MOTION OF TWO WEAKLY COUPLED NONLINEAR OSCILLATORS,

Abstract

The purpose of this investigation was to establish the existence of almost periodic solutions for analytic dynamical systems consisting of two weakly coupled oscillators and to describe some qualitative features of these solutions. Hamiltonian formalism was used in the mathematics of this dynamical problem to realize simplicity of presentation and to agree with much of the literature concerning the problem. The method consisted primarily in the application of an invariant curve theorem due to Moser. The basic problem was given in terms of a Hamiltonian with the usual displacement and momentum variables. By changing to action-angle variables, by selecting a particular value of the energy and by eliminating time from the equations of motion, the study of the free oscillations of the two weakly coupled oscillators was reduced to the consideration of a one dimensional oscillator which is weakly forced with periodic forcing.

Document Details

Document Type
Technical Report
Publication Date
Sep 04, 1964
Accession Number
AD0617480

Entities

People

  • Raimond A. Struble
  • Thomas G. Proctor

Organizations

  • North Carolina State University

Tags

DTIC Thesaurus Topics

  • Displacement
  • Equations
  • Equations Of Motion
  • Formulas (Mathematics)
  • Literature
  • Mathematics
  • Mechanics
  • Oscillation
  • Oscillators

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Electronics Engineering