XU Xiao-ming, ZHONG Wan-xie. Symplectic Conservation Integration of Rigid Body Dynamics With Quaternion Parameters[J]. Applied Mathematics and Mechanics, 2014, 35(1): 1-11. doi: 10.3879/j.issn.1000-0887.2014.01.001
Citation: XU Xiao-ming, ZHONG Wan-xie. Symplectic Conservation Integration of Rigid Body Dynamics With Quaternion Parameters[J]. Applied Mathematics and Mechanics, 2014, 35(1): 1-11. doi: 10.3879/j.issn.1000-0887.2014.01.001

Symplectic Conservation Integration of Rigid Body Dynamics With Quaternion Parameters

doi: 10.3879/j.issn.1000-0887.2014.01.001
Funds:  The National Basic Research Program of China (973 Program)(2009CB918501)
  • Received Date: 2013-10-07
  • Rev Recd Date: 2013-11-03
  • Publish Date: 2014-01-15
  • 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.
  • loading
  • [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))
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (1807) PDF downloads(2557) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return