The Electromagnetic Three-Body Problem With Radiation Terms - Derivation of Equations of Motion (I)

Abstract

The primary purpose of the present paper is to continue the previous investigations of the author and apply the technique from the two-body problem of classical electrodynamics to the three-body problem. We derive equations of motion with radiation terms which are neutral type nonlinear differential equations with statedependent delays. The derivation approach is analogous to that of the two body-problem, which allows a unified consideration of the problem for any number of bodies. In the next paper, we prove the existence of periodic solution of the three-body problem and in such a way the Bohr-Sommerfeld postulate for stationary states is confirmed.