I
nd
o
ne
s
ia
n J
o
urna
l o
f
E
lect
rica
l En
g
ineering
a
nd
Co
m
pu
t
er
Science
Vo
l.
24
,
No
.
3
,
Dec
em
b
er
2
0
2
1
,
p
p
.
1
3
0
7
~
1
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1
4
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SS
N:
2
5
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4
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24
.i
3
.
pp
1
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0
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1307
J
o
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na
l ho
m
ep
a
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e
:
h
ttp
:
//ij
ee
cs.ia
esco
r
e.
co
m
Diff
e
rential
equa
t
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ns o
f
mo
tion o
f
a
ma
terial po
int
i
n t
he
perpendic
ula
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ne t
o
t
he plane
of
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g
ra
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itating
di
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heni
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ul Ra
k
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ina
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a
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a
rida
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m
eno
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a
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1,
3
De
p
a
rtme
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o
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En
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in
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g
M
a
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m
a
ti
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D.
S
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rik
b
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y
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t
Ka
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rsity
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EKTU),
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t'
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m
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ti
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D.
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a
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t
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(EKU),
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t'
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k
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Art
icle
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nfo
AB
S
T
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A
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ticle
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to
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y:
R
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J
u
l
4
,
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0
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1
R
ev
is
ed
Oct
30
,
2
0
2
1
Acc
ep
ted
No
v
1
,
2
0
2
1
Th
is
p
a
p
e
r
p
re
se
n
ts
a
n
a
n
a
ly
ti
c
a
l
so
lu
ti
o
n
o
f
t
h
e
d
iffere
n
ti
a
l
e
q
u
a
ti
o
n
s
o
f
m
o
ti
o
n
o
f
a
m
a
teria
l
p
o
i
n
t
in
t
h
e
p
lan
e
p
e
rp
e
n
d
icu
lar
to
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h
e
p
l
a
n
e
o
f
t
h
e
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ra
v
it
a
ti
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g
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isk
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T
h
e
d
iffere
n
t
ial
e
q
u
a
ti
o
n
s
o
f
t
h
e
p
ro
b
lem
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n
d
e
r
stu
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y
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n
d
th
e
a
p
p
li
e
d
G
il
d
e
n
'
s
m
e
th
o
d
a
r
e
d
e
sc
rib
e
d
in
th
e
wo
r
k
s
o
f
A.
P
o
in
c
a
ré
.
Diffe
re
n
ti
a
l
e
q
u
a
ti
o
n
s
re
fe
r
to
n
o
n
li
n
e
a
r
e
q
u
a
ti
o
n
s.
Th
e
a
n
a
l
y
sis
o
f
m
e
th
o
d
s
fo
r
so
lv
i
n
g
n
o
n
l
in
e
a
r
d
iffere
n
ti
a
l
e
q
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a
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n
s
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s
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o
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t.
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e
m
e
th
o
d
o
lo
g
y
o
f
a
p
p
l
y
in
g
th
e
G
il
d
e
n
m
e
th
o
d
to
t
h
e
so
lu
ti
o
n
o
f
th
e
d
iffere
n
ti
a
l
e
q
u
a
ti
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s
u
n
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r
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o
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sid
e
ra
ti
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n
c
a
n
b
e
a
p
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li
e
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stu
d
ies
o
f
t
h
e
p
r
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b
lem
o
f
t
h
e
m
o
ti
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o
f
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e
les
ti
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l
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o
d
ies
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e
“
d
isk
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m
a
teria
l
p
o
in
t
”
sy
ste
m
in
p
e
rp
e
n
d
icu
lar
p
lan
e
s.
To
id
e
n
ti
f
y
t
h
e
v
a
ri
o
u
s
p
r
o
p
e
rti
e
s
o
f
th
e
g
ra
v
it
a
ti
n
g
d
isk
,
a
n
a
n
a
l
y
ti
c
a
l
re
v
iew
o
f
th
e
sta
te
o
f
th
e
p
ro
b
lem
o
f
t
h
e
m
o
ti
o
n
o
f
a
m
a
teria
l
p
o
in
t
i
n
th
e
field
o
f
a
g
ra
v
it
a
ti
n
g
d
is
k
is ca
rried
o
u
t
.
S
u
m
m
in
g
u
p
t
h
e
p
re
se
n
ted
re
v
iew
o
n
th
e
p
r
o
b
lem
u
n
d
e
r
stu
d
y
,
a
c
o
n
c
lu
si
o
n
is
m
a
d
e
.
Th
e
su
b
sta
n
ti
v
e
f
o
rm
u
latio
n
o
f
th
e
p
r
o
b
lem
is
d
e
sc
rib
e
d
,
wh
ic
h
i
s
f
o
r
m
u
late
d
a
s
fo
ll
o
ws
:
th
e
st
u
d
y
o
f
t
h
e
in
f
lu
e
n
c
e
o
f
d
isk
-
sh
a
p
e
d
b
o
d
ies
o
n
t
h
e
m
o
ti
o
n
o
f
a
m
a
teria
l
p
o
in
t
a
n
d
m
e
th
o
d
s fo
r
th
e
ir
so
lu
ti
o
n
.
K
ey
w
o
r
d
s
:
Dif
f
er
en
tial e
q
u
atio
n
s
Gr
av
itatin
g
d
is
k
Ma
th
em
atica
l m
o
d
el
Mo
tio
n
o
f
a
m
ater
ial
p
o
i
n
t
Per
p
en
d
icu
lar
p
lan
e
Po
ten
tial
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
I
n
d
ir
a
Uv
aliy
e
v
a
Dep
ar
tm
en
t o
f
E
n
g
in
ee
r
in
g
M
ath
em
atics
D.
Ser
ik
b
ay
ev
E
ast Ka
za
k
h
s
tan
T
ec
h
n
ical
Un
iv
e
r
s
ity
6
9
Pro
to
za
n
o
v
Stre
et,
Ust
-
Ka
m
en
o
g
o
r
s
k
,
Kaz
ak
h
s
tan
E
m
ail: in
d
ir
au
v
aliev
a@
g
m
ail.
co
m
1.
I
NT
RO
D
UCT
I
O
N
T
h
e
p
r
o
b
lem
o
f
th
e
m
o
tio
n
o
f
ce
lest
ial
b
o
d
ies
in
th
e
“d
is
k
-
m
ater
ial
p
o
in
t
”
s
y
s
tem
,
in
p
ar
ticu
lar
,
was
o
f
in
ter
est
to
m
an
y
s
cien
tis
ts
.
T
h
e
task
h
as
its
o
wn
p
r
ac
ti
ca
l
ap
p
licatio
n
s
.
T
h
e
m
o
tio
n
o
f
ce
lest
ial
b
o
d
ies
p
er
p
en
d
icu
lar
to
th
e
p
lan
e
o
f
th
e
Gala
x
y
,
o
b
tain
in
g
th
e
tr
a
jecto
r
y
o
f
m
o
tio
n
,
as
well
as
s
tu
d
y
in
g
th
em
f
o
r
s
tab
ilit
y
ca
n
b
e
u
s
ed
in
C
o
s
m
o
n
au
tics
.
I
n
a
d
d
itio
n
,
th
e
m
o
ti
o
n
o
f
ce
lest
ial
b
o
d
ies
in
th
e
p
er
p
en
d
icu
la
r
p
lan
e
o
f
th
e
n
ea
r
-
p
lan
etar
y
d
is
k
s
an
d
th
e
eq
u
ato
r
ial
p
lan
e
o
f
th
e
E
ar
th
is
v
er
y
im
p
o
r
tan
t f
o
r
s
tu
d
y
in
g
th
e
m
ec
h
an
ical
ch
ar
ac
ter
is
tics
o
f
th
e
m
o
tio
n
o
f
s
u
ch
ce
lest
ial
b
o
d
ies as a
co
m
et,
a
m
eteo
r
ite
[
1
]
-
[
3
]
.
W
h
en
s
ettin
g
u
p
n
u
m
er
ical
e
x
p
er
im
en
ts
,
m
at
h
em
atica
l
ca
l
cu
latio
n
s
f
o
r
m
o
d
elin
g
t
h
e
p
l
an
et
Satu
r
n
an
d
o
t
h
er
p
la
n
ets
with
r
in
g
s
,
s
u
ch
as
Ur
an
u
s
,
J
u
p
iter
,
Ne
p
tu
n
e,
also
wh
en
in
ter
p
r
etin
g
t
h
e
p
lan
e
o
f
th
e
g
alax
y
an
d
in
th
e
s
p
ac
e
i
n
d
u
s
tr
y
,
m
o
tio
n
a
r
o
u
n
d
d
is
c
-
s
h
ap
ed
b
o
d
ies,
in
clu
d
in
g
s
elf
-
g
r
a
v
itatin
g
o
n
es,
is
alwa
y
s
co
n
s
id
er
ed
[
4
]
,
[
5
]
.
T
h
e
p
u
r
p
o
s
e
o
f
th
is
r
esear
c
h
is
s
o
lu
tio
n
o
f
d
if
f
e
r
en
tial
eq
u
atio
n
s
o
f
m
o
tio
n
o
f
a
m
ater
ial
p
o
in
t
in
th
e
p
lan
e
p
e
r
p
en
d
icu
lar
to
th
e
p
lan
e
o
f
th
e
g
r
av
itatin
g
d
is
k
.
T
h
e
task
s
o
f
th
is
s
tu
d
y
in
clu
d
e
th
e
f
o
llo
win
g
item
s
:
−
A
p
p
ly
th
e
e
x
p
r
ess
io
n
f
o
r
th
e
p
o
ten
tial o
f
th
e
g
r
av
itatin
g
d
is
k
.
f
o
u
n
d
in
p
r
ev
io
u
s
s
tu
d
ies;
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
5
2
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci,
Vo
l.
24
,
No
.
3
,
Dec
em
b
er
2
0
2
1
:
1
3
0
7
-
1
3
1
4
1308
−
A
p
p
ly
G
ild
en
'
s
m
eth
o
d
to
th
e
in
v
esti
g
ated
s
y
s
tem
“
d
is
k
-
m
ater
ial
p
o
in
t
”
;
−
P
r
esen
t
th
e
s
o
lu
tio
n
an
aly
tically
an
d
ch
ec
k
th
e
co
n
s
is
ten
cy
o
f
th
e
r
esu
lts
o
f
th
e
m
ath
em
atica
l
f
o
u
n
d
atio
n
s
with
th
e
co
m
p
o
n
e
n
ts
o
f
th
e
class
ical
th
eo
r
y
o
f
m
o
tio
n
in
th
e
g
alax
y
.
2.
RE
S
E
ARCH
M
E
T
H
O
D
Un
d
er
ce
lest
ial
b
o
d
ies,
r
ep
r
e
s
en
tatio
n
s
o
f
m
o
v
in
g
c
o
s
m
ic
b
o
d
ies
ar
e
p
o
s
s
ib
le.
T
h
e
m
a
th
em
atica
l
m
o
d
el
o
f
th
e
p
o
te
n
tial
o
f
th
e
g
r
av
itatin
g
d
is
k
in
th
e
co
n
s
id
er
ed
ca
s
e
o
f
m
o
tio
n
o
f
a
m
ater
ia
l
p
o
in
t
in
th
e
p
lan
e
p
er
p
en
d
icu
lar
to
t
h
e
p
lan
e
o
f
t
h
e
g
r
av
itatin
g
d
is
k
ac
co
r
d
in
g
t
o
th
e
L
eg
e
n
d
r
e
f
o
r
m
u
la
h
as th
e
f
o
r
m
(
1
)
,
(
,
,
)
=
2
[
1
⋅
2
2
−
1
2
2
(
)
3
4
4
+
1
8
⋅
4
(
)
5
⋅
6
2
]
(
1
)
wh
er
e
is
:
R
-
th
e
r
ad
iu
s
o
f
th
e
g
r
av
itatin
g
r
o
u
n
d
th
in
d
is
k
;
r
-
th
e
d
is
tan
ce
f
r
o
m
t
h
e
ce
n
ter
o
f
th
e
d
is
k
t
o
th
e
m
ater
ial
p
o
in
t
P
;
θ
-
th
e
an
g
le
b
etwe
en
th
e
r
a
d
iu
s
v
ec
to
r
o
f
th
e
m
ater
ial
p
o
i
n
ts
P
an
d
th
e
p
lan
e
o
f
th
e
d
is
k
.
T
h
e
(
1
)
was
o
b
tai
n
ed
in
v
iew
o
f
th
e
ap
p
licatio
n
o
f
th
e
f
u
n
d
a
m
en
tal
th
eo
r
y
o
f
th
e
p
o
ten
tials
o
f
b
o
d
ies
o
f
ce
lest
ial
m
ec
h
an
ics,
d
etaile
d
in
[
6
]
-
[
9
]
,
as
th
e
c
o
n
ce
p
t o
f
th
e
f
o
r
ce
f
u
n
ctio
n
o
f
th
e
f
ield
o
f
attr
ac
tio
n
,
w
h
ich
is
al
s
o
ca
lled
th
e
p
o
ten
tial
u
s
e
d
.
T
h
e
m
o
v
em
e
n
t
o
f
a
m
ater
ia
l
p
o
in
t
in
th
e
p
lan
e
p
er
p
e
n
d
ic
u
lar
to
th
e
p
lan
e
o
f
th
e
g
r
av
itatin
g
d
is
k
o
cc
u
r
s
u
n
d
er
th
e
ac
tio
n
o
f
g
r
av
itatio
n
al
f
o
r
ce
s
.
T
h
ese
f
o
r
ce
s
ar
e
d
eter
m
in
ed
b
y
New
to
n
'
s
law
o
f
u
n
iv
e
r
s
al
g
r
av
itatio
n
.
T
o
s
o
lv
e
d
if
f
e
r
en
tial
,
th
e
(
2
)
d
escr
ib
in
g
th
e
i
n
v
esti
g
ated
m
o
tio
n
:
{
̈
−
̇
2
=
(
,
)
(
2
̇
)
=
(
2
)
th
e
Gild
en
m
eth
o
d
d
escr
ib
e
d
i
n
th
e
wo
r
k
s
o
f
A.
Po
in
ca
r
é
[
1
0
]
is
ap
p
lied
.
3.
RE
VI
E
W
O
F
T
H
E
RE
SE
A
RCH
Nwa
ig
we
[
1
1
]
d
escr
ib
e
in
d
etail
th
e
r
elev
an
ce
o
f
th
e
in
v
esti
g
ated
p
r
o
b
lem
o
f
th
e
r
eso
n
an
t
r
elatio
n
s
h
ip
,
wh
ic
h
a
r
e
p
e
r
p
en
d
icu
lar
to
th
e
m
ain
p
lan
e
an
d
h
av
e
a
n
alm
o
s
t
p
er
io
d
ic
f
o
r
ce
o
f
ac
tio
n
d
ir
ec
ted
to
th
e
ce
n
ter
o
f
s
y
m
m
et
r
y
o
f
th
e
Gala
x
y
,
wh
ich
ca
n
lead
to
a
s
tar
m
o
v
in
g
awa
y
f
r
o
m
th
e
p
lan
e.
C
ases
in
w
h
ich
th
e
s
tab
le
p
o
s
itio
n
o
f
t
h
e
s
tu
d
ied
m
o
v
e
m
en
t
is
v
io
lated
is
th
e
m
ain
p
r
o
b
lem
.
T
h
is
wo
r
k
clar
if
ies
th
e
lim
itatio
n
s
th
at
ca
n
b
e
im
p
o
s
ed
o
n
th
e
s
h
ap
es
o
f
ellip
tical
g
alax
ies
f
r
o
m
o
b
s
er
v
atio
n
s
o
f
t
h
eir
n
u
clea
r
d
is
k
s
,
an
d
m
ar
k
s
th
e
m
o
s
t
im
p
o
r
tan
t
m
o
m
en
ts
o
f
r
o
tatin
g
s
tar
s
at
l
ar
g
e
r
ad
ii
in
th
e
d
is
k
o
f
a
g
alax
y
with
a
r
o
tatin
g
ce
n
tr
al
b
ar
.
An
y
b
ar
r
e
d
g
alax
y
will
h
av
e
a
r
in
g
o
f
th
ese
s
tar
s
.
A
co
m
p
lete
a
n
aly
s
is
o
f
th
e
im
p
o
r
tan
c
e
o
f
th
is
r
in
g
r
eq
u
ir
es
th
at
th
e
th
eo
r
y
o
f
th
is
ar
ticle
b
e
ex
ten
d
ed
to
in
clu
d
e
s
elf
-
g
r
av
ity
o
f
th
e
d
is
k
.
B
u
t
th
e
m
ec
h
an
is
m
d
is
cu
s
s
ed
h
er
e
ca
n
h
elp
u
s
u
n
d
er
s
tan
d
th
e
cu
r
v
at
u
r
es
an
d
co
r
r
u
g
atio
n
s
in
t
h
e
g
as
d
is
k
s
o
f
g
alax
ies,
th
e
k
in
em
atics o
f
s
tar
s
in
th
e
v
icin
ity
o
f
th
e
Su
n
,
an
d
th
e
s
h
ar
p
e
d
g
es th
at
m
an
y
s
tellar
d
is
k
s
h
av
e.
I
n
th
e
wo
r
k
b
y
B
h
an
d
ar
e
an
d
Pfa
lzn
er
[
1
2
]
,
th
e
in
f
lu
en
ce
o
f
th
e
p
ar
ab
o
lic
p
ass
ag
e
o
f
a
n
o
t
h
er
s
tar
o
n
th
e
ac
cr
etio
n
d
is
k
ar
o
u
n
d
o
n
e
s
tar
was
in
v
esti
g
ated
.
I
n
d
ir
e
ct
co
p
lan
ar
ap
p
r
o
ac
h
,
th
e
d
is
k
is
tid
ally
ex
p
o
s
ed
.
I
n
th
is
p
ap
er
,
th
e
q
u
esti
o
n
o
f
t
h
e
m
u
tu
ally
p
er
p
e
n
d
icu
lar
ar
r
an
g
em
en
t
o
f
th
e
d
is
k
an
d
th
e
o
r
b
it
is
co
n
s
id
er
ed
,
an
d
co
n
clu
s
io
n
s
p
r
esen
ted
ca
n
b
e
ap
p
lied
to
m
o
d
els o
f
d
o
u
b
l
e
s
tar
f
o
r
m
atio
n
.
Acc
o
r
d
in
g
t
o
Fu
jim
o
to
an
d
T
an
ah
ash
i
[
1
3
]
,
th
e
f
r
ee
p
r
ec
ess
io
n
o
f
a
th
in
s
elf
-
g
r
av
itatin
g
d
is
k
o
f
a
co
n
tin
u
o
u
s
m
e
d
iu
m
was
in
v
es
tig
ated
.
T
h
e
ass
u
m
p
tio
n
s
o
f
L
in
d
en
B
ell
th
at
th
e
o
b
s
er
v
ed
b
en
d
in
g
o
f
th
e
o
u
ter
p
ar
ts
o
f
th
e
g
alac
tic
p
lan
e
ca
n
b
e
ex
p
lain
e
d
b
y
th
e
f
r
ee
p
r
ec
ess
io
n
o
f
th
e
Gala
x
y
a
r
e
co
n
f
i
r
m
ed
.
L
ar
g
e
-
s
ca
le
non
-
cir
c
u
lar
g
as
m
o
tio
n
is
g
en
er
ated
f
o
r
g
as
at
a
v
er
t
ical
d
is
tan
ce
f
r
o
m
th
e
g
alac
tic
eq
u
ato
r
ial
p
lan
e.
Mu
ch
atten
tio
n
is
p
aid
to
th
e
alm
o
s
t
p
ar
allel
m
o
tio
n
o
f
th
e
g
alac
ti
c
p
lan
e,
an
d
th
e
in
s
tan
tan
eo
u
s
an
g
u
lar
v
elo
city
is
an
aly
ze
d
wh
e
n
m
o
v
in
g
p
er
p
en
d
icu
lar
to
th
e
a
x
is
o
f
s
y
m
m
etr
y
o
f
th
e
g
alax
y
.
As
s
tated
b
y
I
n
g
r
am
a
n
d
M
o
tta
[
1
4
]
,
th
e
co
n
s
eq
u
e
n
ce
s
o
f
th
e
h
y
p
o
th
esis
th
at
th
e
d
is
k
s
p
o
s
s
es
s
ed
b
y
g
alax
ies
h
av
e
less
g
r
av
ity
th
an
s
tar
s
ar
e
in
v
esti
g
ated
.
T
h
is
i
s
ex
p
lain
ed
b
y
th
e
o
b
tain
e
d
an
aly
tical
s
o
lu
tio
n
o
f
th
e
p
r
o
b
lem
o
f
m
o
tio
n
a
r
o
u
n
d
th
e
g
alac
tic
d
is
k
:
t
h
e
m
o
v
em
e
n
ts
o
u
ts
id
e
th
e
p
lan
e
o
f
th
e
g
al
ax
y
d
if
f
er
in
s
m
all
f
lu
ctu
atio
n
s
f
r
o
m
th
e
m
o
v
em
en
t
o
f
th
e
i
n
ter
n
al
p
a
r
ts
.
Acc
o
r
d
in
g
to
B
ah
ca
ll
[
1
5
]
,
th
e
s
o
lu
tio
n
o
f
two
b
asic
B
o
ltzm
an
n
an
d
Po
is
s
o
n
eq
u
at
io
n
s
in
th
e
p
er
p
e
n
d
icu
lar
ax
i
s
o
f
th
e
g
alac
tic
d
is
k
is
o
b
ta
i
n
ed
.
T
h
e
s
o
lu
tio
n
s
o
b
tain
ed
d
ep
en
d
o
n
th
e
r
atio
o
f
th
e
m
ass
es
o
f
th
e
ce
lest
ial
o
b
jects
u
n
d
er
co
n
s
id
er
atio
n
.
T
h
ese
r
esu
lts
h
av
e
th
eir
o
wn
a
p
p
licatio
n
in
th
e
d
i
s
tr
ib
u
tio
n
o
f
s
tar
lig
h
t
p
er
p
en
d
icu
lar
to
th
e
d
is
k
s
.
T
h
e
co
n
cl
u
s
io
n
s
ar
e
m
ad
e
b
y
an
aly
zin
g
th
e
o
b
t
ain
e
d
ex
ac
t n
u
m
er
ical
an
d
a
p
p
r
o
x
im
ate
an
a
ly
tical
s
o
lu
tio
n
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
Differ
en
tia
l e
q
u
a
tio
n
s
o
f m
o
ti
o
n
o
f a
ma
teri
a
l p
o
in
t in
th
e
p
erp
en
d
icu
la
r
p
la
n
e
…
(
Zh
en
is
g
u
l R
a
kh
metu
llin
a
)
1309
Acc
o
r
d
in
g
to
Po
g
g
io
et
a
l.
[
1
6
]
,
it
was
ass
u
m
ed
th
at
a
co
s
m
ic
f
all
o
n
g
alax
ies
wo
u
ld
lead
to
a
r
eo
r
ien
tatio
n
o
f
th
e
an
g
u
lar
m
o
m
en
tu
m
v
ec
to
r
s
o
f
d
is
k
g
alax
ies.
I
n
s
id
e
th
e
o
p
tical
d
is
k
,
th
e
ef
f
ec
t
o
f
th
is
r
eo
r
ien
tatio
n
is
m
o
d
eled
u
s
in
g
a
co
n
s
tan
tly
ch
a
n
g
in
g
ax
is
y
m
m
etr
ic
r
ep
r
esen
tatio
n
o
f
th
e
p
o
te
n
tial.
T
h
e
co
n
s
id
er
ed
m
o
v
em
e
n
ts
ar
e
p
er
f
o
r
m
ed
at
an
a
n
g
le
in
th
e
p
lan
e
o
f
th
e
d
is
k
.
T
h
e
d
ev
iatio
n
s
o
b
tain
ed
d
e
p
en
d
o
n
th
e
r
ad
i
u
s
at
wh
ic
h
th
e
s
u
r
f
ac
e
d
en
s
ity
o
f
th
e
d
is
k
is
lo
w.
T
h
e
m
a
n
if
estatio
n
s
o
f
th
e
s
tu
d
ied
ef
f
ec
t
m
a
y
b
e
ass
o
ciate
d
with
th
e
in
clin
atio
n
o
f
th
e
c
o
r
e
o
f
th
e
d
is
k
o
f
th
e
Milk
y
W
ay
.
Mo
d
er
n
s
tu
d
ies
o
f
ex
tr
a
g
ala
ctic
m
o
lecu
lar
g
as
r
ea
c
h
th
e
s
ca
le
o
f
g
ian
t
s
tar
-
f
o
r
m
in
g
m
o
lecu
lar
clo
u
d
s
.
In
th
e
wo
r
k
by
Me
id
t
et
a
l
.
[
1
7
]
,
a
m
o
d
el
o
f
th
r
ee
-
d
i
m
en
s
io
n
al
g
as
m
o
tio
n
s
f
o
r
m
e
d
b
y
f
o
r
ce
f
u
n
ctio
n
s
f
r
o
m
th
e
g
r
av
itatio
n
al
in
f
lu
en
ce
o
f
th
e
g
alax
y
was
s
tu
d
ied
an
d
d
ev
el
o
p
ed
.
A
n
aly
zin
g
t
h
e
o
b
tain
ed
m
o
tio
n
m
o
d
els,
we
ca
n
co
n
clu
d
e
th
at
th
e
g
alax
y
im
p
o
s
es
p
r
ef
er
en
ti
al
r
estrictio
n
s
o
n
th
e
p
r
o
b
lem
s
o
f
s
tar
f
o
r
m
atio
n
.
Mo
n
teir
o
et
a
l.
[
1
8
]
a
r
e
d
e
v
o
ted
to
th
e
m
ain
th
e
o
r
etica
l
is
s
u
es
o
f
ce
lest
ial
m
ec
h
an
ics:
M
ea
s
u
r
em
en
t
o
f
th
e
g
alac
tic
p
o
ten
tial,
g
r
av
ity
,
is
o
th
er
m
al
ex
p
an
s
io
n
s
,
s
elf
-
c
o
n
s
is
ten
t
s
o
lu
tio
n
s
f
o
r
ρ
0
,
u
n
ce
r
tain
ties
o
f
lo
ca
l
b
u
l
k
d
en
s
ity
,
ca
lcu
latio
n
o
f
s
u
r
f
ac
e
m
ass
d
en
s
ity
,
s
im
p
le
p
ar
am
e
tr
izatio
n
o
f
p
la
u
s
ib
le
f
u
n
ctio
n
s
Kz
.
Acc
o
r
d
in
g
to
Ma
ts
ak
o
s
an
d
Kö
n
ig
l
[
1
9
]
,
th
e
tim
e
-
d
ep
en
d
en
t
s
ca
le
i
s
d
eter
m
in
ed
f
o
r
th
e
co
n
s
id
er
ed
ca
s
es
o
f
a
d
is
k
h
av
in
g
a
f
lat
o
r
b
ital
co
m
p
o
n
en
t.
I
f
th
e
in
clin
a
tio
n
o
f
th
e
d
is
k
ex
ce
ed
s
th
e
o
p
en
in
g
a
n
g
le
o
f
th
e
d
is
k
,
th
e
n
th
e
tid
al
d
is
p
lace
m
e
n
t
in
s
id
e
th
e
d
is
k
is
tr
an
s
o
n
ic.
I
t
was
f
o
u
n
d
th
at
t
h
e
h
y
d
r
o
d
y
n
am
ic
in
s
tab
ilit
ies
ass
o
ciate
d
with
th
e
in
ter
n
al
s
h
if
t le
d
to
ad
d
itio
n
al
s
ca
tter
in
g
,
wh
ich
will a
llo
w
ch
an
g
in
g
th
e
tim
e
s
ca
le.
As
s
tated
b
y
Asl
an
o
v
[
2
0
]
,
th
e
m
eth
o
d
o
f
s
m
al
l
p
ar
a
m
eter
s
is
ap
p
lied
to
co
n
s
tr
u
ct
p
er
io
d
ic
s
o
lu
tio
n
s
to
th
e
p
r
o
b
lem
b
ein
g
s
o
lv
ed
,
s
y
m
m
etr
ic
in
s
h
ap
e
an
d
s
tr
u
ct
u
r
e
in
th
e
ca
s
e
u
n
d
er
co
n
s
id
er
a
tio
n
.
T
h
e
d
y
n
am
ic
co
m
p
r
ess
io
n
o
f
th
e
b
o
d
y
is
t
ak
en
as
a
s
m
all
p
ar
am
eter
.
T
h
e
m
ain
b
o
d
ies
ar
e
ax
is
y
m
m
etr
ic,
th
e
p
lan
e
o
f
s
y
m
m
etr
y
o
f
wh
ich
is
p
er
p
en
d
icu
lar
to
th
e
ax
is
o
f
s
y
m
m
etr
y
.
In
th
e
w
o
r
k
b
y
Hu
ň
ad
y
et
a
l.
[
2
1
]
,
t
h
e
r
esu
lts
o
f
th
r
ee
ex
p
er
im
e
n
ts
ar
e
p
r
esen
ted
,
in
wh
ich
o
s
cillato
r
y
m
o
tio
n
s
ar
o
u
n
d
a
f
lat
d
is
k
h
a
v
in
g
r
o
tatio
n
ar
e
s
tu
d
ied
.
T
h
ese
r
esu
lts
ar
e
ch
ar
ac
ter
ized
b
y
m
o
r
e
p
r
o
n
o
u
n
ce
d
f
r
e
q
u
en
c
y
r
esp
o
n
s
e
s
p
ec
tr
a.
T
h
e
ess
en
ce
o
f
th
e
wo
r
k
b
y
L
eg
ez
a
[
2
2
]
i
s
ex
p
lain
ed
b
y
its
d
if
f
er
en
ce
f
r
o
m
o
th
er
s
tu
d
ies,
b
y
th
e
f
ac
t
th
at
th
e
p
r
o
b
lem
u
n
d
er
s
tu
d
y
in
p
r
e
v
io
u
s
s
o
u
r
c
es
o
f
o
th
er
au
th
o
r
s
was
in
ter
p
r
eted
o
n
g
e
o
m
etr
ic
s
u
r
f
ac
e
s
o
f
th
e
s
ec
o
n
d
o
r
d
er
.
T
o
o
b
tain
an
a
n
aly
tical
s
o
lu
tio
n
,
class
ical
m
eth
o
d
s
ar
e
u
s
ed
in
th
e
wo
r
k
.
T
h
e
f
u
n
ctio
n
al
o
f
tim
e,
with
th
e
h
elp
o
f
wh
ich
th
e
d
if
f
e
r
en
tial
eq
u
a
tio
n
s
o
f
th
e
s
p
atial
b
r
ac
h
is
tr
o
ch
r
o
n
ar
e
co
n
s
tr
u
cte
d
,
ar
e
d
e
r
iv
ed
a
n
aly
tically
.
T
h
e
r
esear
c
h
r
esu
lts
ar
e
illu
s
tr
ated
g
r
ap
h
ically
.
Stab
le
ac
cr
etio
n
d
is
k
s
ar
e
co
n
s
id
er
ed
,
an
d
in
[
2
3
]
atten
tio
n
is
p
aid
to
th
e
r
o
le
o
f
im
p
o
r
tan
t
elem
en
ts
in
th
e
p
h
y
s
ics
o
f
ac
c
r
etio
n
d
is
k
s
.
Mo
d
elin
g
o
f
th
e
d
is
k
m
ad
e
it
p
o
s
s
ib
le
to
c
o
n
s
tr
u
ct
a
ll
co
m
b
in
atio
n
s
o
f
v
is
co
u
s
an
d
r
ad
iatio
n
p
r
o
ce
s
s
es.
T
h
e
wo
r
k
b
y
Bu
et
a
l
.
[
2
4
]
p
r
esen
ts
a
class
ical
th
eo
r
etica
l
m
ater
ial
o
n
t
h
e
in
ter
ac
tio
n
b
etwe
en
p
ar
ticles
d
ep
en
d
in
g
o
n
th
e
d
is
tan
ce
.
C
o
n
s
id
er
ed
in
ter
ac
tio
n
s
b
etw
ee
n
s
tar
s
an
d
o
th
e
r
g
r
av
itatin
g
m
ass
es
in
th
e
d
y
n
am
ics
o
f
g
r
a
v
itatin
g
s
y
s
tem
s
s
h
o
u
ld
b
e
d
ec
is
iv
e.
T
h
e
p
ap
er
a
n
aly
ze
s
th
e
p
r
o
p
er
ties
o
f
in
d
i
v
id
u
al
s
tar
s
,
th
e
m
o
tio
n
o
f
s
tar
s
,
s
o
lar
an
d
lu
n
ar
ec
lip
s
es
u
s
in
g
th
e
laws
o
f
New
to
n
ian
m
ec
h
an
ics.
T
h
e
wo
r
k
b
y
T
en
jes
et
a
l
[
2
5
]
h
as
a
n
o
v
elty
an
d
r
elev
a
n
ce
in
t
h
at
th
e
r
esear
ch
e
r
s
p
r
o
p
o
s
ed
a
n
ew
m
eth
o
d
f
o
r
th
e
a
n
aly
tical
s
o
lu
tio
n
o
f
g
as
-
d
y
n
am
ic
eq
u
atio
n
s
ab
o
u
t
co
m
p
letely
s
tab
le
m
o
tio
n
s
ar
o
u
n
d
th
e
d
is
k
g
alax
y
.
L
im
itatio
n
s
o
n
th
e
a
p
p
licatio
n
o
f
t
h
e
p
r
o
p
o
s
ed
m
eth
o
d
with
in
th
e
f
r
am
ewo
r
k
o
f
m
ec
h
a
n
ical
an
d
g
eo
m
etr
ic
s
tr
u
ctu
r
es
an
d
p
r
o
p
er
ties
o
f
th
e
d
is
k
ar
e
g
iv
en
.
T
h
e
d
if
f
er
e
n
tial
eq
u
atio
n
s
o
f
v
a
r
io
u
s
tech
n
o
lo
g
ical
p
r
o
ce
s
s
es
an
d
d
eter
m
in
is
tic
ch
ao
tic
s
y
s
tem
s
wer
e
d
ec
i
p
h
er
ed
in
t
h
e
r
esear
c
h
[
2
6
]
-
[
2
9
]
.
T
h
e
m
o
s
t
im
p
o
r
tan
t
is
th
e
s
tu
d
y
o
f
th
e
r
a
n
d
o
m
n
atu
r
e
o
f
ch
a
o
tic
s
ig
n
als an
d
im
ag
es.
In
th
e
w
o
r
k
by
Sid
d
ik
i
et
a
l.
[
3
0
]
,
[
3
1
]
,
co
n
ce
n
tr
ic
r
i
n
g
s
wer
e
ch
o
s
en
f
o
r
th
e
d
is
k
m
o
d
el,
an
d
ca
lcu
latio
n
s
wer
e
p
er
f
o
r
m
e
d
f
o
r
th
e
m
o
m
e
n
ts
o
f
m
o
tio
n
i
n
th
e
n
o
n
lin
ea
r
m
o
d
e
,
it
was
s
h
o
wn
th
at
s
tab
le,
s
tr
o
n
g
ly
c
u
r
v
ed
p
r
ec
ess
in
g
e
q
u
ilib
r
iu
m
s
tates
ar
e
p
o
s
s
ib
le.
T
h
ese
eq
u
ilib
r
iu
m
co
n
f
ig
u
r
atio
n
s
o
b
e
y
th
e
s
ca
lin
g
r
elatio
n
an
d
d
ep
e
n
d
o
n
th
e
d
is
k
f
r
eq
u
e
n
cy
r
esp
o
n
s
e.
T
h
e
m
a
in
r
esu
lt is
th
at
d
u
e
to
s
elf
-
g
r
av
ity
,
th
e
co
n
s
id
er
ed
ty
p
es o
f
d
is
k
s
r
etain
th
ei
r
s
tate
in
a
tem
p
o
r
ar
y
m
o
d
e
i
n
d
ep
e
n
d
en
tly
f
r
o
m
o
u
ts
id
e.
A
n
ew
m
eth
o
d
f
o
r
d
eter
m
in
i
n
g
th
e
m
ass
d
en
s
ity
o
f
th
e
g
a
lactic
d
is
k
s
u
r
f
ac
e
is
s
h
o
wn
in
[
3
2
]
.
T
o
ap
p
ly
th
e
ab
o
v
e
m
eth
o
d
,
it
is
n
ec
ess
ar
y
to
tak
e
in
to
ac
co
u
n
t
th
e
p
h
y
s
ical
ch
ar
ac
ter
is
tics
o
f
th
is
s
y
s
tem
.
T
h
e
an
aly
s
is
is
ca
r
r
ied
o
u
t f
o
r
m
o
r
e
s
u
itab
le
ca
s
es o
f
ap
p
licatio
n
o
f
th
is
m
eth
o
d
.
Acc
o
r
d
in
g
to
Par
k
e
r
[
3
3
]
,
th
e
r
esu
lts
o
f
a
s
tu
d
y
o
f
th
e
p
r
o
p
a
g
atio
n
o
f
h
y
d
r
o
m
ag
n
etic
wa
v
e
s
with
lo
w
f
r
eq
u
e
n
cy
p
h
en
o
m
en
a
a
r
e
p
r
esen
ted
,
an
d
th
e
d
er
iv
atio
n
o
f
th
e
e
q
u
atio
n
th
at
m
a
k
es
u
p
th
e
m
ath
e
m
atica
l
m
o
d
el
o
f
th
is
p
r
o
b
lem
is
o
b
ta
in
ed
.
Fo
r
th
e
r
esu
lts
o
b
tain
ed
,
it
is
im
p
o
r
tan
t
to
tak
e
i
n
to
ac
co
u
n
t
s
elf
-
g
r
av
ity
.
As
s
tated
b
y
Ko
h
et
a
l
.
[
3
4
]
,
a
m
eth
o
d
is
d
escr
ib
ed
th
at
co
m
b
in
es
th
e
s
o
lu
tio
n
o
f
p
r
o
b
lem
s
in
o
n
e
s
y
s
tem
o
f
r
o
tatin
g
an
d
s
tatio
n
ar
y
d
is
k
s
.
T
h
e
p
ap
er
d
escr
ib
es
in
d
etail
t
h
e
co
m
p
a
r
is
o
n
o
f
t
h
e
an
aly
tic
al
s
o
lu
tio
n
with
th
e
o
b
tain
ed
n
u
m
er
ical
im
p
lem
en
t
atio
n
.
Acc
o
r
d
in
g
t
o
Ag
ap
ito
u
et
a
l
.
[
3
5
]
,
th
e
elec
tr
o
m
ag
n
etic
p
r
o
p
er
ties
o
f
a
f
lat
th
i
n
cir
cu
lar
d
is
k
co
n
s
is
tin
g
o
f
co
n
ce
n
tr
ic
r
in
g
s
wer
e
s
tu
d
ied
,
wh
ich
ca
n
l
ea
d
to
th
e
m
an
if
estatio
n
in
class
ical
s
tar
s
.
T
h
e
s
o
lu
tio
n
o
f
n
o
n
lin
ea
r
s
p
ir
al
-
lik
e
p
h
en
o
m
en
a
in
p
r
o
to
p
lan
et
ar
y
d
is
k
s
is
d
escr
ib
ed
in
[
3
6
]
.
T
h
e
p
h
en
o
m
en
o
n
lead
s
to
a
r
ap
id
g
as p
r
o
p
ag
atio
n
in
a
p
e
r
p
en
d
icu
lar
d
ir
ec
ti
o
n
to
th
e
m
id
d
le
p
lan
e
o
f
th
e
d
is
k
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
5
2
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci,
Vo
l.
24
,
No
.
3
,
Dec
em
b
er
2
0
2
1
:
1
3
0
7
-
1
3
1
4
1310
T
h
e
wo
r
k
by
T
en
o
r
io
-
T
ag
le
an
d
B
o
d
e
n
h
eim
er
[
3
7
]
is
d
ev
o
ted
to
th
e
s
tu
d
y
of
t
h
e
i
n
ter
s
tellar
m
ed
iu
m
,
th
eir
d
is
tr
ib
u
tio
n
d
e
n
s
ity
in
th
e
s
p
ir
al
s
tr
u
ctu
r
es
of
th
e
Gala
x
y
,
tak
in
g
i
n
to
ac
co
u
n
t
ch
em
ical
a
n
d
p
h
y
s
ical
p
r
o
p
er
ties
.
As
s
tated
by
Falco
et
al
.
[
3
8
]
,
t
h
e
r
esu
lts
of
th
e
s
tu
d
y
of
t
h
e
co
n
tin
u
ity
eq
u
ati
on
of
th
e
f
lo
w
d
en
s
ity
by
g
eo
d
esic
ch
ar
ac
ter
is
tics
an
d
th
eir
ap
p
r
o
x
im
atio
n
ar
e
p
r
esen
ted
.
Af
ter
an
ad
eq
u
ate
ap
p
r
o
x
im
atio
n
of
th
e
tr
ajec
t
o
r
ies
of
in
d
iv
i
d
u
al
p
h
o
to
n
s
f
o
r
th
is
p
r
o
b
lem
,
ap
p
r
o
x
im
a
te
s
o
lu
tio
n
s
of
th
e
co
n
tin
u
ity
eq
u
atio
n
a
r
e
o
b
tain
ed
.
T
h
e
p
ar
ticl
es
in
t
h
e
m
e
d
iu
m
u
n
d
er
s
tu
d
y
,
m
o
v
in
g
to
war
d
s
th
e
ce
n
ter
of
th
e
d
is
k
in
a
p
er
p
en
d
ic
u
lar
d
ir
ec
ti
o
n
,
r
ec
eiv
e
a
lar
g
e
ac
ce
ler
atio
n
,
wh
ich
is
n
o
t
alm
o
s
t
ju
s
tifie
d
by
t
h
e
r
elativ
is
tic
th
eo
r
y
.
Acc
o
r
d
in
g
to
Gh
o
s
h
an
d
L
a
m
b
[
3
9
]
,
t
h
e
r
esu
lts
ar
e
an
aly
ze
d
,
s
y
s
tem
atize
d
an
d
p
r
esen
ted
,
wh
ich
co
n
s
is
t
in
th
e
lo
ca
tio
n
of
th
e
d
is
k
d
ep
e
n
d
in
g
on
t
h
e
in
te
g
r
a
l
m
ag
n
etic
v
o
ltag
e
ac
tin
g
on
t
h
e
d
is
k
m
ed
iu
m
.
In
p
ap
er
by
Me
r
r
if
ield
[
4
0
]
,
th
e
d
is
tr
ib
u
tio
n
of
t
h
e
lin
e
-
of
-
s
ig
h
t
v
elo
cities
of
a
d
is
k
g
ala
x
y
with
its
o
b
v
e
r
s
e
s
id
e
was
in
v
esti
g
ated
.
In
th
e
p
r
o
b
lem
u
n
d
er
s
tu
d
y
,
th
e
o
b
t
ain
ed
m
ath
e
m
atica
l
ex
p
r
ess
io
n
s
of
th
e
d
en
s
ity
d
is
tr
ib
u
tio
n
m
o
d
el
of
a
Gala
x
y
p
er
p
en
d
ic
u
lar
to
th
e
p
lan
e
le
ad
to
s
ig
n
if
ican
tly
d
if
f
er
e
n
t
f
o
r
m
s
of
th
e
o
b
s
er
v
e
d
ch
an
g
e
in
th
e
law
of
m
o
tio
n
d
ep
en
d
in
g
on
tim
e.
4.
RE
SU
L
T
AND
DI
SCUS
SI
O
N
4
.
1
.
R
o
le
o
f
a
ux
ilia
ry
s
y
m
bo
ls
T
o
s
o
lv
e
d
if
f
er
en
tial
eq
u
atio
n
s
,
we
u
s
e
th
e
Gild
en
m
eth
o
d
d
escr
ib
ed
in
th
e
wo
r
k
s
o
f
A.
Po
in
ca
r
é
[
1
0
]
.
Acc
o
r
d
in
g
to
th
e
p
r
o
p
o
s
ed
ch
o
ice
o
f
t
h
e
in
d
ep
e
n
d
en
t
v
ar
iab
le
A.
Po
in
ca
r
é
s
h
o
u
ld
b
e
tak
en
s
o
th
at
th
e
eq
u
atio
n
s
o
f
m
o
tio
n
h
av
e
a
f
o
r
m
s
im
ilar
t
o
th
e
eq
u
atio
n
s
o
f
m
o
tio
n
o
f
a
m
ater
ial
p
o
in
t
in
t
h
e
p
la
n
e
o
f
t
h
e
d
is
k
.
Fo
r
th
is
,
we
ac
ce
p
t th
e
c
o
n
v
en
tio
n
s
o
f
th
e
Gild
en
m
eth
o
d
[
1
0
]
b
y
(
3
)
:
0
=
√
2
,
(
3
)
wh
er
e
c
is
a
n
ew
co
n
s
tan
t.
I
f
we
tak
e
θ
0
as
an
in
d
ep
en
d
en
t
v
ar
iab
le,
th
en
t
h
e
s
ec
o
n
d
o
f
(
2
)
will
b
e
wr
itten
in
t
h
e
f
o
r
m
an
d
in
s
tead
o
f
th
e
v
a
r
iab
le
t
an
d
th
e
p
o
lar
an
g
le
θ
u
s
in
g
(
3
)
to
e
n
ter
th
e
in
d
ep
e
n
d
en
t v
ar
iab
le
θ
0
an
d
th
e
r
ec
i
p
r
o
ca
l
d
is
tan
ce
u,
th
en
a
tr
an
s
f
o
r
m
ed
s
y
s
tem
o
f
eq
u
atio
n
s
r
e
p
r
ese
n
ti
n
g
th
e
m
at
h
em
atica
l m
o
d
el
is
o
b
tain
(
4
)
an
d
(
5
)
:
2
0
2
=
2
[
(
3
8
−
5
8
2
2
)
⋅
2
−
35
64
2
2
4
]
(
4
)
2
0
2
+
(
0
)
2
−
=
−
[
(
3
2
4
2
2
+
45
2
9
4
4
)
+
(
9
2
4
2
2
−
25
2
7
4
4
)
⋅
2
−
−
175
2
9
4
4
4
]
(
5
)
T
h
e
an
alo
g
y
w
ith
th
e
eq
u
atio
n
o
f
m
o
tio
n
o
f
a
p
o
in
t
in
th
e
p
lan
e
o
f
th
e
d
is
k
will
b
ec
o
m
e
ev
en
m
o
r
e
o
b
v
io
u
s
[
1
0
]
if
we
n
o
te
t
h
at
in
s
u
b
s
eq
u
en
t
ca
lcu
latio
n
s
θ
it
will
d
if
f
er
litt
le
f
r
o
m
θ
0
.
Fro
m
(
5
)
,
ta
k
in
g
in
t
o
ac
co
u
n
t
th
e
o
r
d
er
o
f
s
m
alln
e
s
s
o
f
th
e
ex
p
r
ess
io
n
as
th
e
p
er
t
u
r
b
in
g
f
u
n
ctio
n
,
a
tr
a
n
s
f
o
r
m
ed
m
ath
em
atica
l
m
o
d
el
o
f
th
e
co
n
s
id
er
ed
m
o
tio
n
is
o
b
tain
ed
(
6
)
.
2
0
2
+
−
=
−
[
3
2
4
2
2
+
45
2
9
4
4
+
+
(
9
2
4
2
2
−
25
2
9
4
4
)
2
−
−
175
2
9
4
4
4
]
+
[
1
−
(
0
)
2
]
(
6
)
2
0
2
=
2
[
(
3
8
−
5
8
⋅
2
3
)
2
−
35
64
⋅
2
3
4
]
T
h
e
ch
o
ice
o
f
t
h
e
in
d
ep
en
d
en
t
v
ar
iab
le,
wh
ich
h
as
clea
r
ad
v
an
tag
es,
is
n
o
t
with
o
u
t
its
d
r
awb
ac
k
s
.
T
h
e
co
o
r
d
in
ates
u
a
n
d
θ
ar
e
e
x
p
r
ess
ed
as
f
u
n
ctio
n
s
o
f
u
s
in
g
θ
0
th
e
eq
u
atio
n
s
o
f
s
y
s
tem
(
6
)
,
th
e
le
f
t
-
h
an
d
s
id
es
o
f
wh
ich
h
av
e
a
s
im
p
le
f
o
r
m
2
0
2
an
d
2
0
2
+
+
,
an
d
th
e
r
ig
h
t
-
h
an
d
s
id
es
d
ep
en
d
n
o
t
o
n
l
y
o
n
u
a
n
d
θ
,
b
u
t
also
o
n
θ
0
.
T
h
e
v
a
r
iab
le
is
r
el
ated
to
tim
e
t
b
y
(
3
)
.
I
t
r
em
ain
s
to
ch
o
o
s
e
th
e
f
ir
s
t
ap
p
r
o
x
im
atio
n
b
y
th
e
Gild
en
ch
o
ice
in
th
e
s
am
e
way
as th
e
Kep
l
er
ian
m
o
tio
n
[
1
0
]
.
I
n
th
is
ca
s
e
(
7
):
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
Differ
en
tia
l e
q
u
a
tio
n
s
o
f m
o
ti
o
n
o
f a
ma
teri
a
l p
o
in
t in
th
e
p
erp
en
d
icu
la
r
p
la
n
e
…
(
Zh
en
is
g
u
l R
a
kh
metu
llin
a
)
1311
=
0
=
+
0
+
0
}
,
(
7
)
wh
er
e
,
ar
e
th
e
co
n
s
tan
ts
o
f
in
t
eg
r
atio
n
.
4
.
2
.
O
bta
ini
ng
a
n a
na
ly
t
ica
l so
lutio
n
T
h
e
d
if
f
er
e
n
tial
eq
u
atio
n
o
f
s
y
s
tem
(
6
)
af
ter
s
u
b
s
titu
tio
n
in
to
th
e
r
ig
h
t
s
id
e
o
f
th
e
ex
p
r
es
s
io
n
f
o
r
u
an
d
θ
0
f
r
o
m
(
7
)
,
ex
p
r
ess
ed
t
h
r
o
u
g
h
θ
0
,
ca
n
b
e
tr
a
n
s
f
o
r
m
ed
with
th
e
r
ig
h
t
s
id
e
in
th
e
f
o
r
m
o
f
h
ar
m
o
n
ics
with
co
ef
f
icien
ts
0
,
,
,
=
1
,
7
an
d
ca
n
b
e
d
eter
m
in
ed
b
y
th
e
f
o
llo
win
g
ex
p
r
es
s
io
n
s
d
ep
en
d
in
g
o
n
,
,
(
8
):
0
=
−
15
16
(
)
2
4
,
с
1
=
−
12
16
2
−
345
512
4
2
−
45
512
4
3
,
1
=
3
16
2
−
15
10
(
)
3
4
−
115
512
4
3
−
135
512
4
2
,
2
=
−
70
1
92
(
)
2
4
,
2
=
3
8
(
)
2
2
−
5
8
(
)
4
4
−
345
256
(
)
2
4
2
−
135
256
(
)
2
4
2
,
3
=
15
128
(
)
3
4
−
15
512
4
2
−
15
512
4
3
,
3
=
−
225
128
(
)
3
4
−
225
512
4
−
225
512
4
2
,
с
4
=
0
,
4
=
−
175
128
(
)
2
4
2
−
45
128
(
)
2
4
2
+
15
16
(
)
2
4
−
35
64
(
)
4
4
,
(
8
)
5
=
105
128
(
)
3
4
+
225
512
4
2
+
65
512
4
3
,
5
=
−
105
128
(
)
3
4
−
155
512
4
3
+
15
512
4
2
,
6
=
105
128
(
)
2
4
,
6
=
−
105
256
(
)
2
4
2
+
105
256
(
)
2
4
2
,
7
=
105
512
4
2
−
35
512
4
3
,
7
=
−
35
512
4
3
+
105
512
4
2
.
Simp
lific
atio
n
s
of
th
e
f
ir
s
t
d
if
f
er
en
tial
eq
u
atio
n
of
th
e
s
y
s
tem
(
6
)
tak
in
g
in
to
ac
co
u
n
t
t
h
e
Gild
en
ch
o
ice
(
7
)
lead
it
to
an
in
h
o
m
o
g
en
eo
u
s
lin
ea
r
d
if
f
er
e
n
tial
eq
u
atio
n
of
th
e
s
ec
o
n
d
o
r
d
e
r
(
9
):
2
0
2
+
=
−
[
(
3
16
2
+
9
16
2
2
0
)
(
+
0
+
0
)
2
+
+
(
45
5
1
2
4
−
25
128
4
2
0
−
175
512
4
4
0
)
×
×
(
+
0
+
0
)
4
]
+
(
с
+
0
+
0
)
(
1
−
(
0
)
2
)
(
9
)
s
im
ilar
ly
,
th
e
ab
o
v
e
d
escr
ip
tio
n
o
f
th
e
tr
an
s
f
o
r
m
atio
n
f
o
r
th
e
s
ec
o
n
d
d
if
f
e
r
en
tial
(
6
)
ca
n
b
e
d
eter
m
in
e
d
b
y
t
h
e
f
o
llo
win
g
ex
p
r
ess
io
n
s
d
ep
en
d
in
g
o
n
,
,
.
th
e
co
ef
f
icien
ts
ar
e
d
eter
m
in
ed
b
y
th
e
f
o
llo
win
g
ex
p
r
ess
io
n
s
d
ep
en
d
i
n
g
o
n
,
,
,
,
=
1
,
9
(
10
):
1
=
2
0
1
−
0
2
+
1
2
0
1
1
=
−
15
16
(
с
)
2
2
−
5
2
7
(
)
4
4
+
65
2
9
(
)
2
4
3
−
65
2
8
(
)
2
4
2
+
∑
2
+
2
2
2
7
=
1
+
(
1
0
)
∑
+
1
+
+
1
2
(
+
1
)
6
=
1
+
1
2
∑
+
2
+
+
2
2
(
+
2
)
5
=
1
+
1
2
∑
+
2
−
+
2
2
(
+
2
)
5
=
1
−
1
4
1
1
u
n
d
er
t
h
ese
ass
u
m
p
tio
n
s
,
th
e
s
o
lu
tio
n
ca
n
b
e
r
e
p
r
esen
ted
(
1
1
):
=
0
+
′
+
1
+
2
+
3
+
4
+
5
+
6
+
7
+
8
+
и
9
+
и
10
+
и
11
+
и
12
+
и
13
+
и
14
+
и
15
(1
1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
5
2
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci,
Vo
l.
24
,
No
.
3
,
Dec
em
b
er
2
0
2
1
:
1
3
0
7
-
1
3
1
4
1312
i
n
(
1
1
)
,
ea
ch
ter
m
h
as a
m
ath
e
m
atica
l m
ea
n
in
g
an
d
r
e
p
r
esen
t
s
a
s
o
lu
tio
n
(
1
2
)
.
0
=
0
+
0
,
′
=
0
0
2
+
0
0
+
0
−
2
0
,
1
=
(
−
0
6
0
2
+
0
−
1
4
0
+
1
+
0
−
2
1
4
)
0
+
(
0
6
0
2
+
1
+
0
4
0
+
2
1
+
1
−
0
4
)
0
(
1
2
)
=
(
1
−
2
0
+
(
1
−
2
)
−
2
⋅
(
1
−
2
)
2
)
0
+
(
1
−
2
0
+
(
1
−
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0
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=
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и
=
1
1
−
2
(
0
+
0
)
,
=
9
,
15
Acc
o
r
d
in
g
to
Gild
en
'
s
in
ter
p
r
etatio
n
o
f
th
e
ap
p
licatio
n
o
f
t
h
e
m
eth
o
d
f
r
o
m
[
1
0
]
,
it
is
n
o
ted
th
at
in
s
u
b
s
eq
u
en
t
a
p
p
r
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x
im
atio
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s
o
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ts
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th
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ig
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ig
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etr
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ctio
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d
e
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ee
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ter
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0
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th
at
th
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s
e
o
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ia
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le
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o
es
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ig
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ican
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l
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ir
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as
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th
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ly
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Gild
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en
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o
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e,
is
th
at
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e
q
u
atio
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s
o
f
m
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tio
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ec
o
m
e
lin
ea
r
o
r
in
teg
r
ab
le
b
y
q
u
ad
r
atu
r
es
[
1
0
]
.
T
a
k
in
g
in
t
o
a
cc
o
u
n
t
t
h
at
th
e
o
p
p
o
s
ite
s
tatem
en
t,
an
d
th
e
last
ex
p
r
ess
io
n
s
,
a
g
r
ap
h
ical
v
is
u
a
lizatio
n
o
f
th
e
o
b
tain
e
d
a
n
aly
tical
s
o
lu
tio
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to
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lem
o
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ater
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lar
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av
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ain
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,
th
e
tr
ajec
to
r
y
o
f
m
o
tio
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u
ilt (
Fig
u
r
e
1
)
.
Fig
u
r
e
1
.
T
h
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tr
ajec
to
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p
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CO
NCLU
SI
O
N
T
h
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lest
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th
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A.
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T
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ased
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s
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to
Kep
ler
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t
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to
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im
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d
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ild
e
n
'
s
m
eth
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d
f
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s
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lv
in
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d
if
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a
m
ater
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k
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m
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d
o
l
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ca
n
b
e
s
u
cc
ess
f
u
lly
a
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p
lied
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e
d
ev
elo
p
m
en
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f
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twar
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u
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ical
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tr
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tem
s
f
o
r
a
s
p
ac
ec
r
af
t.
RE
F
E
R
E
NC
E
S
[1
]
A.
L.
Ku
n
i
tsy
n
a
n
d
A.
T.
T
u
re
sh
b
a
e
v
,
“
On
t
h
e
sta
b
il
iza
ti
o
n
of
r
e
lativ
e
e
q
u
il
i
b
riu
m
of
th
e
o
r
b
it
a
l
sta
ti
o
n
at
th
e
c
o
ll
in
e
a
r
l
ib
ra
ti
o
n
p
o
in
t
b
e
y
o
n
d
th
e
m
o
o
n
,
”
2
0
1
5
I
n
ter
n
a
t
io
n
a
l
Co
n
fer
e
n
c
e
on
M
e
c
h
a
n
ics
-
S
e
v
e
n
th
Po
lya
k
h
o
v
's
Rea
d
i
n
g
,
2
0
1
5
,
pp.
1
-
3,
d
o
i:
1
0
.
1
1
0
9
/P
OLYA
KH
OV
.
2
0
1
5
.
7
1
0
6
7
4
4
.
[2
]
J.
A.
Ru
iz
-
De
-
Az
u
a
,
V.
Ra
m
írez
,
H.
P
a
r
k
,
A.
C.
AU
G
é
a
n
d
A.
Ca
m
p
s,
"
As
se
ss
m
e
n
t
of
S
a
telli
te
Co
n
tac
ts
Us
in
g
P
re
d
ictiv
e
Al
g
o
ri
th
m
s
fo
r
Au
t
o
n
o
m
o
u
s
S
a
telli
te
Ne
two
r
k
s,"
in
IEE
E
Acc
e
ss
,
v
o
l.
8,
p
p
.
1
0
0
7
3
2
-
1
0
0
7
4
8
,
2
0
2
0
,
d
o
i:
1
0
.
1
1
0
9
/ACCE
S
S
.
2
0
2
0
.
2
9
9
8
0
4
9
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
Differ
en
tia
l e
q
u
a
tio
n
s
o
f m
o
ti
o
n
o
f a
ma
teri
a
l p
o
in
t in
th
e
p
erp
en
d
icu
la
r
p
la
n
e
…
(
Zh
en
is
g
u
l R
a
kh
metu
llin
a
)
1313
[3
]
H.
M.
I.
Alsh
a
m
y
,
H.
He
n
d
y
,
A.
E.
M
a
k
led
a
n
d
Y.
Z.
El
h
a
lwa
g
y
,
"
S
p
a
c
e
c
ra
ft
Orb
it
a
l
m
a
n
e
u
v
e
r
F
li
g
h
t
D
y
n
a
m
ics
S
imu
latio
n
a
n
d
Ve
rifi
c
a
ti
o
n
,
"
2
0
1
9
Ni
n
th
I
n
ter
n
a
ti
o
n
a
l
Co
n
fer
e
n
c
e
on
I
n
telli
g
e
n
t
C
o
mp
u
ti
n
g
a
n
d
In
f
o
rm
a
ti
o
n
S
y
ste
ms
(
ICICIS
)
,
p
p
.
3
4
3
-
3
4
9
,
2
0
1
9
,
d
o
i:
1
0
.
1
1
0
9
/ICICIS
4
6
9
4
8
.
2
0
1
9
.
9
0
1
4
7
0
2
.
[4
]
X.
Nin
g
,
M.
G
u
i,
J.
F
a
n
g
,
G.
Li
u
a
n
d
W.
Wu
,
"A
No
v
e
l
Au
t
o
n
o
m
o
u
s
Ce
les
ti
a
l
Na
v
ig
a
ti
o
n
M
e
t
h
o
d
Us
in
g
S
o
lar
Os
c
il
latio
n
Ti
m
e
De
lay
M
e
a
su
re
m
e
n
t,
"
in
IEE
E
T
ra
n
sa
c
ti
o
n
s
on
Aer
o
sp
a
c
e
a
n
d
El
e
c
tro
n
ic
S
y
ste
ms
,
v
o
l.
54,
n
o
.
3,
pp.
1
3
9
2
-
1
4
0
3
,
Ju
n
e
2
0
1
8
,
d
o
i
:
1
0
.
1
1
0
9
/T
AES
.
2
0
1
8
.
2
7
9
1
0
3
8
.
[5
]
V.
As
lan
o
v
a
n
d
A.
Led
k
o
v
,
"
Ch
a
o
ti
c
m
o
ti
o
n
of
a
p
a
ss
iv
e
s
p
a
c
e
o
b
jec
t
d
u
r
in
g
its
c
o
n
tac
tl
e
ss
io
n
b
e
a
m
tran
sp
o
rtati
o
n
,
"
2
0
2
0
In
ter
n
a
ti
o
n
a
l
C
o
n
fer
e
n
c
e
on
I
n
fo
rm
a
ti
o
n
T
e
c
h
n
o
l
o
g
y
a
n
d
N
a
n
o
tec
h
n
o
lo
g
y
(I
T
NT
)
,
p
p
.
1
-
6,
2
0
2
0
,
d
o
i:
1
0
.
1
1
0
9
/I
TNT4
9
3
3
7
.
2
0
2
0
.
9
2
5
3
1
8
5
.
[6
]
E.
On
o
r
i,
"
E
lem
e
n
tary
c
e
les
ti
a
l
m
e
c
h
a
n
ics
u
sin
g
M
a
tl
a
b
,
"
in
C
o
mp
u
ti
n
g
in
S
c
ien
c
e
&
En
g
in
e
e
rin
g
,
v
o
l.
3,
n
o
.
6,
pp.
48
-
53,
No
v
.
-
De
c
.
2
0
0
1
,
d
o
i:
1
0
.
1
1
0
9
/5
9
9
2
.
9
6
3
4
2
7
.
[7
]
X.
Nin
g
,
M.
G
u
i,
J.
F
a
n
g
,
G.
Li
u
a
n
d
Y.
Da
i,
"A
No
v
e
l
Diffe
re
n
ti
a
l
D
o
p
p
ler
M
e
a
su
re
m
e
n
t
-
Aid
e
d
Au
t
o
n
o
m
o
u
s
Ce
les
ti
a
l
Na
v
ig
a
ti
o
n
M
e
th
o
d
f
o
r
S
p
a
c
e
c
ra
ft
Du
rin
g
A
p
p
r
o
a
c
h
P
h
a
se
,
"
in
IE
EE
T
ra
n
sa
c
ti
o
n
s
on
Aer
o
sp
a
c
e
a
n
d
El
e
c
tro
n
ic
S
y
ste
ms
,
v
o
l.
5
3
,
no.
2,
pp.
5
8
7
-
5
9
7
,
A
p
ril
2
0
1
7,
d
o
i:
1
0
.
1
1
0
9
/T
AE
S
.
2
0
1
7
.
2
6
5
1
5
5
8
.
[8
]
D.
Ra
in
e
,
“
Ne
wto
n
ian
M
e
c
h
a
n
ics
:
A
M
o
d
e
ll
in
g
A
p
p
r
o
a
c
h
,
”
S
tyl
u
s
Pu
b
li
s
h
in
g
L
L
C
.
pp.
2
1
1
-
2
4
2
,
2
0
2
1
.
[9
]
A.
B.
Kh
a
sh
imo
v
,
"
Dia
g
n
o
st
ics
of
li
n
e
a
r
p
h
a
se
d
a
rra
y
fr
o
m
n
e
a
r
-
fi
e
ld
d
a
ta
u
si
n
g
it
e
ra
ti
v
e
re
g
u
lariz
a
ti
o
n
,
"
2
0
1
7
2
n
d
In
ter
n
a
t
io
n
a
l
Ur
a
l
Co
n
fer
e
n
c
e
on
M
e
a
su
re
me
n
ts
(Ur
a
lCo
n
)
,
p
p
.
3
3
0
-
3
3
5
,
2
0
1
7
,
d
o
i
:
1
0
.
1
1
0
9
/URALCON
.
2
0
1
7
.
8
1
2
0
7
3
2
.
[1
0
]
A.
D.
Bry
u
n
o
,
“
M
o
d
e
rn
M
e
th
o
d
s
of
Ce
les
ti
a
l
M
e
c
h
a
n
ics
,
”
M
e
c
h
a
n
i
c
s
of
S
o
li
d
s
,
v
o
l.
56,
n
o
.
1,
p
p
.
84
-
94,
2
0
2
1
,
d
o
i:
1
0
.
3
1
0
3
/
S
0
0
2
5
6
5
4
4
2
1
0
1
0
0
5
2
.
[1
1
]
D.
Nw
a
ig
we
,
“
On
th
e
c
o
n
v
e
rg
e
n
c
e
of
WKB
a
p
p
ro
x
ima
ti
o
n
s
of
th
e
d
a
m
p
e
d
M
a
t
h
ieu
e
q
u
a
ti
o
n
,
”
J
o
u
rn
a
l
of
M
a
t
h
e
ma
ti
c
a
l
Ph
y
sic
s
,
v
o
l.
6
2
,
no
6,
J
u
n
e
2
0
2
1
,
d
o
i
:
1
0
.
1
0
6
3
/
1
.
5
1
4
5
2
6
7
.
[1
2
]
A.
Bh
a
n
d
a
re
,
a
n
d
S
.
P
fa
lzn
e
r,
“
D
ES
TINY:
Da
tab
a
se
fo
r
th
e
Eff
e
c
t
s
o
f
S
Tellar
e
n
c
o
u
n
ters
o
n
d
Isk
s
a
n
d
p
laN
e
tary
sy
ste
m
s,”
Co
mp
u
t
a
ti
o
n
a
l
Astro
p
h
y
sic
s
a
n
d
C
o
sm
o
lo
g
y
,
v
o
l.
6
,
n
o
3
,
p
p
.
1
-
8
,
2
0
1
9
,
d
o
i:
1
0
.
1
1
8
6
/s4
0
6
6
8
-
0
1
9
-
0
0
3
0
-
3
.
[1
3
]
M
.
F
u
ji
m
o
t
o
a
n
d
Y.
Tan
a
h
a
sh
i,
“
Ro
l
li
n
g
M
o
ti
o
n
s
o
f
In
ters
te
ll
a
r
G
a
s
in
th
e
G
a
lax
y
,”
Pu
b
li
c
a
ti
o
n
s
o
f
th
e
Astro
n
o
mic
a
l
S
o
c
iety
o
f
J
a
p
a
n
,
v
o
l.
2
3
,
n
o
.
1
3
,
p
p
.
7
-
12
,
1
9
7
1
.
[1
4
]
A.
In
g
ra
m
,
a
n
d
S
.
M
o
tt
a
,
“
A
re
v
i
e
w
o
f
q
u
a
si
-
p
e
rio
d
ic
o
sc
il
latio
n
s
fro
m
b
lac
k
h
o
le
X
-
ra
y
b
in
a
ries
:
Ob
se
rv
a
ti
o
n
a
n
d
th
e
o
ry
,
”
Ne
w
Astro
n
o
my
Rev
iews
,
v
o
l
.
8
5
,
p
p
.
1
0
1
5
2
4
,
2
0
1
9
,
d
o
i:
1
0
.
1
0
1
6
/
j.
n
e
wa
r.
2
0
2
0
.
1
0
1
5
2
4
.
[1
5
]
J.
N.
Ba
h
c
a
ll
,
“
Th
e
d
istr
ib
u
ti
o
n
o
f
sta
rs
p
e
rp
e
n
d
i
c
u
lar
to
g
a
lac
ti
c
d
is
k
,”
T
h
e
Astr
o
p
h
y
sic
a
l
J
o
u
rn
a
l,
v
o
l.
2
7
6
,
p
p
.
156
-
1
6
8
,
1
9
8
4
[1
6
]
E.
P
o
g
g
io
e
t
a
l.
,
“
Ev
i
d
e
n
c
e
o
f
a
d
y
n
a
m
ica
ll
y
e
v
o
lv
i
n
g
G
a
lac
ti
c
w
a
rp
,
”
Na
t
Astro
n
,
v
o
l.
4
,
p
p
.
5
9
0
–
5
9
6
,
2
0
2
0
,
d
o
i:
1
0
.
1
0
3
8
/s
4
1
5
5
0
-
0
2
0
-
1
0
1
7
-
3
.
[1
7
]
S
.
E.
M
e
id
t,
e
t
a
l.
,
“
A
m
o
d
e
l
f
o
r
th
e
o
n
se
t
o
f
se
lf
-
g
ra
v
it
a
ti
o
n
a
n
d
sta
r
fo
rm
a
ti
o
n
i
n
m
o
lec
u
lar
g
a
s
g
o
v
e
rn
e
d
b
y
g
a
lac
ti
c
fo
rc
e
s.
I.
Clo
u
d
-
sc
a
le
g
a
s
m
o
ti
o
n
s
,”
T
h
e
Astro
p
h
y
sic
a
l
J
o
u
rn
a
l
,
v
o
l
.
8
5
4
,
n
o
.
2
,
p
p
.
1
0
9
-
1
2
1
,
2
0
1
8
,
d
o
i:
1
0
.
3
8
4
7
/
1
5
3
8
-
4
3
5
7
/aa
a
2
9
0
.
[1
8
]
H.
M
o
n
teiro
,
D.
A.
Ba
rr
o
s,
W.
S.
Dia
s
a
n
d
J.
R.
D.
Lép
i
n
e
,
“
T
h
e
Distrib
u
ti
o
n
o
f
Op
e
n
Clu
ste
rs
in
t
h
e
G
a
lax
y
,”
a
rXiv p
re
p
ri
n
t
a
rX
iv:2
1
0
4
.
0
0
1
3
4
,
2
0
2
1
.
[1
9
]
T.
M
a
tsa
k
o
s,
a
n
d
A.
Kö
n
i
g
l,
“
T
h
e
g
ra
v
i
tatio
n
a
l
in
tera
c
ti
o
n
b
e
twe
e
n
p
lan
e
ts
o
n
i
n
c
li
n
e
d
o
r
b
it
s
a
n
d
p
r
o
to
p
lan
e
tary
d
isk
s
a
s
th
e
o
rig
i
n
o
f
p
rim
o
rd
ial
sp
in
-
o
rb
it
m
isa
li
g
n
m
e
n
ts,”
T
h
e
A
stro
n
o
mic
a
l
J
o
u
rn
a
l
,
v
o
l
.
1
5
3
,
n
o
2
,
p
p
.
5
3
-
6
0
,
2
0
1
7
F
e
b
ru
a
ry
,
d
o
i:
1
0
.
3
8
4
7
/1
5
3
8
-
3
8
8
1
/1
5
3
/
2
/6
0
.
[2
0
]
V.
S
.
As
lan
o
v
,
“
A
sp
l
it
ti
n
g
o
f
c
o
ll
in
e
a
r
li
b
ra
ti
o
n
p
o
i
n
ts
i
n
c
ircu
l
a
r
re
stricte
d
th
re
e
-
b
o
d
y
p
ro
b
lem
b
y
a
n
a
rti
ficia
l
e
lec
tro
sta
ti
c
field
,”
No
n
li
n
e
a
r Dy
n
a
mic
s
,
v
o
l.
1
0
3
,
n
o
.
3
,
p
p
.
2
4
5
1
-
2
4
6
0
,
2
0
2
1
,
d
o
i:
1
0
.
1
0
0
7
/s1
1
0
7
1
-
021
-
0
6
2
2
6
-
4
.
[2
1
]
R.
Hu
ň
a
d
y
,
P
.
P
a
v
e
l
k
a
a
n
d
P
.
Le
n
g
v
a
rs
k
ý
,
“
Vib
ra
ti
o
n
a
n
d
m
o
d
a
l
a
n
a
ly
sis
o
f
a
ro
tatin
g
d
isc
u
sin
g
h
ig
h
-
sp
e
e
d
3
D
d
ig
it
a
l
ima
g
e
c
o
rre
lati
o
n
,”
M
e
c
h
a
n
ica
l
S
y
ste
ms
a
n
d
S
i
g
n
a
l
P
ro
c
e
ss
in
g
,
v
o
l
.
1
21
,
p
p
.
2
0
1
-
2
1
4
,
2
0
1
9
,
d
o
i:
1
0
.
1
0
1
6
/
j.
y
m
ss
p
.
2
0
1
8
.
1
1
.
0
2
4
.
[2
2
]
V.P
.
Le
g
e
z
a
,
“
Bra
c
h
isto
c
h
ro
n
ic
M
o
ti
o
n
o
f
a
M
a
teria
l
P
o
in
t
o
n
a
Tran
sc
e
n
d
e
n
tal
S
u
rfa
c
e
,
”
In
t
A
p
p
l
M
e
c
h
,
v
o
l.
5
6
,
p
p
.
3
5
8
–
3
6
6
,
2
0
2
0
,
d
o
i:
1
0
.
1
0
0
7
/
s1
0
7
7
8
-
0
2
0
-
0
1
0
1
9
-
5
.
[2
3
]
N.
I.
S
h
a
k
u
ra
e
t
a
l
.
,
“
Ac
c
re
ti
o
n
p
ro
c
e
ss
e
s
in
a
stro
p
h
y
sic
s
,”
Ph
y
sic
s
-
Us
p
e
k
h
i,
vol
.
6
2
,
n
o
.
1
1
,
p
p
.
1
1
2
6
-
1
1
4
1
,
2
0
1
9
,
d
o
i:
1
0
.
3
3
6
7
/u
f
n
e
.
2
0
1
9
.
0
4
.
0
3
8
6
4
7
.
[2
4
]
Yi.
Bu
,
D.
S
.
M
u
rra
y
,
Y.
Din
g
,
Y.
Hu
a
n
g
,
a
n
d
Y.
Z
h
a
o
,
“
M
e
a
su
rin
g
t
h
e
sta
b
il
it
y
o
f
sc
ien
ti
fic
c
o
ll
a
b
o
ra
ti
o
n
,”
S
c
ien
to
me
trics
,
v
o
l.
1
1
4
,
n
o
.
2
,
p
p
.
4
6
3
-
4
7
9
,
2
0
1
8
,
d
o
i:
1
0
.
1
0
0
7
/s1
1
1
9
2
-
0
1
7
-
2
5
9
9
-
0
.
[2
5
]
P
.
Ten
jes
,
T
.
Tu
v
i
k
e
n
e
,
A.
Tam
m
,
R.
Kip
p
e
r,
a
n
d
E.
Tem
p
e
l
,
“
S
p
iral
a
rm
s
a
n
d
d
isc
sta
b
il
it
y
i
n
th
e
An
d
r
o
m
e
d
a
g
a
lax
y
,
”
Astr
o
n
o
my
&
Astro
p
h
y
si
c
s
,
v
o
l.
6
0
0
,
2
0
1
7
,
d
o
i:
1
0
.
1
0
5
1
/
0
0
0
4
-
6
3
6
1
/2
0
1
6
2
9
9
9
1
.
[2
6
]
A.
T.
Ha
sh
im
a
n
d
B.
D.
Ja
li
l,
“
Co
lo
r
ima
g
e
e
n
c
ry
p
ti
o
n
b
a
se
d
o
n
c
h
a
o
ti
c
sh
it
k
e
y
i
n
g
wit
h
lo
ss
le
ss
c
o
m
p
re
ss
io
n
,”
In
ter
n
a
t
io
n
a
l
J
o
u
r
n
a
l
o
f
El
e
c
tric
a
l
a
n
d
C
o
mp
u
ter
En
g
in
e
e
rin
g
(IJ
ECE
)
,
v
o
l.
1
0
,
n
o
.
6
,
p
p
.
5
7
3
6
-
5
7
4
8
,
2
0
2
0
,
d
o
i
:
1
0
.
1
1
5
9
1
/i
jec
e
.
v
1
0
i
6
.
p
p
5
7
3
6
-
5
7
4
8.
[2
7
]
Z.
Ra
k
h
m
e
tu
ll
in
a
,
R.
M
u
k
h
a
m
e
d
o
v
a
,
R.
M
u
k
a
sh
e
v
a
a
n
d
E
.
Aitmu
k
h
a
n
b
e
t
o
v
a
,
“
M
a
th
e
m
a
ti
c
a
l
M
o
d
e
l
fo
r
Cli
n
ica
l
De
c
isio
n
S
u
p
p
o
rt
S
y
ste
m
Us
in
g
G
e
n
e
ti
c
Alg
o
rit
h
m
,”
2
0
2
0
4
t
h
In
ter
n
a
ti
o
n
a
l
S
y
mp
o
siu
m
o
n
M
u
lt
id
isc
i
p
li
n
a
ry
S
tu
d
ies
a
n
d
I
n
n
o
v
a
ti
v
e
T
e
c
h
n
o
l
o
g
ies
(IS
M
S
IT
)
,
2
0
2
0
,
p
p
.
1
-
5
,
d
o
i:
1
0
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IT
5
0
6
7
2
.
2
0
2
0
.
9
2
5
5
1
5
0
.
[2
8
]
I.
Uv
a
l
y
iev
a
,
S
.
Be
lg
i
n
o
v
a
a
n
d
A.
Ism
u
k
h
a
m
e
d
o
v
a
,
“
De
v
e
lo
p
m
e
n
t
a
n
d
imp
lem
e
n
tati
o
n
o
f
t
h
e
a
lg
o
ri
th
m
o
f
d
iffere
n
ti
a
l
d
iag
n
o
stics
,”
2
0
1
8
IEE
E
1
2
th
I
n
ter
n
a
t
io
n
a
l
Co
n
fer
e
n
c
e
o
n
A
p
p
l
ica
ti
o
n
o
f
I
n
fo
rm
a
t
io
n
a
n
d
Co
mm
u
n
ica
ti
o
n
T
e
c
h
n
o
l
o
g
ies
(AI
CT
)
,
2
0
1
8
,
p
p
.
1
-
6
,
d
o
i
:
1
0
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1
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0
9
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CAICT.
2
0
1
8
.
8
7
4
7
1
1
6
.
[2
9
]
K.
K.
Ng
u
y
e
n
a
n
d
T.
T
.
Ng
u
y
e
n
,
“
Th
e
se
n
so
rles
s
c
o
n
tro
l
sy
ste
m
fo
r
c
o
n
tro
ll
in
g
t
h
e
sp
e
e
d
o
f
d
irec
t
c
u
rre
n
t
m
o
t
o
r
,”
In
d
o
n
e
sia
n
J
o
u
r
n
a
l
o
f
El
e
c
trica
l
En
g
i
n
e
e
rin
g
a
n
d
Co
mp
u
ter
S
c
i
e
n
c
e
(IJ
EE
CS
)
,
v
o
l
.
1
6
,
n
o
.
3
,
p
p
.
1
1
7
1
-
1
1
7
8
,
2
0
1
9
,
d
o
i:
1
0
.
1
1
5
9
1
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jee
c
s.v
1
6
.
i
3
.
p
p
1
1
7
1
-
1
1
7
8
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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:
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4
7
5
2
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci,
Vo
l.
24
,
No
.
3
,
Dec
em
b
er
2
0
2
1
:
1
3
0
7
-
1
3
1
4
1314
[3
0
]
A.
U
.
S
id
d
i
k
i,
O.
G
e
rh
a
rd
a
n
d
M
.
Arn
a
b
o
ld
i
,
“
S
e
lf
-
g
ra
v
it
a
ti
n
g
wa
rp
e
d
d
isc
s
a
ro
u
n
d
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p
e
rm
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ss
iv
e
b
lac
k
h
o
les
,”
M
o
n
th
ly
N
o
ti
c
e
s
o
f
t
h
e
R
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y
a
l
A
stro
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o
mic
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l
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iety
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o
l.
3
9
8
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.
2
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.
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[3
1
]
A.
U.
S
i
d
d
i
k
i,
“
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ra
v
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ti
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s
Ar
o
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rm
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ss
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e
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k
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lac
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lei
,”
Do
c
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ra
l
d
isse
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n
,
2
0
0
9
.
[3
2
]
J.
Bu
c
h
,
S
.
C.
J.
Leu
n
g
,
J.
J.
F
a
n
,
“
Us
in
g
G
a
ia
DR2
to
c
o
n
stra
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rk
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sity
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o
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rn
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o
f
Co
sm
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n
d
A
stro
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rticle
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h
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s
,
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l.
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0
1
9
,
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o
.
4
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p
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9
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9
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4
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2
6
.
[3
3
]
E.
N.
P
a
rk
e
r,
“
G
a
lac
ti
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e
ffe
c
ts
o
f
th
e
c
o
sm
ic
-
ra
y
g
a
s
,”
S
p
a
c
e
S
c
ien
c
e
Rev
iews
,
v
o
l
.
9
,
n
o
.
5
,
p
p
.
6
5
1
-
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1
2
,
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9
6
9
,
d
o
i:
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0
.
1
0
0
7
/B
F
0
0
1
7
4
0
3
2
.
[3
4
]
C.
G
.
Ko
h
,
P
.
P
.
S
z
e
,
a
n
d
T.
T
.
De
n
g
,
“
Nu
m
e
rica
l
a
n
d
a
n
a
ly
ti
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m
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th
o
d
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r
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ter
n
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ti
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n
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l
J
o
u
r
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d
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tru
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t
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re
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3
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.
1
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.
1
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,
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0
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6
,
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o
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0
.
1
0
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6
/
j.
ij
so
lstr.
2
0
0
5
.
0
5
.
0
1
3
.
[3
5
]
V.
Ag
a
p
it
o
u
,
J.
C
.
P
a
p
a
l
o
izo
u
a
n
d
C.
Terq
u
e
m
,
“
Be
n
d
in
g
in
sta
b
il
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ies
i
n
m
a
g
n
e
ti
z
e
d
a
c
c
re
ti
o
n
d
isc
s
,”
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o
n
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l
y
No
ti
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e
s o
f
t
h
e
Ro
y
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l
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o
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mic
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l
S
o
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iety
,
v
o
l.
2
9
2
,
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o
.
3
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p
.
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3
1
-
6
4
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ra
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9
2
.
3
.
6
3
1
.
[3
6
]
A.
C.
B
o
ley
a
n
d
R.
H.
Du
rise
n
,
“
Hy
d
ra
u
li
c
/sh
o
c
k
ju
m
p
s
in
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ro
t
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lan
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tary
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is
k
s
,”
T
h
e
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p
h
y
sic
a
l
J
o
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rn
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l
,
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l.
641
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.
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o
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0
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8
6
/5
0
0
3
9
6
.
[3
7
]
G
.
Ten
o
rio
-
Tag
le
a
n
d
P
.
Bo
d
e
n
h
e
ime
r,
“
Larg
e
-
sc
a
le
e
x
p
a
n
d
in
g
su
p
e
rstru
c
t
u
re
s
in
g
a
lax
ies
,”
A
n
n
u
a
l
re
v
iew
o
f
a
stro
n
o
my
a
n
d
a
stro
p
h
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sic
s
,
v
o
l.
26
,
n
o
.
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p
.
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.
2
6
.
0
9
0
1
8
8
.
0
0
1
0
4
5
.
[3
8
]
V.
D.
F
a
lco
,
E.
Ba
tt
ista
,
S
.
Ca
p
o
z
z
iello
,
a
n
d
M
.
D.
Lau
re
n
ti
s
,
“
G
e
n
e
r
a
l
re
lativ
isti
c
P
o
y
n
ti
n
g
-
Ro
b
e
rtso
n
e
ffe
c
t
t
o
d
iag
n
o
se
wo
rm
h
o
les
e
x
isten
c
e
:
S
tatic
a
n
d
s
p
h
e
rica
ll
y
sy
m
m
e
tri
c
c
a
se
,
”
Ph
y
sic
a
l
Rev
iew
D.
,
v
o
l.
1
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1
,
n
o
.
1
0
,
p
p
.
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0
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0
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o
i:
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y
s
Re
v
D.1
0
1
.
1
0
4
0
3
7
.
[3
9
]
P
.
G
h
o
sh
a
n
d
F
.
K.
Lam
b
,
“
Ac
c
re
ti
o
n
b
y
r
o
tatin
g
m
a
g
n
e
ti
c
n
e
u
t
ro
n
sta
rs.
II
-
Ra
d
ial
a
n
d
v
e
rti
c
a
l
stru
c
tu
re
o
f
t
h
e
tran
siti
o
n
z
o
n
e
in
d
isk
a
c
c
re
ti
o
n
,”
T
h
e
Astro
p
h
y
sic
a
l
J
o
u
r
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a
l
,
v
o
l.
2
3
2
,
p
p
.
2
5
9
-
2
7
6
,
1
9
7
9
.
[4
0
]
M
.
R.
M
e
rrif
iel
d
,
“
T
h
e
k
i
n
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m
a
ti
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e
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lax
ies
,
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n
d
th
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tu
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G
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lac
ti
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H
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la
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r
,”
M
o
n
th
ly
No
ti
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e
s o
f
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h
e
Ro
y
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l
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o
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l
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o
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iety
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l.
2
6
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,
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o
.
1
,
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p
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2
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B
I
O
G
RAP
H
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E
S O
F
AUTH
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RS
Zh
e
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E
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ti
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ri
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t
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z
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k
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tec
h
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ica
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n
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y
(EKT
U),
Us
t
-
Ka
m
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n
o
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rs
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k
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B.
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g
.
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M
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g
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n
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P
h
.
D.
d
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s
in
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-
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ra
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z
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k
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rsity
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1
9
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2
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1
,
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sp
e
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ti
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ly
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S
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b
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As
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c
iate
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r
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Train
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g
.
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r
re
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rc
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tere
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teria
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lar p
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o
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ti
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g
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n
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e
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rsity
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n
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,
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h
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A
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o
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iate
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ro
fe
ss
o
r
in
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t
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m
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,
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z
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k
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sta
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2
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6
.
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r
re
se
a
rc
h
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tere
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lu
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o
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m
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o
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ti
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m
s,
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ro
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o
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ta m
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l
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a
th
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t
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ll
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g
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r
id
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h
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n
g
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a
n
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h
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d
e
g
re
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s
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-
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ra
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k
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i
n
2
0
0
0
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0
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n
d
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1
5
,
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sp
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ti
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ly
.
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h
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a
s b
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a
n
As
so
c
iate
P
ro
fe
ss
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f
th
e
De
p
a
rtme
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t
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M
a
th
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ti
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s"
of
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2
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6
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r
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se
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rc
h
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tere
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o
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ter
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a
ti
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l
m
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c
tu
re
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d
s,
d
o
u
b
ly
c
o
n
n
e
c
ted
,
p
o
we
r
sy
ste
m
sta
b
il
it
y
,
li
n
e
a
r
sto
k
e
s
d
iffere
n
ti
a
l
p
ro
b
lem
.
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