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首先介绍了圆型限制性三体问题的非线性常微分运动方程组,利用定性分析方法、级数解法和数值解法,系统地介绍了这个问题的求解分析方法,相应地给出了共线平动点附近的力学特性、条件周期(和拟周期)轨道,并通过分析一个周期处的状态转移矩阵(Monodromy矩阵)分析了各类轨道的稳定性以及几种周期和拟周期轨道之间的关系。另外,还给出了圆型限制型三体模型下Halo轨道的牛顿迭代算法。
Firstly, the nonlinear ordinary differential equations of motion for a circular constrained three-body problem are introduced. By means of qualitative analysis, series solution and numerical solution, the solution and analysis of this problem are systematically introduced. The dynamic characteristics near the moving point, the conditional period (and the quasi-periodic) orbit, and analyzes the stability of various orbits and the relationship between several periodic and quasi-periodic orbits by analyzing the state transition matrix (Monodromy matrix) at one period . In addition, the Newton iteration algorithm of Halo orbit in a circular constrained three-body model is also given.