三体轨道动力学研究进展

三体系统轨道动力学问题是航天动力学领域中的经典问题, 具有丰富的理论与工程意义, 并将在人类由近地延伸到深空的航天活动过程中起到至关重要的作用. 本文回顾并总结了三体系统轨道动力学相关研究进展, 并结合未来的深空探测的发展趋势, 展望了三体系统轨道动力学研究中的热点与挑战. 首先阐述了三体问题的研究背景及意义, 简要回顾了三体系统动力学模型的发展历程. 其次, 系统概述了三体系统平衡点附近的局部运动特性, 介绍了平衡点附近周期轨道解析与数值求解方法, 给出了拟周期运动的最新进展. 同时总结了共振轨道、循环轨道、自由返回轨道等三类三体系统全局周期运动的动力学特性与研究进展. 再次, 从不变流形理论和弱稳定边界理论两个方面综述了三体系统中低能量转移与捕获轨道设计的研究进展. 最后, 综述了三体系统轨道动力学在编队飞行、导航星座设计两方面的应用, 并展望了全月面覆盖轨道设计、三体系统下的小推力轨道优化和三体系统的三角平衡点开发利用中值得关注的轨道动力学与控制问题. 

PROGRESS OF THREE-BODY ORBITAL DYNAMICS STUDY

The orbital dynamics in the three-body system is a classical problem in the field of astrodynamics. It has rich theoretical and engineering significance, and have played an important role in the process of space activities extending from near-earth space to deep space. This paper reviews and summarizes the progress of the study of orbital dynamics in the three-body system. Combined with the development trend of deep space exploration in the future, the hotspots and challenges in the research of three-body orbital dynamics are prospected. First, the research background and significance of the three-body problem are surveyed, and the development of the dynamics model of the three-body system is briefly reviewed. Secondly, characteristics of the local motion near the equilibrium point in the three-body problem are systematically summarized. The analytical and numerical methods for periodic orbits are introduced. The latest development of quasi-periodic motion is discussed. Meanwhile, the characteristics and research progress of global periodic motions in the three-body system including resonance orbits, cycler trajectories, and free return orbits are summarized. Next, the research progress of the low-energy transfer and capture trajectory design in the three-body system is analyzed from two aspects of invariant manifold theory and weak stability boundary theory. Finally, the applications of orbital dynamics in the three-body system in formation flight and navigation constellation design are summarized. Several orbital dynamics and control problems in the design of landing trajectories for full lunar-surface coverage, the low thrust orbit optimization of the three-body system, and the utilization of non-linear equilibrium points in the three-body system are addressed for future study.