On the Linearization of the Geodetic Boundary Value Problem,

Abstract

The geodetic boundary value problem consists in determining an unknown closed surface from the boundary values of an external potential and its gradient. A rigorous mathematical formulation of this problem is given leading to a system of non-linear integro-differential equations. The formalism of differentiation in function spaces is applied yielding a linearized version which involves no further neglections and approximations. Tensor calculus is used in linearizing the various differential geometric quantities. The results are specialized to a linearization with respect to the equipotential sphere in which case the formulas of Stokes and Vening Meinesz are simultaneously obtained. (Author)

Document Details

Document Type
Technical Report
Publication Date
May 01, 1971
Accession Number
AD0728632

Entities

People

  • Peter Meissl

Organizations

  • Ohio State University

Tags

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Value Problems
  • Calculus
  • Calculus Of Variations
  • Differential Equations
  • Equations
  • Mathematics

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis

Technology Areas

  • Space