多体系统动力学微分-代数方程L-稳定方法

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

针对多体系统动力学微分-代数方程形式,在时间区间上构造L-稳定方法,分别基于等距节点、Chebyshev节点和Legendre节点等非等距节点建立求解格式,依据Ehle定理及猜想,与Padé逼近式对比得到待定矩阵和向量,从而获得L-稳定求解公式,循环求解过程采用Newton迭代法计算.以平面双连杆机械臂系统为例,使用L-稳定方法进行数值仿真,通过改变时间区间节点数和步长对各个指标结果进行比较,并与经典Runge-Kutta法对比.结果表明,该方法具有稳定性好、精度高等优点,适用于长时间情况下的多体系统动力学仿真.

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.