约束多体系统的基于离散零空间的隐式龙格库塔法

Implicit Runge-Kutta method based on the discrete null space method for constrained multibody systems

将离散零空间理论应用于多体系统动力学方程的数值计算,可降低多体系统动力学方程的维数。通过给出离散零空间理论与IRK法相结合的一般数学框架,提出了多体系统动力学的基于离散零空间理论的IRK法。数值算例表明:该算法可获得较满意的数值结果,约束违约程度很小,三种积分算法算例的范数均在10-16之内。

Applying the discrete null space method to deal with the equations of motion for multibody systems,it is feasible to further reduce the number of unknowns.In this paper,a scheme combining with the discrete null space method(DNS) and the implicit Runge-Kutta methods(IRK) is formulated,and the IRK based on the DNS for multibody dynamic systems is proposed.The application shows that using the proposed method,the simulation results are satisfied and the violation of constraints is very small.This method provides an effective approach to the numerical calculation of the equations of motion for multibody systems.