The Jacobi's principle of stationary full action and its consequences

Abstract

The purpose of this article is to extend the applicability of the stationarity principle of the full Jacobi action to non-conservative natural systems and to derive equations of motion corresponding to this extended principle. To this end, in addition to the well-known variation of the Jacobi action with respect to coordinates, we propose independently variating time. Small variations in coordinates and time depend on the point on the true trajectory with the usual boundary conditions.