平面3N体问题的中心构型

The Central Configurations of Planar 3N-body Problems

对于N体问题,中心构型具有非常重要的作用。1772年,拉格朗日描述了3体问题的一个周期解既各质点位于等边三角形的顶点处以适当的角速度围绕质心旋转。L.M.Perko和E.L.W alter证明了当N≥4时,N个质点位于正N边形的顶点处以适当的角速度围绕质心旋转是N体问题的一个周期解的充要条件为各质点的质量相等。本文主要研究了平面3N体问题存在正多边形套中心构型的充分和必要条件。

For N- body problems, a central configuration plays an important role. In 1772, Lagrange described a periodic solution of the three - body problem, that is to say, three masses at the vertices of an equilateral triangle rotate about their common center of mass with an appropriate angular velocity. Then, L. M. Perko and E. L. Walter proved that when N≥4, N masses at the vertices of a regular polygon rotating about their common center of mass with an appropriate angular ,-elocity is the sufficient and necessary condition for a periodic solution of the N - body problem if and only if the masses are equal. This paper mainly concentrates on the necessary and suffi- cient conditions for the nested - polygonal central configuration of planar 3N - body problems.