连续小推力作用下的共线平动点

侯锡云; 刘林

doi:10.6052/0459-1879-12-191

连续小推力作用下的共线平动点

侯锡云^1,2, ,,
刘林^1,2

1.
南京大学天文与空间科学学院,南京210093
2. 南京大学空间环境与航天动力学研究所,南京210093

基金项目: 国家自然科学基金(10903002),教育部新世纪优秀人才基金(NCET-11-0223)和国家高技术研究发展计划(2012AA121602)资助项目.

详细信息

通讯作者:
侯锡云,副教授,主要研究方向:动力天文与轨道力学.E-mail:silence@nju.edu.cn

中图分类号: V448.2
计量
- 文章访问数: 2344
- HTML全文浏览量: 64
- PDF下载量: 872
出版历程
- 收稿日期: 2012-07-03
- 修回日期: 2012-09-15
- 刊出日期: 2013-03-17

COLLINEAR LIBRATION POINTS WITH CONTINUOUS LOW THRUST

Hou Xiyun^1,2, ,,
Liu Lin^1,2

1.
School of Astronomy and Space Science, Nanjing University, Nanjing 210093, China
2. Institute of Space Environment and Astrodynamics, Nanjing University, Nanjing 210093, China

Funds: The project was supported by the National Natural Science Foundation of China (10903002), New Century Excellent Talents in University (NCET-11-0223) and the National High Technology Research and Development Program of China (2012AA121602).

摘要

摘要: 研究了圆型限制性三体问题的平动点在连续小推力作用下的具体位置和动力学特征的变化. 研究表明,随着小推力方向在空间中的变化,平动点的具体位置也会发生相应的变化,文章详细阐述了这些变化的特征.针对航天任务中应用较多的共线平动点L1和L2,研究了其附近运动的稳定性状态,给出了线性条件稳定解,并在此基础上,构造了条件稳定解的高阶形式,将其结果与数值积分轨道进行了比对,两者符合得很好. 最后,进一步研究了共线平动点附近周期轨道族的演化状态,由于连续小推力引入的非对称性,周期轨道族会发生分岔现象.
- 圆型限制性三体问题 /
- 平动点 /
- 周期轨道
Abstract: Collinear libration points of the restricted three-body problem with constant low thrust are studied. Varying the direction of the low thrust, the positions of the collinear libration points vary correspondingly. The set of the point L1 or L2 forms the shape of an elliptical “sphere” in space while the set of the point L3 forms the shape of a “banana”. The triangular libration points are also studied to show how they are connected with the collinear libration point L3. Concentrating on the points L1 and L2, linear solutions of the motions around them are obtained. Due to the asymmetry introduced by the low thrust, the linear solution has a form different from that of the unperturbed case. High order analytical solutions are also constructed. These solutions are compared with numerically integrated orbits. The comparison shows good agreement with each other. At last, periodic families around these two points are studied. These families include the planar and the vertical Lyapunov families, the halo family and another special periodic family. Bifurcation phenomena of these families are described.
- circular restricted three-body problem /
- libration point /
- periodic orbit

HTML全文

参考文献(22)

Dunham DW, Farquhar RW. Libration point missions, 1978-2002. In: Gómez G, Lo MW, Masdemont JJ, eds. Proceedings of the Conference on Libration Point Orbits and Applications, Singapore: World Scientific, 2003. 45-73

Farquhar RW, Dunharn DW, Guo Y, et al. Utilization of libration points for human explorations in the sun-earth- moon system and beyond. Acta Astronautica, 2004, 55 (3-9): 687-700

Broschart SB, Chung MJ, Hatch SJ, et al. Preliminary trajectory design for the Artemis Lunar Mission, AAS 09- 382, Astrodynamics Specialist Conference, Pittsburgh, Pennsylvania, USA, 2009

Hoffman TL. GRAIL: Gravity Mapping the Moon. In: Proceedings of the 2009 IEEE Aerospace Conference, Big Sky, MT, USA, March 7-14, 2009, 1-7: 293-300

吴伟仁,崔平远,乔栋等. 嫦娥二号日地拉格朗日L2点探测轨道设计与实施. 科学通报,2012,57:1987-1991 (Wu Weiren, Cui Pingyuan, Qiao Dong, et al. Design and performance of exploring trajectory to Sun-Earth L2 point for Chang'E-2 mission. Chin Sci Bull, 2012, 57: 1987-1991 (in Chinese))

Gómez G, Llibre J, Martínez R, et al. Dynamics and Mission Design near Libration Point Orbits, Vol. I, Fundamentals: The Case of Collinear Libration Points. Singapore: World Scientific, 2001

Gómez G, Llibre J, Martínez R, et al. Dynamics and Mission Design near Libration Point Orbits, Vol. III, Advanced Methods for Collinear Points. Singapore: World Scientific, 2001

Jorba A, Masdemond J. Dynamics in the center manifold of the collinear points of the restricted three-body problem. Physica D, 1999, 132: 189-213

赵军,蔡志勤,齐朝晖. 基于平动点轨道的绳系卫星编队重构仿真. 系统仿真学报,2011,23(12):2805-2811 (Zhao Jun, Cai Zhiqin, Qi Zhaohui. Simulation of reconfiguration of tethered satellite formations in libration point orbits. it Journal of System Simulation, 2011, 23(12): 2805-2811 (in Chinese))

张汉清,李言俊,张科. 一种新的共线平动点拟周期轨道稳定保持策略. 宇航学报,2012,33(3):318-324 (Zhang Haiqing, Li Yanjun, Zhang Ke. A novel station-keeping strategy for quasi-periodic orbits in the vicinity of collinear libration points. Journal of Astronautics, 2012, 33(3): 318-324 (in Chinese))

Chen Y, Baoyin H, Li JF. Trajectory design for the moon departure libration point mission in full ephemeris model. Science China Technological Sciences, 2011, 54: 2924-2934

Baoyin H, McInnes CR. Solar sail halo orbits at the sun-earth artificial L1 point. Celestial Mechanics and Dynamical Astronomy, 2006, 94: 155-171

Simo J, McInnes CR. Solar sail trajectories at the Earth-Moon Lagrange Points. In: Proc. of 59th International Astronautical Congress (IAC'08), Glasgow, Scotland, 2008

Simo J, McInnes CR. Designing displaced lunar orbits using low-thrust Propulsion. Journal of Guidance, Control and Dynamics, 2010, 33: 259-265

Farrés A, Jorba À. Solar sail surfing along families of equilibrium points. Acta Astronautica, 2008, 63: 249-257

Farrés A, Jorba À. Dynamics of a solar sail near a halo orbit. Acta Astronautica, 2010, 67: 979-990

Farrés A, Jorba À. Periodic and quasi-periodic motions of a solar sail close to sl1 in the earth-sun system. Celestial Mechanics and Dynamical Astronomy, 2010, 107: 233-253

McInnes CR. Artificial lagrange points for a partially reflecting flat solar sail. Journal of Guidance, Control and Dynamics, 1999, 22: 185-187

Baig S, McInnes CR. Artificial halo orbits for low-thrust propulsion Spacecraft. Celestial Mechanics and Dynamical Astronomy, 2009, 104: 321-335

Hou XY, Liu L. On lyapunov families around collinear libration points. The Astronomical Journal, 2009, 137: 4577-4585

Hénon M. Vertical stability of periodic orbits in the restricted Problem. Celestial Mechanics, 1973, 8: 269-272

Mondelo JM. Contribution to the study of fourier methods for quasi-periodical functions and the vicinity of the collinear libration points. [PhD Thesis]. Barcelona, Spain: Universitat de Barcelona, 2001