Geography Reference
In-Depth Information
A + B cos V 2 = f
f
Λ 1 =
(23.8d)
B
C l − Λ 2 G l =
− Λ 2 B 2 2
( A + B ) 2
Λ 2 ( A + B cos V ) 2
0
=0
(23.8e)
g 2
0
A + B cos V 2 = g
A + B
Λ 1 =
(23.8f)
B
2 :=
2
Box 23.3 (Conformal mapping of the torus
M
T
A,B onto the central plane parallel to
2 and onto the circular cylinder
2
T π/ 2
M
C
A + B ).
f
f
B
A + B cos V
Λ 1 ( V )= Λ 2 ( V ) ∀V ↔
=
(23.9a)
( A + B ) B
A + B cos V
g =
Λ 1 ( V )= Λ 2 ( V )
V
(23.9b)
B 2 arctan A B
+ln c f
2 B
A 2
B 2 tan V
ln f =
A 2
(23.9c)
2
B 2 arctan A
]
2 B
A 2
B
B 2 tan V
f ( V )= c f exp [
A 2
(23.9d)
2
− B 2 arctan A
+ c g
A + B
− B 2 tan V
B
A 2
A 2
g ( V )=2 B
(23.9e)
2
f (0) = A + B = c f
(23.9f)
f ( V )=( A + B ) exp
− B 2 arctan A
2 B
− B 2 tan V
B
A 2
A 2
(23.9g)
2
g (0) = 0 = c g
(23.9h)
B 2 arctan A
A + B
B
B 2 tan V
A 2
A 2
g ( V )=2 B
(23.9i)
2
Box 23.4 (Equiareal mapping of the torus M
2 := T
2 A,B onto the central plane parallel to
T π/ 2 M
2 and onto the circular cylinder C
A + B ).
ff = B ( A + B cos V )
Λ 1 Λ 2 ( V )=1
V
(23.10a)
B
A + B ( A + B cos V )
Λ 1 Λ 2 ( V )=1 ∀V ↔ g =
(23.10b)
1
2 f 2 = ABV + B 2 + c f
(23.10c)
f = 2 ABV + B 2 sin V +2 c f
(23.10d)
B 2
A + B sin V + c g
AB
A + B V +
g ( V )=
(23.10e)
 
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