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Relative equilibria for the generalized rigid body

Hernández-Garduño, Antonio and Lawson, Jeffrey K. and Marsden, Jerrold E. (2005) Relative equilibria for the generalized rigid body. Journal of Geometry and Physics, 53 (3). pp. 259-274. ISSN 0393-0440.

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This paper gives necessary and sufficient conditions for the (n-dimensional) generalized free rigid body to be in a state of relative equilibrium. The conditions generalize those for the case of the three-dimensional free rigid body, namely that the body is in relative equilibrium if and only if its angular velocity and angular momentum align, that is, if the body rotates about one of its principal axes. For the n-dimensional rigid body in the Manakov formulation, these conditions have a similar interpretation. We use this result to state and prove a generalized Saari’s Conjecture (usually stated for the N-body problem) for the special case of the generalized rigid body.

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Additional Information:© 2004 Elsevier B.V. All rights reserved. JKL was supported by an ROA supplement to JEM’s grant NSF-DMS0204474. He thanks Control and Dynamical Systems at Caltech and Mathematics and Computer Science at St. Mary’s College of Maryland for their hospitality. JKL would also like to thank Manuele Santoprete for his comments
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Subject Keywords:Relative equilibrium; Generalized rigid body; Saari’s Conjecture
Classification Code:MSC: 37J15; 70E15
Record Number:CaltechAUTHORS:20100810-145729296
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19378
Deposited By: Ruth Sustaita
Deposited On:10 Aug 2010 23:31
Last Modified:26 Dec 2012 12:18

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