Stabilization of rigid body dynamics by the Energy-Casimir method

Abstract

We show how the Energy-Casimir method can be used to prove stabilizability of the angular momentum equations of the rigid body about its intermediate axis of inertia, by a single torque applied about the major or minor axis. We also show how this system has associated with it, a Lie-Poisson bracket which is invariant under SO(3) for small feedback, but is invariant under SO(2, 1) for feedback large enough to achieve stability.