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 state-dependent 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.