4-Body Problem of Classical Electrodynamics - Derivation of Equations of Motion (I)
Keywords:
Classical electrodynamics, 4-body problemAbstract
The primary purpose of the present paper is to continue the our previous investigations and apply the technique from the 2-body and 3-body problems of classical electrodynamics to the 4-body problem. First, we extend the problem for $N$ charged particles based on our previous results and introducing radiation terms. Moreover, we justify the radiation time within the framework of non-standard analysis. The equations of motion are neutral type nonlinear differential equations with state dependent delays. In the next papers we prove the existence-uniqueness of a periodic solution. In this way we hope to explain the existence of Lithium atom and Hydrogen molecules.
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