Kinematics for rolling a Lorentzian sphere

We derive the equations of motion for the n-dimensional Lorentzian sphere (one-sheet hyperboloid) rolling, without slipping and twisting, over the affine tangent space at a point. Both manifolds are endowed with semi-Riemannian metrics, induced by the Lorentzian metric on the embedding manifold which is the generalized Minkowski space. The kinematic equations turn out to be a nonlinear control system evolving on a connected subgroup of the Poincaré group. The controls correspond to the choice of the curves along which the Lorentzian sphere rolls. Controllability of this rolling system will be proved by showing that the corresponding distribution is bracket-generating.