Geography Reference
In-Depth Information
Section 15-4.
Section
15-4
introduces by four corollaries the left
Cauchy-Green tensor
and the
dilatation fac-
tor
for both the
UTM reference frame
as well as the
Gauss-Krueger reference frame
with the
values (
15.2
)and(
15.3
) based upon the geometry of the “Geodetic Reference System 1980”
(
Moritz 1984
). Such a result was achieved by (i) minimizing the total distance distortion or (ii)
minimizing the total areal distortion with the identical result.
UTM:
3
.
5
◦
,
+3
.
5
◦
]
[80
◦
S
,
84
◦
N]
,
[
−
l
E
,
+
l
E
]
×
[
B
S
,B
N
]=[
−
×
(15.2)
ρ
=0
.
999578
(scale reduction factor 1 : 2370)
,
Gauss-Krueger:
[
−l
E
,
+
l
E
]
×
[
B
S
,B
N
]=[
−
2
◦
,
+2
◦
]
×
[80
◦
S
,
80
◦
N]
,
(15.3)
ρ
=0
.
999 864
(scale reduction factor 1: 7353).
(The symbols S, N, E, and W as indices denote South, North, East, and West.)
Section 15-5.
Examples are the subject of Sect.
15-5
. In particular, compare with Figs.
15.6
,
15.7
,
15.8
,
15.9
,
15.10
,
15.11
,
15.12
,
15.13
,
15.14
,
15.15
,and
15.16
dealing with the
transverse Mercator projection
.
Section 15-6.
Strip transformations
of conformal coordinates of type
Gauss-Krueger
as well as of type
UTM
are finally the subject of Sect.
15-6
.
Appendix
In Appendix
D
, we outline the theory of the
Cauchy-Green deformation tensor
and its related
general
eigenvalue-eigenvector problem
, in particular, its conformal structure, which leads us to
three forms of the related
Korn-Lichtenstein equations
.
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