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

Vasil Angelov

doi:10.53006/rna.833345

Abstract

In the present paper, the spin equations for the three-body problem of classical electrodynamics are introduced. They should be considered jointly with 3-body equations of motion derived in a previous paper of the author. The system of spin equations is an overdetermined one. It is shown that the independent spin equations are nine in number as many as the components of the unknown spin functions. The system obtained will be solved by the fixed-point method in the next paper.

Highlights

The present paper is one of the series devoted to study of the three-body problem of classical electrodynamics
In [5] we have formulated 3-dimensional three-body problem with radiation terms and in [6] we have proved the existence-uniqueness of periodic solution based on the previous results for two-body problem [2], [3]
In a similar way we extend the results from [4] applying the interaction presentation for N-body problem from [1] and derive spin equations for three charged particles

Summary

Introduction

The present paper is one of the series devoted to study of the three-body problem of classical electrodynamics. Lorentz parts we call the summands in the right-hand sides of the spin equations which take into account for a given particle the inuence of the rest ones. 2. Preliminary Results for3-Body Problem Equations of Motion with Radiation Terms and their Relations to Spin Equations. Following the approach from [4] and [10] we introduce spin equations jointly with equations of motion with radiation terms derived in [5] for three-body problem: dλ(r1) ds. In [6] an existence-uniqueness of a periodic solution of (2.1) is proved

Derivation of the Spin Equations

The Last Three Equations are Consequences of the First Three Ones