一种改进的轨道动力学模型

杨梦洁; 袁建平

doi:10.6052/0459-1879-14-298

一种改进的轨道动力学模型

西北工业大学航天飞行动力学技术重点实验室, 西安 710072

详细信息

作者简介:
杨梦洁,硕士研究生,主要研究方向:轨道动力学,姿态动力学.E-mail: yangmengjiesc@126.com

中图分类号: V412.4
计量
- 文章访问数: 1421
- HTML全文浏览量: 223
- PDF下载量: 1019
出版历程
- 收稿日期: 2014-09-27
- 修回日期: 2014-10-26
- 刊出日期: 2015-01-17

AN IMPROVED MODEL OF ORBITAL DYNAMICS

National Key Laboratory of Aerospace Flight Dynamics, Northwestern Polytechnical University, Xi'an 710072, China

摘要

摘要: 航天器的矢径可以分解为矢径模和单位矢量的乘积,利用该性质将传统轨道动力学方程分解为矢径模和矢径方向的动力学方程组,实现了航天器位置信息的分离;针对两个方程分别采用常数变易法和四元数描述方法,将轨道动力学模型转化为线性无奇异的方程组,同时得到了7 个新轨道变量,且建立了新轨道变量与惯性系下航天器位置速度信息以及轨道六要素之间的相互转换关系. 该轨道模型适用于任意形式的推力和摄动,避免了奇异性,且在虚拟时间的意义下,航天器的旋转角速度只取决于法向力;在常值推力和变推力的情况下,对该模型进行了数值验证,验证了新模型的可适用性、数值稳定性以及计算精度高的优势.
- 轨道模型 /
- 连续推力轨道 /
- 轨道机动 /
- 常数变易法 /
- 四元数
Abstract: The radius vector of spacecraft can be decomposed into the product of the mold and the unit vector. Using this property, the traditional orbital dynamics equation can be transformed into two equations which describe the mold's and direction's motions separately. The mold's equation can be converted to a linear equation without singularity by introducing the inverse of the mold; and using the variation of constants method, the linear equation can be reduced to one-order. As for the direction's equation, the quaternion description is suitable. This equation can be completely solved. Through the above handling methods, we obtain a new orbital dynamic model which contains seven equations. In the sense of the virtual time, the angular velocity of the spacecraft depends only on the normal force. This new orbital model is applicable to any form of thrust or perturbation. At the same time, we get seven new stable variables which completely equivalent to the kepler elements. And the transforming relationship has been established. In the end of this article, we verify the accuracy and applicability of the new model in the cases of constant and variable thrusts.
- orbital model /
- continuous thrust /
- orbital maneuvering /
- changing constant /
- quaternion

HTML全文

参考文献(18)

袁建平, 朱战霞. 空间操作与非开普勒运动. 宇航学报, 2009, 30(1): 42-46 (Yuan Jianping, Zhu Zhanxia. Space operations and non-Keplerian orbit motion. Journal of Astronautics, 2009, 30(1): 42-46 (in Chinese))

王萍, 袁建平, 范剑峰. 关于非开普勒轨道的讨论. 宇航学报, 2009, 30(1): 37-41 (Wang Ping, Yuan Jiangping, Fan Jianfeng. A discussion on non-Keplerian orbit. Journal of Astronautics, 2009, 30(1): 37-41 (in Chinese))

Stiefel EL, Scheifele G. Linear and Regular Celestial Mechanics. Berlin, New York, Springer-Verlag, 1971: 18-33

Vitins M. Kepler motion and gyration. Celestial Mechanics, 1978, 17(2): 173-192

曹静, 袁建平, 罗建军. 陀螺进动与强迫进动轨道. 力学学报, 2013, 45(3): 406-411(Cao Jing, Yuan Jianping, Luo Jianjun. Gyroscopic precession and forced precession orbit. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(3): 406-411 (in Chinese))

Peláez J, Hedo JM, de Andrés PR. A special perturbation method in orbital dynamics. Celest Mech Dyn Astr, 2007, 97(2): 131-150

Baú G, Bombardelli C, Peláez J. A new set of integrals of motion to propagate the perturbed two-body problem. Celest Mech Dyn Astr, 2013, 116(3): 53-78

Junkins JL, Turner JD. On the analogy between orbital dynamics and rigid body dynamics. The Journal of the Astronautical Science, 1979, 17(4): 345-358.

Battin RH. An introduction to the mathematics and methods of astrodynamics. AIAA, 2001: 408-415

章仁为. 卫星轨道姿态动力学与控制. 北京: 北京航空航天大学出版社, 1998: 157-176 (Zhang Renwei. Satellite Attitude Dynamics and Control. Beijing: Beijing University of Aeronautics and Astronautics Press, 1998: 157-176 (in Chinese))

赵育善, 师鹏. 航天器飞行动力学建模理论与方法. 北京: 北京航空航天大学出版社, 2012: 5-27 (Zhao Yushan, Shi Peng. Spacecraft Flight Dyna- mics Modeling Theory and Methods. Beijing: Beijing University of Aeronautics and Astronautics Press, 2012: 5-27 (in Chinese))

袁建平, 李俊峰, 和兴锁等. 航天器相对运动轨道动力学. 北京: 中国宇航出版社, 2013: 101-139 (Yuan Jianping, Li Junfeng, He Xingsuo, et al. Relative Orbit Dynamics of Spacecraft. Beijing: China Aerospace Press. 2013: 101-139(in Chinese))

刘暾, 赵钧. 空间飞行器动力学. 哈尔滨: 哈尔滨工业大学出版社, 2007: 12-14, 102-114 (Liu Dun, Zhao Jun. Spacecraft Dynamics. Harbin: Harbin Institute of Technology Press. 2007: 12-14, 102-114(in Chinese))

肖业伦. 航天器飞行动力学原理. 北京: 宇航出版社, 1995: 26-45 (Xiao Yelun. Spacecraft Dynamics Theory. Beijing: Aerospace Press. 1995: 26-45 (in Chinese))

王伟, 袁建平, 罗建军等. 赤道平面J2束缚轨道研究. 中国科学: 物理学, 力学, 天文学, 2013, 43(3): 309-317 (Wang Wei, Yuan Jianping, Luo Jianjun, et al. Anatomy of J2 bounded orbits in equatorial plane. Scientia Sinica Physica, Mechanica & Astronomica, 2013, 43(3): 309-317 (in Chinese))

Robert JM, Malcolm M, James B, et al. Survey of highly-non-keplerian orbits with low-thrust propulsion. Journal of Guidance, Control, and Dynamics, 2011, 34(3): 645-666

程国采. 四元数法及其应用. 长沙: 国防科技大学出版社, 1991 (Cheng Guocai. Quaternion Theory and Application. Changsha: National University of Defense Technology Press, 1991 (in Chinese))

曹静, 袁建平. 空间飞行器轨道相对运动动力学及应用研究. [博士论文]. 西安: 西北工业大学, 2013 (Cao Jing, Yuan Jianping. Kinetics and applied research of spacecraft orbit relative motion. [PhD Thesis]. Xi'an: Northwestern Polytechnical University. 2013 (in Chinese))