Abstract
In Chapter 3 we briefly discussed the energy-momentum method for analyzing stability of relative equilibria of mechanical systems. In the nonholonomic case, while energy is conserved, momentum generally is not. In some cases, however, the momentum equation is integrable, leading to invariant surfaces that make possible an energy-momentum analysis similar to that in the holonomic case. When the momentum equation is not integrable, one can get asymptotic stability in certain directions, and the stability analysis is rather different from that in the holonomic case. Nonetheless, to show stability we will make use of the conserved energy and the dynamic momentum equation.
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© 2015 Springer-Verlag New York
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Bloch, A.M. (2015). Stability and Structure of Nonholonomic Systems. In: Krishnaprasad, P., Murray, R. (eds) Nonholonomic Mechanics and Control. Interdisciplinary Applied Mathematics, vol 24. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-3017-3_8
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DOI: https://doi.org/10.1007/978-1-4939-3017-3_8
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4939-3016-6
Online ISBN: 978-1-4939-3017-3
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