Recent Developments in the Geodetic Boundary Value Problem,

Abstract

The report reviews progress in the mathematical formulation and treatment of the geodetic boundary-value problem, in particular, the existence and uniqueness theorems of L. Hormander and the gravity space approach due to F. Sanso. The method of Hormander uses a very advanced inverse function theorem of nonlinear functional analysis. Sanso has transformed Molodensky's free boundary-value problem into a fixed boundary-value problem in gravity space, thereby essentially reducing the mathematical complexity. As a linear approximation, the gravity space approach gives identical superior for treating questions of existence and uniqueness of the solution, although it is restricted to the pure gravitational case without centrifugal force. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1977
Accession Number
ADA053187

Entities

People

  • Helmut Moritz

Organizations

  • Ohio State University

Tags

Communities of Interest

  • Air Platforms
  • Energy and Power Technologies
  • Materials and Manufacturing Processes
  • Space

DTIC Thesaurus Topics

  • Air Force
  • Banach Space
  • Boundary Value Problems
  • Cartesian Coordinates
  • Centrifugal Force
  • Coordinate Systems
  • Differential Equations
  • Equations
  • Functional Analysis
  • Geodesy
  • Gravity
  • Integral Equations
  • Latitude
  • Longitude
  • Partial Differential Equations
  • Reference Ellipsoids
  • Spherical Harmonics

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Space Exploration and Orbital Mechanics.

Technology Areas

  • Space
  • Space - Orbital Debris