Newton´s law and nonholonomic systems

We consider nonholonomic control systems on Riemannian manifolds. Such systems evolve on sub-bundles of tangent bundles, defined by the nonholonomic constraints. This paper promotes the view of such systems as the restriction to the nonholonomic sub-bundle of “Newton-law” type problems on the entire tangent bundle, defined by, in general, non-Riemannian connections. These connections should be related to specific geometric properties of the nonholonomic system. We define a particular class of connections based on special symmetry properties, and demonstrate the validity of the construction through three examples