PROGRESS OF THREE-BODY ORBITAL DYNAMICS STUDY
-
摘要: 三体系统轨道动力学问题是航天动力学领域中的经典问题, 具有丰富的理论与工程意义, 并将在人类由近地延伸到深空的航天活动过程中起到至关重要的作用. 本文回顾并总结了三体系统轨道动力学相关研究进展, 并结合未来的深空探测的发展趋势, 展望了三体系统轨道动力学研究中的热点与挑战. 首先阐述了三体问题的研究背景及意义, 简要回顾了三体系统动力学模型的发展历程. 其次, 系统概述了三体系统平衡点附近的局部运动特性, 介绍了平衡点附近周期轨道解析与数值求解方法, 给出了拟周期运动的最新进展. 同时总结了共振轨道、循环轨道、自由返回轨道等三类三体系统全局周期运动的动力学特性与研究进展. 再次, 从不变流形理论和弱稳定边界理论两个方面综述了三体系统中低能量转移与捕获轨道设计的研究进展. 最后, 综述了三体系统轨道动力学在编队飞行、导航星座设计两方面的应用, 并展望了全月面覆盖轨道设计、三体系统下的小推力轨道优化和三体系统的三角平衡点开发利用中值得关注的轨道动力学与控制问题.Abstract: 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.
-
Keywords:
- three-body problem /
- orbital dynamics /
- periodic motion /
- capture trajectory /
- transfer trajectory
-
-
[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
计量
- 文章访问数: 2406
- HTML全文浏览量: 383
- PDF下载量: 556
下载:
