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焦博涵, 党朝辉. 基于二阶CW方程的引力波探测编队构形设计[J]. 深空探测学报(中英文), 2023, 10(3): 257-267. DOI: 10.15982/j.issn.2096-9287.2023.20230012
引用本文: 焦博涵, 党朝辉. 基于二阶CW方程的引力波探测编队构形设计[J]. 深空探测学报(中英文), 2023, 10(3): 257-267. DOI: 10.15982/j.issn.2096-9287.2023.20230012
JIAO Bohan, DANG Zhaohui. Formation Design of for Space Gravitational Wave Detection Based on Second Order CW Equation[J]. Journal of Deep Space Exploration, 2023, 10(3): 257-267. DOI: 10.15982/j.issn.2096-9287.2023.20230012
Citation: JIAO Bohan, DANG Zhaohui. Formation Design of for Space Gravitational Wave Detection Based on Second Order CW Equation[J]. Journal of Deep Space Exploration, 2023, 10(3): 257-267. DOI: 10.15982/j.issn.2096-9287.2023.20230012

基于二阶CW方程的引力波探测编队构形设计

Formation Design of for Space Gravitational Wave Detection Based on Second Order CW Equation

  • 摘要: 针对基于CW(Clohessy-Wiltshire)方程所设计的空间引力波探测编队在二体非线性引力场下的臂长发散问题,提出了一种基于二阶CW方程的编队构形设计方法。推导了二阶CW方程的微分形式,利用摄动法得到了二阶CW方程的近似解析解,并以此为基础证明了完美空间圆形绕飞轨道的不存在性,分析了基于CW方程所设计的标称构形的发散原因;基于二阶CW方程与能量匹配周期条件以航天器相位角为优化变量构建了编队构形优化模型,建立了基于全局优化算法和模式搜索算法的多约束构形优化方法;以“太极”任务为背景对优化结果进行了仿真验证。仿真表明:所提出的优化方法能够将编队臂长的平均误差降低至0.32%、最大误差降低至0.44%。

     

    Abstract: To solve the problem of arm length divergence of space gravitational wave detection formation based on CW equation in two-body nonlinear gravitational field, a formation configuration design method based on second-order CW equation was proposed. Firstly, the differential form of the second-order CW equation was derived, and the approximate analytical solution of the second-order CW equation was obtained by perturbation method. Then, the non-existence of circular flying orbit was proved, and the divergence reason of the nominal configuration based on CW equation was analyzed. Secondly, based on second-order CW equation and the energy matching period condition, the formation configuration optimization model was constructed with the phase angles of the spacecraft as optimization variables, and the multi-constraint configuration optimization method based on the global optimization algorithm and the pattern search algorithm was established. Finally, the optimization results were verified by simulation based on the Taiji mission. Simulation results show that the proposed optimization method can reduce the average error of formation arm length to 0.32% and the maximum error to 0.44 %.

     

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