Low-thrust, optimal strategies are investigated for making a smooth landing on a uniformly rotating, homogeneous rectangular parallelepiped while avoiding the sharp corners during the approach. The individual effects of principal spherical harmonic coefficients on the stability against impact are determined numerically. An iterative predictor-corrector algorithm is utilized to find a direct and retrograde family of equatorial orbits. Stability analysis of equatorial orbits confirms the fact that retrograde orbits are less prone to disturbances than direct orbits. For an optimal landing, each approach trajectory begins from a stable equatorial orbit, and terminates at a prescribed landing point. The optimality conditions are given by Euler-Lagrange equations, and the associated two-point boundary value problem is solved by a collocation method with additional path constraints, and its results are compared with those of a direct nonlinear programming search technique. It is observed that a smaller energy expenditure is required for a landing made further away from the initial location such that sufficient time is allowed for the spacecraft to remain in an unforced orbital trajectory for a majority of the trajectory. A sample inclined orbit is also studied for a possible non-planar optimal approach in the body-fixed frame, and further investigated for various landing locations.

研究了低推力的最佳策略，以在均匀旋转的均匀长方体上平稳着陆，同时避免进近时出现尖角。数值确定主要球谐系数对冲击稳定性的影响。利用迭代预测器-校正器算法来找到赤道轨道的直接和逆行系列。赤道轨道的稳定性分析证实了这样一个事实，即逆行轨道比直接轨道更不容易受到干扰。为了获得最佳着陆，每个进场轨迹都从稳定的赤道轨道开始，并在指定的着陆点处终止。最优条件由Euler-Lagrange方程给出，并通过附加路径约束的搭配方法解决了相关的两点边值问题，并将其结果与直接非线性规划搜索技术的结果进行了比较。可以看出，离初始位置更远的着陆需要较小的能量消耗，从而使航天器有足够的时间在大部分轨迹上保持在非受力轨道轨迹中。还研究了一个样本倾斜轨道，以研究在人体固定框架中可能的非平面最佳进近，并进一步研究了各种着陆位置。可以看出，离初始位置更远的着陆需要较小的能量消耗，从而使航天器有足够的时间在大部分轨迹上保持在非受力轨道轨迹中。还研究了一个样本倾斜轨道，以研究在人体固定框架中可能的非平面最佳进近，并进一步研究了各种着陆位置。可以看出，离初始位置更远的着陆需要较小的能量消耗，从而使航天器有足够的时间在大部分轨迹上保持在非受力轨道轨迹中。还研究了一个样本倾斜轨道，以研究在人体固定框架中可能的非平面最佳进近，并进一步研究了各种着陆位置。