Constrained Systems and Analytical Mechanics in Spases with Torsion

Abstract

A system with anholonomic constraints where the trajectories of physical degrees of freedom are autoparallels on a manifold equipped with a general Cartan connection is discussed. A variational principle for the autoparallel trajectories is derived from the d'Alambert-Lagrange principle for anholonomic constrained systems. A geometrical (coordinate-independent) formulation of the variational principle is given. Its relation to Sedov's anholonomic variational principle for dissipative systems and to Poincar\'e's variational principle in anholonomic reference frames is established. A modification of Noether's theorem due to the torsion force is studied. A non-local action whose extrema contain the autoparallels is proposed. The action can be made local by adding auxiliary degrees of freedom coupled to the original variables in a special way.