Published 1991
| public
Book Section - Chapter
The Rotor and the Pendulum
- Creators
- Holm, Darryl D.
- Marsden, Jerrold E.
- Others:
- Donato, P.
- Duval, C.
- Elhadad, J.
- Tuynman, G. M.
Chicago
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.
Additional Information
© 1991, In Honor of J.-M. SouriauAdditional details
- Eprint ID
- 19403
- Resolver ID
- CaltechAUTHORS:20100812-075154192
- Created
-
2010-08-13Created from EPrint's datestamp field
- Updated
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2019-10-03Created from EPrint's last_modified field
- Series Name
- Progress in Mathematics
- Series Volume or Issue Number
- 99