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Stabilization of rigid body dynamics by internal and external torques. (English) Zbl 0781.70020

The stabilization of a rigid body dynamics by external torques (gas jets) and internal torques (momentum wheels) is discussed. The starting point is a generalization of the stabilizing quadratic feedback law for a single external torque recently analyzed in a previous paper by two of the authors [A. M. Bloch and J. E. Marsden, Syst. Control Lett. 14, No. 4, 341-346 (1990; Zbl 0701.93083)]. It is shown 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 the other two authors [P. S. Krishnaprasad, Nonlinear Anal., Theory Methods Appl. 9, 1011-1035 (1985; Zbl 0626.70028); and G. Sánchez de Alvarez, Ph. D. Diss. (1986)]. Stabilization with a single rotor by using the energy-Casimir method is established. It is shown also how to realize the external torque feedback equations using internal torques. Finally, a formula for the amplitude drift for the rigid body- rotor system, when it is perturbed away from a stable equilibrium, is given and it is shown how to compensate for this.

MSC:

70Q05 Control of mechanical systems
70E15 Free motion of a rigid body
70M20 Orbital mechanics
70H05 Hamilton’s equations
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