圆型限制性三体问题相对运动解析研究

Analytical Solutions for Relative Motion in the Circular Restricted Three-Body Problem

针对圆型限制性三体问题共线平动点附近周期/拟周期轨道下的相对运动问题,提出一种新的、通用的解析研究方法。在周期/拟周期轨道近似解析解的基础上,结合微分修正方法,获得了精确的周期/拟周期轨道。对周期/拟周期轨道的单值矩阵进行分析,同时借鉴Floquet理论核心思想,建立了六个相对运动模态,并将相对运动表示为六个相对运动模态的线性组合,获得了相对运动的近似解析解。最后在地-月系统圆型限制性三体问题下,以L1点作为研究对象,分别以Halo轨道、Lissajous轨道和Lyapunov轨道为参考轨道,对相对运动模态和相对运动进行仿真分析,说明了相对运动模态的正确性以及相对运动近似解析解的有效性。

Aiming at the problem of relative motion near the collinear libration points in the circular restricted three-body problem of the Earth-Moon system,which is of great value both in theory and applications,a general method is proposed for the relative motion near the periodic/quasi-periodic orbits in the vicinity of the collinear libration points.Based on the first-order analytical solutions,the precise orbits are obtained through differential correction approach.The monodromy matrix is analyzed and then six modes of relative motion are extracted by referencing the Floquet theory.The relative motion can be described as a linear combination of these modes and then the approximate analytical solutions are obtained.The simulations of these modes and relative motion with Halo orbits,Lissajous orbits and Lyapunov orbits as the reference orbits respectively in the vicinity of Earth-Moon L1 points are made and the validity of the six modes and the analytical solutions for relative motion is proved.