包含引力辅助变轨的三体Lambert问题求解算法

罗钦钦; 韩潮

包含引力辅助变轨的三体Lambert问题求解算法

罗钦钦,
韩潮

北京航空航天大学宇航学院, 北京 100191

基金项目: 国家自然科学基金资助项目(11002008); 国家重点基础研究发展计划资助项目(2009CB723906)

详细信息

中图分类号: V412.4
计量
- 文章访问数: 2366
- HTML全文浏览量: 136
- PDF下载量: 964
- 被引次数: 0
出版历程
- 收稿日期: 2012-05-10
- 修回日期: 2013-05-07
- 网络出版日期: 2013-05-31

Solution algorithm of the three-body lambert problem with gravity assist maneuver

School of Astronautics, Beijing University of Aeronautics and Astronautics, Beijing 100191, China

摘要

摘要: 对包含引力辅助变轨的三体Lambert问题提出了一种数值求解算法,分为转移轨道初始设计和终值搜索两部分.采用伪状态理论,通过简单迭代求解高精度的转移轨道初始设计结果,在此基础之上,通过数值积分在更复杂的摄动环境中,计算精确的转移轨道和一二阶状态转移矩阵,并利用二阶微分修正算法搜索最终解.经过数值算例检验,这种方法具有较高的效率和鲁棒性,可以有效解决三体系统中引力辅助转移轨道的高敏感性问题.
- 引力辅助 /
- 三体系统 /
- Lambert问题 /
- 伪状态 /
- 微分修正
Abstract: A new numerical solution algorithm for the three-body Lambert problem with gravity assist maneuver was developed. The algorithm was divided into two parts, the initial solution design and the searching for the final solution. The pseudostate theory was adopted to get the initial solution of the three-body Lambert problem. Based on that, the transfer trajectory and the state transition matrix were calculated by numerical integration in the real dynamic model. A second order differential-correction method was employed to find the final solution. The numerical examples were used to test the reliability and the efficiency of the algorithm.
- gravity assist /
- three-body system /
- Lambert problem /
- pseudostate /
- differential-correction

HTML全文

参考文献(17)

[1]	Battin R H,Vaughan R M.An elegant Lambert algorithm[J].Journal of Guidance,Control and Dynamics,1984,7:662-670
[2]	Bate R,Mueller D,White J.Fundamentals of astrodynamics[M].New York:Dover Publications,1971:177-275
[3]	韩潮,谢华伟.空间交会中多圈Lambert变轨算法研究[J].中国空间科学技术,2004(5):9-14 Han Chao,Xie Huawei.Research on algorithm of Loopy lambert transfer in space rendezvous[J].China Space Science Technology,2004(5):9-14 (in Chinese)
[4]	彭坤,徐世杰.一种无奇异的求解Lambert变轨的普适变量法[J].北京航空航天大学学报,2010,36(4):399-402 Peng Kun,Xu Shijie.Singularity free universal variables method to solve Lambert transfer[J].Journal of Beijing University of Aeronautics and Astronautics,2010,36(4):399-402 (in Chinese)
[5]	Gooding R H.A procedure for the solution of Lambert's orbital boundary-value problem[J].Celestial Mechanics and Dynamical Astronomy,1990,48:145-165
[6]	Kriz J.A uniform solution of the Lambert problem[J].Celestial Mechanics,1976,14(4):509-513
[7]	Nelson S L.Alternative approach to the solution of Lamberts problem[J].Journal of Guidance,Control,and Dynamics,1992,15(4):1003-1009
[8]	Arlulkar P V,Naik S D.Solution based on dynamical approach for multiple-revolution Lambert problem[J].Journal of Guidance,Control,and Dynamics,2011,34(3):920-923
[9]	Avanzini G.A simple Lambert algorithm[J].Journal of Guidance,Control,and Dynamics,2008,31(6):1587-1594
[10]	He Q,Li J,Han C.Multiple-revolution solutions of the transverse-eccentricity-based Lambert problem[J].Journal of Guidance,Control,and Dynamics,2010,33(1):265-268
[11]	D'Amario L,Bynes D,Sackett L.Optimization of multiple flyby trajectories[C] //AAS/AIAA Astrodynamics Specialists Conference,Provincetown,Mass,AIAA Paper 79-162,1979
[12]	Sukhanov A,Prado A F B A.Lambert problem solution in the Hill model of motion[J].Celestial Mechanics and Dynamical Astronomy,2004,90:331-354
[13]	Jesicak M,Ocampo C.Automated generation of symmetric lunar free-return trajectories[J].Journal of Guidance,Control and Dynamics,2011,34(1):98-106
[14]	Okutsu M,Longuski J.Mars free returns via grivity assist from Venus[J].Journal of Spacecraft and Rockets,2002,39(1): 31-36
[15]	徐明,谭田,李志武,等.Lambert转移中途修正的全局概率最优策略[J].北京航空航天学报,2012,38(5):574-578 Xu Ming,Tan Tian,Li Zhiwu,et al.Optimal correction strategy during Lambert transfer from view of probability[J].Journal of Beijing University of Aeronautics and Astronautics,2012, 38(5):574-578(in Chinese)
[16]	Byrnes D V.Application of the pseudostate theory to the three-body Lambert problem[J].Journal of the Astronautical Sciences,1989,37:221-232
[17]	Wilson S W.A pseudostate theory for the approximation of three-body trajectories[R].TRW Note No.60-FMT-765 (11176-H304-R0-00),1969