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三体动力学系统动平衡点附近存在的周期轨道在空间探测任务中有着重要的应用价值.本文研究了流形不相交三体系统周期轨道间的转移问题,提出了一种结合流形和引力辅助技术的转移轨道设计方法.首先通过定义近拱点庞加莱映射搜索周期轨道不变流形的近拱点,然后给出了任意初始状态达到一定双曲超速所需速度增量的计算方法,从而得到了最佳逃逸流形和捕获流形的选择依据,并结合等高线图法与近拱点庞加莱映射分析了周期轨道利用该方式进行逃逸或捕获的性质.在此基础上,基于受摄三体模型建立了流形逃逸点到捕获点转移轨道的优化模型,通过微分修正策略将优化模型化简为仅有两个参数的无约束优化问题,并采用单纯形算法进行了求解.以地球-火星和地球-金星转移为例对所提方法的有效性进行了验证,数值结果表明:结合流形和引力辅助技术可有效降低周期轨道间转移的能量消耗.
Periodic orbits existing near the dynamic equilibrium point of the three-body dynamical system have an important application value in the mission of space exploration.In this paper, we study the problem of periodic orbit transition between three-body systems with manifold disjointness, Assisting technology transfer trajectory design method.Firstly, the approximate apodization point of the periodic orbitally invariant manifolds is searched by defining the apodization Poincaré mapping, and then the method of calculating the increment of velocity needed to reach a certain hyperbolic speeding in any initial state is given , The optimal escape form and capture manifold are obtained, and the properties of the periodic orbit using this method to escape or capture are analyzed based on the contour map method and the Poincaré mapping near the arch point , An optimization model of manifold escape trajectory to capture point transition trajectory was established based on the three-body model. The optimization model was reduced to an unconstrained optimization problem with only two parameters by using the differential correction strategy, and the simplex algorithm was used The validity of the proposed method is verified by taking Earth-Mars and Earth-Venus transitions as an example. The numerical results show that the combination of manifold and gravity-assisted technique Reduce energy consumption between periodic orbit transfer.