On the one-dimensional symmetric two-body problem of classical electrodynamics

Abstract

The functional-differential equation which describes the one-dimensional symmetric motion of two charged particles in the framework of classical electrodynamics is considered. In the case of the charges of a like sign it is proved that the global solution exists and it is specified uniquely by the instantaneous initial data, if the classical energy at the initial moment is sufficiently small. In the case of the charges of opposite sign there are additional restrictions on the initial data. The estimates are given which allow one to obtain an approximate description of motion.