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Basic Equations of Differential Geodesy

  • Joseph Zund

Abstract

In this chapter we will apply the leg calculus as developed in Chapters IV and V to the geometry of the geopotential field of the Earth. This will yield the basic equations of differential geodesy. Our discussion is essentially a major reworking of the material contained in Hotine’s treatise, i.e. [Chapters 12 and 20], however, we make no use of the (ω,ϕ; N) coordinate system which he employed in his analysis. Consequently, our approach is more general and many of his derivations may be recast in a more lucid and less restrictive form, and our results are applicable to any choice of a local coordinate system involved in the local isometric imbedding of the family of equipotential surfaces Σ:= {S,S′,S″, …} in E3 in which S:= S3, and Γ:=Γ3 is a normal congruence of curves, ΓΣ, having the third leg vector v as its unit tangent.

Keywords

Basic Equation Local Coordinate System Covariant Differentiation Equipotential Surface Local Gravity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Joseph Zund
    • 1
  1. 1.Department of Mathematical SciencesNew Mexico State UniversityLas CrucesUSA

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