Noether's theory for non-conservative generalised mechanical systems

Abstract

Noether's theorem and Noether's inverse theorem for generalised mechanical systems described by Lagrangian functions of the second order and non-conservative forces are established. The existence of the first integral depends on the existence of solutions of the generalised Noether-Bessel-Hagen equation. The theory is based on the idea that the transformations of time and generalised coordinates together with non-conservative forces determine the transformations of velocities and accelerations. An illustrative problem is discussed.