刚体动力学的四元数表示及保辛积分  

Symplectic Conservation Integration of Rigid Body Dynamics With Quaternion Parameters

作　　者：徐小明[1] 钟万勰[1] 

机构地区：[1]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

出　　处：《应用数学和力学》2014年第1期1-11,共11页Applied Mathematics and Mechanics

基　　金：国家重点基础研究发展计划(973计划)(2009CB918501)~~

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.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 approdmated 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 vari- ation principle. The numerical results of heavy tops are satisfying in precision and efficiency.

关 键 词：分析结构力学 四元数 刚体动力学 保辛积分 重陀螺 

分 类 号：TP391.9[自动化与计算机技术—计算机应用技术]