Geography Reference
In-Depth Information
6
o
9
o
12
o
15
o
56
o
56
o
55
o
55
o
54
o
54
o
53
o
53
o
52
o
52
o
51
o
51
o
50
o
50
o
49
o
49
o
48
o
48
o
47
o
47
o
Harmonic Map with Tissot Ellipses
B=[46 , 56 ], Bo=51
o
o
o
o
o
(7.5 , 10.5 );(10.5 , 13.5 );(13.5 , 16.5 )
o
o
o
o
o
o
L=[(4.5 , 7.5 );
]
46
o
46
o
Equidistant Meridian
6
o
,
9
o
,
12
o
,
15
o
6
o
9
o
12
o
15
o
[46
◦
,
+56
◦
]; [4
.
5
◦
,
7
.
5
◦
]or[7
.
5
◦
,
10
.
5
◦
]
or
[10
.
5
◦
,
13
.
5
◦
]
or
Fig. 22.5.
Special harmonic map of the region (
B,L
)
∈{
[13
.
5
◦
,
16
.
5
◦
]
6
◦
,
9
◦
,
12
◦
,
15
◦
}
,B
0
=51
◦
}
L
0
∈{
or pushforward
(
x, y
)in
I
l
=
dS
2
=
N
2
(cos
B
)
2
dL
2
+
M
2
dB
2
by means of the
right Jacobi map
J
r
such that the
right Cauchy-Green deformation tensor
C
r
=
J
r
G
l
J
r
is generated.
The matrix pairs
•
are subject of simultaneous diagonalization. Table
22.2
introduces the computation of the
left Cauchy-Green deformation tensor
C
l
:Table
22.26
out-
lines the derivation of
left eigenvalues Λ
1
,
2
by means of solving the general characteristic equation
|
{
G
l
,
C
l
}
,
{
C
r
,
G
r
}
Λ
l
G
l
=0.Table
22.27
summarizes the computation of the left eigenspace analysis by
the derivation of
left eigenvectors
C
l
−
|
constituting the
left Frobenius matrix
F
l
.Incon-
trast, Table
22.28
starts from the computation of the
right Cauchy-Green deformation tensor
C
l
:
Table
22.29
aims at deriving the
right eigenvalues λ
1
,
2
by means of solving the general character-
istic equation
{
F
1
l
,
F
2
l
}
Λ
r
G
r
= 0. We complete the right eigenspace analysis by deriving the
right
eigenvector {
F
1
r
,
F
2
r
}
which constitute the
right Frobenius matrix
F
r
.
|
C
r
−
|
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