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

LI Bowen; DING Jieyu; LI Yanan

doi:10.21656/1000-0887.400038

Volume 40 Issue 7

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LI Bowen, DING Jieyu, LI Yanan. An L-Stable Method for Differential-Algebraic Equations of Multibody System Dynamics[J]. Applied Mathematics and Mechanics, 2019, 40(7): 768-779. doi: 10.21656/1000-0887.400038

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

doi: 10.21656/1000-0887.400038

¹School of Mathematics and Statistics, Qingdao University, Qingdao, Shandong 266071, P.R.China;²Center for Computational Mechanics and Engineering Simulation, Qingdao University, Qingdao, Shandong 266071, P.R.China

Funds: The National Natural Science Foundation of China（11472143；11772166）

Received Date: 2019-01-17
Rev Recd Date: 2019-02-09
Publish Date: 2019-07-01

Abstract

Abstract

An L-stable method over time intervals for differential-algebraic equations of multibody system dynamics was presented. The solution scheme was established based on equidistant nodes and non-equidistant nodes such as Chebyshev and Legendre nodes. According to Ehle’s theorem and conjecture, the unknown matrix and vector in the L-stable solution formula were obtained through comparison with the Padé approximation. The Newtonian iteration method was used during the solution process. The planar 2-link manipulator system was taken as an example, and the results from the L-stable method were compared for different node numbers in the time interval and different steps in the simulation, with those from the classic Runge-Kutta method. The comparison shows that, the proposed method has the advantages of good stability and high precision, and is suitable for multibody system dynamics simulation under long-term conditions.
- multibody system dynamics,
- L-stable method,
- differential-algebraic equation,
- Padé approximation,
- stability

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References(17)

References

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