This article proposes a low-thrust reconfiguration strategy for formation flying based on the Jordan normal form and evaluates its performance based on the required control acceleration and fuel cost. First, the relative dynamics of reconfiguration is disposed by Jordan decomposition to describe the unstable component, i.e., the drift velocity along the track direction, which is not explicit in eigenstructure. Next, the initial states of the Jordan-reduced dynamics are regarded as orbital invariants without control to characterize a formation configuration, similar to the definition of orbital elements that are invariants of the unperturbed Keplerian orbit. Based on the derived differential form of ISJD with control, the reconfiguration trajectory is parameterized by a functional integral, the existence of which is then proved analytically by the proposed polynomial series method. The specified optimal trajectories are yielded by the practical Radau pseudospectral method numerically. Finally, the effects of reconfiguring positions and relative orbital orientation on the required acceleration and fuel cost are investigated using a technique for order preference based on similarity to the ideal solution.

中文翻译：

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基于Jordan范式的编队飞行小推力重构策略及优化

本文提出了一种基于Jordan范式的编队飞行低推力重构策略，并基于所需的控制加速度和燃料成本对其性能进行了评估。首先，重构的相对动力学通过Jordan分解来描述不稳定分量，即沿轨道方向的漂移速度，这在特征结构中是不明确的。接下来，Jordan-reduced 动力学的初始状态被视为不受控制的轨道不变量来表征地层配置，类似于作为未受扰动的开普勒轨道不变量的轨道元素的定义。基于具有控制的 ISJD 的导出微分形式，重构轨迹由函数积分参数化，然后通过所提出的多项式级数方法分析证明其存在。指定的最佳轨迹是由实际的 Radau 伪谱方法以数值方式产生的。最后，使用基于与理想解决方案相似性的顺序偏好技术研究了重新配置位置和相对轨道方向对所需加速度和燃料成本的影响。