The dynamics of coupled planar rigid bodies. II. Bifurcations, periodic solutions, and chaos

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

Abstract

We give a complete bifurcation and stability analysis for the relative equilibria of the dynamics of three coupled planar rigid bodies. We also use the equivariant Weinstein-Moser theorem to show the existence of two periodic orbits distinguished by symmetry type near the stable equilibrium. Finally we prove that the dynamics is chaotic in the sense of Poincaré-Birkhoff-Smale horseshoes using the version of Melnikov's method suitable for systems with symmetry due to Holmes and Marsden.

Key words

Geometric mechanics reduction stability chaos rigid body dynamics periodic orbits 

AMS subject classification

58F 

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Copyright information

© Plenum Publishing Corporation 1989

Authors and Affiliations

  • Y. -G. Oh
    • 1
  • N. Sreenath
    • 2
  • P. S. Krishnaprasad
    • 2
  • J. E. Marsden
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeley
  2. 2.Department of Electrical Engineering and the Systems Research CenterUniversity of MarylandCollege Park

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