Contracting Forced Lagrangian and Contact Lagrangian Systems: application to nonholonomic systems with symmetries

In this paper we address the problem of identifying contracting systems among dynamical systems appearing in mechanics. First, we introduce a sufficient condition to identify contracting systems in a general Riemannian manifold. Then, we apply this technique to establish that a particular type of dissipative forced mechanical system is contracting, while stating immediate consequences of this fact for its stability. Finally, we use the previous results to study the stability of particular types of Contact and Nonholonomic systems.