Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations

Abstract

A method for the analysis of perturbations of integrable planar systems of differential equations is developed. Concentrating on the case in which the unperturbed system is Hamiltonian and the perturbation introduces dissipation and time-periodic forcing, the global solution curves of the unperturbed system are used in regular perturbation calculations to locate subharmonic orbits and homoclinic orbits and to characterize the bifurcations in which they are created as external parameters are varied. The results are applied to Duffing's equation and applications to the chaotic motions of buckled elastic beams undergoing periodic excitation are given.

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Document Details

Document Type
Technical Report
Publication Date
Jul 15, 1981
Accession Number
ADA103564

Entities

People

  • Bernie D. Greenspan
  • Philip Holmes

Organizations

  • University of California, Berkeley

Tags

Communities of Interest

  • Air Platforms
  • Autonomy

DTIC Thesaurus Topics

  • Abstracts
  • Applied Mathematics
  • Applied Mechanics
  • Computations
  • Differential Equations
  • Dissipation
  • Equations
  • Excitation
  • Frequency
  • Integrals
  • Mathematics
  • Mechanics
  • New York
  • Partial Differential Equations
  • Perturbations
  • Sequences
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Control Systems Engineering.

Technology Areas

  • Space
  • Space - Orbital Debris