Lie aspects of the dynamics of self-gravitating ellipsoids in n dimensions.

In this paper we study the dynamics of self-gravitating ellipsoids in n dimensions, from the point of view of the Poisson structure of the dual of a suitable Lie algebra. When n=3 this was done by Rosenteel. In this setting we describe explicitly the ring of invariant functions. In the two-dimensional case we apply a technique due to Pedersen to find globally defined Darboux coordinates on the coadjoint orbits. Finally we derive a characterization of tensors coming from potentials, and use it to exhibit the dynamical equations of the ellipsoid in the Hamiltonian form. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]