Geoscience Reference
In-Depth Information
Chapter 7
Establishment of Geodetic Coordinate
Systems
To describe the state of an object, we have to make clear what it is referenced to. In
the context of geodetic surveying, other than choosing a reference, one still needs to
carry out spatial positioning and orientation and specify the unit of measurement
(such as time scale, spatial scale, etc.). Therefore, it is necessary to establish a
terrestrial reference coordinate system (also known as reference system or coordi-
nate system, which are interpreted as synonyms here). Mathematically, it is unrea-
sonable to judge the merits and demerits of a coordinate system. Nevertheless, from
a physical and functional perspective, we should choose the proper reference
system, taking into account the operability and convenience of the issues being
studied.
This chapter discusses the principles for establishing classical and modern
geodetic coordinate systems, establishes the transformation models between differ-
ent coordinate systems, and provides an overview of the geodetic coordinate
systems in China and throughout the world.
7.1 Euler Angles in Geodetic Coordinate Systems
7.1.1 Vector Analysis in Coordinate Transformations
In Fig. 7.1 , two spatial Cartesian coordinate systems are introduced, O-XYZ and
O-X 0 Y 0 Z. Our discussion involves only the coordinate transformations under rota-
tion, so their origins are assumed to be coincident. The direction angles of the
coordinate axes OX 0 , OY 0 , and OZ 0 of O-X 0 Y 0 Z 0 with respect to the axes OX, OY, OZ
of the coordinate system O-XYZ are
α 1 ,
ʲ 1 ,
ʳ 1 ;
α 2 ,
ʲ 2 ,
ʳ 2 ; and
α 3 ,
ʲ 3 ,
ʳ 3 , respectively.
r denote the radius vector of a point M in space in relation to the coordinate
system O-XYZ and
Let
~
r 0 represent the radius vector of the same point in space relative
~
X 0 Y 0 Z 0 ; then it is obvious that:
to the system O
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