Non-holonomic Lagrangian and Hamiltonian Mechanics: an intrinsic approach

A geometrical approach to lagrangian and hamiltonian non-holonomic dynamics is proposed. The construction relies on a revisitation of the Poincaré-Cartan 1-form, leading to the introduction of the concepts of lagrangian and hamiltonian pairs and to the implementation of a non--holonomic Legendre map. The relationship with the standard "extrinsic" approach is outlined. A unified canonical framework, joining both lagrangian and hamiltonian aspects is proposed.