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

Abstract EN

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.