Geography Reference
In-Depth Information
Left principal stretches:
tr[C
l
G
−
l
]
4det[C
l
G
−
l
]
,
(tr [C
l
G
−
l
])
2
=
1
2
Λ
1
,
2
=
Λ
2
±
−
(5.151)
±
C
l
G
−
l
=
,
1
cos
2
2
2sin
2
2
1
2
1
cos
2
2
1
tr [C
l
G
−
l
]=
1+cos
2
2
,
det [C
l
G
−
l
]=1
,
(5.152)
cos
2
2
1+cos
2
Δ
2
,
2
1
cos
4
2
−
4cos
4
Δ
2
(tr[C
l
G
−
l
])
2
−
4det[C
l
G
−
l
]=
⎡
⎣
1+cos
2
Δ
⎤
1+cos
2
Δ
2
2
=
1
2
1
cos
2
2
4cos
4
Δ
2
⎦
Λ
1
,
2
=
Λ
2
2
±
−
(5.153)
±
⇒
Λ
1
Λ
2
=1
.
With this box, we finish the discussion of the polar (normal) aspect of the mapping “sphere to
tangential plane”. In the chapter that follows, let us discuss the transverse aspect.
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