Holm, Darryl D. and Marsden, Jerrold E. (1991) The Rotor and the Pendulum. In: Proceedings of Colloquium in honor of Jean-Marie Souriau. Progress in Mathematics (99). Birkhauser Boston , pp. 189-203. ISBN 0817635815 http://resolver.caltech.edu/CaltechAUTHORS:20100812-075154192
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Abstract
We show that Euler's equations for a free rigid body, and for a rigid body with a controlled feedback torque each red lice to the classical simple pendulum equation under an explicit cylindrical coordinate change of variables. These examples illustrate several ideas in Hamiltonian mechanics: LiePoisson reduction, cotangent bundle reduction, singular Lie-Poisson maps, deformations of Lie algebras, brackets R3, simplifications obtained by utilizing the representation-dependence of Lie-Poisson reduction, and controlling instability by inducing global bifurcations among a set of equilibria using a control parameter.
| Item Type: | Book Section |
|---|---|
| Additional Information: | © 1991, In Honor of J.-M. Souriau |
| Record Number: | CaltechAUTHORS:20100812-075154192 |
| Persistent URL: | http://resolver.caltech.edu/CaltechAUTHORS:20100812-075154192 |
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. |
| ID Code: | 19403 |
| Collection: | CaltechAUTHORS |
| Deposited By: | Ruth Sustaita |
| Deposited On: | 13 Aug 2010 17:00 |
| Last Modified: | 26 Dec 2012 12:18 |
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