ON CONSTRAINED MECHANICAL SYSTEMS: D'ALEMBERT'S AND GAUSS' PRINCIPLES

A geometric formulation of the classical principles of D'Alembert and Gauss in analytical mechanics is given, and their equivalence for possibly non-Riemannian mechanical systems is shown, in the case of ideal holonomic constraints. This is done by means of a Gauss' function, which is defined in a natural way on the bundle of two-jets on the configuration space, and which gives the "intensity" of the "reaction forces" of the constraints. It is originated by a metric structure on the bundle of semibasic forms on the phase space determined by the Finslerian kinetic energy functions of the mechanical system. © 1989 American Institute of Physics.