平面4N体问题的扭转正多边形套周期解

Periodical Solutions of Planar 4N-body Problems of Twist Polygon Set

研究平面4N体问题的扭转正多边形套周期解。如果这些天体分别位于3个同心圆上,并且形成正N边形与正2N边形的的多边形套,那么平面4N体问题存在周期解的充分必要条件是同一个圆上的质点的质量相等。

In this paper,the periodical solutions of planar 4N-body problems of twist polygon set are discussed. If the celestial bodies are located at three concentric circles,and take the shape of a twist polygon set with regular polygon,then the planar 4N-body problems have periodical solutions if and only if the celestial bodies have equal masses in the same circle.