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本文基于圆型限制性三体模型(Circular Restricted Three Body Problem,CR3BP)研究由地球飞往Halo轨道的转移轨道设计问题,并提出一种定时中途修正的闭环策略。研究Halo轨道稳定性,得到Floquet乘子与Halo轨道幅值的关系,并折衷选择适合探测任务的Halo轨道幅值。定义不同于以往研究的Poincaré映射用以计算Halo轨道的稳定流形,根据该不变流形的几何性质得到6类单脉冲轨道转移方式。以被文献中忽略的间接轨道转移方式为基础,应用离散线性随机系统的不完全信息最优控制理论给出修正策略,并经由Monte-Carlo模拟给出修正结果的统计信息。
In this paper, the problem of transfer orbit design from Earth to Halo orbit is studied based on the Circular Restricted Three Body Problem (CR3BP), and a closed-loop strategy with time-phased correction is proposed. Studying the Halo orbital stability, the relationship between the Floquet multiplier and the Halo orbit amplitude is obtained, and the Halo orbital amplitude suitable for the detection task is chosen ecologically. The definition of Poincaré mapping, which is different from previous studies, is used to calculate the stable manifolds of the Halo orbit. According to the geometric properties of the invariant manifolds, six types of single-pulse orbital transitions are obtained. Based on the indirect orbital transfer mode neglected in the literature, the modified strategy is given by applying the theory of optimal information control of discrete linear stochastic systems, and the statistical information of the corrected results is given through Monte-Carlo simulation.