Volume 32 Issue 06
Jun.  2006
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Fu Shihui, Wang Qi. Numerical method for Lyapunov exponents of multibody systems with constraints[J]. Journal of Beijing University of Aeronautics and Astronautics, 2006, 32(06): 742-746. (in Chinese)
Citation: Fu Shihui, Wang Qi. Numerical method for Lyapunov exponents of multibody systems with constraints[J]. Journal of Beijing University of Aeronautics and Astronautics, 2006, 32(06): 742-746. (in Chinese)

Numerical method for Lyapunov exponents of multibody systems with constraints

  • Received Date: 17 Jun 2005
  • Publish Date: 30 Jun 2006
  • Dynamic equations of multibody systems with constraints induced by the first kind of Lagrange’s equations are nonlinear differential-algebraic equations. To be solved numerically, nonlinear differential-algebraic equations were transformed into ordinary differential equations with the augmentation approach. Ordinary differential equations and their Jacobian matrix were given in the matrix form to improve computational efficiency. A numerical method of Lyapunov exponents of nonlinear dynamics of multibody systems was demonstrated. An example was given to analysis dynamical behavior of two multibody systems with topological tree and non-tree configuration, such as bifurcation and chaos by calculating Lyapunov exponents along with Poincare maps and phase graphs.

     

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  • [1] Oseledec V I. A multiplicative ergodic theorem:Lyapunov characteristic numbers for dynamical systems[J]. Trans Moscow Math Soc, 1968,19:197-231 [2] Benettin G, Galgani A,Giorgilli G, et al. Lyapunov exponents for smooth dynamical systems and Hamiltonian systems:a method for computing all of them, part1:theory[J]. Meccanica, 1980,15:9-20 [3] 王琪,黄克累,陆启韶. 树形多体系统动力学的数值分析方法[J]. 固体力学学报,1999, 20(4):363-367 Wang Qi, Huang Kelei, Lu Qishao. A numerical algorithm for nonlinear dynamical analysis of multibody systems with topological tree configuration[J]. Acta Mechanica Solida Sinica,1999,20(4):363-367(in Chinese) [4] 金俐,王琪,陆启韶. 树形多体Hamilton 系统的Lyapunov 指数计算方法 . 北京航空航天大学学报,2001,27(2):230-232 Jin Li, Wang Qi, Lu Qishao. Numerical algorithm for calculating Lyapunov exponents of multibody Hamilton systems with topological tree configuration[J]. Journal of Beijing University of Aeronautics and Astronautics, 2001,27(2):230-232(in Chinese) [5] 张彦梅,王琪,陆启韶. 带约束非线性多体系统动力学方程数值分析方法 . 应用力学学报,2002,19(3):54-58 Zhang Yanmei, Wang Qi, Lu Qishao. Numerical analytical method for nonlinear dynamical equations of multibody systems with constraints[J]. Chinese Journal of Applied Mechanics, 2002,19(3):54-58(in Chinese) [6] Baumgarte J. Stabilization of constraints and integrals of motionin dynamical systems[J]. Comp Meth in Appl Mech and Engineering, 1972,1:1-16 [7] 王琪, 陆启韶. 多体系统Lagrange方程数值算法的研究进展[J].力学进展,2001,31(1), 9-17 Wang Qi, Lu Qishao. Advances in the numerical methods for Lagrange’s equations of multibody systems[J]. Advances in Mechanics, 2001,31(1), 9-17(in Chinese) [8] Parker Thomas S, Chua Leon O. Practical numerical algorithms for chaotic systems[M]. Beijing:World Publishing Corp,1992,74
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