Periodic Solutions of Hamiltonian Systems: A Survey,

Abstract

Hamiltonian systems of ordinary differential equations model the motion of a discrete mechanical system. During the past few years there has been a considerable amount of progress in the study of periodic solutions of such systems with many new ideas and methods of solution being introduced. The purpose of this paper is to survey these recent developments and their connection with some earlier results. In particular the main results that have been obtained will be stated and an indication will be given of their proofs. A few open questions will also be mentioned. In conclusion it should be mentioned that one of the main sources of inspiration for the development of Hamiltonian mechanics was the field of celestial mechanics. In this field, one encounters Hamiltonians which possess singularities. We believe celestial mechanics is a very interesting and possibly fertile proving ground for the further development of the ideas and methods described in this study.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1979
Accession Number
ADA093444

Entities

People

  • Paul H. Rabinowitz

Organizations

  • University of Wisconsin Madison Department of Mathematics

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Boundary Value Problems
  • Calculus
  • Calculus Of Variations
  • Celestial Mechanics
  • Differential Equations
  • Differential Geometry
  • Energy
  • Equations
  • Euler Equations
  • Geometry
  • Mechanics
  • Orbits
  • Periodic Functions
  • Point Theorem
  • Potential Energy
  • Variational Methods
  • Variational Principles

Readers

  • Calculus or Mathematical Analysis
  • Systems Analysis and Design