Low-energy Earth–Moon transfers involving manifolds through isomorphic mapping ☆
Low-energy Earth–Moon transfers involving manifolds through isomorphic mapping ☆
复制标题
通过同构映射涉及流形的低能地月传输☆
DOI：
10.1016/j.actaastro.2013.05.009
复制
发表时间：
2013
影响因子：
3.5
通讯作者：
P. Teofilatto
中科院分区：
文献类型：
--
作者：
M. Pontani;P. Teofilatto
几十年来，分析和设计低能量转移到月球一直是一个非常感兴趣的主题。基于通过共线平动点所在区域的凌日现象，对内外转移进行了长期研究，一些空间飞行任务已经利用了这些研究的结果。基于同构映射，提出了一种低能地月使命分析的几何方法。轨迹的同构映射允许周期轨道和相关的不变流形的视觉的、直观的表示，其对应于从与周期轨道相关联的曲线发出的管。考虑了两种类型的地月飞行任务。第一个使命由以下弧段组成：㈠从圆形低地球轨道转移轨道到与L1处的李雅普诺夫轨道（对应于特定能级）相关的稳定不变流形; ㈡转移轨道沿着与L1处的李雅普诺夫轨道相关的不稳定流形，最后注入绕月周期轨道。第二项使命由以下弧线组成：从圆形低地球轨道转移轨道到与L1处的李雅普诺夫轨道（对应于特定能级）相关的稳定不变流形;转移轨道沿着与L1处的李雅普诺夫轨道相关的不稳定流形，最后注入绕月捕获（非周期）轨道。在这两种情况下，都需要三个速度脉冲来进行转移：第一个在沿着低地球轨道的未知初始点，第二个在稳定流形上注入，第三个在最终（周期或捕获）轨道上注入。最终的目标是找到最优化参数，这些参数由速度脉冲的位置、方向和幅度表示，使得传递的总Δ v最小化。这项工作证明了如何同构映射（在两个不同的形式）可以有利地采用优化这样的传输，通过确定在几何的方式所需的优化参数，最大限度地减少所需的delta-v预算执行传输。
Analysis and design of low-energy transfers to the Moon has been a subject of great interest for decades. Exterior and interior transfers, based on the transit through the regions where the collinear libration points are located, have been studied for a long time and some space missions have already taken advantage of the results of these studies. This paper is concerned with a geometrical approach for low-energy Earth-to-Moon mission analysis, based on isomorphic mapping. The isomorphic mapping of trajectories allows a visual, intuitive representation of periodic orbits and of the related invariant manifolds, which correspond to tubes that emanate from the curve associated with the periodic orbit. Two types of Earth-to-Moon missions are considered. The first mission is composed of the following arcs: (i) transfer trajectory from a circular low Earth orbit to the stable invariant manifold associated with the Lyapunov orbit atL1(corresponding to a specified energy level) and (ii) transfer trajectory along the unstable manifold associated with the Lyapunov orbit atL1, with final injection in a periodic orbit around the Moon. The second mission is composed of the following arcs: (i) transfer trajectory from a circular low Earth orbit to the stable invariant manifold associated with the Lyapunov orbit atL1(corresponding to a specified energy level) and (ii) transfer trajectory along the unstable manifold associated with the Lyapunov orbit atL1, with final injection in a capture (non-periodic) orbit around the Moon. In both cases three velocity impulses are needed to perform the transfer: the first at an unknown initial point along the low Earth orbit, the second at injection on the stable manifold, the third at injection in the final (periodic or capture) orbit. The final goal is in finding the optimization parameters, which are represented by the locations, directions, and magnitudes of the velocity impulses such that the overall delta-v of the transfer is minimized. This work proves how isomorphic mapping (in two distinct forms) can be profitably employed to optimize such transfers, by determining in a geometrical fashion the desired optimization parameters that minimize the delta-v budget required to perform the transfer.