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The energy-momentum method for the stability of non-holonomic systems

Zenkov, Dmitry V. and Bloch, Anthony M. and Marsden, Jerrold E. (1998) The energy-momentum method for the stability of non-holonomic systems. Dynamics and Stability of Systems, 13 (3). pp. 123-165. ISSN 0268-1110 . http://resolver.caltech.edu/CaltechAUTHORS:20101026-090010743

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Abstract

In this paper, we analyze the stability of relative equilibria of non-holonomic systems (that is, mechanical systems with non-integrable constraints such as rolling constraints). In the absence of external dissipation, such systems conserve energy, but nonetheless can exhibit both neutrally stable and asymptotically stable, as well as linearly unstable relative equilibria. To carry out the stability analysis, we use a generalization of the energy-momentum method combined with the Lyapunov-Malkin theorem and the center manifold theorem. While this approach is consistent with the energy-momentum method for holonomic systems, it extends it in substantial ways. The theory is illustrated with several examples, including the rolling disk, the roller racer and the rattleback top


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http://dx.doi.org/10.1080/02681119808806257 DOIUNSPECIFIED
http://www.informaworld.com/smpp/content~db=all?content=10.1080/02681119808806257PublisherUNSPECIFIED
http://www.cds.caltech.edu/~marsden/bib/1998/03-ZeBlMa1998/AuthorUNSPECIFIED
Additional Information:© 1998, Research partially supported by National Science Foundation PYI grant DMS–94–96221 and AFOSR grant F49620-96-1-0100. Research partially supported by National Science Foundation PYI grant DMS–94–96221, AFOSR grant F49620-96-1-0100, a Guggenheim Fellowship and the Institute for Advanced Study. Research partially supported by the National Science Foundation. We would like to thank J. Burdick, P. Crouch, W. Koon, P. Krishnaprasad, and R. Murray for helpful comments and suggestions.
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NSFDMS-94-96221
AFOSRF49620-96-1-0100
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Deposited By: Ruth Sustaita
Deposited On:02 Dec 2010 00:07
Last Modified:26 Dec 2012 12:33

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