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Design of Natural Loose Formation Flying around Halo Orbits

机译：绕晕轨道飞行的天然松散编队设计

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Two spacecraft or more are assumed to be in a state of loose formation flying around a collinear Lagrangian point in the Sun-Earth circular restricted three-body problem (CR3BP) system. The orbit reference of choice for the leader is a halo orbit, and the followers are assumed to follow nearby and be constrained either geometrically or in size. This type of formation could be useful in the future for constructing space ports, space telescopes, astronomical spacecraft requiring sun shields and, with greater numbers, spacecraft swarm missions. The formation design method is constructed by firstly seeking the local coordinate system from the monodromy matrix through extraction of the independent bases that span the space of the halo orbit. To nullify diverging and converging motion, we confine the relative motion to within the periodic subspaces. We observe two modes of relative motion within these subspaces, long-term and short-term motion. In this study, we approximate the long-term motion by deriving a discrete formulation of independent directions based on the eigenvectors of the monodromy matrix, while for the short-term motion we approximate the fundamental set solutions using Fourier series and additional linear functions. Since the size of the formation discussed is significantly smaller than that of the halo orbit, the formation design method can fundamentally be stated as a process of linearly combining these approximations to achieve the desired formation. Consequently, use of this approach transforms formation design from a differential equation problem into an algebraic one, and furthermore enables the long-term and short-term motion design problems to be handled either jointly or separately. A set of design examples is presented to demonstrate the validity of the design method.
机译：假定两个或两个以上的航天器处于散布状态，绕太阳-地球圆形受限三体问题（CR3BP）系统中的共线拉格朗日点飞行。引导者选择的轨道参考是晕圈轨道，并且假定跟随者跟随附近，并且受到几何形状或大小的限制。这种构造在将来可能会用于建造太空港口，太空望远镜，需要遮阳罩的天文航天器以及数量更多的飞船群任务。地层设计方法是通过首先从单峰矩阵中搜索局部坐标系，并通过提取跨越晕圈空间的独立基础来构造的。为了使发散和收敛运动无效，我们将相对运动限制在周期子空间内。我们在这些子空间中观察到两种相对运动模式，即长期运动和短期运动。在这项研究中，我们通过根据单峰矩阵的特征向量推导独立方向的离散公式来近似长期运动，而对于短期运动，我们使用傅立叶级数和其他线性函数近似基本集解。由于讨论的地层的尺寸明显小于晕圈轨道的尺寸，因此，地层设计方法可以从根本上说是将这些近似值线性组合以实现所需地层的过程。因此，这种方法的使用将地层设计从微分方程问题转换为代数问题，并且还使长期和短期运动设计问题可以共同或分别处理。提出了一组设计实例，以证明设计方法的有效性。

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