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.

Topics
Analytical mechanics, Gaussian processes
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© 1989 American Institute of Physics.
1989
American Institute of Physics
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