## 留言板

 引用本文: 徐小明, 钟万勰. 基于四元数表示的多体动力学系统及其保辛积分算法[J]. 应用数学和力学, 2014, 35(10): 1071-1080.
XU Xiao-ming, ZHONG Wan-xie. Symplectic Integration for Multibody Dynamics Based on Quaternion Parameters[J]. Applied Mathematics and Mechanics, 2014, 35(10): 1071-1080. doi: 10.3879/j.issn.1000-0887.2014.10.001
 Citation: XU Xiao-ming, ZHONG Wan-xie. Symplectic Integration for Multibody Dynamics Based on Quaternion Parameters[J]. Applied Mathematics and Mechanics, 2014, 35(10): 1071-1080.

## 基于四元数表示的多体动力学系统及其保辛积分算法

##### doi: 10.3879/j.issn.1000-0887.2014.10.001

###### 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）;钟万勰（1934—），男，浙江德清人，教授，中科院院士（E-mail: zwoffice@dlut.edu.cn）.
• 中图分类号: TP391.9;O313.3

## Symplectic Integration for Multibody Dynamics Based on Quaternion Parameters

• 摘要: 将四元数引入多体动力学系统，用以描述刚体转动分量，继而据此将问题转入约束动力学领域，建立相关的Lagrange体系.然后引入作用量并进行有限元近似，并保证格点上严格满足约束条件，则根据分析结构力学基本理论，可导出逐步积分的递推格式，并且积分保辛.该法具有未知数少、计算量小等优点，数值结果令人满意.
•  [1] 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)) [2] 张树侠, 孙静. 捷联式惯性导航系统[M]. 北京: 国防工业出版社, 1992.(ZHANG Shu-xia, SUN Jing.Strap-Down Inertial Navigation System [M]. Beijing: National Defence Industry Press, 1992.(in Chinese)) [3] Wendlandt J M, Marsden J E. Mechanical integrators derived from a discrete variational principle[J].Physica D: Nonlinear Phenomena,1997,106(3): 223-246. [4] Betsch P, Siebert R. Rigid body dynamics in terms of quaternions: Hamiltonian formulation and conserving numerical integration[J].International Journal for Numerical Methods in Engineering,2009,79(4): 444-473. [5] Nielsen M B, Krenk S. Conservative integration of rigid body motion by quaternion parameters with implicit constraints[J].International Journal for Numerical Methods in Engineering,2012,〖STHZ〗 92(8): 734-752. [6] 徐小明, 钟万勰. 刚体动力学的四元数表示及保辛积分[J]. 应用数学和力学, 2014,〖STHZ〗35(1): 1-11.(XU Xiao-ming, ZHONG Wan-xie. Symplectic integration of rigid body motion by quaternion parameters[J].Applied Mathematics and Mechanics,2014,35(1): 1-11.(in Chinese)) [7] 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,〖STHZ〗4(3): 193-200.(ZHONG Wan-xie, GAO Qiang. Integration of constrained dynamical system via analytical structrural mechanics[J].Jounal of Dynamics and Control,2006,4(3): 193-200.(in Chinese)) [8] 钟万勰. 应用力学的辛数学方法[M]. 北京: 高等教育出版社, 2006.(ZHONG Wan-xie.Symplectic Method in Applied Mechanics [M]. Beijing: Higher Education Press, 2006.(in Chinese)) [9] Goldstein H, Poole C, Safko J.Classical Mechanics [M]. 3rd ed. Boston: Addison Wesley, 2002.

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##### 出版历程
• 收稿日期:  2014-06-25
• 修回日期:  2014-08-20
• 刊出日期:  2014-10-15

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