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

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

2011-01-17

arxiv.org/abs/1101.3153v1

Int. J. Geom. Methods Mod. Phys. 8 (2011) 897-923

Mathematics

Differential Geometry

25 pages

Scientific paper

10.1142/S0219887811005452

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.

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