Relative equilibria of a rigid satellite in a circular Keplerian orbit

We examine relative equilibria of a rigid body free to rotate about its center of mass which is constrained to follow a Keplerian orbit in a central gravitational field. We derive a noncanonical Hamiltonian formulation of this system and show how it relates to the noncanonical system for an unconstrained rigid body in a hierarchy of approximations of the two-body problem. For a particular approximation of the potential, the Keplerian system is equivalent to the classical approximation typically seen in the literature. We determine relative equilibria for this approximation and derive stability conditions for both arbitrary and axisymmetric bodies.