多体系统动力学方程违约修正的数值计算方法

A numerical method for constraint stabilization of dynamic equations of multi-body systems

多体系统动力学方程为微分代数方程,一般将其转化成常微分方程组进行数值计算,在数值积分的过程中约束方程的违约会逐渐增大。本文对具有完整、定常约束的多体系统,在修改的带乘子Lagrange正则形式的方程的基础上,根据Baumgarte提出的违约修正的方法,给出了一种多体系统微分代数方程违约修正法和系统的动力学方程的矩阵表达式。通过对曲柄-滑块机构的数值仿真,计算结果表明本文给出的方法在计算精度和计算效率上好于Baumgarte提出的两种违约修正的方法。

Dynamic equations of multi-body systems with holonomic constraints are differential-algebraic equations.In order to be solved numerically,they are generally transformed into ordinary differential equations by differentiating constraint equations.However,during the numerical integration of those ordinary differential equations,the constraints are violated more and more.In this paper, a new method of constraint stabilization is put forward based on Baungarte's stabilization.According to the method,the dynamic equations of multi-body systems with holonomic and steady constraints are given in the matrix form of modified Lagrange's canonical equations with multipliers.The numerical simulation of a slider-crank mechanism shows that the computational precision of this method is higher than that of other methods.And the numerical simulation for long is not false,which benefits to the numerical calculation of Lyapunov exponents of multi-body systems.