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
=
nΛ
,
(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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