Manifold dynamics in the Earth–Moon system via isomorphic mapping with application to spacecraft end-of-life strategies
Manifold dynamics in the Earth–Moon system via isomorphic mapping with application to spacecraft end-of-life strategies
复制标题
通过同构映射研究地月系统中的流形动力学及其在航天器寿命终止策略中的应用
DOI：
10.1016/j.actaastro.2014.08.029
复制
发表时间：
2014
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;M. Giancotti;P. Teofilatto
最近，流形动力学对于地月系统和替代多体环境中的低能量任务的分析和设计越来越重要。对于月球任务，基于共线平动点L1和L2所在区域的凌日的外部和内部传输已经进行了很长时间的研究，并且一些太空任务已经利用了这些研究成果。本文重点讨论用于低能量任务分析的特殊同构映射的定义和使用。在圆形受限三体问题的背景下，采用一组方便的柱坐标来描述航天器动力学（即位置和速度），用于模拟地月系统中的航天器运动。这种轨迹的同构映射允许识别和直观地表示周期轨道和相关的不变流形，这些不变流形对应于从与周期轨道相关的曲线发出的管。异斜连接，即属于两个不同周期轨道的稳定流形和不稳定流形的轨迹，可以通过这种表示很容易地检测到。本文说明了使用同构映射来查找（a）周期轨道，（b）两个李雅普诺夫轨道（第一个 atL1 和第二个 atL2）发出的轨迹之间的异宿连接，以及（c）L1 处的李雅普诺夫轨道和特定不稳定月球轨道发出的轨迹之间的异宿连接。异斜轨迹是以零推进剂成本行进的渐近轨迹。在实际情况中，需要适度的 delta-v 预算来执行沿流形的传输。这种情况意味着通过组合属于流形的不同类型的轨迹弧来执行复杂任务的可能性。这项工作还研究了流形动力学的可能应用，为绕地球运行的航天器定义合适、方便的寿命终止策略。确定了七个不同的选项，并将航天器置于最终处置轨道，即（a）月球捕获轨道，（b）月球撞击轨道，（c）稳定的月球周期轨道，或（d）永远不会接近地球或月球的外轨道。利用将速度变化与航天器能量联系起来的两个显着特性，用于确定执行七个转移轨迹所需的速度脉冲的最佳位置、大小和方向。每个报废策略的整体性能是根据飞行时间和推进剂预算来评估的。
Recently, manifold dynamics has assumed an increasing relevance for analysis and design of low-energy missions, both in the Earth–Moon system and in alternative multibody environments. With regard to lunar missions, exterior and interior transfers, based on the transit through the regions where the collinear libration pointsL1andL2are 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 focused on the definition and use of a special isomorphic mapping for low-energy mission analysis. A convenient set of cylindrical coordinates is employed to describe the spacecraft dynamics (i.e. position and velocity), in the context of the circular restricted three-body problem, used to model the spacecraft motion in the Earth–Moon system. This isomorphic mapping of trajectories allows the identification and 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. Heteroclinic connections, i.e. the trajectories that belong to both the stable and the unstable manifolds of two distinct periodic orbits, can be easily detected by means of this representation. This paper illustrates the use of isomorphic mapping for finding (a) periodic orbits, (b) heteroclinic connections between trajectories emanating from two Lyapunov orbits, the first atL1, and the second atL2, and (c) heteroclinic connections between trajectories emanating from the Lyapunov orbit atL1and from a particular unstable lunar orbit. Heteroclinic trajectories are asymptotic trajectories that travels at zero-propellant cost. In practical situations, a modest delta-v budget is required to perform transfers along the manifolds. This circumstance implies the possibility of performing complex missions, by combining different types of trajectory arcs belonging to the manifolds. This work studies also the possible application of manifold dynamics to defining suitable, convenient end-of-life strategies for spacecraft orbiting the Earth. Seven distinct options are identified, and lead to placing the spacecraft into the final disposal orbit, which is either (a) a lunar capture orbit, (b) a lunar impact trajectory, (c) a stable lunar periodic orbit, or (d) an outer orbit, never approaching the Earth or the Moon. Two remarkable properties that relate the velocity variations with the spacecraft energy are employed for the purpose of identifying the optimal locations, magnitudes, and directions of the velocity impulses needed to perform the seven transfer trajectories. The overall performance of each end-of-life strategy is evaluated in terms of time of flight and propellant budget.