Generalization of direct and inverse Noether's theorem in generalized mechanics

Djordje Mušicki

Theoretical and applied mechanics, Tome 21 (1995) no. 1, p. 91

Résumé

In this article we have formulated Emmy Noether's theorem in generalized mechanics, which relates to the general case and is valid for arbitrary physical systems with nonpotential forces, without any additional assumptions. Here the starting point are such transformations of generalized coordinates and time which depend on higher order derivatives with respect to time, where the gauge function is also included, not assuming invariance of action in the absolute or extended sense. In this way we obtained the corresponding Noether theorem for such systems in a more general form, also the inverse Noether theorem and the corresponding Killing equations. Next, the case of degenerate systems is analyzed based on Dirac's theory, highlighting the differences from the usual case, as well as quasi-conservative systems, which can be reduced to those describable by a variational principle.