L-Stable Method for Differential-Algebraic Equations of Multibody System Dynamics

An L-stable method over time intervals for differential-algebraic equations (DAEs) of multibody system dynamics is presented in this paper. The solution format is established based on equidistant nodes and nonequidistant nodes such as Chebyshev nodes and Legendre nodes. Based on Ehle’s theorem and c...

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Bibliographic Details
Published in:Mathematical problems in engineering 2019-01, Vol.2019 (2019), p.1-11
Main Authors: Li, Bowen, Li, Yanan, Ding, Jieyu
Format: Article
Language:English
Subjects:
Accuracy
Algebra
Chebyshev approximation
Computational mathematics
Differential equations
Dynamic stability
Iterative methods
Lagrange multiplier
Mathematical analysis
Mathematical problems
Matrix algebra
Matrix methods
Methods
Multibody systems
Nodes
Numerical analysis
Ordinary differential equations
Pade approximation
Runge-Kutta method
System dynamics
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Summary:An L-stable method over time intervals for differential-algebraic equations (DAEs) of multibody system dynamics is presented in this paper. The solution format is established based on equidistant nodes and nonequidistant nodes such as Chebyshev nodes and Legendre nodes. Based on Ehle’s theorem and conjecture, the unknown matrix and vector in the L-stable solution formula are obtained by comparison with Pade approximation. Newton iteration method is used during the solution process. Taking the planar two-link manipulator system as an example, the results of L-stable method presented are compared for different number of nodes in the time interval and the step size in the simulation, and also compared with the classic Runge-Kutta method, A-stable method, Radau IA, Radau IIA, and Lobatto IIIC methods. The results show that the method has the advantages of good stability and high precision and is suitable for multibody system dynamics simulation under long-term conditions.
ISSN:1024-123X
1563-5147
DOI:10.1155/2019/9283461