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Stabilization of Rigid Body Dynamics by Internal and External Torques

Bloch, A. M. and Krishnaprasad, P. S. and Marsden, J. E. and De Alvarez, G. Sanchez (1992) Stabilization of Rigid Body Dynamics by Internal and External Torques. Automatica, 28 (4). pp. 745-756. ISSN 0005-1098. doi:10.1016/0005-1098(92)90034-D.

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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). Our starting point is a generalization of the stabilizing quadratic feedback law for a single external torque recently analyzed in Bloch and Marsden [Proc. 27th IEEE Conf. Dec. and Can., pp. 2238-2242 (1989b); Sys. Can. Letts., 14,341-346 (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 [Nonlin. Ana. Theory Methods and App., 9, 1011-1035 (1985)] and Sanchez de Alvarez [Ph.D. Diss. (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 [Am. J. Phys., 59, 394-398 (1990)J, 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.

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Additional Information:© 1992 International Federation of Automatic Control. Received 11 September 1990; revised 13 June 1991; revised 1 October 1991; received in final form 13 January 1992. The original version of this paper was not presented at any IFAC meeting. This paper was recommended for publication in revised form by Associate Editor A. Isidori under the direction of Editor H. Kwakernaak.Department of Mathematics, The Ohio State University, Columbus, OH 43210, U.S.A. Research supported in part by grants from the NSF and AFOSR, by MSI at Cornell University and by a seed grant from the Ohio State University. Department of Electrical Engineering and Systems Research Center, University of Maryland, College Park, MD 20742, U.S.A. Research partially supported by the AFOSR University Research Initiative Program under grants AFOSR-87-0073 and AFOSR-90-0105, by the National Science Foundation's Engineering Research Centers Program NSFD CDR 8803012, and by the Army Research Office through the Mathematical Sciences Institute of Cornell University. Department of Mathematics, University of California, Berkeley, CA 94720, U.S.A. Research partially supported by DOE Contract DE-FG03-88ER-25064. II Department de Matematicas, Facultad de Cienclas, Universidad Los Andes, Merida, Venezuela.
Funding AgencyGrant Number
MSI/Cornell UniversityUNSPECIFIED
Ohio State UniversityUNSPECIFIED
Air Force Office of Scientific Research (AFOSR)AFOSR-87-0073
Air Force Office of Scientific Research (AFOSR)AFOSR-90-0105
NSFCDR 8803012
Department of Energy (DOE)DE-FG03-88ER-25064
Army Research Office (ARO)UNSPECIFIED
Universidad Los Andes, Merida, VenezuelaUNSPECIFIED
Subject Keywords:Stabilizers; feedback control; satellite control; attitude control; dynamic stability
Issue or Number:4
Record Number:CaltechAUTHORS:20100713-155533584
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19041
Deposited By: Ruth Sustaita
Deposited On:14 Jul 2010 19:28
Last Modified:08 Nov 2021 23:49

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