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Special Issues
Mathematical Problems in Engineering
/
2012
/
Article
/
Tab 4
/
Research Article
Semianalytic Integration of High-Altitude Orbits under Lunisolar Effects
Table 4
Averaged moon direction coefficients
𝑡
𝑗
,
𝑘
. Here,
𝑐
≡
c
o
s
𝐽
,
𝑠
≡
s
i
n
𝐽
, and
𝑒
≡
𝑒
☾
.
𝑗
𝑘
𝑡
𝑗
,
𝑘
2
0
3
1
−
2
𝑒
2
1
4
(
2
−
3
𝜎
2
)
(
2
−
3
𝑠
2
3
)
−
3
𝜎
𝜅
𝑐
𝑠
c
o
s
𝑁
+
4
𝜎
2
𝑠
2
c
o
s
2
𝑁
±
1
3
1
−
2
𝑒
2
1
4
𝜎
𝜅
(
2
−
3
𝑠
2
1
)
+
2
(
1
−
2
𝜎
2
1
)
𝑐
𝑠
c
o
s
𝑁
−
4
𝜎
𝜅
𝑠
2
c
o
s
2
𝑁
±
2
3
1
−
2
𝑒
2
1
4
𝜎
2
(
2
−
3
𝑠
2
1
)
+
𝜎
𝜅
𝑐
𝑠
c
o
s
𝑁
+
4
(
2
−
𝜎
2
)
𝑠
2
c
o
s
2
𝑁
3
0
0
±
1
𝑒
1
4
(
4
−
5
𝜎
2
)
c
o
s
(
𝑁
+
𝜔
☾
5
)
−
2
𝜎
𝜅
𝑠
c
o
s
(
2
𝑁
+
𝜔
☾
)
±
2
𝑒
[
𝜎
𝜅
c
o
s
(
𝑁
+
𝜔
☾
)
+
(
1
−
2
𝜎
2
)
𝑠
c
o
s
(
2
𝑁
+
𝜔
☾
)
]
±
3
𝑒
9
4
𝜎
2
c
o
s
(
𝑁
+
𝜔
☾
9
)
+
2
𝜎
𝜅
𝑠
c
o
s
(
2
𝑁
+
𝜔
☾
)
4
0
3
8
(
8
−
4
0
𝜎
2
+
3
5
𝜎
4
)
−
1
5
2
(
4
−
7
𝜎
2
)
𝜎
𝜅
𝑠
c
o
s
𝑁
±
1
3
8
(
4
−
7
𝜎
2
3
)
𝜎
𝜅
+
8
(
4
−
2
9
𝜎
2
+
2
8
𝜎
4
)
𝑠
c
o
s
𝑁
±
2
3
8
(
6
−
7
𝜎
2
)
𝜎
2
+
3
2
(
3
−
7
𝜎
2
)
𝜎
𝜅
𝑠
c
o
s
𝑁
±
3
9
8
𝜎
3
9
𝜅
+
8
(
3
−
4
𝜎
2
)
𝜎
2
𝑠
c
o
s
𝑁
±
4
3
8
𝜎
4
+
3
2
𝜎
3
𝜅
𝑠
c
o
s
𝑁