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The right eigenvectors of the right Cauchy-Green deformation tensor normalized with respect to
the right metric tensor G
r
=I
2
can be represented by
λ
1
)
e
1
λ
2
)
e
2
f
r
1
=
−
C
12
e
2
+(
C
22
−
,f
r
2
=
−
C
12
e
1
+(
C
11
−
C
12
+(
C
22
−
C
12
+(
C
11
−
,
(F.74)
λ
1
)
2
λ
2
)
2
2
,δ
αβ
}
namely with respect to the orthonormal basis
{
e
1
,e
2
}
which spans
{
R
. The coordinates
of the eigenvectors
{
f
r
1
,
f
r
2
}
generate the orthonormal matrix
F
r
=
cos
ϕ
sin
ϕ
=[
f
r
1
,
f
r
2
]
,
(F.75)
−
sin
ϕ
cos
ϕ
such that
C
12
2
C
12
2
C
12
C
11
C
22
− C
11
−
(
C
11
− C
22
)
2
+(2
C
12
)
2
,
cot
ϕ
=
tan
ϕ
=
λ
2
)
=
C
22
.
(F.76)
−
(
C
22
−
−
End of Corollary.
Fig. F.4.
Vertical weighted mean of the generalized Lambert projection and the generalized Sanson-Flamsteed
projection of the biaxial ellipsoid
E
2
A,B
, squared relative eccentricity
E
2
=0
.
1, weight parameters
α
=0
.
5,
β
=1
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