三体模型下二维平面地月转移轨道设计与特性分析
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摘要
为提高地月转移轨道搜索速度和提供精确的初值猜测,在三体模型下研究了双脉冲地月转移轨道的快速设计方法及其轨道特性。首先基于三体模型建立了地心旋转系下地月转移轨道系统模型,选择物理意义明显的地月转移加速速度增量和地心旋转系对准角作为控制变量;其次在二体模型假设下给出控制变量的初值估计方法,提出了不同运行方向地月转移轨道的搜索策略,并采用序列二次规划算法对4种类型地月转移轨道进行求解,分析其控制变量差异;最后分析了转移时间、近地点高度和近月点高度对地月转移轨道的影响,以及月球引力对二体模型下初值估计的修正量。仿真结果表明,本文提出的设计方法能快速准确地搜索出指定类型的地月转移轨道,同时其轨道特性分析结论可为后续月球探测任务地月转移轨道选择提供依据。
To improve the speed of trans-lunar trajectory search and provide the accurate initial value guess,the fast design method and the orbital characteristics of two-impulse trans-lunar trajectory were studied in this paper. First,the system model of trans-lunar trajectory in geocentric rotating frame was established based on the three-body model,and the velocity increment of trans-lunar injection and alignment angle in geocentric rotating frame were selected as the control variables,which had explicit physical meanings. Then,an initial estimation method for control variables was given based on the hypothesis of two-body model,and a search strategy for trans-lunar trajectories with different moving directions were proposed. Sequential quadratic programming algorithm was applied to solve four types of trans-lunar trajectories and the variations of the control variables were analyzed.In the end,the influences of the transfer time,the perigee altitude and the perilune altitude on trans-lunar trajectory were analyzed,and the corrections of two-body model initial values caused by lunar gravity were derived. The simulation results showed that the proposed design method could rapidly and accurately search the specified type of trans-lunar trajectory,and the obtained trajectory characteristics could provide references for trans-lunar trajectory selection in future lunar exploration missions.
To improve the speed of trans-lunar trajectory search and provide the accurate initial value guess,the fast design method and the orbital characteristics of two-impulse trans-lunar trajectory were studied in this paper. First,the system model of trans-lunar trajectory in geocentric rotating frame was established based on the three-body model,and the velocity increment of trans-lunar injection and alignment angle in geocentric rotating frame were selected as the control variables,which had explicit physical meanings. Then,an initial estimation method for control variables was given based on the hypothesis of two-body model,and a search strategy for trans-lunar trajectories with different moving directions were proposed. Sequential quadratic programming algorithm was applied to solve four types of trans-lunar trajectories and the variations of the control variables were analyzed.In the end,the influences of the transfer time,the perigee altitude and the perilune altitude on trans-lunar trajectory were analyzed,and the corrections of two-body model initial values caused by lunar gravity were derived. The simulation results showed that the proposed design method could rapidly and accurately search the specified type of trans-lunar trajectory,and the obtained trajectory characteristics could provide references for trans-lunar trajectory selection in future lunar exploration missions.
引文
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[17]贺波勇,沈红新,李海阳.地月转移轨道设计的改进微分校正方法[J].国防科技大学学报,2014,36(6):60-64.He B Y,Shen H X,Li H Y.An improved differential correction method for trans-lunar orbit design[J].Journal of National University of Defense Technology,2014,36(6):60-64.(in Chinese)
[18]贺波勇.载人登月转移轨道偏差传播分析与中途修正方法研究[D].长沙:国防科技大学,2006.He B Y.Analysis of Transfer Orbit Deviation Propagation and Mid-Course Correction for Manned Lunar Landing[D].Changsha:National University of Defense Technology,2006.(in Chinese)
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[20]周文艳,杨维廉.月球探测器转移轨道的特性分析[J].空间科学学报,2004,24(5):354-359.Zhou W Y,Yang W L.Analysis of the characteristics of the transfer trajectory of lunar explorer[J].Chinese Journal of Space Science,2004,24(5):354-359.(in Chinese)
[2]何巍,徐世杰.地月低能转移轨道设计方法研究[J].宇航学报,2006,27(5):965-969.He W,Xu S J.Research on low energy transfer trajectory design method between earth and moon[J].Journal of Astronautics,2006,27(5):965-969.(in Chinese)
[3]张汉清,李言俊.利用平动点流形设计地月转移轨道的研究[J].测控技术,2011,30(3):94-97.Zhang H Q,Li Y J.Research on using libration point manifolds to design earth-moon transfer trajectory[J].Measurement and Control Technology,2011,30(3):94-97.(in Chinese)
[4]徐明,徐世杰.小推力航天器的地月低能转移轨道[J].航空学报,2008,29(4):781-787.Xu M,Xu S J.Low-energy trajectory from earth to moon for low-thrust spacecraft[J].Acta Aeronautica Et Astronautica Sinica,2008,29(4):781-787.(in Chinese)
[5]Manned Spacecraft Center.Apollo 11 mission report[R].NASA,MSC-00171,1969.
[6]周文艳,杨维廉.嫦娥二号卫星轨道设计[J].航天器工程,2010,19(5):24-28.Zhou W Y,Yang W L.Orbit design for Chang’e-2 lunar orbiter[J].Spacecraft Engineering,2010,19(5):24-28.(in Chinese)
[7]黄文德,郗晓宁,王威.基于双二体假设的载人登月混合轨道特性分析及设计[J].国防科技大学学报,2010,32(4):61-67.Huang W D,Xi X N,Wang W.Characteristic analysis and design of hybrid trajectory for manned lunar landing mission based on double two body model[J].Journal of National University of Defense Technology,2010,32(4):61-67.(in Chinese)
[8]Peng Q B,Shen H X,Li H Y.Free return orbit design and characteristics analysis for manned lunar mission[J].Science China,Technological Sciences,2011,54(12):3243-3250.
[9]Jesick M,Ocampo C.Automated generation of symmetric lunar free-return trajectories[J].Journal of Guidance,Control,and Dynamics,2011,34(1):98-106.
[10]Hou X Y,Zhao Y H,Liu L.Free return trajectories in lunar mission[J].Chinese Astronomy and Astrophysics,2013,37:183-194.
[11]张科,谭明虎,吕梅柏,等.圆型限制性三体问题中双脉冲地月转移轨道设计研究[J].西北工业大学学报,2015,33(1):110-114.Zhang K,Tan M H,Lv Meibo,et al.Calculating two-impulse earth-moon transfers in the circular restricted three-body problem[J].Journal of Northwestern Polytechnical University,2015,33(1):110-114.(in Chinese)
[12]李立涛,张振民,杨涤.奔月转移轨道的快速设计方法研究[J].航空学报,2003,24(2):152-156.Li L T,Zhang Z M,Yang D.Study of rapid design method for cislunar transfer trajectory[J].Acta Aeronautica Et Astronautica Sinica,2003,24(2):152-156.
[13]林晓辉,孙兆伟,杨涤.地月转移轨道的快速设计方法研究[J].哈尔滨工业大学学报,2005,37(2):234-237.Lin X H,Sun Z W,Yang D.Fast design method for transfer orbit of lunar probe[J].Journal of Harbin Institute of Technology,2005,37(2):234-237.(in Chinese)
[14]Luo Q Q,Yin J F,Han C.Design of Earth-Moon free-return trajectories[J].Journal of Guidance,Control,and Dynamics,2013,36(1):263-271.
[15]高玉东,郗晓宁,王威.地月空间飞行轨道分层搜索设计[J].宇航学报,2006,27(6):1157-1161.Gao Y D,Xi X N,Wang W.Cislunar trajectory design using searching step by step method[J].Journal of Astronautics,2006,27(6):1157-1161.(in Chinese)
[16]杨维廉.发射极月卫星的转移轨道研究[J].航天器工程,1997,6(3):19-33.Yang W L.Research on transfer orbit for probe on polar moon orbit[J].Spacecraft Engineering,1997,6(3):19-33.(in Chinese)
[17]贺波勇,沈红新,李海阳.地月转移轨道设计的改进微分校正方法[J].国防科技大学学报,2014,36(6):60-64.He B Y,Shen H X,Li H Y.An improved differential correction method for trans-lunar orbit design[J].Journal of National University of Defense Technology,2014,36(6):60-64.(in Chinese)
[18]贺波勇.载人登月转移轨道偏差传播分析与中途修正方法研究[D].长沙:国防科技大学,2006.He B Y.Analysis of Transfer Orbit Deviation Propagation and Mid-Course Correction for Manned Lunar Landing[D].Changsha:National University of Defense Technology,2006.(in Chinese)
[19]Gill P E,Murray W,Saunders M A.Snopt:an SQP algorithm for large-scale constrained optimization[J].SIAM J.Optim.,2002,12:979-1006.
[20]周文艳,杨维廉.月球探测器转移轨道的特性分析[J].空间科学学报,2004,24(5):354-359.Zhou W Y,Yang W L.Analysis of the characteristics of the transfer trajectory of lunar explorer[J].Chinese Journal of Space Science,2004,24(5):354-359.(in Chinese)