On the dynamics of a rigid body in the hyperbolic space

SALVAI, MARCOS

JOURNAL OF GEOMETRY AND PHYSICS

ELSEVIER SCIENCE BV

Año: 2000 vol. 36 p. 126 - 139

0393-0440

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.