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Stabilization of rigid body dynamics by the Energy-Casimir method. (English) Zbl 0701.93083

Summary: We show how the Energy-Casimir method [see V. Arnol’d, Ann. Inst. Fourier 16, No.1, 319-361 (1966; Zbl 0148.453)] 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.

MSC:

93D15 Stabilization of systems by feedback
70E99 Dynamics of a rigid body and of multibody systems
34D05 Asymptotic properties of solutions to ordinary differential equations

Citations:

Zbl 0148.453
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References:

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