Global Positioning System Reference
In-Depth Information
tan
a
cos
(
σ − α
)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
2
=
(A.23)
k
σ − β
tan
b
cos
(
)
2
=
(A.24)
k
tan
c
cos
(
σ − γ
)
2
=
(A.25)
k
L'Huilier-Serret Formulas
tan
s
−
a
tan
s
−
b
tan
s
−
c
·
·
2
2
2
M
=
(A.26)
[34
tan
s
2
Lin
—
0.1
——
Sho
*PgE
tan
ε
tan
s
2
4
=
M
·
(A.27)
tan
2
−
−
ε
4
cot
s
a
=
M
·
(A.28)
2
tan
2
−
ε
4
cot
s
−
b
=
M
·
(A.29)
2
[34
tan
2
−
ε
4
cot
s
−
c
=
M
·
(A.30)
2
The symbol
ε
denotes the spherical angular excess. The area of spherical triangle can
be expressed as
εr
2
∆ =
(A.31)
where
r
denotes the radius of the sphere.
A.2 ROTATION MATRICES
Rotations between coordinate systems are very conveniently expressed in terms of
rotation matrices. The rotation matrices
1
0
0
R
1
(
θ
)
=
0
cos
θ
sin
θ
(A.32)
0
−
sin
θ
cos
θ
