Generalized Dynamics of the Mass Point with Internal Degrees of Freedom

Abstract

An equation of motion of the mass point with internal degrees of freedom in scalar potential $U$ depending on relative coordinates and time, velocity and accelerations is obtained both for non-relativistic and relativistic case. In non-relativistic case a generalization of the energy conservation law follows, if $\partial U/\partial t=0$ fulfilled. A concept of work is generalized to relativistic case, leading to corresponding integral of motion, if $\partial U/\partial \tau =0$ fulfilled, where $\tau$ is proper time of the point. In neglecting an internal degrees of freedom and absence of interaction this integral of motion gives standard Special Relativity.

Talk presented at 15-th International Conference and School "Foundation & Advances in Nonlinear Science", September 20-23, 2010 (Minsk, Belarus)