Geography Reference
In-Depth Information
For the deformation tensor of first order, we specialize C l =J l G r J l . In detail, we note
α
r
=
,
(19.2)
f ( Δ )
J l = D Λ αD Δ α
= n 0
, G r = r 2 0
= f 2 ( Δ )0
,
(19.3)
0 f ( Δ )
D Λ rD Δ r
01
01
c 11 = n 2 f 2 ( Δ ) , 12 =0 , 21 =0 , 22 = f 2 ( Δ ) ,
(19.4)
1
κ 1 =
A 1 (1 − E 2 )
M =
E 2 sin 2 Φ ) 3 / 2 (meridian radius) ,
(1
(19.5)
1
κ 2 =
A 1
N =
E 2 sin 2 Φ ) 1 / 2 (radius of curvature in the prime vertical) ,
(1
G l = N 2 cos 2 Φ 0
M 2 = N 2 sin 2 Δ 0
M 2 ,
(19.6)
0
0
and finally, we note the principal stretches
Λ 1 = c 11 /G 11 =
N sin Δ , Λ 2 = c 22 /G 22 = f ( Δ )
nf ( Δ )
.
(19.7)
M
Fig. 19.1. Mapping the ellipsoid-of-revolution to the cone, polar aspect, line-of-contact
 
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