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. https://resolver.caltech.edu/CaltechAUTHORS:20100913-092725646
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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.
| Item Type: | Article | ||||||||||||
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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.). | ||||||||||||
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| Subject Keywords: | Geometric mechanics; reduction; stability; chaos; rigid body dynamics; periodic orbits | ||||||||||||
| Issue or Number: | 3 | ||||||||||||
| Classification Code: | AMS: 58F | ||||||||||||
| DOI: | 10.1007/BF01053929 | ||||||||||||
| Record Number: | CaltechAUTHORS:20100913-092725646 | ||||||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20100913-092725646 | ||||||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||
| ID Code: | 19888 | ||||||||||||
| Collection: | CaltechAUTHORS | ||||||||||||
| Deposited By: | Ruth Sustaita | ||||||||||||
| Deposited On: | 16 Sep 2010 21:30 | ||||||||||||
| Last Modified: | 08 Nov 2021 23:55 |
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