The equation of motion in of generalized point charges interacting via the -dimensional Coulomb potential, which contains for a constant magnetic field, is considered. Planar exact solutions of the equation are found if either negative charges and their masses are equal or and the charges are different. They describe a motion of negative charges along identical orbits around the positive immobile charge at the origin in such a way that their coordinates coincide with vertices of regular polygons centered at the origin. Bounded solutions converging to an equilibrium in the infinite time for the considered equation without a magnetic field are also obtained. A condition permitting the existence of such solutions is proposed.

中文翻译：

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不同尺寸的平衡，正多边形和库仑型动力学

运动中的方程的广义点电荷经由交互-维库仑势，其包含用于考虑到恒定的磁场。如果方程为负，则找到方程的平面精确解 电荷和它们的质量相等或 而且收费是不同的。他们描述了负电荷沿着原点周围正固定不动电荷的相同轨道运动的方式，使得它们的坐标与以原点为中心的正多边形的顶点重合。对于所考虑的方程式，在没有磁场的情况下，也可以获得在无限时间内收敛到平衡的有界解。提出了允许存在这种解决方案的条件。