The Energy-Momentum Method for the Stability of Nonholonomic Systems
Abstract
In this paper we analyze the stability of relative equilibria of nonholonomic systems (that is, mechanical systems with nonintegrable 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 the rolling disk, the roller racer, and the rattleback top.
Additional Information
Research [D.V.Z.] partially supported by National Science Foundation PYI grant DMS-91-57556 and AFOSR grant F49620-96-1-0100. Research [A.M.B.] partially supported by National Science Foundation PYI grant DMS-91-57556, AFOSR grant F49620-96-1-0100, a Guggenheim Fellowship and the Institute for Advanced Study. Research [J.E.M.] partially supported by DOE contract DEFG0395-ER25251.Files
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Additional details
- Eprint ID
- 28133
- Resolver ID
- CaltechCDSTR:1997.010
- Created
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2007-12-19Created from EPrint's datestamp field
- Updated
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2019-10-03Created from EPrint's last_modified field
- Caltech groups
- Control and Dynamical Systems Technical Reports