A Simplified Path Searching and Correcting Method for the Calculation of Initial Value of Libration Periodic Orbit
-
摘要: 在限制性三体问题中,路径搜索修正法是一种基于平动点周期轨道垂直穿越Poincare截面的几何对称性计算平面及空间平动点周期轨道近似初值的方法.采用路径搜索修正法的一种简化形式,在圆形限制性三体模型中,对地月系中几种典型的平面及空间周期轨道近似初值进行了计算.结果表明,该简化方法得到的周期轨道近似初值不唯一,由近似初值经微分修正得到的精确结果中通常同时存在Halo轨道和大幅值逆行轨道(DRO).进一步分析表明,在某些临界初值下,精确结果中Halo轨道将消失,同时可能出现平面Lyapunov轨道及Vertical轨道.上述计算中,搜索初值与结果中轨道类型的对应关系值得进一步研究.Abstract: In the restricted three-body problem, the path searching and correcting method is often used to calculate the approximate initial value of planar and three-dimensional periodic orbit. In this paper, in view of the Circular Restricted Three-Body Problem (CRTBP), a simplified mode of this method is applied to calculate the approximate initial value of several ordinary kinds of periodic orbit. The results show that the approximate initial value obtained by the simplified method is not unique, and the precise initial values derived from the unique values above using differential correction method often include both Halo and DRO (Distant Retrograde Orbit) orbits. Moreover, under certain boundary initial values, Halo orbit will disappear from the results and the planar Lyapunov orbit or Vertical orbit will appears. The relationship between these initial values using in this method and the certain kinds of orbit needs further study.
-
[1] RICHARDSON D L. Analytic construction of periodic orbits about the collinear points[J]. Celest. Mech., 1980, 22(3):241-253 [2] ANGEL J, MASDEMONT J. Dynamics in the center manifold of the collinear points of the restricted three body problem[J]. Phys. D, 1999, 132(1/2):189-213 [3] GOMEZ G, LIBRE J, MARTINEZ R, et al. Dynamics and mission design near libration points[M]. Singapore:World Scientific Publishing Company, 2001 [4] HIRANI A N, RUSSELL R P. Approximations of distant retrograde orbits for mission design[C]. 16th AAS/AIAA Space Flight Mechanics Meeting. San Diego:AAS Publications Office, 2006 [5] RUSSELL R P. Global search for planar and three-dimensional periodic orbits near Europa[J]. J. Astronaut. Sci., 2006, 54(2):199-226 [6] TAN M H, ZHANG K, LV M B, et al. Transfer to long term distant retrograde orbits around the moon[J]. Acta Astronaut., 2014, 98:50-63 [7] YUAN Jianping, ZHAO Yushan, TANG Geshi, et al. Spacecraft Orbit Design of Deep Space Flight[M]. Beijing:China Astronautic Publishing House, 2014:184-190(袁建平, 赵育善, 唐歌实, 等. 航天器深空飞行轨道设计[M]. 北京:中国宇航出版社, 2014:184-190) [8] MENG Yunhe, ZHANG Yuedong, CHEN Qifeng. Dynamics and Control of Spacecraft Near Libration Points[M]. Beijing:Science Press, 2015:48-52(孟云鹤, 张跃东, 陈琪锋. 平动点航天器动力学与控制[M]. 北京:科学出版社, 2015:48-52) [9] ZHANG Yuedong. Research on Relative Motion Dynamics and Control of Libration Points Spacecrafts[D]. Changsha:National University of Defense Technology, 2012:18-28(张跃东. 平动点航天器相对运动动力学与控制研究[D]. 长沙:国防科学技术大学, 2012:18-28) [10] MENG Yunhe, CHEN Qifeng. Outline design and performance analysis of navigation constellation near earth-moon libration point[J]. Acta Phys. Sin., 2014, 63(24):248402(孟云鹤, 陈琪锋. 地月平动点导航星座的概要设计与性能分析[J]. 物理学报, 2014, 63(24):248402) [11] STRAMACCHIA M, COLOMBO C, BERNELLIZAZZERA F. Distant retrograde orbits for space-based near earth objects detection[J]. Adv. Space Res., 2016, 58:967-988 [12] LIU P, HOU X Y, TANG J S, et al. Application of two special orbits in the orbit determination of lunar satellites[J]. Res. Astron. Astrophys., 2014, 14(10):1307-1328 [13] BEZROUK C, PARKER J. Long duration stability of distant retrograde orbits[C]//AAS/AIAA Astrodynamics Specialist Conference. South Carolina:American Astronautical Society, 2013 [14] XU Ming, XU Shijie. Stability analysis and transiting trajectory design for retrograde orbits around moon[J]. J. Astronaut., 2009, 30(5):1785-1791(徐明, 徐世杰. 绕月飞行的大幅值逆行轨道研究[J]. 宇航学报, 2009, 30(5):1785-1791) [15] HOU Xiyun, LIU Lin. The dynamics and applications of the collinear libration points in deep space exploration[J]. J. Astronaut., 2008, 29(3):736-747(侯锡云, 刘林. 共线平动点的动力学特征及其在深空探测中的应用[J]. 宇航学报, 2008, 29(3):736-747) [16] LU Songtao, ZHAO Yushan. The improvement of Richardson's three order approximate analytical solution of Halo orbit[J]. J. Astronaut., 2009, 30(3):863-869(卢松涛, 赵育善. Halo轨道Richardson三阶近似解析解的改进[J]. 宇航学报, 2009, 30(3):863-869) [17] LIU Lin, HOU Xiyun, WANG Haihong. On characteristics of collinear libration points and their applications in deep space exploration[J]. Progress Astron., 2006, 24(2):174-182(刘林, 侯锡云, 王海红. 关于共线平动点的特征及其在深空探测中的应用[J]. 天文学进展, 2006, 24(2):174-182) [18] XU Ming, XU Shijie. The application of libration points and Halo orbits in the Earth-Moon system to space mission design[J]. J. Astronaut., 2006, 27(4):695-699(徐明, 徐世杰. 地elax——elax月系平动点及Halo轨道的应用研究[J]. 宇航学报, 2006, 27(4):695-699)
点击查看大图
计量
- 文章访问数: 668
- HTML全文浏览量: 69
- PDF下载量: 66
- 被引次数: 0