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

Abstract

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.

25 pages

References in corpus (2)

• Anholonomic frames in constrained dynamics
• Reduction of invariant constrained systems using anholonomic frames

Cited by in corpus (6)

• Noether Symmetries as a geometric criterion to select theories of gravity
• Conservation of energy and momenta in nonholonomic systems with affine constraints
• Hamiltonization of solids of revolution through reduction
• A Geometric Characterization of Certain First Integrals for Nonholonomic Systems with Symmetries
• Isotropic submanifolds and the inverse problem for mechanical constrained systems
• Geodesic extensions of mechanical systems with nonholonomic constraints