Geography Reference
In-Depth Information
S 2 R , conformal coordinates generated by the universal stereographic
projection, solution of the boundary value problem, departing point Frankfurt, arrival point Taipeh, time given
for constant speed movement with respect to the arrival point
Fig. E.1. Maupertuis gauged geodesic on
Box E.1 (The conformal coordinates as functions of spherical longitude and spherical latitude
and the factor of conformality).
(i) Universal Polar Stereographic Projection (UPS):
q 1 =2 R tan π
cos Λ, q 2 =2 R tan π
sin Λ,
Φ
2
Φ
2
4
4
(E.41)
λ =cos 2 π
=
Φ
2
4 R 2
4 R 2 +( q 1 ) 2 +( q 2 ) 2 ,
4
(E.42)
16 R 4
d s 2 =
(4 R 2 +( q 1 ) 2 +( q 2 ) 2 ) 2 [(d q 1 ) 2 +(d q 2 ) 2 ] .
(E.43)
 
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