṗ1ϕ̇	NOUN
ejpam-2252	140	18	(	(	PUNCT
ejpam-2252	140	19	15	15	NUM
ejpam-2252	140	20	)	)	PUNCT
ejpam-2252	140	21	if	if	SCONJ
ejpam-2252	140	22	ε	ε	PROPN
ejpam-2252	140	23	�	�	PROPN
ejpam-2252	140	24	ϕ̇	ϕ̇	PRON
ejpam-2252	140	25	�	�	PROPN
ejpam-2252	140	26	4	4	NUM
ejpam-2252	140	27	+	+	NUM
ejpam-2252	140	28	�	�	PROPN
ejpam-2252	140	29	ϕ̈	ϕ̈	PROPN
ejpam-2252	140	30	�	�	PROPN
ejpam-2252	140	31	2	2	NUM
ejpam-2252	140	32	6=	6=	ADP
ejpam-2252	140	33	0	0	NUM
ejpam-2252	140	34	,	,	PUNCT
ejpam-2252	140	35	we	we	PRON
ejpam-2252	140	36	obtain	obtain	VERB
ejpam-2252	140	37	the	the	DET
ejpam-2252	140	38	pole	pole	NOUN
ejpam-2252	140	39	point	point	NOUN
ejpam-2252	140	40	from	from	ADP
ejpam-2252	140	41	the	the	DET
ejpam-2252	140	42	above	above	ADJ
ejpam-2252	140	43	system	system	NOUN
ejpam-2252	140	44	as	as	SCONJ
ejpam-2252	140	45	follows	follow	VERB
ejpam-2252	140	46	:	:	PUNCT
ejpam-2252	140	47			NOUN
ejpam-2252	140	48			PROPN
ejpam-2252	140	49			PROPN
ejpam-2252	140	50			PROPN
ejpam-2252	140	51			PROPN
ejpam-2252	140	52			NOUN
ejpam-2252	140	53			PROPN
ejpam-2252	140	54			PROPN
ejpam-2252	140	55			PROPN
ejpam-2252	140	56			PROPN
ejpam-2252	140	57			PROPN
ejpam-2252	140	58	�	�	PROPN
ejpam-2252	140	59	ε2	ε2	PROPN
ejpam-2252	140	60	�	�	PROPN
ejpam-2252	140	61	ϕ̇(t	ϕ̇(t	PROPN
ejpam-2252	140	62	)	)	PUNCT
ejpam-2252	140	63	�	�	PROPN
ejpam-2252	140	64	4	4	NUM
ejpam-2252	140	65	+	+	CCONJ
ejpam-2252	140	66	ε	ε	PROPN
ejpam-2252	140	67	�	�	PROPN
ejpam-2252	140	68	ϕ̈(t	ϕ̈(t	PROPN
ejpam-2252	140	69	)	)	PUNCT
ejpam-2252	140	70	�	�	PROPN
ejpam-2252	140	71	2	2	NUM
ejpam-2252	140	72	�	�	PROPN
ejpam-2252	140	73	q1(t	q1(t	PART
ejpam-2252	140	74	)	)	PUNCT
ejpam-2252	140	75	=	=	SYM
ejpam-2252	140	76	�	�	PROPN
ejpam-2252	140	77	ε2	ε2	PROPN
ejpam-2252	140	78	�	�	PROPN
ejpam-2252	140	79	ϕ̇(t	ϕ̇(t	PROPN
ejpam-2252	140	80	)	)	PUNCT
ejpam-2252	140	81	�	�	PROPN
ejpam-2252	140	82	4	4	NUM
ejpam-2252	140	83	+	+	CCONJ
ejpam-2252	140	84	ε	ε	PROPN
ejpam-2252	140	85	�	�	PROPN
ejpam-2252	140	86	ϕ̈(t	ϕ̈(t	PROPN
ejpam-2252	140	87	)	)	PUNCT
ejpam-2252	140	88	�	�	PROPN
ejpam-2252	140	89	2	2	NUM
ejpam-2252	140	90	�	�	PROPN
ejpam-2252	140	91	p1(t	p1(t	PART
ejpam-2252	140	92	)	)	PUNCT
ejpam-2252	140	93	+	+	ADJ
ejpam-2252	140	94	ϕ̇(t	ϕ̇(t	ADJ
ejpam-2252	140	95	)	)	PUNCT
ejpam-2252	140	96	�	�	PROPN
ejpam-2252	140	97	εϕ̈(t)ṗ1(t	εϕ̈(t)ṗ1(t	PROPN
ejpam-2252	140	98	)	)	PUNCT
ejpam-2252	141	1	+	+	CCONJ
ejpam-2252	141	2	ε	ε	PROPN
ejpam-2252	141	3	2	2	NUM
ejpam-2252	141	4	�	�	PROPN
ejpam-2252	141	5	ϕ̇(t	ϕ̇(t	PROPN
ejpam-2252	141	6	)	)	PUNCT
ejpam-2252	141	7	�	�	PROPN
ejpam-2252	141	8	2	2	NUM
ejpam-2252	141	9	ṗ2(t	ṗ2(t	PROPN
ejpam-2252	141	10	)	)	PUNCT
ejpam-2252	141	11	�	�	PROPN
ejpam-2252	141	12	�	�	PROPN
ejpam-2252	141	13	ε2	ε2	PROPN
ejpam-2252	141	14	�	�	PROPN
ejpam-2252	141	15	ϕ̇(t	ϕ̇(t	PROPN
ejpam-2252	141	16	)	)	PUNCT
ejpam-2252	141	17	�	�	PROPN
ejpam-2252	141	18	4	4	NUM
ejpam-2252	141	19	+	+	CCONJ
ejpam-2252	141	20	ε	ε	PROPN
ejpam-2252	141	21	�	�	PROPN
ejpam-2252	141	22	ϕ̈(t	ϕ̈(t	PROPN
ejpam-2252	141	23	)	)	PUNCT
ejpam-2252	141	24	�	�	PROPN
ejpam-2252	141	25	2	2	NUM
ejpam-2252	141	26	�	�	PROPN
ejpam-2252	141	27	q2(t	q2(t	PROPN
ejpam-2252	141	28	)	)	PUNCT
ejpam-2252	141	29	=	=	SYM
ejpam-2252	141	30	�	�	PROPN
ejpam-2252	141	31	ε2	ε2	PROPN
ejpam-2252	141	32	�	�	PROPN
ejpam-2252	141	33	ϕ̇(t	ϕ̇(t	PROPN
ejpam-2252	141	34	)	)	PUNCT
ejpam-2252	141	35	�	�	PROPN
ejpam-2252	141	36	4	4	NUM
ejpam-2252	141	37	+	+	CCONJ
ejpam-2252	141	38	ε	ε	PROPN
ejpam-2252	141	39	�	�	PROPN
ejpam-2252	141	40	ϕ̈(t	ϕ̈(t	PROPN
ejpam-2252	141	41	)	)	PUNCT
ejpam-2252	141	42	�	�	PROPN
ejpam-2252	141	43	2	2	NUM
ejpam-2252	141	44	�	�	PROPN
ejpam-2252	141	45	p2(t	p2(t	NOUN
ejpam-2252	141	46	)	)	PUNCT
ejpam-2252	141	47	−εϕ̇(t	−εϕ̇(t	NUM
ejpam-2252	141	48	)	)	PUNCT
ejpam-2252	141	49	�	�	PROPN
ejpam-2252	141	50	�	�	PROPN
ejpam-2252	141	51	ϕ̇(t	ϕ̇(t	PROPN
ejpam-2252	141	52	)	)	PUNCT
ejpam-2252	141	53	�	�	PROPN
ejpam-2252	141	54	2	2	NUM
ejpam-2252	141	55	ṗ1(t)−	ṗ1(t)−	PROPN
ejpam-2252	141	56	ϕ̈(t)ṗ2(t	ϕ̈(t)ṗ2(t	X
ejpam-2252	141	57	)	)	PUNCT
ejpam-2252	141	58	�	�	PROPN
ejpam-2252	141	59	so	so	SCONJ
ejpam-2252	141	60	that	that	SCONJ
ejpam-2252	141	61	the	the	DET
ejpam-2252	141	62	point	point	NOUN
ejpam-2252	141	63	q	q	NOUN
ejpam-2252	141	64	is	be	AUX
ejpam-2252	141	65	instant	instant	ADJ
ejpam-2252	141	66	in	in	ADP
ejpam-2252	141	67	the	the	DET
ejpam-2252	141	68	plane	plane	NOUN
ejpam-2252	141	69	pε	pε	NOUN
ejpam-2252	141	70	.	.	PUNCT
ejpam-2252	142	1	acknowledgements	acknowledgement	VERB
ejpam-2252	142	2	the	the	DET
ejpam-2252	142	3	authors	author	NOUN
ejpam-2252	142	4	thank	thank	VERB
ejpam-2252	142	5	the	the	DET
ejpam-2252	142	6	readers	reader	NOUN
ejpam-2252	142	7	of	of	ADP
ejpam-2252	142	8	european	european	PROPN
ejpam-2252	142	9	journal	journal	PROPN
ejpam-2252	142	10	of	of	ADP
ejpam-2252	142	11	pure	pure	ADJ
ejpam-2252	142	12	and	and	CCONJ
ejpam-2252	142	13	applied	applied	ADJ
ejpam-2252	142	14	mathematics	mathematic	NOUN
ejpam-2252	142	15	,	,	PUNCT
ejpam-2252	142	16	for	for	ADP
ejpam-2252	142	17	making	make	VERB
ejpam-2252	142	18	our	our	PRON
ejpam-2252	142	19	journal	journal	NOUN
ejpam-2252	142	20	successful	successful	ADJ
ejpam-2252	142	21	.	.	PUNCT
ejpam-2252	143	1	references	reference	NOUN
ejpam-2252	143	2	[	[	X
ejpam-2252	143	3	1	1	NUM
ejpam-2252	143	4	]	]	PUNCT
ejpam-2252	143	5	m.	m.	NOUN
ejpam-2252	143	6	akar	akar	PROPN
ejpam-2252	143	7	,	,	PUNCT
ejpam-2252	143	8	s.	s.	PROPN
ejpam-2252	143	9	yüce	yüce	PROPN
ejpam-2252	143	10	,	,	PUNCT
ejpam-2252	143	11	and	and	CCONJ
ejpam-2252	143	12	n.	n.	PROPN
ejpam-2252	143	13	kuruoğlu	kuruoğlu	PROPN
ejpam-2252	143	14	.	.	PUNCT
ejpam-2252	144	1	one	one	NUM
ejpam-2252	144	2	-	-	PUNCT
ejpam-2252	144	3	parameter	parameter	NOUN
ejpam-2252	144	4	planar	planar	ADJ
ejpam-2252	144	5	motion	motion	NOUN
ejpam-2252	144	6	in	in	ADP
ejpam-2252	144	7	the	the	DET
ejpam-2252	144	8	galilean	galilean	PROPN
ejpam-2252	144	9	plane	plane	NOUN
ejpam-2252	144	10	.	.	PUNCT
ejpam-2252	145	1	international	international	ADJ
ejpam-2252	145	2	electronic	electronic	ADJ
ejpam-2252	145	3	journal	journal	NOUN
ejpam-2252	145	4	of	of	ADP
ejpam-2252	145	5	geometry	geometry	NOUN
ejpam-2252	145	6	(	(	PUNCT
ejpam-2252	145	7	iejg	iejg	PROPN
ejpam-2252	145	8	)	)	PUNCT
ejpam-2252	145	9	,	,	PUNCT
ejpam-2252	145	10	6(1	6(1	NUM
ejpam-2252	145	11	):	):	PUNCT
ejpam-2252	145	12	79–88	79–88	NUM
ejpam-2252	145	13	,	,	PUNCT
ejpam-2252	145	14	2013	2013	NUM
ejpam-2252	145	15	.	.	PUNCT
ejpam-2252	146	1	[	[	X
ejpam-2252	146	2	2	2	NUM
ejpam-2252	146	3	]	]	PUNCT
ejpam-2252	146	4	m.	m.	NOUN
ejpam-2252	146	5	akbıyık	akbıyık	PROPN
ejpam-2252	146	6	.	.	PUNCT
ejpam-2252	147	1	moving	move	VERB
ejpam-2252	147	2	coordinate	coordinate	NOUN
ejpam-2252	147	3	system	system	NOUN
ejpam-2252	147	4	and	and	CCONJ
ejpam-2252	147	5	euler	euler	X
ejpam-2252	147	6	savary	savary	ADJ
ejpam-2252	147	7	formula	formula	NOUN
ejpam-2252	147	8	on	on	ADP
ejpam-2252	147	9	galilean	galilean	PROPN
ejpam-2252	147	10	plane	plane	NOUN
ejpam-2252	147	11	.	.	PUNCT
ejpam-2252	148	1	master	master	NOUN
ejpam-2252	148	2	thesis	thesis	PROPN
ejpam-2252	148	3	,	,	PUNCT
ejpam-2252	148	4	yıldız	yıldız	PROPN
ejpam-2252	148	5	technical	technical	PROPN
ejpam-2252	148	6	university	university	PROPN
ejpam-2252	148	7	graduate	graduate	NOUN
ejpam-2252	148	8	school	school	NOUN
ejpam-2252	148	9	of	of	ADP
ejpam-2252	148	10	natural	natural	ADJ
ejpam-2252	148	11	and	and	CCONJ
ejpam-2252	148	12	applied	applied	ADJ
ejpam-2252	148	13	sciences	science	NOUN
ejpam-2252	148	14	,	,	PUNCT
ejpam-2252	148	15	2012	2012	NUM
ejpam-2252	148	16	.	.	PUNCT
ejpam-2252	149	1	[	[	X
ejpam-2252	149	2	3	3	X
ejpam-2252	149	3	]	]	X
ejpam-2252	149	4	w.	w.	PROPN
ejpam-2252	149	5	blaschke	blaschke	PROPN
ejpam-2252	149	6	and	and	CCONJ
ejpam-2252	149	7	h.r	h.r	PROPN
ejpam-2252	149	8	.	.	PROPN
ejpam-2252	149	9	müller	müller	PROPN
ejpam-2252	149	10	.	.	PUNCT
ejpam-2252	149	11	ebene	ebene	PROPN
ejpam-2252	149	12	kinematik	kinematik	PROPN
ejpam-2252	149	13	.	.	PUNCT
ejpam-2252	150	1	verlag	verlag	PROPN
ejpam-2252	150	2	oldenbourg	oldenbourg	PROPN
ejpam-2252	150	3	,	,	PUNCT
ejpam-2252	150	4	münchen	münchen	NOUN
ejpam-2252	150	5	,	,	PUNCT
ejpam-2252	150	6	1956	1956	NUM
ejpam-2252	150	7	.	.	PUNCT
ejpam-2252	151	1	[	[	X
ejpam-2252	151	2	4	4	NUM
ejpam-2252	151	3	]	]	PUNCT
ejpam-2252	151	4	a.	a.	NOUN
ejpam-2252	151	5	a.	a.	NOUN
ejpam-2252	151	6	ergin	ergin	NOUN
ejpam-2252	151	7	.	.	PUNCT
ejpam-2252	152	1	on	on	ADP
ejpam-2252	152	2	the	the	DET
ejpam-2252	152	3	one	one	NUM
ejpam-2252	152	4	-	-	PUNCT
ejpam-2252	152	5	parameter	parameter	NOUN
ejpam-2252	152	6	lorentzian	lorentzian	ADJ
ejpam-2252	152	7	motion	motion	NOUN
ejpam-2252	152	8	.	.	PUNCT
ejpam-2252	153	1	communications	communication	NOUN
ejpam-2252	153	2	,	,	PUNCT
ejpam-2252	153	3	faculty	faculty	NOUN
ejpam-2252	153	4	of	of	ADP
ejpam-2252	153	5	science	science	NOUN
ejpam-2252	153	6	,	,	PUNCT
ejpam-2252	153	7	university	university	NOUN
ejpam-2252	153	8	of	of	ADP
ejpam-2252	153	9	ankara	ankara	PROPN
ejpam-2252	153	10	,	,	PUNCT
ejpam-2252	153	11	series	series	PROPN
ejpam-2252	153	12	a	a	DET
ejpam-2252	153	13	40	40	NUM
ejpam-2252	153	14	,	,	PUNCT
ejpam-2252	153	15	59–66,1991	59–66,1991	NUM
ejpam-2252	153	16	.	.	PUNCT
ejpam-2252	154	1	[	[	X
ejpam-2252	154	2	5	5	X
ejpam-2252	154	3	]	]	X
ejpam-2252	154	4	h.	h.	PROPN
ejpam-2252	154	5	es	es	PROPN
ejpam-2252	154	6	.	.	PROPN
ejpam-2252	154	7	motions	motion	NOUN
ejpam-2252	154	8	and	and	CCONJ
ejpam-2252	154	9	nine	nine	NUM
ejpam-2252	154	10	different	different	ADJ
ejpam-2252	154	11	geometry	geometry	NOUN
ejpam-2252	154	12	.	.	PUNCT
ejpam-2252	155	1	phd	phd	NOUN
ejpam-2252	155	2	thesis	thesis	PROPN
ejpam-2252	155	3	,	,	PUNCT
ejpam-2252	155	4	ankara	ankara	PROPN
ejpam-2252	155	5	university	university	PROPN
ejpam-2252	155	6	graduate	graduate	PROPN
ejpam-2252	155	7	school	school	NOUN
ejpam-2252	155	8	of	of	ADP
ejpam-2252	155	9	natural	natural	ADJ
ejpam-2252	155	10	and	and	CCONJ
ejpam-2252	155	11	applied	applied	ADJ
ejpam-2252	155	12	sciences	science	NOUN
ejpam-2252	155	13	,	,	PUNCT
ejpam-2252	155	14	2003	2003	NUM
ejpam-2252	155	15	.	.	PUNCT
ejpam-2252	156	1	references	reference	NOUN
ejpam-2252	156	2	342	342	NUM
ejpam-2252	157	1	[	[	X
ejpam-2252	157	2	6	6	NUM
ejpam-2252	157	3	]	]	PUNCT
ejpam-2252	157	4	g.	g.	PROPN
ejpam-2252	157	5	helzer	helzer	PROPN
ejpam-2252	157	6	.	.	PUNCT
ejpam-2252	158	1	special	special	ADJ
ejpam-2252	158	2	relativity	relativity	NOUN
ejpam-2252	158	3	with	with	ADP
ejpam-2252	158	4	acceleration	acceleration	NOUN
ejpam-2252	158	5	,	,	PUNCT
ejpam-2252	158	6	the	the	DET
ejpam-2252	158	7	american	american	PROPN
ejpam-2252	158	8	mathematical	mathematical	PROPN
ejpam-2252	158	9	monthly	monthly	ADV
ejpam-2252	158	10	,	,	PUNCT
ejpam-2252	158	11	107(3	107(3	NUM
ejpam-2252	158	12	)	)	PUNCT
ejpam-2252	158	13	,	,	PUNCT
ejpam-2252	158	14	219–237	219–237	NUM
ejpam-2252	158	15	,	,	PUNCT
ejpam-2252	158	16	2000	2000	NUM
ejpam-2252	158	17	.	.	PUNCT
ejpam-2252	159	1	[	[	X
ejpam-2252	159	2	7	7	X
ejpam-2252	159	3	]	]	X
ejpam-2252	159	4	f.	f.	PROPN
ejpam-2252	159	5	j.	j.	PROPN
ejpam-2252	159	6	herranz	herranz	PROPN
ejpam-2252	159	7	and	and	CCONJ
ejpam-2252	159	8	m.	m.	NOUN
ejpam-2252	159	9	santader	santader	NOUN
ejpam-2252	159	10	.	.	PUNCT
ejpam-2252	160	1	homogeneous	homogeneous	ADJ
ejpam-2252	160	2	phase	phase	NOUN
ejpam-2252	160	3	spaces	space	VERB
ejpam-2252	160	4	:	:	PUNCT
ejpam-2252	160	5	the	the	DET
ejpam-2252	160	6	cayley	cayley	ADJ
ejpam-2252	160	7	-	-	PUNCT
ejpam-2252	160	8	klein	klein	NOUN
ejpam-2252	160	9	framework	framework	NOUN
ejpam-2252	160	10	,	,	PUNCT
ejpam-2252	160	11	http://arxiv.org/pdf/physics/9702030v1.pdf	http://arxiv.org/pdf/physics/9702030v1.pdf	NOUN
ejpam-2252	160	12	.	.	PUNCT
ejpam-2252	161	1	[	[	X
ejpam-2252	161	2	8	8	NUM
ejpam-2252	161	3	]	]	X
ejpam-2252	161	4	f.	f.	PROPN
ejpam-2252	161	5	klein	klein	PROPN
ejpam-2252	161	6	.	.	PROPN
ejpam-2252	162	1	über	über	PROPN
ejpam-2252	162	2	die	die	VERB
ejpam-2252	162	3	sogenante	sogenante	ADV
ejpam-2252	162	4	nicht	nicht	NOUN
ejpam-2252	162	5	-	-	PUNCT
ejpam-2252	162	6	euklidische	euklidische	NOUN
ejpam-2252	162	7	geometrie	geometrie	NOUN
ejpam-2252	162	8	,	,	PUNCT
ejpam-2252	162	9	gesammelte	gesammelte	NOUN
ejpam-2252	162	10	mathematische	mathematische	PROPN
ejpam-2252	162	11	abhandlungen	abhandlungen	PROPN
ejpam-2252	162	12	,	,	PUNCT
ejpam-2252	162	13	254	254	NUM
ejpam-2252	162	14	-	-	SYM
ejpam-2252	162	15	305	305	NUM
ejpam-2252	162	16	,	,	PUNCT
ejpam-2252	162	17	1921	1921	NUM
ejpam-2252	162	18	.	.	PUNCT
ejpam-2252	163	1	[	[	X
ejpam-2252	163	2	9	9	NUM
ejpam-2252	163	3	]	]	X
ejpam-2252	163	4	f.	f.	PROPN
ejpam-2252	163	5	klein	klein	PROPN
ejpam-2252	163	6	.	.	PUNCT
ejpam-2252	164	1	vorlesungen	vorlesungen	PROPN
ejpam-2252	164	2	über	über	PROPN
ejpam-2252	164	3	nicht	nicht	NOUN
ejpam-2252	164	4	-	-	PUNCT
ejpam-2252	164	5	euklidische	euklidische	NOUN
ejpam-2252	164	6	geometrie	geometrie	NOUN
ejpam-2252	164	7	,	,	PUNCT
ejpam-2252	164	8	springer	springer	NOUN
ejpam-2252	164	9	,	,	PUNCT
ejpam-2252	164	10	berlin	berlin	PROPN
ejpam-2252	164	11	,	,	PUNCT
ejpam-2252	164	12	1928	1928	NUM
ejpam-2252	164	13	.	.	PUNCT
ejpam-2252	165	1	[	[	X
ejpam-2252	165	2	10	10	NUM
ejpam-2252	165	3	]	]	X
ejpam-2252	165	4	r.	r.	PROPN
ejpam-2252	165	5	salgado	salgado	PROPN
ejpam-2252	165	6	.	.	PUNCT
ejpam-2252	165	7	space	space	NOUN
ejpam-2252	165	8	-	-	PUNCT
ejpam-2252	165	9	time	time	NOUN
ejpam-2252	165	10	trigonometry	trigonometry	NOUN
ejpam-2252	165	11	.	.	PUNCT
ejpam-2252	166	1	aapt	aapt	PROPN
ejpam-2252	166	2	topical	topical	ADJ
ejpam-2252	166	3	conference	conference	NOUN
ejpam-2252	166	4	:	:	PUNCT
ejpam-2252	166	5	teaching	teach	VERB
ejpam-2252	166	6	general	general	ADJ
ejpam-2252	166	7	relativity	relativity	NOUN
ejpam-2252	166	8	to	to	ADP
ejpam-2252	166	9	undergraduates	undergraduate	NOUN
ejpam-2252	166	10	,	,	PUNCT
ejpam-2252	166	11	aapt	aapt	PROPN
ejpam-2252	166	12	summer	summer	NOUN
ejpam-2252	166	13	meeting	meeting	NOUN
ejpam-2252	166	14	,	,	PUNCT
ejpam-2252	166	15	syrauce	syrauce	PROPN
ejpam-2252	166	16	university	university	PROPN
ejpam-2252	166	17	,	,	PUNCT
ejpam-2252	166	18	ny	ny	PROPN
ejpam-2252	166	19	,	,	PUNCT
ejpam-2252	166	20	july	july	PROPN
ejpam-2252	166	21	20	20	NUM
ejpam-2252	166	22	-	-	PUNCT
ejpam-2252	166	23	21,22	21,22	NUM
ejpam-2252	166	24	-	-	PUNCT
ejpam-2252	166	25	26	26	NUM
ejpam-2252	166	26	.	.	PUNCT
ejpam-2252	166	27	2006	2006	NUM
ejpam-2252	166	28	.	.	PUNCT
ejpam-2252	167	1	[	[	X
ejpam-2252	167	2	11	11	NUM
ejpam-2252	167	3	]	]	PUNCT
ejpam-2252	167	4	m.	m.	NOUN
ejpam-2252	167	5	a.	a.	PROPN
ejpam-2252	167	6	f.	f.	PROPN
ejpam-2252	167	7	sanjuan	sanjuan	PROPN
ejpam-2252	167	8	.	.	PROPN
ejpam-2252	167	9	group	group	PROPN
ejpam-2252	167	10	contraction	contraction	NOUN
ejpam-2252	167	11	and	and	CCONJ
ejpam-2252	167	12	nine	nine	NUM
ejpam-2252	167	13	cayley	cayley	ADJ
ejpam-2252	167	14	-	-	PUNCT
ejpam-2252	167	15	klein	klein	NOUN
ejpam-2252	167	16	geometries	geometries	PROPN
ejpam-2252	167	17	,	,	PUNCT
ejpam-2252	167	18	international	international	ADJ
ejpam-2252	167	19	journal	journal	NOUN
ejpam-2252	167	20	of	of	ADP
ejpam-2252	167	21	theoretical	theoretical	ADJ
ejpam-2252	167	22	physics	physics	NOUN
ejpam-2252	167	23	,	,	PUNCT
ejpam-2252	167	24	23(1	23(1	NOUN
ejpam-2252	167	25	)	)	PUNCT
ejpam-2252	167	26	,	,	PUNCT
ejpam-2252	167	27	1984	1984	NUM
ejpam-2252	167	28	.	.	PUNCT
ejpam-2252	168	1	[	[	X
ejpam-2252	168	2	12	12	NUM
ejpam-2252	168	3	]	]	PUNCT
ejpam-2252	168	4	m.	m.	NOUN
ejpam-2252	168	5	spirova	spirova	PROPN
ejpam-2252	168	6	.	.	PUNCT
ejpam-2252	169	1	propellers	propeller	NOUN
ejpam-2252	169	2	in	in	ADP
ejpam-2252	169	3	affine	affine	NOUN
ejpam-2252	169	4	cayley	cayley	ADJ
ejpam-2252	169	5	-	-	PUNCT
ejpam-2252	169	6	klein	klein	NOUN
ejpam-2252	169	7	planes	plane	NOUN
ejpam-2252	169	8	,	,	PUNCT
ejpam-2252	169	9	journal	journal	NOUN
ejpam-2252	169	10	of	of	ADP
ejpam-2252	169	11	geometry	geometry	NOUN
ejpam-2252	169	12	.	.	PUNCT
ejpam-2252	170	1	93	93	NUM
ejpam-2252	170	2	,	,	PUNCT
ejpam-2252	170	3	164	164	NUM
ejpam-2252	170	4	-	-	SYM
ejpam-2252	170	5	167	167	NUM
ejpam-2252	170	6	,	,	PUNCT
ejpam-2252	170	7	2009	2009	NUM
ejpam-2252	170	8	.	.	PUNCT
ejpam-2252	171	1	[	[	X
ejpam-2252	171	2	13	13	NUM
ejpam-2252	171	3	]	]	X
ejpam-2252	171	4	h.	h.	PROPN
ejpam-2252	171	5	urban	urban	PROPN
ejpam-2252	171	6	.	.	PUNCT
ejpam-2252	172	1	über	über	PROPN
ejpam-2252	172	2	drei	drei	PROPN
ejpam-2252	172	3	zwanglaufiggegeneinander	zwanglaufiggegeneinander	NOUN
ejpam-2252	172	4	bewegte	bewegte	PROPN
ejpam-2252	172	5	cayley	cayley	PROPN
ejpam-2252	172	6	/	/	SYM
ejpam-2252	172	7	klein	klein	PROPN
ejpam-2252	172	8	-	-	PUNCT
ejpam-2252	172	9	ebenen	ebenen	PROPN
ejpam-2252	172	10	.	.	PUNCT
ejpam-2252	172	11	geometriae	geometriae	PROPN
ejpam-2252	172	12	dedicata	dedicata	PROPN
ejpam-2252	172	13	,	,	PUNCT
ejpam-2252	172	14	53:187–199	53:187–199	PROPN
ejpam-2252	172	15	,	,	PUNCT
ejpam-2252	172	16	1994	1994	NUM
ejpam-2252	172	17	.	.	PUNCT
ejpam-2252	173	1	[	[	X
ejpam-2252	173	2	14	14	NUM
ejpam-2252	173	3	]	]	PUNCT
ejpam-2252	173	4	i.	i.	NOUN
ejpam-2252	173	5	m.	m.	PROPN
ejpam-2252	173	6	yaglom	yaglom	PROPN
ejpam-2252	173	7	.	.	PUNCT
ejpam-2252	174	1	a	a	DET
ejpam-2252	174	2	simple	simple	ADJ
ejpam-2252	174	3	non	non	ADJ
ejpam-2252	174	4	-	-	ADJ
ejpam-2252	174	5	euclidean	euclidean	ADJ
ejpam-2252	174	6	geometry	geometry	NOUN
ejpam-2252	174	7	and	and	CCONJ
ejpam-2252	174	8	its	its	PRON
ejpam-2252	174	9	physical	physical	ADJ
ejpam-2252	174	10	basis	basis	NOUN
ejpam-2252	174	11	.	.	PUNCT
ejpam-2252	175	1	springer	springer	NOUN
ejpam-2252	175	2	-	-	PUNCT
ejpam-2252	175	3	verlag	verlag	PROPN
ejpam-2252	175	4	,	,	PUNCT
ejpam-2252	175	5	new	new	PROPN
ejpam-2252	175	6	york	york	PROPN
ejpam-2252	175	7	,	,	PUNCT
ejpam-2252	175	8	1979	1979	NUM
ejpam-2252	175	9	.	.	PUNCT