## 留言板

 引用本文: 赵维加, 潘振宽, 王艺兵. 多体系统动力学微分/代数方程约束误差小扰动自我稳定方法[J]. 应用数学和力学, 2000, (1): 94-98.
Zhao Weijia, Pan Zhenkuan, Wang Yibing. An Automatic Constraint Violation Stabilization Method for Differential/Algebraic Equations of Motion Multibody System Dynamics[J]. Applied Mathematics and Mechanics, 2000, (1): 94-98.
 Citation: Zhao Weijia, Pan Zhenkuan, Wang Yibing. An Automatic Constraint Violation Stabilization Method for Differential/Algebraic Equations of Motion Multibody System Dynamics[J]. Applied Mathematics and Mechanics, 2000, (1): 94-98.

• 中图分类号: O313

## An Automatic Constraint Violation Stabilization Method for Differential/Algebraic Equations of Motion Multibody System Dynamics

• 摘要: 多体系统动力学微分/代数混合方程组又称为Euler-Lagrange方程.其数值积分的困难之一是由违约引起的数值不稳定.基于对约束方程左部的Tylor展开,根据积分步长提出了一种能对约束误差自动修正的小扰动违约稳定方法.该方法大大改善了传统违约修正法的数值性态,并具有简单、实用、高效的特点.最后对该方法与传统增广方法及其违约修正方法进行了数值比较.
•  [1] 洪嘉振.多体系统计算动力学[Z].上海:上海交大科技交流室,1989. [2] Wehage R A,Haug EJ.Generalized coordinates partitioning for dimension reduction in analysis ofconstrained dynamic systems[J].ASMEJof Mechanical Design,1982,104. [3] Singh RP,Likins P W.Singular value decomposition for constrained dynamic systems[J].ASMEJof Applied Mechanics,1985,52. [4] Kam man J W,Huston R L.Constrained multibody system dynamics—An automated approach[J],Jof Computers and Structures,1984,18(6). [5] Kim S S,Vanderploeg M J.QR decomposition for state space representation of constrained mechanical dynamic systems[J].ASMEJof Mech Trans and Auto in Design,1986,108. [6] Liang C G,Lance G M.A differential null space method for constrained dynamic analysis[J].ASME J of Mech Trans and Auto in Design,1987,109. [7] Nikravesh P E.Computer Aided Analysis of Mechanical Systems[M].Englewood Cliffs,N JPrentice-Hall,1987. [8] Potra F A,Rheinbolt W C.On the numericalsolution of Euler-Lagrange equations[J].Mechanicsof Structures & Machines,1991,19(1). [9] Campbell B S,Leimkuhler B.Differentiation of constraintsin differential/algebraic equations[J].Mechanics of Structures & Machines,1991,19(1). [10] Yen J,Haug EJ,Tak T O.Numerical methods for constrained equations of motion in mechani calsystem dynamics[J].Mechanics of Structures & Machines,1991,19(1). [11] Petzold L R,Potra F A.ODAE methods for the numerical solution of Eurer-Lagrange equations[J].J of Applied Numerical Mathematics,1992,10. [12] 赵维加,潘振宽,洪嘉振,等.多体系统动力学微分代数方程组的一类紧凑算法[J].青岛大学学报(自然科学版),1995,18(3):22~28. [13] 赵维加,潘振宽,洪嘉振,等.多体系统动力学微分代数方程组的一类缩并算法[J].纺织高校基础科学学报,1995,18(3):234~239. [14] 赵维加,潘振宽,洪嘉振,等.多体系统动力学微分代数方程组数值积分方法[J].力学进展,1996,26(1):28~40.

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##### 出版历程
• 收稿日期:  1997-12-21
• 修回日期:  1999-10-30
• 刊出日期:  2000-01-15

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