三体问题的封闭形式近似
Closed Form Approximations For The Three Body Problem
摘要：
本文发展了一种求解含有非球对称质量的三体问题的方法。这个问题可以追溯到庞加莱时代，并且无疑是经典力学中最古老的未解问题之一。庞加莱的格言全面地证明，由于所涉及的不稳定性的性质，这个问题确实是无法解决的。因此，我们驳斥了寻找精确解的想法。相反，我们开发封闭形式的解析近似的精确解。我们将解决的情况下，所有涉及的质量有球对称的质量分布的问题。解决的方法将包括使用一个单一的质量，以复制两个单独的质量对每个机构的影响。解的推导将涉及Lamberts波函数的使用，并且解将包括表示为显式时间函数的位置矢量。
英文摘要：
In this paper, an approach is developed to solve the three body problem involving masses which posses spherical symmetry. The problem dates back to the times of Poincare, and is undoubtedly one of the oldest of unsolved problems of classical mechanics. The Poincares Dictum comprehensively proves that the problem is truly insolvable as a result of the nature of the instabilities involved. We therefore refute the idea of finding exact solutions. Instead, we develop closed form analytical approximations in place of exact solutions. We will solve the problem for the case when all the masses involved have spherically symmetric mass distributions. The method of solution would include the use of a single mass to replicate the effect of two individual masses on each body. The derivation of solutions will involve the use of the Lamberts wave function and the solution will comprise of the position vectors expressed as explicit time functions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
