  This paper deals with conservation laws for mechanical systems with
nonholonomic constraints. It uses a Lagrangian formulation of nonholonomic
systems and a Cartan form approach. We present what we believe to be the most
general relations between symmetries and first integrals. We discuss the
so-called nonholonomic Noether theorem in terms of our formalism, and we give
applications to Riemannian submanifolds, to Lagrangians of mechanical type, and
to the determination of quadratic first integrals.
