中文摘要：

对航天器集群编队最优单脉冲机动问题进行了研究．针对不同的任务约束，基于非线性相对运动的周期性条件，以解析的思路分别研究了机动时刻给定和机动时刻未定情况下集群编队的最优单脉冲机动问题．对于机动时刻给定的情况，从高斯变分方程和基于能量匹配条件的拉格朗日乘子法两个角度分别进行了探讨，将问题转化为对一元二次方程求极值或对一个单零点非线性方程求根；对于机动时刻未定的情况，将问题转化为对一个多零点非线性方程求根，通过傅里叶一贝塞尔级数展开可以得到任意高阶近似解．对于每种情况，推导得到二范数意义下能量最省对应的最优参考长半轴，以及所施加的最优速度脉冲．数值仿真验证了本文方法的正确性，并对仿真结果进行了解释和分析．

英文摘要：

The optimal single-impulse maneuver for spacecraft cluster flight is studied in this paper. Based on Gauss＇ variational equations, the optimal conditions and solutions for time-fixed and time-unfixed case are provided via the periodic condition of nonlinear relative motion. For the time-fixed case, the problem is also treated from the perspective of energy matching condition. In this case, the problem is transformed into seeking for the extremum of a quadratic equation or the solution of a single-root algebraic equation, and the optimal semimajor axis is derived, as well as the optimai velocity impulse. For the time-unfixed case, the problem can be solved by numerical algorithms or transformed into pursuing for the solution of a multi-root algebraic equation＇ with the aid of Fourier-Bessel functions. In the end, the proposed method is validated by several carded out illustrating examples.