Note on uniqueness for a one-dimensional two-body problem of classical electrodynamics

Abstract

A previous paper [Ann. Phys.21, 122 (1963)] gave a mathematical analysis of a two-body problem of classical electrodynamics incorporating retarded interactions (for the case of two charged particles remaining on the x axis). It was shown that the future trajectories would be uniquely determined, and well behaved, if past histories of the particles were given satisfying certin conditions, including a Lipschitz condition on the velocities. However, this Lipschitz condition has since become suspect as possibly unreasonable. The present note shows that it was, in fact, also superfluous.