Department of Physics, The University of Texas at Arlington, Arlington, TX 76019, USA.
Rep Prog Phys. 2014 Jun;77(6):065901. doi: 10.1088/0034-4885/77/6/065901. Epub 2014 Jun 10.
The three-body problem, which describes three masses interacting through Newtonian gravity without any restrictions imposed on the initial positions and velocities of these masses, has attracted the attention of many scientists for more than 300 years. In this paper, we present a review of the three-body problem in the context of both historical and modern developments. We describe the general and restricted (circular and elliptic) three-body problems, different analytical and numerical methods of finding solutions, methods for performing stability analysis and searching for periodic orbits and resonances. We apply the results to some interesting problems of celestial mechanics. We also provide a brief presentation of the general and restricted relativistic three-body problems, and discuss their astronomical applications.
三体问题描述了三个质量在牛顿引力作用下相互作用，而对这些质量的初始位置和速度没有任何限制。三百多年来，这个问题吸引了许多科学家的关注。本文在历史和现代发展的背景下，对三体问题进行了综述。我们描述了三体问题的一般情况和限制情况（圆形和椭圆形），以及求解方法的不同分析和数值方法，用于进行稳定性分析和搜索周期轨道和共振的方法。我们将结果应用于一些有趣的天体力学问题。我们还简要介绍了三体问题的一般和限制相对论情况，并讨论了它们在天文学中的应用。
