Relative equilibria for the generalized rigid body
Hernández-Garduño, A., J. K. Lawson, and J. E. Marsden
Journal of Geometry and Physics, 53, (2005), 259-274
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.