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力学学报  2015 

航天器集群编队最优单脉冲机动

DOI: 10.6052/0459-1879-14-386, PP. 799-806

Keywords: 集群编队飞行,单脉冲机动,周期性条件,航天器相对运动

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Abstract:

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-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.

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