Symmetry and conservation laws in non-holonomic Mechanics

A geometric environment for the study of non-holonomic lagrangian systems is developed. A definition of admissible displacement valid in the presence of arbitrary nonlinear kinetic constraints is proposed. The meaning of ideality for non-strictly mechanical systems is analysed. The concepts of geometric and/or dynamical symmetry of a constrained system are discussed and embodied in a subsequent non-holonomic formulation of Noether theorem. A revisitation of the results in an extrinsic variational language is worked out. A couple of examples and an Appendix illustrating some properties of the manifold of admissible kinetic states are presented. Keywords: Non-holonomic constraints, Conservation laws, Variational principles in physics