Quasi-Exact Coulomb Dynamics of n Charges n - 1 of Which Are Equal

Abstract EN

For n ≥ 3 point charges n - 1 of which are negative and equal quasi-exact periodic solutions of their Coulomb equation of motion are found.

These solutions describe a motion of the negative charges around a coordinate axis in such a way that their coordinates coincide with vertices of a regular polygon in planes perpendicular to the axis along which the positive charge moves.

The Weinstein and center Lyapunov theorems are utilized.