多体系统动力学微分/代数方程组的一类新的数值分析方法<sup>*</sup>

王艺兵; 赵维加; 潘振宽

多体系统动力学微分/代数方程组的一类新的数值分析方法^*

青岛大学自动化系, 青岛 266071

基金项目: * 国家自然科学基金;山东省自然科学基金

计量
- 文章访问数: 2270
- HTML全文浏览量: 119
- PDF下载量: 612
- 被引次数: 0
出版历程
- 收稿日期: 1996-07-18
- 刊出日期: 1997-09-15

A New Algorithm for Solving Differential/Algehraic Equations of Multibody System Dynamics

Department of Automation, Qingdao University, Qingdao 266071, P. R. China

摘要

摘要: 本文讨论了多体系统动力学微分/代数混合方程组的数值离散问题.首先把参数t并入广义坐标讨论,简化了方程组及其隐含条件的结构,并将其化为指标1的方程组.然后利用方程组的特殊结构,引入一种局部离散技巧并构造了相应的算法.算法结构紧凑,易于编程,具有较高的计算效率和良好的数值性态,且其形式适合于各种数值积分方法的的实施.文末给出了具体算例.
- 多体系统 /
- 动力学 /
- 微分/代数方程 /
- 数值解
Abstract: The second order Euler-Lagrange equations are transformed to a set of first orderdifferentiallalgebraic equations. which are then transformed to state equations by usinglocul parameterization. The corresponding discretization method is presented. and theresults can be used to implementation of various numerical integration methods. Anumerical example is presented finally.
- multibody systems /
- differential/algebraic equations /
- numerical analysis /

HTML全文

参考文献(13)

[1]	E.J.Haug.Computer Aided Kinemanics and Dynamics of Mechanical Systems.Vol.1:Basic Methods.Ally & Bacon.Boston-MA(1989).
[2]	F.A.Potra and W.C.Rheinbolt.On the numerical solution of Euler-Lagrangeequations.Mechamics of Structures & Machimes.19-1(1991).1～18.
[3]	J.W.Baumgarte.A new method of stabilization for holonomic constraints,J.AppliedMechanics.50(1983),869～870.
[4]	R.P.Singh and P.W.Likins.Singular value decomposition for constrained dynamicalsystems.J.Applied Mechanics.52(1985),943～948.
[5]	S.S.Kim and M.J.Vanderploeg.QR decomposition for state space representation ofconstrained mechanical dynamic systems.J.,Mech.Tran.& Auto.in Design.108(1986).168～183.
[6]	C.G.Liang and G.M.Lance.A differential null space method for constrained dynamicanalysis,J.,Mech.Tran.& Auto.in Design,109(1987),405～411.
[7]	O.P.Agrawal and S.Saigal.Dynamic analysis of multibody systems using tangentcoordinates.Computers & Structures.31.3(1989),349～355.
[8]	J.W.Kamman and R.L.Huston,Constrained multibody systems-An automate dapproach.Computers & Structures.18,4(1984).999～1112.
[9]	F.A.Potra and J.Yen,Implicit integration for Euler-Lagrange equations via tangentspace parameterization.Mechamics of Structures & Machiunes,19,1(1991),77～98.
[10]	洪嘉振、刘延柱,离散系统动力学计算方法,力学进展,19(2)(1989),205-210.
[11]	王德人,《非线性方程解法和最优化方法》,人民教育出版社,北京(1980).
[12]	潘振宽,柔性多体系统动力学建模理论与数值方法研究,上海交大博士学位论文(1992).
[13]	潘振宽、赵维加、洪嘉振、刘延柱,多体系统动力学微分/代数方程数值方法,力学进展,26(1)(1996),28-40.