提高多体系统离散时间传递矩阵法计算精度的研究

Improvement of the Accuracy of Computation for the Discrete Time Transfer Matrix Method of Multibody System

深入探讨多体系统离散时间传递矩阵法对平面、空间刚体 光滑铰多体系统运动响应的研究。提出提高该方法计算精度和计算稳定性的方法 ,导出相应的多端刚体传递矩阵。设计了角坐标的迭代循环 ,该变量不必采用近似形式 ,因而提高了计算精度和计算稳定性。其它方法有 :1)增加泰勒展开式的高阶项 ;2 )合理选择将速度、加速度表示为位移的线性函数的方法 (本文简称线性化方法 ) ;3)合理确定迭代循环的初值等。对 4种多体系统进行了计算机仿真研究 。

The movement of multi-rigid-body system interconnected by smooth hinge moving in space and plane are deeply studied with the discrete time transfer matrix method of multibody system. The methods for improving the accuracy and stability of computation for this method are presented and the corresponding transfer matrix of multi-endpoint rigid body is derived. The central idea is to design the iteration for angle coordinates, which can be expressed accurately. Other methods are, such as 1. increasing the high-order terms of the Taylor series in the geometric equations; 2. choosing properly the linear method of velocity and acceleration and 3. deciding properly the initial value of the iteration. The computational simulation of four kinds of multibody systems show that the method presented in this paper has obvious effect on improving the accuracy and stability of computation.