On the dynamics of a rigid body in the hyperbolic space

Abstract

Let H be the three-dimensional hyperbolic space and let G be the identity component of the isometry group of H. It is known that some aspects of the dynamics of a rigid body in H contrast strongly with the Euclidean case, due to the lack of a subgroup of translations in G. We present the subject in the context of homogeneous Riemannian geometry, finding the metrics on G naturally associated with extended rigid bodies in H. We concentrate on the concept of dynamical center, characterizing it in various ways.