I
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rna
t
io
na
l J
o
urna
l o
f
E
lect
rica
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Co
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I
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v7
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p
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-
2001
1994
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o
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:
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ttp
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ar
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:
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id
1.
I
NT
RO
D
UCT
I
O
N
Desig
n
o
f
a
s
p
ac
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r
af
t
o
r
s
atellite
attitu
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e
co
n
tr
o
l
b
y
an
al
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r
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tatio
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m
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r
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m
ain
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r
esear
ch
f
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d
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t
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s
.
Ash
o
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p
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p
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co
n
tr
o
l
m
o
m
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g
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o
s
b
ased
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tr
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m
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-
o
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l
m
a
n
eu
v
er
f
o
r
ag
ile
(
r
ig
id
)
s
a
tell
ite
[
1
]
.
C
h
ab
o
t
a
n
d
Sch
a
u
b
p
r
esen
ted
a
s
p
h
er
ical
ac
tu
ato
r
f
o
r
s
atelli
te
attit
u
d
e
c
o
n
tr
o
l th
at
co
v
er
s
m
o
d
eli
n
g
,
s
i
m
u
latio
n
o
f
a
ttit
u
d
e
co
n
tr
o
l
o
f
a
r
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id
b
o
d
y
s
y
s
te
m
m
o
tio
n
as
w
e
ll
as
co
m
p
ar
is
o
n
w
it
h
a
co
n
f
i
g
u
r
atio
n
o
f
t
h
r
ee
r
ea
ctio
n
w
h
ee
l
s
[
2
]
.
in
[
3
]
,
Stev
en
s
o
n
an
d
Sc
h
au
b
u
s
ed
r
ig
id
b
o
d
y
ap
p
r
o
ac
h
i
n
th
e
attit
u
d
e
co
n
tr
o
l
d
ev
el
o
p
m
e
n
t
p
r
io
r
to
d
o
test
b
ed
ex
p
er
i
m
e
n
t
o
f
r
e
m
o
te
elec
tr
o
s
tatic
ch
ar
g
e
co
n
tr
o
l.
R
ez
an
ez
h
ad
i
n
[
4
]
p
r
esen
ted
T
a
k
ag
i
-
Su
g
e
n
o
f
u
zz
y
-
b
ased
attitu
d
e
co
n
tr
o
ller
in
o
r
d
er
to
r
ed
u
ce
th
r
u
s
ter
f
u
e
l
co
n
s
u
m
p
tio
n
an
d
in
cr
ea
s
e
lo
n
g
ev
i
t
y
o
f
s
a
tellite.
P
ar
ticle
s
w
ar
m
o
p
ti
m
iza
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alg
o
r
ith
m
is
u
s
ed
to
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ce
li
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it
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cle
o
n
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h
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f
u
zz
y
s
y
s
te
m
.
P
ir
o
u
z
m
an
d
in
[
5
]
p
r
o
p
o
s
ed
a
m
o
d
el
r
ef
er
en
ce
ad
ap
tiv
e
s
y
s
te
m
-
b
a
s
ed
r
o
b
u
s
t
m
o
d
el
p
r
ed
ictiv
e
co
n
tr
o
ller
f
o
r
th
r
ee
d
eg
r
ee
o
f
f
r
ee
d
o
m
s
atellite
atti
tu
d
e
co
n
tr
o
l
s
y
s
te
m
.
W
h
ils
t
th
e
co
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tr
o
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g
ain
is
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b
tain
ed
th
r
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o
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tim
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li
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m
atr
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x
in
eq
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alit
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ap
p
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.
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h
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k
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m
atics
o
f
a
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o
d
y
r
o
tatio
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m
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i
s
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at
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m
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m
b
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f
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p
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th
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g
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t
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r
o
u
p
,
3
SO
.
Am
o
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g
p
ar
a
m
e
ter
iza
tio
n
s
o
f
t
h
e
r
o
tatio
n
m
atr
i
x
,
a
p
ar
am
eter
izat
io
n
u
s
i
n
g
q
u
ater
n
io
n
i
s
t
h
e
o
n
l
y
p
ar
a
m
eter
izat
io
n
w
it
h
f
o
u
r
p
ar
a
m
eter
s
.
He
n
ce
,
it
ca
n
r
ep
r
esen
t
g
lo
b
al
attitu
d
e
o
f
a
r
ig
id
b
o
d
y
r
o
tatio
n
al
m
o
tio
n
.
Ho
w
e
v
e
r
,
a
p
h
y
s
ical
attit
u
d
e,
w
h
ic
h
is
r
ep
r
esen
ted
in
a
u
n
iq
u
e
r
o
tatio
n
m
atr
i
x
v
al
u
e,
is
r
ep
r
esen
ted
b
y
t
w
o
v
al
u
es
i
n
q
u
ater
n
io
n
,
i.e
.
a
p
air
an
tip
o
d
al
v
alu
e.
T
h
is
f
ac
t
i
m
p
lies
d
i
f
f
icu
lties
o
n
t
h
e
s
tab
ilit
y
g
u
ar
a
n
tee
o
f
t
h
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q
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ater
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i
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n
b
ased
attitu
d
e
co
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tr
o
l s
y
s
te
m
[
6
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
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C
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I
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N:
2
0
8
8
-
8708
A
s
ymp
to
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S
ta
b
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f Q
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a
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-
b
a
s
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A
ttit
u
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C
o
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o
l S
ystem
w
ith
….
(
Ha
r
r
y
S
ep
ta
n
to
)
1995
Ma
n
y
r
esear
c
h
ef
f
o
r
ts
h
a
v
e
b
ee
n
ad
d
r
ess
ed
o
n
th
e
d
esig
n
o
f
q
u
ater
n
io
n
b
ased
attit
u
d
e
co
n
tr
o
l
s
y
s
te
m
:
Ma
cKu
n
i
s
et
al
in
[
7
]
d
ev
elo
p
ed
an
ad
ap
tiv
e
n
eu
r
al
n
et
w
o
r
k
b
ased
attit
u
d
e
co
n
tr
o
ller
f
o
r
s
atellite
th
at
is
ac
tu
a
ted
b
y
co
n
tr
o
l
m
o
m
e
n
t
g
y
r
o
s
,
w
h
er
e
ex
ter
n
al
d
is
t
u
r
b
an
ce
as
w
e
ll
as
d
is
tu
r
b
an
ce
o
f
th
e
co
n
tr
o
l
m
o
m
e
n
t
g
y
r
o
s
’
tac
h
o
m
eter
ar
e
co
n
s
id
er
ed
;
C
a
lv
o
et
al.
p
r
o
p
o
s
ed
an
ad
ap
tiv
e
f
u
zz
y
co
n
tr
o
ller
f
o
r
m
o
m
e
n
tu
m
w
h
ee
l
ac
t
u
ated
s
atellite
a
n
d
it
s
p
er
f
o
r
m
an
ce
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s
co
m
p
ar
ed
w
i
th
a
cu
s
to
m
P
D
co
n
tr
o
ller
[
8
]
;
in
[
9
]
,
Sep
tan
to
et
al
p
r
o
p
o
s
ed
a
co
n
tin
u
o
u
s
s
c
h
e
m
e
o
f
q
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ater
n
io
n
b
ased
co
n
tr
o
ller
th
at
e
m
p
lo
y
s
au
g
m
e
n
ted
d
y
n
a
m
ic;
to
n
a
m
e
a
f
e
w
.
I
n
[
1
0
]
,
a
co
n
tin
u
o
u
s
s
c
h
e
m
e
o
f
q
u
ater
n
io
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-
b
ased
co
n
tr
o
l
s
y
s
te
m
th
at
h
as
s
a
tu
r
ati
o
n
f
u
n
ctio
n
is
also
p
r
o
p
o
s
ed
w
it
h
b
o
u
n
d
ed
n
e
s
s
o
f
s
o
lu
tio
n
g
u
ar
an
tee.
I
n
t
h
is
p
a
p
er
,
th
e
s
y
s
te
m
h
a
s
b
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n
f
u
r
th
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al
y
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d
to
h
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v
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o
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er
g
u
ar
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n
tee,
i.e
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as
y
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p
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ticall
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tab
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T
h
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o
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an
izatio
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llo
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m
at
i
ca
l
p
r
elim
i
n
ar
ies
i
n
cl
u
d
in
g
m
o
d
elin
g
o
f
th
e
s
ate
llit
e
d
y
n
a
m
ics
a
n
d
k
in
e
m
atic
ar
e
p
r
esen
ted
i
n
t
h
e
n
ex
t
s
ec
tio
n
.
Sectio
n
3
p
r
esen
t
s
t
h
e
p
r
o
b
lem
f
o
r
m
u
latio
n
a
n
d
m
et
h
o
d
o
lo
g
y
.
T
h
e
m
a
in
co
n
tr
ib
u
tio
n
o
f
t
h
is
p
ap
er
w
ill
b
e
p
r
esen
ted
in
Sectio
n
4
.
Dis
cu
s
s
io
n
an
d
n
u
m
er
ical
s
i
m
u
la
tio
n
s
ar
e
also
p
r
esen
ted
in
Sect
io
n
5
.
Sectio
n
6
p
r
o
v
id
es th
e
co
n
cl
u
d
in
g
r
e
m
ar
k
s
.
2.
B
ACK
G
RO
UND
AN
D
P
RE
L
I
M
I
NARI
E
S
2
.
1
.
M
a
t
he
m
a
t
ica
l P
re
li
m
ina
ries
So
m
e
m
at
h
e
m
atica
l
n
o
tatio
n
s
w
ill
b
e
u
s
ed
i
n
t
h
e
r
e
s
t
o
f
p
ap
er
.
R
is
t
h
e
s
et
o
f
al
l
r
ea
l
n
u
m
b
er
s
.
nm
R
is
th
e
s
et
o
f
all
nm
m
atr
i
x
th
at
all
o
f
its
en
tr
y
ar
e
r
ea
l
n
u
m
b
er
s
,
w
h
er
e
0
,
nm
Z
,
Z
is
th
e
s
et
o
f
al
l
in
te
g
er
n
u
m
b
er
s
an
d
0
Z
is
th
e
s
e
t
o
f
all
p
o
s
itiv
e
in
te
g
er
n
u
m
b
er
s
.
C
o
n
s
id
er
a
m
a
tr
ix
nm
R
R
,
h
en
ce
T
R
d
en
o
tes
tr
an
s
p
o
s
e
o
f
R
an
d
R
d
eter
m
in
a
n
t
o
f
R
.
Ma
tr
ix
n
n
n
n
I
R
d
en
o
tes
th
e
id
en
t
it
y
o
f
nn
m
atr
ix
.
Su
p
p
o
s
e
th
er
e
is
a
co
lu
m
n
m
atr
i
x
n
C
R
,
h
en
ce
C
d
en
o
tes
2
-
n
o
r
m
o
f
C
.
Ma
tr
ix
0
nm
d
en
o
tes
nm
m
atr
i
x
th
at
all
o
f
its
e
n
tr
y
ar
e
ze
r
o
.
I
n
th
i
s
p
ap
er
,
a
v
ec
to
r
is
d
ef
in
ed
as in
(
1
)
.
T
l
l
rr
F
(
1
)
w
h
er
e:
r
d
en
o
tes
th
e
v
ec
to
r
o
f
r
,
l
F
is
a
co
lu
m
n
s
m
atr
ix
co
n
s
is
t
s
o
f
th
r
ee
u
n
it
v
ec
to
r
1
ˆ
l
,
2
ˆ
l
an
d
3
ˆ
l
th
at
a
r
e
ass
o
ciate
d
w
it
h
th
e
in
er
tial
r
e
f
er
en
ce
f
r
a
m
e,
a
n
d
3
l
r
R
is
a
co
lu
m
n
m
atr
i
x
w
h
o
s
e
t
h
r
ee
co
m
p
o
n
en
t
s
o
f
r
th
at
ar
e
ex
p
r
ess
ed
(
d
ec
o
m
p
o
s
ed
)
in
to
th
e
in
er
tial r
e
f
er
en
ce
f
r
a
m
e,
l
F
.
B
esid
es
s
u
p
er
s
cr
ip
t
l
(
s
u
b
s
cr
ip
t
l
)
th
at
ar
e
as
s
o
ciate
d
w
it
h
t
h
e
in
er
tial
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e
f
er
en
ce
f
r
a
m
e,
th
i
s
p
ap
er
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s
e
s
s
u
p
er
s
cr
ip
t
b
(
s
u
b
s
cr
ip
t
b
)
an
d
s
u
p
er
s
cr
ip
t
d
(
s
u
b
s
cr
ip
t
d
)
ass
o
ciate
d
w
ith
th
e
s
atel
lite
’
s
f
i
x
ed
b
o
d
y
f
r
a
m
e
an
d
s
atellite
’
s
d
esire
d
f
r
a
m
e,
r
esp
ec
tiv
el
y
.
Fo
r
b
r
ev
it
y
,
t
h
e
s
atellite’
s
f
ix
ed
b
o
d
y
f
r
a
m
e,
th
e
in
er
tial
r
ef
er
e
n
ce
f
r
a
m
e
a
n
d
th
e
s
atelli
te’
s
d
esi
r
ed
f
r
a
m
e
m
a
y
b
e
w
r
itte
n
as
b
o
d
y
f
r
a
m
e,
i
n
er
tial
f
r
a
m
e
an
d
d
esire
d
f
r
a
m
e,
r
esp
ec
tiv
el
y
.
2
.
2
.
Dy
na
m
ic
a
n
d K
ine
m
a
t
ics o
f
Sp
a
ce
cr
a
f
t
I
n
t
h
is
p
ap
er
,
m
o
tio
n
o
f
a
s
ate
llit
e
i
s
r
e
g
ar
d
ed
as
a
r
i
g
id
b
o
d
y
m
o
tio
n
.
D
y
n
a
m
ic
o
f
a
r
ig
id
s
atellite
is
g
iv
e
n
b
y
E
u
ler
E
q
u
atio
n
,
[
1
1
]
.
T
h
e
d
y
n
a
m
ic
o
f
a
s
atellite
t
h
a
t is ex
p
r
ess
ed
i
n
b
F
is
r
ep
r
esen
ted
in
(
2
)
.
b
b
b
b
b
b
l
b
l
b
l
b
l
b
l
J
JJ
(
2
)
w
h
er
e
th
e
s
y
m
m
etr
ic
p
o
s
iti
v
e
d
ef
in
ite
m
atr
i
x
33
J
R
is
th
e
s
atellite
in
er
tia
m
o
m
e
n
t
ab
o
u
t
it
s
ce
n
t
er
o
f
m
as
s
th
at
is
lo
ca
ted
in
t
h
e
o
r
ig
i
n
o
f
b
F
,
(
k
g
.
m
2
)
;
3
b
bl
R
is
th
e
a
n
g
u
lar
v
el
o
cit
y
v
ec
to
r
o
f
b
F
w
i
th
r
esp
ec
t
t
o
l
F
w
h
ic
h
is
d
ec
o
m
p
o
s
ed
in
b
F
,
(
r
ad
.
s
-
1
)
;
an
d
3
R
is
th
e
to
tal
e
x
ter
n
a
l
co
n
tr
o
l
to
r
q
u
e
ab
o
u
t
its
ce
n
ter
o
f
m
as
s
th
at
i
s
lo
ca
ted
i
n
t
h
e
o
r
ig
i
n
o
f
b
F
,
(
N.
m
)
b
bl
d
en
o
tes
a
s
k
e
w
-
s
y
m
m
etr
ic
m
atr
ix
o
f
b
bl
,
i.e
.
th
e
c
o
lu
m
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
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0
8
8
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8708
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J
E
C
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Vo
l.
7
,
No
.
4
,
A
u
g
u
s
t
2
0
1
7
:
1
9
9
4
–
2
0
0
1
1996
m
atr
i
x
o
f
v
ec
to
r
bl
th
at
is
e
x
p
r
ess
ed
in
b
F
,
w
h
er
e
1
2
3
T
b
b
b
b
b
l
b
l
b
l
b
l
an
d
32
31
21
0
0
0
bb
b
l
b
l
b
b
b
b
l
b
l
b
l
bb
b
l
b
l
.
I
n
ad
d
itio
n
,
b
bl
d
en
o
tes f
ir
s
t d
er
iv
ati
v
e
o
f
b
bl
w
it
h
r
esp
ec
t to
ti
m
e
.
Satellite
at
tit
u
d
e
r
ep
r
esen
tatio
n
i
n
(
u
n
it)
q
u
ater
n
io
n
t
h
at
d
e
n
o
tes
t
h
e
at
titu
d
e
o
f
t
h
e
s
atel
lite
b
o
d
y
f
r
a
m
e
b
F
w
it
h
r
e
s
p
ec
t
to
t
h
e
in
er
tial
f
r
a
m
e
l
F
is
g
i
v
en
b
y
T
T
b
l
b
l
bl
q
,
w
h
er
e
bl
R
,
3
bl
R
an
d
2
1
T
b
l
b
l
b
l
.
I
n
ad
d
itio
n
,
all
atti
tu
d
e
r
ep
r
esen
tat
io
n
s
in
q
u
ater
n
io
n
r
eg
ar
d
ed
in
th
i
s
p
ap
er
,
in
cl
u
d
in
g
bl
q
,
ar
e
m
e
m
b
er
o
f
th
e
u
n
it sp
h
er
e
o
r
d
er
3
,
34
0
1
2
3
:
T
S
a
a
a
a
R
2
2
2
2
0
2
2
3
1
a
a
a
a
.
No
w
,
co
n
s
id
er
a
k
in
e
m
atic
s
E
q
u
atio
n
r
ep
r
e
s
en
ted
i
n
q
u
ater
n
io
n
g
i
v
en
b
y
(
3
)
-
(
5
)
.
T
T
b
d
b
d
b
d
q
(
3
)
W
h
er
e
1
2
Tb
b
d
b
d
b
d
(
4
)
1
2
b
b
d
b
d
b
d
b
d
I
(
5
)
No
te
th
at
bd
q
r
ep
r
esen
ts
t
h
e
atti
tu
d
e
b
F
w
it
h
r
esp
ec
t to
d
F
,
bd
q
is
also
r
eg
a
r
d
ed
as th
e
attit
u
d
e
er
r
o
r
b
et
w
ee
n
t
h
e
s
atellite
b
o
d
y
f
r
a
m
e
b
F
an
d
th
e
s
atellite
d
esire
d
o
r
tar
g
et
f
r
am
e
d
F
.
Sin
ce
th
e
in
f
o
r
m
atio
n
f
r
o
m
a
n
attit
u
d
e
s
en
s
o
r
is
w
it
h
r
esp
ec
t
to
th
e
i
n
er
tial
f
r
a
m
e
l
F
,
i.e
.
bl
q
an
d
th
e
tar
g
et
attit
u
d
e
is
also
w
it
h
r
esp
ec
t
to
l
F
,
i.e
.
dl
q
,
h
en
ce
t
h
e
attit
u
d
e
er
r
o
r
bd
q
is
o
b
tain
ed
f
o
r
m
q
u
a
ter
n
io
n
m
u
ltip
li
ca
tio
n
b
et
w
ee
n
bl
q
an
d
dl
q
as g
i
v
e
n
i
n
(
6
)
.
1
b
d
d
l
b
l
l
d
b
l
q
q
q
q
q
(
6
)
w
h
er
e
1
d
l
l
d
qq
is
th
e
in
v
er
s
e
o
f
dl
q
.
No
te
th
at
s
i
n
ce
th
e
att
itu
d
e
is
co
n
s
i
d
er
ed
as
a
u
n
it
q
u
ater
n
io
n
,
w
h
er
e
th
e
q
u
ater
n
io
n
n
o
r
m
2
1
T
d
l
d
l
d
l
dl
q
,
th
e
n
q
u
a
ter
n
io
n
i
n
v
er
s
e,
*
1
dl
dl
dl
q
q
q
,
is
eq
u
al
to
t
h
e
q
u
ater
n
io
n
co
n
j
u
g
ate,
*
T
T
d
l
d
l
dl
q
.
3.
P
RO
B
L
E
M
DE
F
I
NIT
I
O
N
AND
M
E
T
H
O
DO
L
O
G
Y
C
o
n
s
id
er
th
e
s
p
ac
ec
r
af
t
(
2
)
a
n
d
t
h
e
co
n
tr
o
ller
(
7
)
p
r
o
p
o
s
ed
in
[
1
1
]
,
w
h
er
e
bd
33
:
RR
d
en
o
tes
s
at
u
r
atio
n
f
u
n
ctio
n
w
it
h
s
at
u
r
atio
n
le
v
el
0
.
T
h
e
s
atu
r
atio
n
f
u
n
ctio
n
is
d
ef
i
n
ed
ele
m
e
n
t
-
w
is
e
bd
i
,
1
,
2
,
3
i
,
1
2
3
T
b
d
b
d
b
d
b
d
,
in
p
ar
ticu
lar
g
i
v
en
b
y
(
8
)
.
Fo
r
co
n
v
e
n
ien
ce
co
n
s
i
d
er
atio
n
,
b
d
X
.
Dea
d
zo
n
e
f
u
n
ctio
n
X
is
d
ef
i
n
ed
as
X
b
d
X
,
h
en
ce
b
b
d
b
d
X
b
l
kL
.
I
n
ad
d
itio
n
,
th
e
co
n
tr
o
l
ler
(
7
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
C
E
I
SS
N:
2
0
8
8
-
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A
s
ymp
to
tic
S
ta
b
ilit
y
o
f Q
u
a
tern
io
n
-
b
a
s
ed
A
ttit
u
d
e
C
o
n
tr
o
l S
ystem
w
ith
….
(
Ha
r
r
y
S
ep
ta
n
to
)
1997
b
b
d
b
d
X
b
d
b
d
kL
,
k
R
,
33
L
R
(
7
)
1
2
3
T
b
d
b
d
b
d
b
d
,
,
,
,
bd
i
b
d
b
d
b
d
i
i
i
bd
i
(
8
)
T
h
e
d
esig
n
ed
atti
tu
d
e
co
n
tr
o
l
s
y
s
te
m
is
f
o
r
th
e
ca
s
e
o
f
co
n
s
t
an
t
atti
tu
d
e
tr
ac
k
in
g
,
i.e
.
b
T
d
d
l
b
d
d
l
R
0
d
d
b
d
l
R
,
w
h
er
e
bd
R
is
th
e
r
o
tatio
n
m
atr
ix
t
h
at
r
ep
r
esen
ts
t
h
e
attit
u
d
e
er
r
o
r
b
etw
ee
n
t
h
e
s
atelli
te
b
o
d
y
f
r
a
m
e
b
F
an
d
t
h
e
s
a
tellite
d
es
ir
ed
o
r
tar
g
et
f
r
a
m
e
d
F
.
R
o
tatio
n
m
atr
i
x
bd
R
is
a
m
e
m
b
er
o
f
s
p
ec
ial
o
r
th
o
g
o
n
al
g
r
o
u
p
o
r
d
er
3
,
i.e
.
33
33
3
:
,
1
T
bd
R
S
O
R
R
R
I
R
R
.
I
n
[
1
1
]
,
th
er
e
is
r
elatio
n
b
et
w
e
e
n
r
o
tatio
n
m
atr
i
x
bd
R
an
d
q
u
ater
n
io
n
bd
q
as g
iv
e
n
b
y
E
q
u
atio
n
(
9
)
.
2
2
2
22
TT
b
d
b
d
b
d
b
d
b
d
b
d
b
d
b
d
RI
(
9
)
Def
ini
t
io
n
1
L
et
3
3
6
ES
RR
is
th
e
s
et
o
f
all
s
o
lu
tio
n
s
o
f
a
co
n
tr
o
l
s
y
s
te
m
.
L
et
E
is
th
e
s
et
th
at
co
n
s
is
ts
o
f
all
n
o
n
-
eq
u
ilib
r
i
u
m
s
o
l
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tio
n
0
E
s
u
c
h
t
h
at
0
E
E
E
,
w
h
er
e
00
EE
.
I
f
th
e
f
o
llo
w
i
n
g
s
tate
m
en
t
s
ar
e
s
atis
f
ied
:
a.
yE
,
0
,
0
V
y
V
y
b.
0
,0
y
E
V
y
c.
0
E
is
th
e
lar
g
est i
n
v
ar
ian
t
s
et
in
:0
y
E
V
y
th
en
0
E
is
th
e
lo
ca
ll
y
as
y
m
p
to
tic
all
y
s
tab
le
s
e
t.
Re
m
a
r
ks
1
.
T
h
e
s
tab
ilit
y
n
o
tio
n
i
n
Def
in
it
io
n
1
is
n
o
t
a
s
tan
d
ar
d
s
tab
ilit
y
i
n
t
h
e
s
en
s
e
o
f
L
y
ap
u
n
o
v
wh
ic
h
is
u
s
ed
to
g
u
ar
a
n
tee
s
tab
ilit
y
o
f
a
p
o
in
t.
I
n
s
tead
,
L
aSalle
’
s
in
v
ar
ia
n
ce
p
r
in
cip
le
th
eo
r
e
m
i
n
co
n
j
u
n
ctio
n
w
ith
L
y
ap
u
n
o
v
f
u
n
ctio
n
p
r
o
p
er
ties
is
u
s
ed
to
g
u
ar
an
tee
s
tab
ilit
y
o
f
th
e
s
et.
O
n
e
m
a
y
s
aid
t
h
at
L
aSal
le’
s
t
h
eo
r
e
m
ex
ten
d
s
L
y
ap
u
n
o
v
’
s
th
eo
r
e
m
s
in
ce
,
n
at
u
r
all
y
,
it c
an
b
e
u
s
ed
f
o
r
th
e
s
y
s
te
m
t
h
at
h
as a
n
eq
u
il
ib
r
iu
m
s
e
t
[
1
2
]
.
T
h
e
m
ain
o
b
j
ec
tiv
e
o
f
t
h
is
p
ap
er
is
to
f
i
n
d
n
ec
ess
ar
y
co
n
d
i
tio
n
s
o
f
t
h
e
s
y
s
te
m
t
h
at
co
n
s
i
s
ts
o
f
t
h
e
r
ig
id
s
p
ac
ec
r
af
t
(
2
)
an
d
th
e
co
n
tr
o
ller
(
9
)
s
u
ch
th
at
as
y
m
p
to
tic
s
tab
ilit
y
g
u
ar
an
tee
a
s
in
Def
i
n
it
io
n
1
is
ac
h
iev
ed
.
T
h
r
o
u
g
h
L
y
ap
u
n
o
v
s
tab
ilit
y
m
e
th
o
d
,
co
n
d
itio
n
s
o
f
th
e
attit
u
d
e
co
n
tr
o
l
s
y
s
te
m
p
ar
am
eter
s
w
ill
b
e
r
esu
lted
.
I
n
ad
d
itio
n
,
s
o
m
e
n
u
m
er
ical
s
i
m
u
latio
n
s
ar
e
d
o
n
e
to
illu
s
tr
ate
it
s
p
er
f
o
r
m
a
n
ce
.
4.
M
AIN RES
UL
T
T
heo
re
m
1
C
o
n
s
id
er
th
e
q
u
ater
n
io
n
-
b
ase
d
s
p
ac
ec
r
af
t
attitu
d
e
co
n
tr
o
l
s
y
s
te
m
co
n
s
i
s
ts
o
f
&
2
)
,
(
7
)
an
d
Def
i
n
itio
n
1
,
w
h
er
e
,
b
b
d
b
l
yq
.
T
h
e
s
et
33
0
,:
T
Tb
b
d
b
d
b
d
b
l
E
q
S
R
33
0
,
1
,
0
b
b
d
b
d
b
l
th
at
co
n
s
i
s
ts
o
f
t
w
o
eq
u
ilib
r
iu
m
p
o
in
ts
o
f
t
h
e
s
y
s
te
m
is
l
o
ca
ll
y
as
y
m
p
to
ticall
y
s
tab
le
an
d
it sati
s
f
ies t
h
e
f
o
llo
w
i
n
g
p
r
o
p
er
ties
a.
T
h
er
e
ex
is
t
p
o
s
iti
v
e
k
an
d
s
y
m
m
etr
ic
d
ef
i
n
ite
p
o
s
iti
v
e
m
at
r
ix
L
s
u
ch
t
h
at
f
u
l
f
ills
th
e
i
n
e
q
u
alit
y
m
i
n
0
kL
,
w
h
er
e
m
i
n
L
is
m
i
n
i
m
u
m
E
i
g
e
n
v
a
lu
e
o
f
L
b.
T
h
e
s
atu
r
atio
n
li
m
it
f
u
l
f
il
ls
1
0
3
c.
T
h
er
e
ex
is
t in
i
tial c
o
n
d
itio
n
0
,
0
b
b
d
b
l
q
t
t
E
s
u
ch
t
h
at
co
n
s
tr
ain
t
(
1
0
)
is
f
u
l
f
i
lled
2
2
0
,
0
b
b
l
X
t
t
t
(
1
0
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
J
E
C
E
Vo
l.
7
,
No
.
4
,
A
u
g
u
s
t
2
0
1
7
:
1
9
9
4
–
2
0
0
1
1
998
P
r
o
o
f
:
C
o
n
s
id
er
th
e
L
y
ap
u
n
o
v
f
u
n
ct
i
o
n
ca
n
d
id
ate
g
i
v
en
i
n
E
q
u
atio
n
(
1
1
)
to
s
h
o
w
s
et
s
tab
il
it
y
o
f
0
E
.
1
2
T
b
T
b
b
d
b
d
b
l
b
l
V
k
J
(
1
1
)
w
h
er
e
0
V
,
f
o
r
all
0
k
.
No
te
t
h
at,
i
n
s
t
ea
d
o
f
bd
q
,
o
n
l
y
bd
is
ap
p
ea
r
ed
in
(
1
1
)
s
in
ce
bd
is
in
h
er
en
tl
y
i
n
bd
.
Fu
r
th
er
m
o
r
e,
th
e
ti
m
e
d
er
iv
at
iv
e
o
f
V
is
g
i
v
en
b
y
(
1
2
)
.
T
b
b
b
T
b
b
b
b
d
b
d
b
d
b
d
b
d
b
l
b
l
b
l
b
d
b
d
X
b
l
V
k
J
k
L
(
1
2
)
Fro
m
th
e
f
ac
ts
t
h
at
3
0
d
dl
an
d
0
T
b
T
b
b
d
b
d
b
l
b
l
,
h
en
c
e
(
1
3
)
is
s
atis
f
ied
.
b
T
b
T
b
b
l
X
b
l
b
l
V
k
L
(
1
3
)
I
f
L
is
a
s
y
m
m
etr
ic
d
e
f
in
ite
p
o
s
it
iv
e
m
a
tr
ix
,
t
h
en
(
1
4
)
is
f
u
l
f
ille
d
.
2
m
i
n
bb
b
l
X
b
l
V
k
L
(
1
4
)
No
te
th
at
th
e
co
n
s
tr
ai
n
t
(
1
0
)
im
p
lies
0
V
,
if
m
i
n
0
kL
.
L
et
33
,
:
,
0
bb
b
d
b
l
b
d
b
l
q
S
V
q
R
.
T
h
en
0
V
,
if
0
b
bl
.
I
n
ad
d
itio
n
,
s
in
ce
co
n
s
tr
ain
t
(
1
0
)
is
h
o
ld
,
0
b
bl
i
m
p
lies
0
X
.
No
te
th
at
0
b
bl
3
0
b
bl
an
d
0
X
3
0
X
.
Su
b
s
tit
u
ti
n
g
th
e
s
e
v
al
u
es to
t
h
e
s
y
s
te
m
(
2
)
an
d
(
7
)
it w
o
u
ld
r
esu
lt
0
bd
.
T
h
er
ef
o
r
e,
0
E
.■
Re
m
a
r
ks
2
I
n
ac
co
r
d
in
g
to
P
r
o
p
o
s
itio
n
1
in
[
1
0
]
,
th
e
attitu
d
e
co
n
tr
o
l
s
y
s
te
m
is
lo
ca
ll
y
L
ip
s
c
h
it
z
in
33
,
T
Tb
b
d
b
d
b
d
b
l
qS
R
.
Hen
ce
,
a
p
r
er
e
q
u
is
ite
co
n
d
i
tio
n
f
o
r
L
y
ap
u
n
o
v
th
eo
r
e
m
u
tili
za
t
io
n
is
f
u
lf
i
lled
.
Re
m
a
r
ks
3
T
h
e
s
tab
ilit
y
a
n
al
y
s
i
s
p
r
esen
t
ed
in
t
h
is
p
ap
er
is
n
o
clai
m
o
f
g
lo
b
al
s
tab
ilit
y
.
I
n
ad
d
iti
o
n
,
g
lo
b
al
s
tab
ilit
y
clai
m
i
n
[
1
3
]
is
in
co
r
r
ec
t
s
in
ce
th
er
e
ar
e
eq
u
ilib
r
iu
m
p
o
in
t
s
o
th
er
t
h
an
0
E
,
i.e
.
33
,:
T
Tb
b
d
b
d
b
d
b
l
qS
R
33
0
,
0
b
b
l
b
d
b
d
X
.
No
te
th
at
t
h
i
s
f
ac
t
is
an
i
m
p
licatio
n
o
f
th
e
ch
o
s
e
n
s
at
u
r
atio
n
li
m
it
th
at
f
u
lf
i
lls
1
0
3
.
5.
DIS
CU
SS
I
O
N
AND
NUM
E
RICA
L
E
XAM
P
L
E
S
T
h
e
r
esu
lt
p
r
esen
ted
i
n
t
h
e
p
r
ev
io
u
s
s
ec
tio
n
p
r
o
v
id
es
ad
v
an
ce
m
e
n
t
i
n
to
t
w
o
d
ir
ec
tio
n
s
.
First,
its
as
y
m
p
to
ti
c
s
tab
ili
t
y
g
u
ar
a
n
tee
p
r
esen
ts
a
s
tr
o
n
g
er
s
tab
ilit
y
g
u
ar
a
n
tee
t
h
an
t
h
e
s
tab
ilit
y
g
u
ar
an
tee
p
r
ese
n
ted
in
[
1
0
]
,
i.e
.
b
o
u
n
d
ed
n
es
s
o
f
s
o
lu
tio
n
g
u
ar
a
n
tee.
Seco
n
d
,
t
h
i
s
r
esu
l
t
co
r
r
ec
ts
th
e
g
lo
b
al
s
ta
b
ilit
y
clai
m
i
n
[
1
3
]
,
as st
ated
in
R
e
m
ar
k
s
3
.
I
n
ad
d
itio
n
to
th
e
th
eo
r
etica
l
r
esu
lt,
t
h
e
at
titu
d
e
co
n
tr
o
l
s
y
s
t
e
m
’
s
p
er
f
o
r
m
a
n
ce
w
i
ll
b
e
ill
u
s
tr
ated
v
ia
s
i
m
u
lat
io
n
s
th
a
t
ar
e
r
u
n
t
h
r
o
u
g
h
th
r
ee
s
ce
n
ar
io
s
p
r
esen
ted
i
n
T
ab
le
1
an
d
th
e
r
est
ar
b
itra
r
y
-
c
h
o
s
e
n
p
ar
a
m
e
ter
s
ar
e
g
iv
e
n
in
T
ab
le
2
.
Sim
u
lat
i
o
n
r
esu
lt
s
ar
e
r
ep
r
esen
ted
in
F
ig
u
r
e
1
an
d
Fi
g
u
r
e
2
.
T
h
e
s
i
m
u
la
tio
n
o
f
Sce
n
ar
io
1
is
r
u
n
w
it
h
n
o
n
-
ze
r
o
in
i
tial
o
f
an
g
u
lar
v
elo
cit
y
b
bl
.
W
h
ils
t
i
n
Scen
ar
io
2
,
th
e
s
i
m
u
lat
io
n
is
r
u
n
w
it
h
ze
r
o
in
itial
o
f
an
g
u
lar
v
elo
cit
y
b
bl
.
Fig
u
r
e
1
(
a)
,
Fig
u
r
e
1
(
b
)
an
d
Fig
u
r
e
2
(
b
)
v
er
if
y
t
h
at
th
e
d
e
s
ig
n
ed
co
n
tr
o
ller
s
s
a
tis
f
y
t
h
e
T
h
eo
r
e
m
1
.
I
n
p
ar
ticu
lar
f
o
r
Sc
en
ar
io
2
,
it
is
v
er
y
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
C
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n
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ci
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ACK
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WL
E
D
G
E
M
E
NT
S
First
a
u
t
h
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r
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is
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to
ac
k
n
o
w
l
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g
e
A
b
d
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l
Kar
i
m
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MT
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Hea
d
o
f
P
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r
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m
s
a
n
d
Facili
ties
Div
is
io
n
,
Satellite
T
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n
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lo
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e
n
ter
L
A
P
A
N
f
o
r
s
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p
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tin
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.
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n
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t
h
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s
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p
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ted
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y
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en
elitian
Un
g
g
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la
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P
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g
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r
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a
n
T
in
g
g
i (
P
UPT
)
Kem
e
n
r
is
tek
d
i
k
ti 2
0
1
7
.
RE
F
E
R
E
NC
E
S
[1
]
K.
A
sh
o
k
,
R.
A
d
it
y
a
,
H.
K.
Jo
g
lek
a
r,
M
.
S
.
S
iv
a
,
N.
K.
P
h
il
i
p
,
“
CM
G
C
o
n
f
ig
u
ra
ti
o
n
a
n
d
S
tee
rin
g
A
p
p
ro
a
c
h
f
o
r
S
p
a
c
e
c
ra
f
t
Ra
p
id
M
a
n
e
u
v
e
rs
”
,
IFA
C
-
Pa
p
e
rs
On
L
in
e
,
v
o
l.
4
9
,
n
o
.
1
,
p
p
.
1
1
8
-
1
2
3
,
2
0
1
6
.
[2
]
J.
Ch
a
b
o
t,
H.
S
c
h
a
u
b
,
“
S
p
h
e
rica
l
M
a
g
n
e
ti
c
Dip
o
le
A
c
tu
a
to
r
f
o
r
S
p
a
c
e
c
ra
f
t
A
tt
it
u
d
e
Co
n
tr
o
l
”
,
J
.
Gu
id
.
C
o
n
tr
o
l.
Dy
n
.
,
v
o
l.
3
9
,
n
o
.
4
,
p
p
.
9
1
1
-
9
1
5
,
2
0
1
6
.
[3
]
D.
S
tev
e
n
so
n
,
H.
S
c
h
a
u
b
,
“
El
e
c
tro
sta
ti
c
S
p
a
c
e
c
ra
f
t
Ra
te
a
n
d
A
tt
it
u
d
e
Co
n
tro
l
-
Ex
p
e
rim
e
n
tal
Re
su
lt
s
a
n
d
P
e
rf
o
rm
a
n
c
e
Co
n
sid
e
ra
ti
o
n
s
”
,
Act
a
Astro
n
a
u
t.
,
v
o
l.
1
1
9
,
p
p
.
22
-
3
3
,
2
0
1
6
.
[4
]
S
.
Re
z
a
n
e
z
h
a
d
,
“
De
si
g
n
o
f
F
u
z
z
y
Op
ti
m
ize
d
Co
n
tro
ll
e
r
f
o
r
S
a
telli
te
A
tt
it
u
d
e
Co
n
tro
l
b
y
Tw
o
S
t
a
te
a
c
tu
a
to
r
to
re
d
u
c
e
L
i
m
it
C
y
c
l
e
b
a
se
d
o
n
T
a
k
a
g
i
-
S
u
g
e
n
o
M
e
th
o
d
”
,
In
t
.
J
.
El
e
c
tr.
Co
mp
u
t.
En
g
.
,
v
o
l.
4
,
n
o
.
2
,
p
p
.
3
0
3
-
3
1
3
,
2
0
1
4
.
[5
]
F
.
P
iro
u
z
m
a
n
d
,
“
Ro
b
u
st
M
o
d
e
l
P
re
d
ictiv
e
Co
n
tro
l
Ba
se
d
o
n
M
RA
S
f
o
r
S
a
tel
li
te
A
tt
it
u
d
e
Co
n
tro
l
S
y
ste
m
”
,
In
t.
J
.
El
e
c
tr.
Co
mp
u
t.
E
n
g
.
,
v
o
l
.
4
,
n
o
.
1
,
p
p
.
8
1
-
9
2
,
2
0
1
4
.
[6
]
S
.
P
.
Bh
a
t,
D
.
S
.
Be
rn
ste
in
,
“
A
to
p
o
lo
g
ica
l
Ob
stru
c
t
io
n
to
Co
n
ti
n
u
o
u
s
G
lo
b
a
l
S
tab
i
li
z
a
ti
o
n
o
f
Ro
t
a
ti
o
n
a
l
M
o
ti
o
n
a
n
d
t
h
e
Un
w
in
d
i
n
g
P
h
e
n
o
m
e
n
o
n
”
,
S
y
st.
C
o
n
tr
o
l
L
e
tt
.
,
v
o
l.
3
9
,
n
o
.
1
,
p
p
.
6
3
-
7
0
,
2
0
0
0
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
C
E
I
SS
N:
2
0
8
8
-
8708
A
s
ymp
to
tic
S
ta
b
ilit
y
o
f Q
u
a
tern
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n
-
b
a
s
ed
A
ttit
u
d
e
C
o
n
tr
o
l S
ystem
w
ith
….
(
Ha
r
r
y
S
ep
ta
n
to
)
2001
[7
]
W
.
M
a
c
k
u
n
is,
F
.
L
e
v
e
,
P
.
M
.
P
a
t
re
,
N.
F
it
z
-
c
o
y
,
W
.
E.
Dix
o
n
,
“
Ad
a
p
ti
v
e
Ne
u
ra
l
Ne
tw
o
rk
-
b
a
s
e
d
S
a
telli
te
A
tt
it
u
d
e
Co
n
tr
o
l
i
n
t
h
e
P
re
se
n
c
e
o
f
CM
G
Un
c
e
rtain
ty
”
,
Aer
o
sp
.
S
c
i.
T
e
c
h
n
o
l.
,
v
o
l.
5
4
,
p
p
.
2
1
8
-
2
2
8
,
2
0
1
6
.
[8
]
D.
Ca
lv
o
,
T
.
Av
il
é
s,
V
.
L
a
p
u
e
rta,
A
.
Lav
e
ró
n
-
S
im
a
v
il
la,
“
F
u
z
z
y
Atti
tu
d
e
Co
n
tr
o
l
f
o
r
a
N
a
n
o
sa
telli
te
in
L
o
w
Earth
Orb
it
”
,
Exp
e
rt
S
y
st.
A
p
p
l.
,
v
o
l.
5
8
,
p
p
.
1
0
2
-
1
1
8
,
2
0
1
6
.
[9
]
H.
S
e
p
tan
to
,
B.
R.
T
ril
a
k
so
n
o
,
A
.
S
y
a
i
c
h
u
-
ro
h
m
a
n
,
R.
E.
P
o
e
tro
,
A
.
R.
Ib
ra
h
im
,
“
No
n
li
n
e
a
r
Co
n
ti
n
u
o
u
s
Qu
a
tern
io
n
-
b
a
se
d
A
tt
it
u
d
e
Co
n
t
ro
l
ler
C
o
m
p
o
sin
g
A
u
g
m
e
n
ted
D
y
n
a
m
ic
”
,
ICIC
Exp
re
ss
L
e
tt
.
,
v
o
l.
8
,
n
o
.
1
1
,
p
p
.
3
2
4
5
–
3
2
5
0
,
2
0
1
4
.
[1
0
]
H.
S
e
p
tan
to
,
R.
T
.
Ba
m
b
a
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g
,
A
.
S
y
a
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u
-
ro
h
m
a
n
,
R.
E.
P
o
e
tr
o
,
A
.
R.
Ib
ra
h
im
,
“
Qu
a
tern
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-
Ba
se
d
A
tt
it
u
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e
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tr
o
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S
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st
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m
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si
g
n
o
f
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in
g
le an
d
C
o
o
p
e
ra
ti
v
e
S
p
a
c
e
c
ra
f
ts :
B
o
u
n
d
e
d
n
e
ss
o
f
S
o
lu
ti
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n
A
p
p
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a
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h
”
,
2
0
1
4
.
[1
1
]
P
.
C.
H
u
g
h
e
s,
S
p
a
c
e
c
ra
ft
At
ti
tu
d
e
Dy
n
a
mic
s
.
M
i
n
e
o
la,
Ne
w
Yo
rk
:
Do
v
e
r
P
u
b
li
c
a
ti
o
n
s,
I
n
c
.
,
2
0
0
4
.
[1
2
]
H.
K.
Kh
a
li
l,
No
n
li
n
e
a
r S
y
ste
ms
,
2
n
d
Ed
it
io
n
.
P
re
n
ti
c
e
Ha
ll
,
1
9
9
6
.
[1
3
]
H.
S
e
p
tan
to
,
B.
R.
T
ril
a
k
so
n
o
,
A
.
S
y
a
ich
u
-
ro
h
m
a
n
,
a
n
d
R.
E.
P
o
e
tr
o
,
“
T
h
e
S
a
t
u
ra
te
d
Qu
a
ter
n
io
n
Co
n
tro
l
L
a
w
wit
h
Ap
p
li
c
a
ti
o
n
f
o
r
S
p
a
c
e
c
ra
ft
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rm
a
ti
o
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Fl
y
i
n
g
”
,
P
r
o
c
.
2
0
1
2
I
EE
E
Co
n
f
.
Co
n
tro
l
.
S
y
st.
In
d
.
In
f
o
rm
a
ti
c
s
,
p
p
.
5
9
–
6
3
,
2
0
1
2
.
B
I
O
G
RAP
H
I
E
S
O
F
AUTH
O
RS
H
a
r
r
y
S
e
p
ta
n
to
re
c
e
i
v
e
d
th
e
BS
c
d
e
g
re
e
f
ro
m
En
g
in
e
e
rin
g
P
h
y
si
c
s,
In
stit
u
t
T
e
k
n
o
lo
g
i
Ba
n
d
u
n
g
in
2
0
0
2
.
He
re
c
e
iv
e
d
M
S
c
d
e
g
re
e
a
n
d
P
h
D f
ro
m
S
c
h
o
o
l
o
f
El
e
c
tri
c
a
l
En
g
in
e
e
rin
g
a
n
d
E
n
g
in
e
e
rin
g
,
In
stit
u
t
T
e
k
n
o
lo
g
i
Ba
n
d
u
n
g
in
2
0
1
0
a
n
d
2
0
1
5
,
re
sp
e
c
ti
v
e
ly
.
C
u
rre
n
tl
y
,
h
e
is
a
re
se
a
r
c
h
e
r
in
S
a
telli
te
T
e
c
h
n
o
lo
g
y
Ce
n
ter,
Na
t
io
n
a
l
I
n
stit
u
te
o
f
Ae
ro
n
a
u
ti
c
s
a
n
d
S
p
a
c
e
(L
A
P
AN
).
His
c
u
rre
n
t
re
se
a
rc
h
in
tere
sts
in
c
lu
d
e
sa
telli
te
a
tt
it
u
d
e
c
o
n
tro
ll
e
r
d
e
sig
n
,
w
h
e
e
l
d
riv
e
e
lec
tro
n
ics
f
o
r
sa
telli
te’s
re
a
c
ti
o
n
w
h
e
e
l
a
n
d
so
f
tw
a
re
si
m
u
lato
r
d
e
v
e
lo
p
m
e
n
t
f
o
r
sa
telli
te atti
tu
d
e
c
o
n
tro
l
sy
ste
m
s.
Djo
k
o
S
u
p
r
ija
n
to
r
e
c
e
iv
e
d
h
is
P
h
D
f
o
rm
K
y
u
sh
u
Un
iv
e
rsit
y
in
2
0
0
7
.
Cu
rre
n
tl
y
,
h
e
is
a
le
c
tu
re
r
a
n
d
m
e
m
b
e
r
o
f
Co
m
b
in
a
to
rial
M
a
th
e
m
a
ti
c
s
R
e
se
a
r
c
h
Div
isio
n
,
F
a
c
u
lt
y
o
f
M
a
th
e
m
a
ti
c
s
a
n
d
Na
tu
ra
l
S
c
ien
c
e
s,
In
stit
u
t
T
e
k
n
o
l
o
g
i
Ba
n
d
u
n
g
.
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