刚体动力学的四元数表示及保辛积分

徐小明; 钟万勰

doi:10.3879/j.issn.1000-0887.2014.01.001

刚体动力学的四元数表示及保辛积分

doi: 10.3879/j.issn.1000-0887.2014.01.001

大连理工大学工程力学系工业装备结构分析国家重点实验室, 辽宁大连 116024

基金项目: 国家重点基础研究发展计划（973计划）（2009CB918501）

详细信息

作者简介:
徐小明（1986—），男，辽宁东港人，博士生（通讯作者. E-mail: xxm@mail.dlut.edu.cn）

中图分类号: TP391.9; O313.3
计量
- 文章访问数: 2050
- HTML全文浏览量: 154
- PDF下载量: 2568
- 被引次数: 0
出版历程
- 收稿日期: 2013-10-07
- 修回日期: 2013-11-03
- 刊出日期: 2014-01-15

Symplectic Conservation Integration of Rigid Body Dynamics With Quaternion Parameters

State Key Laboratory of Structural Analysis of Industrial Equipment; Department of Engineering Mechanics, Dalian University of Technology, Dalian, Liaoning 116024, P.R.China

Funds: The National Basic Research Program of China (973 Program)(2009CB918501)

摘要

摘要: 基于刚体定点转动的四元数表示，运用分析结构力学方法，引入离散系统作用量代替四元数微分方程，并在积分点严格满足四元数模等于1的约束条件，进行时间积分．则按分析结构力学理论，不但达到了积分的保辛且区段内部约束条件也可在变分原理意义下近似满足对重陀螺进行数值仿真，结果满意.
- 分析结构力学 /
- 四元数 /
- 刚体动力学 /
- 保辛积分 /
- 重陀螺
Abstract: A numerical method was proposed with the quaternion representation of rigid body dynamics. Based on the analytical structural mechanics, the action of differential system was introduced for the time integration of the approximated discrete system and the constraint that the norm of quaternion kept constant at 1 was satisfied strictly at the grid points of integration. As was interpreted in the theory of analytical structural mechanics, the numerical integration was symplectic conservative and the constraint was satisfied approximately in the sense of variation principle. The numerical results of heavy tops are satisfying in precision and efficiency.
- analytical structural mechanics /
- quaternion /
- rigid body dynamics /
- symplectic conservation integration /
- heavy top

HTML全文

参考文献(10)

[1]	肖尚彬. 四元数方法及其应用[J]. 力学进展, 1993,23(2): 249-260.(XIAO Shang-bin. The method of quaternion and its application[J].Advances in Mechanics,1993,23(2): 49-260.(in Chinese))
[2]	Goldstein H. Classical Mechanics [M]. 2nd ed. Addison-Wesley, 1980.
[3]	程国采. 四元数法及其应用[M]. 长沙: 国防科技大学出版社, 1991.(CHENG Guo-cai. The Method of Quaternion and Its Application [M]. Changsha: National University of Defence Technology Press, 1991.(in Chinese))
[4]	钟万勰. 应用力学的辛数学方法[M]. 北京: 高等教育出版社, 2006.(ZHOGN Wan-xie. Symplectic Method in Applied Mechanics [M]. Beijing: Higher Education Press, 2006.(in Chinese))
[5]	钟万勰, 高强. 约束动力系统的分析结构力学积分[J]. 动力学与控制学报, 2006,4(3): 193-200.(ZHONG Wan-xie, GAO Qiang. Integration of constrained dynamical system via analytical structrural mechanics[J]. Journal of Dynamics and Control,2006,4(3): 193-200.(in Chinese))
[6]	Hairer E, Lubich Ch, Wanner G. Geometric-Preserving Algorithms for Ordinary Differential Equations[M]. Springer, 2006.
[7]	Zienkiewicz O C, Taylor R. The Finite Element Method [M]. 4th ed. New York: McGraw-Hill, 1989.
[8]	钟万勰, 姚征. 时间有限元与保辛[J]. 机械强度, 2005,27(2): 178-183.(ZHONG Wan-xie, YAO Zheng. Time domain FEM and symplectic conservation[J]. Journal of Mechanical Strength,2005,27(2): 178-183.(in Chinese))
[9]	周江华, 苗育红, 李宏, 孙国基. 四元数在刚体姿态仿真中的应用研究[J]. 飞行力学, 2000,18(4): 28-33.(ZHOU Jiang-hua, MIAO Yu-hong, LI Hong, SUN Guo-ji. Research of attitude simulation using quaternion[J]. Flight Dynamics,2000,18(4): 28-33.(in Chinese))
[10]	姚征, 钟万勰. 椭圆函数的精细积分算法[J]. 数值计算与计算机应用, 2008,29(4): 251-260.(YAO Zheng, ZHONG Wan-xie. Time improved precise integration method for elliptic functions[J]. Journal on Numerical Methods and Computer Applications,2008,29(4): 251-260.(in Chinese))