A NEW LOOK AT CLASSICAL MECHANICS OF CONSTRAINED SYSTEMS

A geometric formulation of Classical Analytical Mechanics, especially suited to the study of non-holonomic systems is proposed. The argument involves a preliminary study of the geometry of the space of kinetic states of the system, followed by a revisitation of Chetaev's definiti on of virtual work, viewed here as a cornerstone for the implementatio n of the principle of determinism. Applications to ideal non-holonomic systems (equivalence between d'Alembert's and Gauss' principles, equa tions of motion) are explicitely worked out.