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 definition of virtual work, viewed here as a cornerstone for the implementation of the principle of determinism. Applications to ideal non-holonomic systems are explicitly worked out.