Third-Order Clairaut Equation for a Rotating Body of Arbitrary Density and Its Application to Marine Geodesy.

Abstract

This report derives the Clairaut equations, which govern the deformation of the equipotential surfaces within a rotating mass in hydrostatic equilibrium, as ordinary differential equations containing up to third-order terms in a small parameter. This has been achieved by (a) eliminating the two integral terms which appeared in the original formulation, and (b) by expanding the equipotential surfaces into a power series of a small parameter which is essentially the ratio between the rotational and potential energy of the body.

Document Details

Document Type
Technical Report
Publication Date
Nov 08, 1974
Accession Number
ADA001304

Entities

People

  • Paolo Lanzano
  • Zdenek Kopal

Organizations

  • United States Naval Research Laboratory

Tags

DTIC Thesaurus Topics

  • Arrhenius Equation
  • Differential Equations
  • Energy
  • Equations
  • Integrals
  • Mathematical Analysis
  • Mathematics
  • Potential Energy
  • Power Series

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