Minimal energy configurations of gravitationally interacting rigid bodies

Consider a collection of n rigid, massive bodies interacting according to their mutual gravitational attraction. A relative equilibrium motion is one where the entire configuration rotates rigidly and uniformly about a fixed axis in R³. Such a motion is possible only for special positions and orientations of the bodies. A minimal energy motion is one which has the minimum possible energy in its fixed angular momentum level. While every minimal energy motion is a relative equilibrium motion, the main result here is that a relative equilibrium motion of n≥ 3 disjoint rigid bodies is never an energy minimizer. This generalizes a known result about point masses to the case of rigid bodies.