Spin Three-Body Problem of Classical Electrodynamics with Radiation Terms (I) Derivation of Spin Equations

The paper is devoted to extension of Synge equations describing motion of two mass charged particles in the frame of classical relativistic electrodynamics including radiation terms and spin equations. In previous papers we have derived equations of motion just with radiation terms. Our radiation terms correspond to the Dirac physical assumptions but they differ from Dirac’s terms on the mathematical derivation. They generate neutral type equations of motion with both retarded and advanced arguments. Here we consider two-body problem with spin following the Corben’s technique. As in the original Synge model the number of the spin equations is more than the number of the unknown functions. We prove that six spin equations are a consequence of the rest ones and in this manner we obtain six equations for the six unknown spin functions. This consequence is in weak sense obtained by scalar multiplication.