Two-dimensional Coulomb dynamics of two and three equal negative charges in the field of two equal fixed positive charges

Abstract

Periodic and bounded for positive time solutions of the planar Coulomb equation of motion for two and three identical negative charges in the field of two equal fixed positive charges are found. The systems possess equilibrium configurations to which the found bounded solutions converge in the infinite time limit. The periodic solutions are obtained with the help of the Lyapunov center theorem.