Mechanical Hamiltonization of unreduced $\ddot{I}•$-simple Chaplygin systems

Abstract

In this paper, we prove that the trajectories of unreduced $\ddot{I}•$-simple Chaplygin kinetic systems are reparametrizations of horizontal geodesics with respect to a modified Riemannian metric. Furthermore, our proof is constructive and these Riemannian metrics, which are not unique, are obtained explicitly in interesting examples. We also extend these results to $\ddot{I}•$-simple Chaplygin mechanical systems (not necessarily kinetic).