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中文核心期刊
Volume 53 Issue 5
May  2021
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Li Xiangyu, Qiao Dong, Cheng Yu. PROGRESS OF THREE-BODY ORBITAL DYNAMICS STUDY[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(5): 1223-1245. doi: 10.6052/0459-1879-20-367
Citation: Li Xiangyu, Qiao Dong, Cheng Yu. PROGRESS OF THREE-BODY ORBITAL DYNAMICS STUDY[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(5): 1223-1245. doi: 10.6052/0459-1879-20-367

PROGRESS OF THREE-BODY ORBITAL DYNAMICS STUDY

doi: 10.6052/0459-1879-20-367
  • Received Date: 2020-10-23
  • Publish Date: 2021-05-18
  • The orbital dynamics in the three-body system is a classical problem in the field of astrodynamics. It has rich theoretical and engineering significance, and have played an important role in the process of space activities extending from near-earth space to deep space. This paper reviews and summarizes the progress of the study of orbital dynamics in the three-body system. Combined with the development trend of deep space exploration in the future, the hotspots and challenges in the research of three-body orbital dynamics are prospected. First, the research background and significance of the three-body problem are surveyed, and the development of the dynamics model of the three-body system is briefly reviewed. Secondly, characteristics of the local motion near the equilibrium point in the three-body problem are systematically summarized. The analytical and numerical methods for periodic orbits are introduced. The latest development of quasi-periodic motion is discussed. Meanwhile, the characteristics and research progress of global periodic motions in the three-body system including resonance orbits, cycler trajectories, and free return orbits are summarized. Next, the research progress of the low-energy transfer and capture trajectory design in the three-body system is analyzed from two aspects of invariant manifold theory and weak stability boundary theory. Finally, the applications of orbital dynamics in the three-body system in formation flight and navigation constellation design are summarized. Several orbital dynamics and control problems in the design of landing trajectories for full lunar-surface coverage, the low thrust orbit optimization of the three-body system, and the utilization of non-linear equilibrium points in the three-body system are addressed for future study.

     

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  • [1]
    Valtonen M, Karttunen H. The Three-Body Problem. Cambridge: Cambridge University Press, 2006
    [2]
    Sundman KF. Mémoire sur le problème des trois corps. Acta Mathematica, 1913,36(1):105-179
    [3]
    Suvakov M, Dmitrasinovic V. Three classes of newtonian three-body planar periodic orbits. Physical Review Letters, 2013,110(11):114301
    [4]
    Broucke R. Stability of periodic orbits in the elliptic restricted three-body problem. AIAA Journal, 1969,7(6):1003-1009
    [5]
    Huang SS. Very restricted four-body problem. The Astronomical Journal, 1960,65:347
    [6]
    Andreu MA. The quasi-bicircular problem. [PhD Thesis]. Barcelona: University of Barcelona, 1998
    [7]
    Richardson DL. Analytic construction of periodic orbits about the collinear points. Celestial Mechanics and Dynamical Astronomy, 1980,22(3):241-253
    [8]
    Howell KC, Pernicka HJ. Numerical determination of Lissajous trajectories in the restricted three-body problem. Celestial Mechanics, 1987,41(1):107-124
    [9]
    Gómez G, Koon WS, Lo MW, et al. Connecting orbits and invariant manifolds in the spatial restricted three-body problem. Nonlinearity, 2004,17(5):1571-1606
    [10]
    Belbruno E, Carrico J. Calculation of weak stability boundary ballistic lunar transfer trajectories//AIAA/AAS Astrodynamics Specialist Conference, 2000-8-14-17, USA CO, Denver, AIAA 2000-4142
    [11]
    García F, Gómez G. A note on weak stability boundaries. Celestial Mechanics and Dynamical Astronomy, 2007,97(2):87-100
    [12]
    Belbruno E, Gidea M, Topputo F. Weak stability boundary and invariant manifolds. SIAM Journal on Applied Dynamical Systems, 2010,9(3):1061-1089
    [13]
    Richardson DL. Halo orbit formulation for the ISEE-3 mission. Journal of Guidance, Control, and Dynamics, 1980,3(6):543-548
    [14]
    Belbruno EA, Miller JK. Sun-perturbed Earth-to-moon transfers with ballistic capture. Journal of Guidance, Control, and Dynamics, 1993,16(4):770-775
    [15]
    吴伟仁, 王琼, 唐玉华 等. "嫦娥4号"月球背面软着陆任务设计. 深空探测学报, 2017,4(2):111-117

    (Wu Weiren, Wang Qiong, Tang Yuhua, et al. Design of Chang'e-4 lunar farside soft-landing mission. Journal of Deep Space Exploration, 2017,4(2):111-117 (in Chinese))
    [16]
    Brown EW. An Introductory Treatise on the Lunar Theory. NY: Dover Publications Inc., 1896
    [17]
    Farquhar RW. The control and use of libration-point satellites. NASA Technical Report, NASA TR R-346, 1970
    [18]
    Nicholson FT. Effect of solar perturbation on motion near the collinear earth-moon libration points. AIAA Journal, 1967,5(12):2237-2241
    [19]
    刘林, 王歆. 月球探测器轨道力学. 北京: 国防工业出版社, 2006

    (Liu Lin, Wang Xin. Beijing: National Defense Industry Press (in Chinese))
    [20]
    Lewallen JM, Tapley BD. Solar influence on satellite motion near the stable earth-moon libration points. AIAA Journal, 2015,2(4):728-732
    [21]
    Li XY, Qiao D, Macdonald M. Energy-saving capture at Mars via backward-stable orbits. Journal of Guidance, Control, and Dynamics, 2019,42(5):1-10
    [22]
    Makó Z, Szenkovits F, Salamon J, et al. Stable and unstable orbits around Mercury. Celestial Mechanics and Dynamical Astronomy, 2010,108(4):357-370
    [23]
    Ma X, Li JF. Distant quasi-periodic orbits around Mercury. Astrophysics and Space Science, 2013,343(1):83-93
    [24]
    Campagnola S, Lo M. BepiColombo gravitational capture and the elliptic restricted three-body problem. Proceedings in Applied Mathematics and Mechanics, 2008,7(1):1030905-1030906
    [25]
    Schechter HB. Three-dimensional nonlinear stability analysis of the Sun-perturbed Earth-moon equilateral points. AIAA Journal, 2008,6(7):1223-1228
    [26]
    Gómez G, Llibre J, Martínez R, et al. Study on orbits near the triangular libration points in the perturbed restricted three body problem. Final Report Fundacio Empresa i Ciencia, Spain: Barcelona, 1987
    [27]
    Castelli R. Regions of prevalence in the coupled restricted three-body problems approximation. Communications in Nonlinear Science and Numerical Simulation, 2012,17(2):804-816
    [28]
    Andreu MA, Simó C. Translunar halo orbits in the quasi-bicircular problem//The Dynamics of Small Bodies in the Solar System. Springer, Dordrecht, 1999: 309-314
    [29]
    Andreu MA. Dynamics in the center manifold around $L_2$ in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy, 2002,84(2):105-133
    [30]
    Guzman JJ. Spacecraft trajectory design in the context of a coherent restricted four-body problem. [PhD Thesis]. Lafayette: Perdue University, 2001
    [31]
    Shang HB, Wu XY, Cui PY. Periodic orbits in the doubly synchronous binary asteroid systems and their applications in space missions. Astrophysics and Space Science, 2015,355(1):69-87
    [32]
    Li XY, Qiao D, Barucci MA. Analysis of equilibria in the doubly synchronous binary asteroid systems concerned with non-spherical shape. Astrodynamics, 2018,2(2):133-146
    [33]
    Li XY, Qiao D, Li P. Bounded trajectory design and self-adaptive maintenance control near non-synchronized binary systems comprised of small irregular bodies. Acta Astronautica, 2018,152:768-781
    [34]
    Szebehely V. Theory of Orbits: The Restricted Problem of Three Bodies. New York and London: Academic Press, 1967
    [35]
    Jorba A, Villanueva J. On the persistence of lower dimensional invariant tori under quasiperiodic perturbations. Journal of Nonlinear Science, 1997,7(5):427-473
    [36]
    Farquhar RW, Kamel AA. Quasi-periodic orbits about the translunar libration point. Celestial Mechanics, 1973,7(4):458-473
    [37]
    Gómez G, Marcote M. High-order analytical solutions of Hill's equations. Celestial Mechanics and Dynamical Astronomy, 2006,94(2):197-211
    [38]
    Howell KC. Three-dimensional, periodic, 'halo' orbits. Celestial Mechanics & Dynamical Astronomy, 1984,32(1):53-71
    [39]
    Folta DC, Woodard M, Howell KC, et al. Applications of multi-body dynamical environments: The ARTEMIS transfer trajectory design. Acta Astronautica, 2012,73:237-249
    [40]
    Simo C. On the analytical and numerical approximation of invariant manifolds. In Modern Methods in Celestial Mechanics, Eds. D. Benest, C. Froeschlé, Editions Frontières, 1990: 285-329
    [41]
    Alessi EM. The role and usage of libration point orbits in the Earth — Moon system. [PhD Thesis]. Barcelona: University of Barcelona, 2010
    [42]
    Colombo G. The stabilization of an artificial satellite at the inferior conjunction point of the Earth-Moon system. Journal of the Astronautical Sciences, 1961,6(1):213
    [43]
    Breakwell JV, Kamel AA, Ratner MJ. Station-keeping for a translunar communication station. Celestial Mechanics, 1974,10(3):357-373
    [44]
    Howell KC, Pernicka HJ. Station-keeping method for libration point trajectories. Journal of Guidance, Control, and Dynamics, 1993,16(1):713-723
    [45]
    Pernicka HJ. The numerical determination of nominal libration point trajectories and development of a station-keeping strategy. [PhD Thesis]. Lafayette: Purdue University, 1990
    [46]
    Dunham DW, Roberts CE. Stationkeeping techniques for libration point satellites. Journal of the Astronautical Sciences, 2001,49(1):127-144
    [47]
    Farquhar RW, Muhonen DP, Newman CR, et al. Trajectories and orbital maneuvers for the first libration-point satellite. Journal of Guidance, Control, and Dynamics, 1980,3(6):549-554
    [48]
    Howell KC, Marchand BG. Control strategies for formation flight in the vicinity of the libration points. Journal of Guidance, Control, and Dynamics, 2005,28(6):1210-1219
    [49]
    Gómez G, Howell KC, Masdemont J, et al. Station-keeping strategies for translunar libration point orbits. Advances in the Astronautical Sciences, 1998,99(2):949-967
    [50]
    Pavlak TA, Howell KC. Strategy for long-term libration point orbit stationkeeping in the Earth-Moon system//Proceedings of the AAS/AIAA Astrodynamics Specialist Conference, 2011-7-31-8-4, Girdwood, Alaska, AAS Paper 11-516
    [51]
    Folta DC, Woodard M, Cosgrove D. Stationkeeping of the first Earth-Moon libration orbiters: The ARTEMIS mission//Proceedings of the AAS/AIAA Astrodynamics Specialist Conference, 2011-07-31—08-04, Girdwood, Alaska, AAS Paper 11-515
    [52]
    Gómez G, Mondelo JM. The dynamics around the collinear equilibrium points of the RTBP. Physica D Nonlinear Phenomena, 2001,157(4):283-321
    [53]
    Baresi N, Scheeres DJ. Quasi-periodic invariant tori of time-periodic dynamical systems: Applications to small body exploration// Proceedings of the International Astronautical Congress, 2016-9-26-30, Mexico, Guadalajara
    [54]
    Kolemen E, Kasdin NJ, Gurfil P. Multiple Poincaré sections method for finding the quasiperiodic orbits of the restricted three body problem. Celestial Mechanics and Dynamical Astronomy, 2012,112(1):47-74
    [55]
    Campagnola S, Lo MW, Newton P. Subregions of motion and elliptic Halo orbits in the elliptic restricted three-body problem. Advances in the Astronautical Sciences, 2008,130(2):1541-1555
    [56]
    Peng H, Xu SJ. Stability of two groups of multi-revolution elliptic halo orbits in the elliptic restricted three-body problem. Celestial Mechanics and Dynamical Astronomy, 2015,123:279-303
    [57]
    Ferrari F, Lavagna M. Periodic motion around libration points in the elliptic restricted three-body problem. Nonlinear Dynamics, 2018,93(2):453-462
    [58]
    Whitley R, Davis DC, Burke L, et al. Earth-Moon near rectilinear halo and butterfly orbits for lunar surface exploration//AAS/AIAA Astrodynamics Specialist Conference, 2018-8-19-23, USA, UT, Snowbird, AAS 18-406
    [59]
    Hénon M, Guyot M. Stability of periodic orbits in the restricted problem//In: Giacaglia G.E.O. ed. Periodic Orbits, Stability and Resonances. Dordrecht: Springer, 1970, 349-374
    [60]
    Capdevila L, Guzzetti D, Howell KC. Various transfer options from Earth into distant retrograde orbits in the vicinity of the Moon. Advances in the Astronautical Sciences, 2014,152(1):3659-3678
    [61]
    Russell RP. Global search for planar and three-dimensional periodic orbits near Europa. Journal of the Astronautical Sciences, 2006,54(2):199-226
    [62]
    Escribano TV. Spacecraft transfer trajectory design exploiting resonant orbits in multi-body environments. [PhD Thesis]. Lafayette: Purdue University, 2013
    [63]
    Vaquero M, Howell KC. Design of transfer trajectories between resonant orbits in the Earth-Moon restricted problem. Acta Astronautica, 2014,94(1):302-317
    [64]
    Antoniadou KI, Voyatzis G. Resonant periodic orbits in the exoplanetary systems. Astrophysics and Space Science, 2014,349(2):657-676
    [65]
    Anderson RL, Campagnola S, Lantoine G. Broad search for unstable resonant orbits in the planar circular restricted three-body problem. Celestial Mechanics and Dynamical Astronomy, 2016,124(2):177-199
    [66]
    张文博, 成跃, 王宁飞. 地月系统循环轨道初步设计与特性分析. 航空学报, 2015,36(7):2197-2206

    (Zhang Wenbo, Cheng Yue, Wang Ningfei. Preliminary design and characteristic analysis of cycler orbits in Earth-Moon system. Acta Aeronautica ET Astronautica Sinica, 2015,36(7):2197-2206 (in Chinese))
    [67]
    Aldrin B. Cyclic trajectory concepts//SAIC presentation to the interplanetary rapid transit study meeting, Jet Propulsion Laboratory. California: 1985,28
    [68]
    Kauffman J. A successful failure: NASA's crisis communications regarding Apollo 13. Public Relations Review, 2001,27(4):437-448
    [69]
    黄文德, 郗晓宁, 王威 等. 基于双二体假设的载人登月自由返回轨道特性分析及设计. 宇航学报, 2010,31(5):1297-1303

    (Huang Wende, Xi Xiaoning, Wang Wei, et al. Characteristic analysis and design of free return orbit for lunar manned landing based on the double two-body model. Journal of Astronautics, 2010,31(5):1297-1303 (in Chinese))
    [70]
    彭祺擘, 沈红新, 李海阳. 载人登月自由返回轨道设计及特性分析. 中国科学: 技术科学, 2012,42(3):333-341

    (Peng Qibo, Shen Hongxin, Li Haiyang. Free return orbit design and characteristics analysis for manned lunar mission. Science China Technique Science, 2012,42(3):333-341 (in Chinese))
    [71]
    王丹阳, 邓辉. 地月自由返回轨道设计. 中国空间科学技术, 2017,37(1):57-65

    (Wang Danyang, Deng Hui. Cislunar free return trajectory design. Chinese Space Science and Technology, 2017,37(1):57-65 (in Chinese))
    [72]
    侯锡云, 赵玉晖, 刘林. 月球探测中的无动力返回轨道. 天文学报, 2012,53(4):308-318

    (Hou Xiyun, Zhao Yuhui, Liu Lin. Free return trajectories in lunar missions. Acta Astronomica Sinica, 2012,53(4):308-318 (in Chinese))
    [73]
    谢晨月, 袁泽龙, 王建春 等. 基于人工神经网络的湍流大涡模拟方法. 力学学报, 2021,53(1):1-16

    (Xie Chenyue, Yuan Zelong, Wang Jianchun, et al. Artificial neural network-based subgrid-scale models for large-eddy simulation of turbulence. Chinese Journal of Theoretical and Applied Mechanics, 2021,53(1):1-16 (in Chinese))
    [74]
    刘铖, 胡海岩. 基于李群局部标架的多柔体系统动力学建模与计算. 力学学报, 2021,53(1):213-233

    (Liu Cheng, Hu Haiyan. Dynamic modeling and computation for flexible multibody systems based on the local frame of Lie group. Chinese Journal of Theoretical and Applied Mechanics, 2021,53(1):213-233 (in Chinese))
    [75]
    Parker JS, Anderson RL. Low-Energy Lunar Trajectory Design. John Wiley & Sons, Inc., 2013
    [76]
    Gómez G, Jorba A, Masdemont J, et al. Study of the transfer from the Earth to a halo orbit around the equilibrium point L1. Celestial Mechanics and Dynamical Astronomy, 1993,56(4):541-562
    [77]
    Barden BT, Howell KC, Lo MW. Application of dynamical systems theory to trajectory design for a libration point mission//Astrodynamics Conference, 1996-07-29, Reston, Virigina, AIAA-96-3602
    [78]
    Parker JS. Low-energy ballistic lunar transfers. [PhD Thesis]. Colorado: University of Colorado, 2007
    [79]
    Parker JS, Born GH. Modeling a low-energy ballistic lunar transfer using dynamical systems theory. Journal of Spacecraft and Rockets, 2008,45(6):1269-1281
    [80]
    Gordon DP. Transfer to Earth-Moon L2 halo orbits using lunar proximity and invariant manifolds. [Master Thesis]. Lafayette: Purdue University, 2008
    [81]
    Li MT, Zheng JH. Impulsive lunar halo transfers using the stable manifolds and lunar flybys. Acta Astronautica, 2010,66(9-10):1481-1492
    [82]
    Zeng H, Zhang JR. Design of impulsive Earth-Moon halo transfers: lunar proximity and direct options. Astrophysics and Space Science, 2016,361(10):328
    [83]
    Cheng Y, Gómez G, Masdemont JJ, et al. Study of the transfer between libration point orbits and lunar orbits in Earth-Moon system. Celestial Mechanics & Dynamical Astronomy, 2017,128(4):409-433
    [84]
    Gómez G, Masdemont JJ. Some zero cost transfers between libration point orbits. Advances in the Astronautical Sciences, 2000,105(2):1199-1216
    [85]
    Gómez G, Jorba A, Simo C. Study of the transfer between halo orbits. Acta Astronautica, 1998,43(9/10):493-520
    [86]
    Davis KE, Anderson RL, Scheeres DJ, et al. The use of invariant manifolds for transfers between unstable periodic orbits of different energies. Celestial Mechanics and Dynamical Astronomy, 2010,107(4):471-485
    [87]
    Davis KE, Anderson RL, Scheeres DJ, et al. Optimal transfers between unstable periodic orbits using invariant manifolds. Celestial Mechanics and Dynamical Astronomy, 2011,109(3):241-264
    [88]
    Koon W, Lo M, Marsden JE, et al. Dynamical Systems, the Three-Body Problem and Space Mission Design. Springer-Verlag, Berlin, 2008.
    [89]
    Howell KC, Kakoi M. Transfers between the Earth-Moon and Sun-Earth systems using manifolds and transit orbits. Acta Astronautica, 2006,59(1-5):367-380
    [90]
    Kakoi M, Howell KC, Folta D. Access to Mars from Earth-Moon libration point orbits: Manifold and direct options. Acta Astronautica, 2014,102:269-286
    [91]
    Peng H, Xu SJ. Low-energy transfers to a Lunar multi-revolution elliptic halo orbit. Astrophysics and Space Science, 2015,357(1):1-15
    [92]
    Whitley R, Martinez R. Options for staging orbits in cislunar space//2016 IEEE Aerospace Conference, 2016-3-5-12, USA, MT, Big Sky, 16121824
    [93]
    Davis DC, Phillips SM, Howell KC, et al. Stationkeeping and transfer trajectory design for spacecraft in cislunar space. Advances in the Astronautical Sciences, 2018,162:3483-3502
    [94]
    Guzzetti D, Zimovan EM, Howell KC, et al. Stationkeeping analysis for spacecraft in lunar near rectilinear halo orbits. Advances in the Astronautical Sciences, 2017,160:3199-3218
    [95]
    杜向南, 杨震. 航天器单脉冲机动可达域求解算法. 力学学报, 2020,52(6):1621-1631

    (Du Xiangnan, Yang Zhen. An algorithm for solving spacecraft reachable domain with single-impulse maneuvering. Chinese Journal of Theoretical and Applied Mechanics, 2020,52(6):1621-1631 (in Chinese))
    [96]
    Belbruno E. Examples of the nonlinear dynamics of ballistic capture and escape in the Earth-Moon system//Astrodynamics Conference, 1990-8-20-22, USA, OR, Portland, AIAA-90-2896
    [97]
    Belbruno E. Capture dynamics and chaotic motions in celestial mechanics: With applications to the construction of low energy transfers//Capture Dynamics and Chaotic Motions in Celestial Mechanics: With Applications to the Construction of Low Energy Transfers. Princeton University Press, 2018
    [98]
    Hyeraci N, Topputo F. The role of true anomaly in ballistic capture. Celestial Mechanics and Dynamical Astronomy, 2013,116(2):175-193
    [99]
    Romagnoli D, Circi C. Earth-Moon weak stability boundaries in the restricted three and four body problem. Celestial Mechanics and Dynamical Astronomy, 2009,103(1):79-103
    [100]
    Li J, Sun YS. A survey of weak stability boundaries in the Sun-Mars system. Research in Astronomy and Astrophysics, 2015,15(3):376-392
    [101]
    Topputo F, Belbruno E. Computation of weak stability boundaries: Sun-Jupiter system. Celestial Mechanics and Dynamical Astronomy, 2009,105(1-3):3-17
    [102]
    Koon WS, Marsden JE, Ross SD, et al. Constructing a low energy transfer between Jovian moons//Celestial Mechanics//Dedicated to Donald Saari for His 60th Birthday: Proceedings of an International Conference on Celestial Mechanics, 1999-12-15—19, USA, Illinois, Evanston, 2002,292:129
    [103]
    Hyeraci N, Topputo F. Method to design ballistic capture in the elliptic restricted three-body problem. Journal of Guidance, Control, and Dynamics, 2012,33(6):1814-1823
    [104]
    Luo ZF, Topputo F, Bernelli-Zazzera F, et al. Constructing ballistic capture orbits in the real solar system model, Celestial Mechanics and Dynamical Astronomy, 2014,120(4):433-450
    [105]
    Fantino E, Gómez G, Masdemont JJ, et al. A note on libration point orbits, temporary capture and low-energy transfers. Acta Astronautica, 2010,67(9-10):1038-1052
    [106]
    Belbruno EA, Miller J. A ballistic lunar capture trajectory for the Japanese spacecraft hiten. Jet Propulsion Laboratory, IOM, 1990,312:90-94
    [107]
    Circi C, Teofilatto P. Weak stability boundary trajectories for the deployment of lunar spacecraft constellations. Celestial Mechanics and Dynamical Astronomy, 2006,95(1-4):371-390
    [108]
    Parker JS, Anderson RL, Peterson A. Surveying ballistic transfers to low lunar orbit. Journal of Guidance, Control, and Dynamics, 2013,36(5):1501-1511
    [109]
    Sweetser TH. An estimate of the global minimum DV needed for earth-moon transfer. Advances in the Astronautical Sciences, 1991,75:111-120
    [110]
    Koon WS, Lo MW, Marsden JE, et al. Low energy transfer to the Moon. Celestial Mechanics and Dynamical Astronomy, 2001,81(1-2):63-73
    [111]
    Circi C, Teofilatto P. Effect of planetary eccentricity on ballistic capture in the solar system. Celestial Mechanics and Dynamical Astronomy, 2005,93(1-4):69-86
    [112]
    Mingotti G, Topputo F, Bernelli-Zazzera F. Earth-Mars transfers with ballistic escape and low-thrust capture. Celestial Mechanics and Dynamical Astronomy, 2011
    [113]
    Topputo F, Belbruno E. Earth-Mars transfers with ballistic capture. Celestial Mechanics and Dynamical Astronomy, 2014,121(4):329-346
    [114]
    Li XY, Qiao D. Earth-Phobos transfer with ballistic trajectory in the Sun-Mars system//2018 AIAA SPACE and Astronautics Forum and Exposition, 2018-9-17-19, USA, FL, Orlando, AIAA 2018-5309
    [115]
    Roncoli R, Fujii K. Mission design overview for the gravity recovery and interior laboratory (GRAIL) mission//AIAA/AAS Astrodynamics Specialist Conference, 2010-08-02—05, Canada, Ontario, Toronto, AIAA 2010-8383
    [116]
    Hatch S, Chung M, Kangas J. et al. Trans-Lunar cruise trajectory design of GRAIL (Gravity recovery and interior laboratory) mission//AIAA/AAS Astrodynamics Specialist Conference, 2010-08-02—05, Canada, Ontario, Toronto, AIAA 2010-8394
    [117]
    Héritier A, Howell KC. Dynamical evolution of natural formations in libration point orbits in a multi-body regime. Acta Astronautica, 2014,102:332-340
    [118]
    Héritier A, Howell KC. Natural regions near the collinear libration points ideal for space observations with large formations. Journal of the Astronautical Sciences, 2013,60(1):87-108
    [119]
    Howell KC, Millard LD. Control of satellite imaging formations in multi-body regimes. Acta Astronautica, 2009,64(5-6):554-570
    [120]
    Millard LD. Control of satellite imaging arrays in multi-body regimes. [PhD Thesis]. Lafayette: Purdue University, 2008
    [121]
    Out IA. Formation flying in the Sun-Earth/Moon perturbed restricted three-body problem. [Master's Thesis]. Netherlands: Delft University of Technology Faculty of Aerospace Engineering, 2017
    [122]
    Gómez G, Lo MW, Masdemont JJ, et al. Simulation of formation flight near L2 for the TPF mission//AAS/AIAA Spaceflight Mechanics Meeting, 2001-02-11—15, USA, California, Santa Barbara, AAS 01-305
    [123]
    Howell KC, Marchand BG. Natural and non-natural spacecraft formations near the L1 and L2 libration points in the Sun-Earth/Moon ephemeris system. Dynamics and Stability of Systems, 2005,20(1):149-173
    [124]
    Howell KC, Marchand BG. Formations near the libration points: Design strategies using natural and non-natural arcs//Proceedings of GSFC 2nd International Symposium on Formation Flying Missions and Technologies, 2004-09-14—16, USA, Washington, D.C., 20060048521
    [125]
    Marchand BG. Spacecraft formation keeping near the libration points of the Sun-Earth/Moon system. [PhD Thesis]. Lafayette: School of Aeronautics and Astronautics, Purdue University, 2004
    [126]
    王峰, 陈雪芹, 张世杰 等. 基于改进PEA的日地L2平动点编队飞行高精度位置保持. 宇航学报, 2011,32(5):982-990

    (Wang Feng, Chen Xueqin, Zhang Shijie, et al. Improved PEA-Based high accuracy relative position keeping for spacecraft formation flight in Sun-Earth L2 point. Journal of Astronautics, 2011,32(5):982-990 (in Chinese))
    [127]
    Wong H, Kapila V. Spacecraft formation flying near Sun-Earth L2 lagrange point: trajectory generation and adaptive full-state feedback control//Proceedings of GSFC 2nd International Symposium on Formation Flying Missions and Technologies, 2004-9-14-16, USA, Washington, D.C., 20060048533
    [128]
    姜春生, 王永, 李恒年 等. 日地平动点编队飞行自抗扰轨道维持控制. 空间控制技术与应用, 2017,43(1):49-54, 60

    (Jiang Chunsheng, Wang Yong, Li Hengnian, et al. ADRC-Based orbit maintaining control of spacecraft formation flying around halo orbits about the Sun-Earth libration points. Aerospace Control and Application, 2017,43(1):49-54,60 (in Chinese))
    [129]
    Infeld SI, Josselyn SB, Murray W, et al. Design and control of libration point spacecraft formations. Journal of Guidance, Control, and Dynamics, 2007,30(4):899-909
    [130]
    张燕, 荆武兴. 基于日地月方位信息的月球卫星自主导航. 宇航学报, 2005,26(4):495-498, 523

    (Zhang Yan, Jing Wuxing. Autonomous navigation for lunar satellite based on the optical information of Sun-Earth-Moon. Journal of Astronautics, 2005,26(4):495-498, 523 (in Chinese))
    [131]
    Hill K, Lo MW, Born GH. Linked, autonomous, interplanetary satellite orbit navigation (LiAISON) in lunar halo orbits//AAS/AIAA Astrodynamics Specialist Conference, 2005-08-07—11, USA, California, Lake Tahoe, AAS 05-400
    [132]
    Hill K, Born GH. Autonomous interplanetary orbit determination using satellite-to-satellite tracking. Journal of Guidance, Control, and Dynamics, 2012,30(3):679-686
    [133]
    Hill K, Born GH. Autonomous orbit determination from lunar halo orbits using crosslink range. Journal of Spacecraft and Rockets, 2012,45(3):548-553
    [134]
    Farquhar RW, Dunham DW, Guo YP, et al. Utilization of libration points for human exploration in the Sun-Earth-Moon system and beyond. Acta Astronautica, 2004,55(3-9):687-700
    [135]
    William DP, Caley B, Selena H, et al. Trajectory design considerations for human missions to explore the lunar farside from the Earth-Moon lagrange point EM-L2//AIAA Space 2013 Conference and Exposition, 2013-09-10—12, USA, CA, San Diego, AIAA 2013-5478
    [136]
    孙超, 唐玉华, 李翔宇 等. 地$!-!$月$L_2$点中继星月球近旁转移轨道设计. 深空探测学报, 2017,4(3):264-269, 275

    (Sun Chao, Tang Yuhua, Li Xiangyu, et al. Design of Earth-Moon $L_2$ halo orbit transfer trajectory for relay satellites using lunar flybys. Journal of Deep Space Exploration, 2017,4(3):264-269, 275 (in Chinese))
    [137]
    唐玉华. 地月$L_2$点中继卫星轨道设计与控制问题研究. [博士论文]. 北京: 北京理工大学, 2018

    (Tang Yuhua. Study of trajectory design and control of Earth-Moon $L_2$ relay satellite. [PhD Thesis]. Beijing: Beijing Institute of Technology 2018 (in Chinese))
    [138]
    刘磊, 曹建峰, 胡松杰 等. 地月$L_2$点周期轨道的月球背面覆盖分析. 深空探测学报, 2017,4(4):361-366

    (Liu Lei, Cao Jianfeng, Hu Songjie, et al. Coverage of lunar farside surface of the Earth-Moon $L_2$ periodic orbits. Journal of Deep Space Exploration, 2017,4(4):361-366 (in Chinese))
    [139]
    Zhang L, Xu B. A Universe Light House - Candidate architectures of the libration point satellite navigation system. Journal of Navigation, 2014,67(5):737-752
    [140]
    Zhang L, Xu B. Navigation performance of the libration point satellite navigation system in cislunar space. Journal of Navigation, 2015,68(2):367-382
    [141]
    Zhang L, Xu B. Simplified constellation architecture for the libration point satellite navigation system. Journal of Navigation, 2016,69(5):1082-1096
    [142]
    Daniele R, Christian C. Lissajous trajectories for lunar global positioning and communication systems. Celestial Mechanics and Dynamical Astronomy, 2010,107(4):409-425
    [143]
    Ren Y, Shan JJ. Libration point orbits for lunar global positioning systems. Advances in Space Research, 2013,51(7):1065-1079
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