星际小推力转移轨道快速设计方法

 针对星际探测任务中燃料最省小推力转移轨道问题，提出一种基于标称轨道的快速设计方法。首先以具有相同端点时刻的无摄动标称轨道为参考，对传统的非线性轨道优化模型进行合理变换，将复杂的优化问题简化为可解的两点边值问题；然后基于标称轨道3个独立积分推导出解析的状态转移矩阵，并以此为基础导出了两点边值问题的最优解析解。该方法无需数值迭代，有效地克服了数值优化方法收敛性差、计算效率低的缺点。最后，以探测火星的小推力转移轨道为例对该方法进行了验证，与精确的数值结果相比，该方法计算的燃料消耗误差小于1%。

A Rapid Design Method for Interplanetary Low-thrust Transfer Trajectory

A novel rapid method to design optimal-fuel interplanetary trajectory for low-thrust propulsion is presented based on normal trajectory approach. A simple two-point boundary value problem is formulated using a non-perturbation normal trajectory, which has the same endpoint time with low-thrust trajectory. The analytic state transition matrix is derived using three independent integrations of normal trajectory, and then the optimal solution of two-point boundary problem is obtained. The major advantage of this method is that it provides a more robust and efficient technique for solving interplanetary low-thrust transfer problem than traditional numerical optimization approaches. The rapid method introduced is demonstrated for an Earth-Mars low-thrust transfer application. The fuel cost computed using the proposed method exhibits a very close match (within 1%) with the corresponding fuel cost obtained with a precise numerical optimization approach.