具广义力势n体问题的中心构形(Ⅰ)——基本方程和理论分析

CENTRAL CONFIGURATIONS OF THE n-BOOY PROBLEM WITH A GENERAL FORCE FUNCTION (Ⅰ)——FUNDAMENTAL EQUATIONS AND THEORE TICAL ANALYSIS

本文采用不同于Palmore和Saari的方法研究了具广义力势n体问题的中心构形,把牛顿力势下中心构形的主要结果推广到了k(≠1)次方反比力势,给出了以质点间相互距离为未知量的中心构形方程的导出方法.

Using a method different from those of Palmore and Saari, we study the central configurations of the n-body system in the field of inverse k(≠1) force. The main results about the central configurations in the gravitational field are extended. Besides, the method of deriving the equations of central configurations (with mutual distances as unknown quantities) is illustrated.