基于四元数表示的多体动力学系统及其保辛积分算法

徐小明; 钟万勰

doi:10.3879/j.issn.1000-0887.2014.10.001

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

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(大连理工大学), 辽宁大连 116024

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）;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
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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

Symplectic Integration for Multibody Dynamics Based on Quaternion Parameters

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

摘要

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.
- 分析结构力学 /
- 四元数 /
- 多体动力学 /
- 保辛积分
Abstract: The quaternion representation was introduced into multibody dynamics for the description of rigid body rotation, based on which the constrained dynamics was derived and the relevant Lagrange system was established. Then, the segmental action for discrete systems was introduced and approximated with the finite element method. According to the theory of analytical structural mechanics, the symplectic numerical integration was derived with the constraints strictly satisfied at the integration points and the integration process was symplectic conservative in the sense of variation principle. The proposed method has the characteristics of less calculation and less unknown numbers, which is confirmed with the numerical results of an exemplary multibody hinged system.
- analytical structural mechanics /
- quaternion /
- multibody dynamics /
- symplectic integration

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参考文献(9)

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