具广义力势二体问题

THE TWO-BODY PROBLEM WITH GENERAL ATTRACTION

本文讨论具k(1<k<3)次方反比力势下的二体问题,它可以作为某些球状星团的力学模型.通过研究两体距离与其变化率间的函数关系,得到了许多与牛顿力势情形类似的结果.在有界运动情形下给出了周期运动的充要条件;在无界运动情形下给出了有关力学量趋向各自极限的方式.

Recently the N-body system with the general force funtion derived from the inverse k force law is often investigated. In this paper, we study, in detail, the twobody problem with the above kind of force function, which can be used as a mechanical model of certain globular clusters. A lot of motion properties similar to the ones under the law of gravitation are given. In the case of the bounded motion, some periodicities are shown and an equivalent condition for periodic motion is presented. At the same time, we obtain the limit forms of mechanical quantities for the unbounded motion.