Advertisement

Applied Mathematics and Mechanics

, Volume 21, Issue 1, pp 103–108 | Cite as

An automatic constraint violation stabilization method for differential/ algebraic equations of motion in multibody system dynamics

  • Zhao Weijia
  • Pan Zhenkuan
  • Wang Yibing
Article

Abstract

A new automatic constraint violation stabilization method for numerical integration of Euler-Lagrange equations of motion in dynamics of multibody systems is presented. The parameters a, β used in the traditional constraint violation stabilization method are determined according to the integration time time step size and Taylor expansion method automatically. The direct integration method, the traditional constraint violation stabilization method and the new method presented in this paper are compared finally.

Key words

dynamics of multibody systems Euler-Lagrange equations constraint violation stabilization 

CLC number

O313 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Hong Jiazhen.Computational Dynamics of Multibody Systems [Z]. Shanghai Jiaotong University Science & Technology Exchange Department, 1989.Google Scholar
  2. [2]
    Wehage R A, Haug E J. Generalized coordinates partioning for dimension reduction in analysis of constrained dynamic systems [J].ASME J of Mechanical Design, 1982,104.Google Scholar
  3. [3]
    Singh R P, Likins P W. Singular value decomposition for constrained dynamic systems [J].ASME J of Applied Mechanics, 1985,52.Google Scholar
  4. [4]
    Kamman J W, Huston R L. Constrained multibody system dynamics—An automated approach [J],J of Computers and Structures, 1984,18 (6).Google Scholar
  5. [5]
    Kim S S, Vanderploeg M J. QR decomposition for state space representation of constrained mechanical dynamic systems [J].ASME J of Mech Trans and Auto in Design, 1986,108.Google Scholar
  6. [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.Google Scholar
  7. [7]
    Nikravesh P E.Computer Aided Analysis of Mechanical Systems [M], Englewood Cliffs, N J Prentice-Hall, 1987.Google Scholar
  8. [8]
    Potra F A, Rheinbolt W C. On the numerical solution of Euler-Lagrange equations [J].Mechanics of Structures & Machines, 1991,19 (1).Google Scholar
  9. [9]
    Campbell B S, Leimkuhler B. Differentiation of constraints in differential/algebraic equations [J].Mechanics of Structures & Machines, 1991,19 (1).Google Scholar
  10. [10]
    Yen J, Haug E J, Tak T O. Numerical methods for constrained equations of motion in mechanical system dynamics [J].Mechanics of Structures & Machines, 1991,19 (1).Google Scholar
  11. [11]
    Petzold L R, Potra F A. ODAE methods for the numerical solution of Eurer-Lagrange equations [J].J of Applied Numerical Methematics, 1992,10.Google Scholar
  12. [12]
    Zhao Weijia, Pan Zhenkuan, Hong Jiazhen, et al. A compact algorithm for solving differential/algebraic equations in multibody system dynamics [J].J of Qingdao University (Natural science Edition), 1995,18 (3). (in Chinese)Google Scholar
  13. [13]
    Zhao Weijia, Pan Zhenkuan, Hong Jiazhen, et al. An eliminated algorithm for solving differental/algebraic equations in multibody system dynamics [J].J of Elemental Science of Textile University, 1995,18 (3), (in Chinese)Google Scholar
  14. [14]
    Pan Zhenkuan, Zhao Weijia, Hong Jiazhen, et al. On numerical integration algorithm for differential/algebraic equations in multibody system dynamics [J].Advancements of Mechanics, 1996, (1). (in Chinese)Google Scholar

Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 2000

Authors and Affiliations

  • Zhao Weijia
    • 1
  • Pan Zhenkuan
    • 1
  • Wang Yibing
    • 1
  1. 1.Qingdao UniversityQingdaoP R China

Personalised recommendations