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

The Cartan form for constrained Lagrangian systems and the nonholonomic Noether theorem