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