约束力学系统运动方程积分的数值耗散研究  

Research on Numerical Dissipation of Integration Methods for Motion Equations in Constrained Mechanical Systems

作　　者：马秀腾[1] 陈立平[1] 张云清[1] 

机构地区：[1]华中科技大学CAD中心,武汉430074

出　　处：《系统仿真学报》2009年第20期6373-6377,共5页Journal of System Simulation

基　　金：国家自然科学基金(60736019;60574053)

摘　　要：以数值积分求解约束力学系统指标-2的微分-代数方程(DAEs)为例,介绍了直接积分方法中的Newmark方法和HHT-α方法在约束力学系统仿真中的应用。主要从算法有无数值耗散、耗散量的多少以及如何控制耗散量的角度研究了这两种方法,并与BDF方法、Radau5方法以及ode45的数值耗散量进行了比较,得到的结果对于这些算法的使用,对于商业动力学仿真软件"求解器"中算法的选取有重要的指导意义,同时数值实验也表明辛算法也可以应用到非保守系统,虽然此时辛结构不再保持,但算法"无"数值耗散,可以更好的反映系统能量的变化。The Newmark method and HHT-α method were used in the simulation of constrained mechanical systems, while motion equations of the systems are index-2 DAEs. These two methods were researched in the view of numerical dissipation quantity and how to control it by numerical experiments, and the methods wre compared with BDF, Radau5 method and ode45 solver in the view of numerical dissipation. The results are significant for the use of these methods and for the choosing of solvers in commercial software. Numerical experiments also show that symplectic method can be used in the non-conservative community. Symplectic structure is no longer preserved for non-conservative systems, but symplectic method can capture the decay of the system energy accurately because of no numerical dissipation.

关 键 词：约束力学系统 Newmark方法 HHT-α方法 辛算法 数值耗散 

分 类 号：TP391.9[自动化与计算机技术—计算机应用技术] TP391.77[自动化与计算机技术—计算机科学与技术]