具有奇异位置的多体系统动力学方程的改进算法

多体系统进行数值仿真时,很多选择了微分代数混合方程作为多体系统动力学数学模型.本文在现有的约束稳定化理论基础上,提出了针对具有奇异位置的多体系统动力学方程的改进算法.算法通过修正速度违约和控制稳定项,讨论了具有奇异位置的微分代数混合方程的数值仿真问题并给出了稳定项中相关系数的建议值,从而有效克服了求解混合方程时因为构型奇异给计算造成的困难.算例分别采用改进算法与ADAMS软件进行仿真,计算结果的比较表明了改进算法的有效性.本文给出的基于能量守恒的能量差曲线也证明了改进算法的有效性.

A modified numerical method for dynamical equations of the multibody systems with singularity position

The differential-algebraic equations are often chosen as the mathematical models of the dynamics of multibody systems in order to achieve the numerical emulation for the multibody systems. Based on the existing constraint violation stabilization method, a modified numerical method for the equations with singularity positions is proposed in the present paper. By correcting the violation of the velocity and controlling the stability term in the modified method, the differential-algebraic equations with singularity positions are solved, and the values of the coefficients in the stability term are suggested. Thus,the numerical difficulty, due to the singularity of the multibody systems,is effectively eliminated. The contrast between the numerical results of the example using the modified method and the ADAMS soft demonstrates the effectiveness of the proposed modified method. The balance based on the law of conservation of energy also proves the effectiveness of the method.