Document Type

Post-Print

Publication Date

3-2005

Abstract

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.

Document Object Identifier (DOI)

10.1016/j.geomphys.2004.06.007

Publication Information

Journal of Geometry and Physics

Included in

Mathematics Commons

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