Halo轨道族延拓方法及特性研究

对Halo轨道周期和运动范围等特性的研究是平动点任务设计的首要前提。针对大幅值Halo轨道和完整Halo轨道族的应用需求及其数值计算问题，面向当前应用广泛的地月系和日-地月系共线平动点，基于延拓法研究了圆型限制性三体问题下的Halo轨道族数值计算和运动学特性，给出了Halo轨道族延拓计算方法。数值仿真了族参数选择对轨道族计算的影响，得到了地月系和日-地月系共线平动点的大范围南北Halo轨道族，同时给出了轨道族的轨道周期变化和空间位置变化特性。研究结果表明，固定延拓步长下，L1点Halo轨道族应选择会合坐标系x坐标作为族参数，L2点Halo轨道族应选择y方向速度或者周期T作为族参数。方法适用于任意三体系统平动点的周期轨道族计算，特别是对其中的状态转移矩阵简单修改后可用于完整力模型下的Halo轨道（族）的数值设计。

Kinetic Characteristics and Continuation Algorithm of Periodic Families

Study on halo orbit period and scope of kinetic characteristics is the premise of halo orbit applications. For the applications and some numerical issues on a big halo orbit and a whole halo family, considering the wide applications of the libration points in the Sun-Earth/Moon and Earth-Moon system, the kinetic characteristics and the continuation algorithm of periodic families were studied under the circular restricted three-body problem. The method of numerical halo family determination by the continuation algorithm was presented. Influences of family parameter selection on family determination were analyzed. Finally, the halo families with a large scope were given in the Sun-Earth/Moon and Earth-Moon system, together with their kinetic characteristics of orbit periods and locations. The results show that the family parameter of x is preferable for an L1 halo family and the y velocity or T is preferable for L2. The method is fit for the numerical halo family determination in any three-body system, especially for those under perturbations by a simple modification of state transition matrix.