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Published 1998 | Accepted Version
Journal Article Open

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

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

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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August 19, 2023
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