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Published 1991 | public
Book Section - Chapter

The Rotor and the Pendulum

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. Souriau

Additional details

Created:
August 19, 2023
Modified:
January 12, 2024