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

Oh, Y.-G and Sreenath, N. and Krishnaprasad, P. S. and Marsden, J. E. (1989) The dynamics of coupled planar rigid bodies. II. Bifurcations, periodic solutions, and chaos. Journal of Dynamics and Differential Equations, 1 (3). pp. 269-298. ISSN 1040-7294. doi:10.1007/BF01053929.

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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.

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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.).
Funding AgencyGrant Number
Department of Energy (DOE)DE-AT03-85ER12097
Air Force Office of Scientific Research (AFOSR)AFOSR-87-0073
Minta Martin Fund for Aeronautical ResearchUNSPECIFIED
Subject Keywords:Geometric mechanics; reduction; stability; chaos; rigid body dynamics; periodic orbits
Issue or Number:3
Classification Code:AMS: 58F
Record Number:CaltechAUTHORS:20100913-092725646
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19888
Deposited By: Ruth Sustaita
Deposited On:16 Sep 2010 21:30
Last Modified:08 Nov 2021 23:55

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