论文标题
在圆形轨道上的最佳低潮溶液的地图集
An Atlas of Optimal Low-Thrust Rephasing Solutions in Circular Orbit
论文作者
论文摘要
在本文中，研究了圆形轨道中的时间和推进剂最佳的低促值重塑问题，以描绘其在地图集中的溶液空间。通过基于Sundman变换开发一组线性的运动方程，并使用最低原理和对称属性来制定两个降低的射击功能，从而减少了解决重新播种问题的关键参数数量。对于时间优势问题，仅确定一个关键参数，而推进剂最佳参数则获得了两个关键参数。对这些参数和射击变量之间关系的数值研究表明，它们可以用某些曲线（或轮廓）地图来描绘它们，并通过分段函数（或线性插值）进行近似。对于相对较短或长期的转换案例，提出了一些分析时间和推进剂 - 最佳解决方案，并与数值解决方案一致。数值结果表明，所提出的解决方案可以提供良好的初始猜测，以解决非线性动力学的低推断性转化问题。此外，性能索引的近似值可以在初步任务设计中使用。
In this paper, the time- and propellant-optimal low-thrust rephasing problems in circular orbit are studied to depict their solution spaces in an atlas. The number of key parameters that settle the rephasing problems is reduced by developing a set of linearized equations of motion based on the Sundman transformation and by formulating two reduced shooting functions using the minimum principle and symmetry properties. Only one key parameter is identified for the time-optimal problem, while two key parameters are obtained for the propellant-optimal one. Numerical investigation of the relationships between these parameters and shooting variables reveals that they can be depicted by some curve (or contour) maps and approximated by piecewise functions (or linear interpolations). For the relatively short- or long-term rephasing cases, some analytical time- and propellant-optimal solutions are proposed and consistent with the numerical solutions. Numerical results demonstrate that the proposed solutions can provide good initial guesses to solve the low-thrust rephasing problems with nonlinear dynamics. Moreover, the approximations of the performance indexes can be used in the preliminary mission design.
