43 2
20G eodetic mapping
Box 20.6 (Coefficients of the solution of the boundary value problem with respect to the Hamilton portrait
η
2
0 := E
2 /(1 − E
2 ) cos
2 B 0 , V
2
0 := 1 + η
2
0 , t 0 := tan B 0 ).
(10 ) = N 0 cos B 0 , (0 1) =
1
V
2
0
N 0 ,
(20 .97 )
(0 2) =
3η
2
0 t 0
2V
4
0
N 0 , (20 ) =
t 0
2
N 0 cos
2 B 0 ,
(20 .98 )
(11) = −
t 0
V
2
0
N 0 cos B 0 ,
(20 .99)
(12) = −
2 + 2 η
2
0 + 9 η
2
0 t
2
0
6V
4
0
N 0 cos B 0 , (21) =
1 − 3t
2
0 + η
2
0
6V
2
0
N 0 cos
2 B 0 ,
(20 .10 0
)
(0 3
) =
η
2
0 (1 − t
2
0 + η
2
0 + 4 η
2
0 t
2
0 )
2V
6
0
N 0 , (3 0
) = −
t
2
0
6
N 0 cos
3 B 0 ,
(20 .10 1)
(13 ) = −
η
2
0 t 0 (7 − 3t
2
0 + 7 η
2
0 + 12 η
2
0 t
2
0 )
6V
6
0
N 0 cos B 0 , (3 1) = −
t 0 (1 − t
2
0 + η
2
0 )
6V
2
0
N 0 cos
3 B 0 , (20 .10 2)
(40 ) =
t 0 (1 − t
2
0 + η
2
0 )
24
N 0 cos
4 B 0 ,
(20 .10 3
)
(22) =
−t 0 (4 + 3 η
2
0 + 9 η
2
0 t
2
0 − η
4
0 )
12V
4
0
N 0 cos
2 B 0 ,
(20 .10 4)
(0 4) =
−η
2
0 t 0 (4 + 17 η
2
0 − 9η
2
0 t
2
0 + 13 η
4
0 + 7
6 η
4
0 t
2
0 )
8V
8
0
N 0 ,
(20 .10 5)
(50 ) = −
t
2
0 (3 − t
2
0 + 3 η
2
0 )
120
N 0 cos
5 B 0 ,
(20 .10 6
)
(41) =
N 0 cos
4 B 0
3
6
0 V
2
0
[
7 − 50t
2
0 + 15 t
4
0 + 2 η
2
0 (7 − 3
7 t
2
0 ) + η
4
0 (7 − 24t
2
0 )] ,
(20 .10 7
)
(3 2) = −
N 0 cos
3 B 0
18 0 V
4
0
[
8 − 40t
2
0 + η
2
0 (16 − 3
1 t
2
0 − 45t
4
0 ) + η
4
0 (8+ 9 t
2
0 )] ,
(20 .10 8
)
(23 ) =
N 0 cos
2 B 0
18 0 V
6
0
[−8 − η
2
0 (7+ 17 4
t
2
0 − 45t
4
0 )+
+
2 η
4
0 (5 − 8
3 t
2
0 − 90t
4
0 ) + 3 η
6
0 (3+ 2 t
2
0 )] ,
(20 .10 9)
(14) = −
N 0 cos B 0
3
6
0 V
8
0
[
8+ 4
η
2
0 (28 − 6
9 t
2
0 )+
+η
4
0 (20 0 − 50 7 t
2
0 + 40 5 t
4
0 ) + 3 η
6
0 (3 2 − 7
7 t
2
0 − 1140t
4
0 )] ,
(20 .110 )
(0 5) =
N 0 η
2
0
40V
10
0
[−4 + 4 t
2
0 + η
2
0 (3 − 98t
2
0 + 15 t
4
0 )+
+
2 η
4
0 (9 − 17 9 t
2
0 + 90 t
4
0 ) + η
6
0 (11 − 256t
2
0 − 13 20 t
4
0 )] .
(20 .111)
20G eodetic mapping
Box 20.6 (Coefficients of the solution of the boundary value problem with respect to the Hamilton portrait
η
2
0 := E
2 /(1 − E
2 ) cos
2 B 0 , V
2
0 := 1 + η
2
0 , t 0 := tan B 0 ).
(10 ) = N 0 cos B 0 , (0 1) =
1
V
2
0
N 0 ,
(20 .97 )
(0 2) =
3η
2
0 t 0
2V
4
0
N 0 , (20 ) =
t 0
2
N 0 cos
2 B 0 ,
(20 .98 )
(11) = −
t 0
V
2
0
N 0 cos B 0 ,
(20 .99)
(12) = −
2 + 2 η
2
0 + 9 η
2
0 t
2
0
6V
4
0
N 0 cos B 0 , (21) =
1 − 3t
2
0 + η
2
0
6V
2
0
N 0 cos
2 B 0 ,
(20 .10 0
)
(0 3
) =
η
2
0 (1 − t
2
0 + η
2
0 + 4 η
2
0 t
2
0 )
2V
6
0
N 0 , (3 0
) = −
t
2
0
6
N 0 cos
3 B 0 ,
(20 .10 1)
(13 ) = −
η
2
0 t 0 (7 − 3t
2
0 + 7 η
2
0 + 12 η
2
0 t
2
0 )
6V
6
0
N 0 cos B 0 , (3 1) = −
t 0 (1 − t
2
0 + η
2
0 )
6V
2
0
N 0 cos
3 B 0 , (20 .10 2)
(40 ) =
t 0 (1 − t
2
0 + η
2
0 )
24
N 0 cos
4 B 0 ,
(20 .10 3
)
(22) =
−t 0 (4 + 3 η
2
0 + 9 η
2
0 t
2
0 − η
4
0 )
12V
4
0
N 0 cos
2 B 0 ,
(20 .10 4)
(0 4) =
−η
2
0 t 0 (4 + 17 η
2
0 − 9η
2
0 t
2
0 + 13 η
4
0 + 7
6 η
4
0 t
2
0 )
8V
8
0
N 0 ,
(20 .10 5)
(50 ) = −
t
2
0 (3 − t
2
0 + 3 η
2
0 )
120
N 0 cos
5 B 0 ,
(20 .10 6
)
(41) =
N 0 cos
4 B 0
3
6
0 V
2
0
[
7 − 50t
2
0 + 15 t
4
0 + 2 η
2
0 (7 − 3
7 t
2
0 ) + η
4
0 (7 − 24t
2
0 )] ,
(20 .10 7
)
(3 2) = −
N 0 cos
3 B 0
18 0 V
4
0
[
8 − 40t
2
0 + η
2
0 (16 − 3
1 t
2
0 − 45t
4
0 ) + η
4
0 (8+ 9 t
2
0 )] ,
(20 .10 8
)
(23 ) =
N 0 cos
2 B 0
18 0 V
6
0
[−8 − η
2
0 (7+ 17 4
t
2
0 − 45t
4
0 )+
+
2 η
4
0 (5 − 8
3 t
2
0 − 90t
4
0 ) + 3 η
6
0 (3+ 2 t
2
0 )] ,
(20 .10 9)
(14) = −
N 0 cos B 0
3
6
0 V
8
0
[
8+ 4
η
2
0 (28 − 6
9 t
2
0 )+
+η
4
0 (20 0 − 50 7 t
2
0 + 40 5 t
4
0 ) + 3 η
6
0 (3 2 − 7
7 t
2
0 − 1140t
4
0 )] ,
(20 .110 )
(0 5) =
N 0 η
2
0
40V
10
0
[−4 + 4 t
2
0 + η
2
0 (3 − 98t
2
0 + 15 t
4
0 )+
+
2 η
4
0 (9 − 17 9 t
2
0 + 90 t
4
0 ) + η
6
0 (11 − 256t
2
0 − 13 20 t
4
0 )] .
(20 .111)