Abstract
The second order Euler-Lagrange equations are transformed to a set of first order differentiallalgebraic equations, which are then transformed to state equations by using local parameierization. The corresponding discretization method is presented, and the results can be used to implementation of various numerical integration methods. A numerical example is presented finally.
Similar content being viewed by others
References
E. J. Haug, Computer Aided Kinematics and Dynamics of Mechanical Systems, Vol. 1: Basic Methods, Ally & Bacon, Boston, MA (1989).
F. A. Potra and W. C. Rheinbolt, On the numerical solution of Euler-Lagrange equations. Mechanics of Structures & Machines, 19, 1 (1991), 1–18.
J. W. Baumgarte, A new method of stabilization for holonomic constraints, J. Applied Mechanics, 50 (1983), 869–870.
R. P. Singh and P. W. Likins, Singular value decomposition for constrained dynamical systems, J. Applied Mechanics, 52 (1985), 943–948.
S. S. Kim and M. J. Vanderploeg. QR decomposition for state space representation of constrained mechanical dynamic systems, J. Mech. Tran. & Auto. in Design, 108 (1986), 168–183.
C. G. Liang and G. M. Lance, A differential null space method for constrained dynamic analysis, J. Mech. Tran. & Auto. in Design, 109 (1987), 405–411.
O. P. Agrawal and S. Saigal, Dynamic analysis of multibody systems using tangent coordinates, Computers & Structures, 31, 3 (1989), 349–355.
J. W. Kamman and R. L. Huston, Constrained multibody systems—An automated approach, Computers & Structures, 18, 4 (1984), 999–1112.
F. A. Potra and J. Yen, Implicit integration for Euler-Lagrange equations via tangent space parameterization, Mechanics of Structures & Machines, 19, 1 (1991), 77–98.
Hong Jiazhen and Liu Yanzhu, Computational dynamics of multibody systems, Advancement of Mechanics, 19, 2 (1989), 205–210. (in Chinese).
Wang Deren, Numerical Methods for Nonlinear Equations and Optimization Techniques, People's Education Press. Beijing (1980). (in Chinese)
Pan Zhenkuan, The modelling theory and numerical study for dynamics of flexible multibody systems, Doctoral dissertation, Shanghai Jiao tong University (1992), (in Chinese)
Pan Zhenkuan, Zhao Weija, Hong Jiazhen and Liu Yanzhu. On numerical techniques for differential/algebraic equations of motion of multibody system dynamics. Advancement of Mechanics, 26, 1 (1996), 28–40. (in Chinese)
Author information
Authors and Affiliations
Additional information
Communicated by Cheng Gengdong
Project supported by Natural Science Foundation of China and Shangdong Province
Rights and permissions
About this article
Cite this article
Yibing, W., Weijia, Z. & Zhenkuan, P. A new algorithm for solving differential/algebraic equations of multibody system dynamics. Appl Math Mech 18, 905–912 (1997). https://doi.org/10.1007/BF00133349
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00133349