A global regularisation of the gravitationalN-body problem
A global regularisation of the gravitationalN-body problem
复制标题
引力N体问题的全局正则化
DOI：
10.1007/bf01227621
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发表时间：
1974
期刊：
影响因子：
--
通讯作者：
D. Heggie
中科院分区：
文献类型：
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作者：
D. Heggie
Aarseth和Zare（1974）的工作被扩展到提供经典引力三体问题的正则化：通过以不依赖于特定构型的方式变换变量，我们得到关于任何粒子对之间碰撞的正则运动方程。唯一例外的情况是那些同时发生一对以上的碰撞和那些至少有一个质量消失的情况。然而，通过相同的原则，如果排除两个原色之间的碰撞，则限制问题在全局上被正则化。数值试验的结果进行了总结，和理论推广提供全球regulationations，第一，扰动三体运动，第二，theN-body问题。一种增加动力系统自由度的方法是该方法的核心，也是附录的主题。
The work of Aarseth and Zare (1974) is extended to provide aglobal regularisation of the classical gravitational three-body problem: by transformation of the variables in a way that does not depend on the particular configuration, we obtain equations of motion which are regular with respect to collisions between any pair of particles. The only cases excepted are those in which collisions between more than one pair occur simultaneously and those in which at least one of the masses vanishes. However, by means of the same principles the restricted problem is regularised globally if collisions between the two primaries are excluded. Results of numerical tests are summarised, and the theory is generalised to provide global regularisations, first, for perturbed three-body motion and, second, for theN-body problem. A way of increasing the number of degrees of freedom of a dynamical system is central to the method, and is the subject of an Appendix.