Horseshoes in Perturbations of Hamiltonian Systems with two Degress of Freedom.

Abstract

This paper concerns Hamiltonian and non-Hamiltonian perturbations of integrable two degree of freedom Hamiltonian systems which contain homoclinic and periodic orbits. Our main example concerns perturbations of the uncoupled system consisting of the simple pendulum and the harmonic oscillator. We show that small coupling perturbations with, possibly, the addition of positive and negative dampling breaks the integrability by introducing horseshoes into the dynamics. (Author)

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1981
Accession Number
ADA103565

Entities

People

  • Jerrold E. Marsden
  • Philip Holmes

Organizations

  • University of California, Berkeley

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Applied Mechanics
  • Calorific Value
  • Celestial Mechanics
  • Computational Science
  • Differential Equations
  • Diffusion
  • Dynamics
  • Energy Bands
  • Energy Transfer
  • Equations
  • Equations Of Motion
  • Mechanics
  • Molecular Mechanics Methods
  • Orbits
  • Oscillators
  • Partial Differential Equations
  • Transverse

Fields of Study

  • Physics

Readers

  • Calculus or Mathematical Analysis
  • Control Systems Engineering.

Technology Areas

  • Space
  • Space - Orbital Debris