基于不变流形的登月轨道设计  

Lunar Landing Trajectory Design Based on Invariant Manifold

作　　者：龚胜平[1] 李俊峰[1] 宝音贺西[1] 高云峰[1] 

机构地区：[1]清华大学航天航空学院,北京110084

出　　处：《应用数学和力学》2007年第2期183-190,共8页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(10672084;10602027)

摘　　要：研究了基于三体问题的不变流形设计低成本登月轨道的问题.考虑了黄道面和白道面之间夹角不为零的三维情况,将太阳_地球_月亮_卫星组成的四体问题分解成由太阳_地球_卫星和地球_月亮_卫星组成的非共面的两个限制三体问题.给出了这两个三体系统Halo轨道不变流形与两轨道面相交处进行小的变轨来设计低成本探月轨道的一般方法.比较结果表明用该方法设计的轨道比传统的Hohmann变轨节省约20%的燃料.从轨道能量的角度分析了用流形设计轨道比Hohmann变轨节省燃料的原因,并给出了理论表达式.该方法对于深空探测轨道设计的能量分析具有普遍的适用性,可为设计提供一个选择参数的标准.The low-energy lunar landing trajectory design using the invariant manifolds of restricted three body problem is studied. Considering angle between the ecliptic plane and lunar orbit plane, the four body problem of Sun-Earth-Moon-spacecraft was divided into two three body problems, the Sun- Earth-spacecraft in the ecliptic plane and the Earth-Moon-spacecraft in the lunar orbit plane. Using the orbit maneuver at the place where the two planes and the invariant manifolds intersect, a general method to design low energy lunar landing trajectory was given. It is found that this method can save the energy by 20% compared with the traditional Hohmann transfer trajectory. The mechanism of the method that can save energy was investigated in the point of view of energy and the expression of the amount of energy saved is given. In addition, some rules of selecting parameters with respect to orbit design were provided. The method of energy analysis can be extended to energy analysis in deep space orbit design.

关 键 词：三体问题 Lagrange点 HALO轨道 不变流形 登月轨道 

分 类 号：V412.4[航空宇航科学与技术—航空宇航推进理论与工程]