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Advances in Mathematical Physics
Volume 2017 (2017), Article ID 6751025, 5 pages
https://doi.org/10.1155/2017/6751025
Research Article

Quasi-Exact Coulomb Dynamics of Charges of Which Are Equal

Institute of Mathematics, Tereshchenkivska 3, Kyiv 01004, Ukraine

Correspondence should be addressed to Wolodymyr Skrypnik

Received 9 December 2016; Accepted 5 February 2017; Published 28 February 2017

Academic Editor: Andrei D. Mironov

Copyright © 2017 Wolodymyr Skrypnik. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

For point charges 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.