The Dynamics of Coupled Planar Rigid Bodies. Part 1. Reduction, Equilibria and Stability,

Abstract

This paper studies the dynamics of coupled planar rigid bodies, concentrating on the case of two or three bodies coupled with a hinge joint. The Hamiltonian structure is non-canonical and is obtained using the methods of reduction, starting from canonical brackets on the cotangent bundle of the configuration space in material representation. The dynamics on the reduced space for two bodies occurs on cylinders in IR(3); stability of the equilibria is studied using the Energy-Casimir method and is confirmed numerically. The phase space of the two bodies contains a homoclinic orbit which produces chaotic solutions when the system is perturbed by a third body. This and a study of periodic orbits are discussed in part II. The number and stability of equilibria and their bifurcations for three bodies as system parameters are varied are studied here; in particular, it is found that there are always 4 or 6 equilibria.

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Document Details

Document Type
Technical Report
Publication Date
Jul 30, 1987
Accession Number
ADA187467

Entities

People

  • J. E. Marsden
  • N. Sreenath
  • P.S.Krishnaprasad
  • Y. G. Oh

Organizations

  • University of Maryland

Tags

Communities of Interest

  • Energy and Power Technologies
  • Space

DTIC Thesaurus Topics

  • Angular Momentum
  • Classification
  • Coordinate Systems
  • Dynamics
  • Electrical Engineering
  • Energy
  • Equations
  • Equations Of Motion
  • Inertia
  • Kinetic Energy
  • Mechanics
  • Molecular Mechanics Methods
  • Moment Of Inertia
  • Momentum
  • Security
  • Three Dimensional
  • Two Dimensional

Readers

  • Control Systems Engineering.

Technology Areas

  • Space
  • Space - Orbital Debris
  • Space - Spacecraft Maneuvers