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The Rotor and the Pendulum

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. No.99. Birkhauser Boston , pp. 189-203. ISBN 0817635815.

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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
Series Name:Progress in Mathematics
Issue or Number:99
Record Number:CaltechAUTHORS:20100812-075154192
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19403
Deposited On:13 Aug 2010 17:00
Last Modified:03 Oct 2019 01:56

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