On constrained mechanical systems: D’Alembert’s and Gauss’ principles

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Abstract
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.

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