Periodic and Bounded Solutions of the Coulomb Equation of Motion of Two and Three Point Charges with Equilibrium in the Line

Abstract

Periodic and bounded solutions of the Coulomb equation of motion in the line are obtained for two and three identical negative point charges in the fields of two and three symmetrically located fixed point charges. The systems possess equilibrium configurations. The Lyapunov, Siegel, Moser, and Weinstein theorems are applied.