Stabilization of rigid body dynamics by internal and external torques

Bloch, A. M., P. S. Krishnaprasad, J. E. Marsden, and G. Sánchez De Alvarez

Automatica, 28, 745-756

Abstract:

In this paper we discuss the stabilization of the rigid body dynamics by external torques (gas jets) and internal torques (momentum wheels). Our starting point is a generalization of the stabilizing quadratic feedback law for a single external torque recently analyzed in Bloch and Marsden [1989b, 1990] with quadratic feedback torques for internal rotors. We show that with such torques, the equations for the rigid body with momentum wheels are Hamiltonian with respect to a Lie-Poisson bracket structure. Further, these equations are shown to generalize the dual-spin equations analyzed by Krishnaprasad [1985] and Sánchez de Alvarez [1986]. We establish stabilization with a single rotor by using the energy-Casimir method. We also show how to realize the external torque feedback equations using internal torques. Finally, extending some work of Montgomery [1990], we derive a formula for the attitude drift for the rigid body-rotor system when it is perturbed away from a stable equilibrium and we indicate how to compensate for this.