We find periodic solutions of the Coulomb d-dimensional (d = 1, 2, 3) equations of motion for two identical negative point charges in the field of four identical positive point charges fixed at vertices of a rectangle. Systems of this kind have equilibrium configurations. Periodic solutions are obtained with the help of the Lyapunov center theorem.

中文翻译：

---

四个相同固定正电荷场中两个相同负电荷的周期性库仑动力学

我们找到的周期解库仑d维（d = 1 ， 2 ， 3）的运动方程为在固定在矩形的顶点四个相同的正的点电荷领域两个相同的负点电荷。这种系统具有平衡配置。借助Lyapunov中心定理获得周期解。