Basic Equations of Differential Geodesy

  • Joseph Zund


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.


Basic Equation Local Coordinate System Covariant Differentiation Equipotential Surface Local Gravity 
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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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