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Stabilization of rigid body dynamics by the Energy-Casimir method

Bloch, Anthony M. and Marsden, Jerrold E. (1990) Stabilization of rigid body dynamics by the Energy-Casimir method. Systems and Control Letters, 14 (4). pp. 341-346. ISSN 0167-6911. doi:10.1016/0167-6911(90)90055-Y.

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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.

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Additional Information:© 1990 Elsevier. Received October 1989. Revised February 1990. Available online 3 March 2003. Research supported in part by NSF Grant DMS-87-01S16, AFOSR Grant AFOSR-ISSA-87-0077, and MSI at Cornell University. Reserach partially supported by AFOSR Grant AFOSR- 89-0226A. and MSI and Cornell University
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)ISSA-87-0077
MSI/Cornell UniversityUNSPECIFIED
Air Force Office of Scientific Research (AFOSR)89-0226A
Subject Keywords:Stabilization; feedback; rigid body; Energy-Casimir; Hamiltonian.
Issue or Number:4
Record Number:CaltechAUTHORS:20100714-145003782
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19053
Deposited By: Ruth Sustaita
Deposited On:15 Jul 2010 00:23
Last Modified:08 Nov 2021 23:49

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