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 non-linear kinetic constraints is proposed. The meaning of ideality for non-strictly mechanical systems is analyzed. 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 few examples and an appendix illustrating some properties of the manifold of admissible kinetic states are presented.