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1
2
1
2 cos 2B,
sin 2 B
3
8
1
2 cos 2B
1
8 cos 4B,
sin 4 B
þ
5
16
15
32 cos 2B
3
16 cos 4B
1
32 cos 6B,
sin 6 B
þ
Hence, it follows that:
3
2
3
4 e 2
3
4 e 2 cos 2B
45
64 e 4
15
16 e 4 cos 2B
e 2 sin 2 B
ð
1
Þ
1
þ
þ
15
64 e 4 cos 4B
175
256 e 6
525
512 e 6 cos 2B
105
256 e 6 cos 4B
35
512 e 6 cos 6B
þ
þ
þ
þ
A 0
B 0 cos 2B
C 0 cos 4B
D 0 cos 6B
E 0 cos 8B
F 0 cos 10B,
þ
þ
ð
5
:
38
Þ
where the coefficients in the equation are:
9
=
;
3
4 e 2
45
64 e 4
175
256 e 6
11025
16384 e 8
43659
65536 e 10
A 0
1
þ
þ
þ
þ
þ
3
4 e 2
15
16 e 4
525
512 e 6
2205
2048 e 8
72765
65536 e 10
B 0
þ
þ
þ
þ
15
64 e 4
105
256 e 6
2205
4096 e 8
10395
16384 e 10
C 0
þ
þ
þ
:
35
512 e 6
315
2048 e 8
31185
131072 e 10
D 0
þ
þ
315
16384 e 8
3465
65536 e 10
E 0
þ
...
639
131072 e 10
F 0
...
These coefficients are all constants for the defined ellipsoid.
Substituting ( 5.38 ) into ( 5.37 ), integration yields:
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