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Published July 1989 | public
Journal Article

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

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.

Additional Information

© 1989 Plenum Publishing Corporation. Received July 22, 1988. This work was partially supported by DOE contract DE-AT03-85ER12097 and by AFOSR-URI grant AFOSR-87-0073 (Y.-G. O. and J. E. M.); and by the National Science Foundation under grant OIR-85-00108, AFOSR-87-0073, and by the Minta Martin Fund for Aeronautical Research (N. S. and P. S. K.).

Additional details

Created:
August 22, 2023
Modified:
October 20, 2023