关于4-体问题中心构型的一点研究

A STUDY ON THE CENTRAL CONFIGURATION IN THE NEWTONIAN 4-BODY PROBLEM OF CELESTIAL MECHANICS

N-体问题的中心构型是应用数学领域广泛研究的问题．关于N-体问题的中心构型已有许多研究结果．但是对于n≥4,其中心构型解的计算是比较困难的．作者运用Wu-Ritt零点分解方法和子结式序列研究了一般的平面4体中心构型问题,给出了这类4体中心构型问题的解析解,从而证明了一类平面牛顿4-体问题的中心构型个数是有限的．

The central configuration in the N-body problem is one of the most studied problems in the field of celestial mechanics and appled mathematics. There are many results about central configurations. In this paper, by using Wu-Ritt method and subresultant sequences, we study a class of Newtonian planar 4-body problem and give a closed form solution. Prom the solution, we prove that the configurations for a class of Newtonian planar 4-body problem is finite.