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.