Stabilization of Rigid Body Dynamics by Internal and External Torques

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1990

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In this paper we discuss the stabilization of the rigid body dynamics by external torques (gas jets) and internal torques (momentum wheels). We compare the stabilizing quadratic quadratic feedback law for a single external torque recently analyzed in Bloch and Marsden [1989b,c] 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 Sanchez 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 stable equilibrium and we indicate how to compensate for this.

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