THE TWO VARIABLE EXPANSION PROCEDURE FOR THE APPROXIMATE SOLUTION OF CERTAIN NON-LINEAR DIFFERENTIAL EQUATIONS,

Abstract

A method is presented for deriving the asymptotic representation valid for large times for the motion of a particle under the influence of a predominantly linear restoring force and small nonlinear perturbations. It is shown that such an asymptotic representation must be a function of two time variables, in order to depict the behavior of the solution. The basic ideas are explained by the liberal use of simple examples, and the method is also applied to two idealized problems in celestial mechanics. (Author)

Document Details

Document Type
Technical Report
Publication Date
Dec 03, 1962
Accession Number
AD0426822

Entities

People

  • J. Kevorkian

Organizations

  • Douglas

Tags

DTIC Thesaurus Topics

  • Astronomy
  • Celestial Mechanics
  • Differential Equations
  • Equations
  • Linear Differential Equations
  • Mathematical Analysis
  • Mathematics
  • Mechanics
  • Nonlinear Differential Equations
  • Particles
  • Perturbations
  • Real Variables
  • Universities

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Geodesy
  • Military History of the United States in the 20th Century.