Geography Reference
In-Depth Information
Fig. 17.4.
Image of the developed cone
Φ
). We therefore obtain the
general mapping equations for conical mappings (
17.2
) with the left Jacobi matrix (
17.3
)andthe
left Cauchy-Green matrix (
17.4
)(G
r
=diag[
r
2
,
1] = diag[
f
2
,
1]). For the reason that both C
l
and
G
r
are diagonal matrices, the left principal stretches are easily computed as follows (
17.5
).
which shall depend only on the latitude
Φ
=
Φ
P
, i.e.
r
=
f
(
π/
2
−
α
r
=
nΛ
,
(17.2)
f
(
Φ
)
J
l
=
n
0
,
(17.3)
0
f
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