机器运动微分方程数值解——解的稳定性与初始运动条件

The Numerical Solution of Differential Equation of Machine motion--Stability of Solution and The Condition of Initial Motion

本文根据常微分方程数值解的理论，结合机器运动方程的特点，讨论了其数值解的稳定性问题。结果表明。该方程不存在固有不稳定性，因此，近似给定初始运动条件求解机器稳定运转规律是可行的。解的稳定性只和计算步长的大小有关。在步长小于最大允许步长的条件下，初值误差引入的解的附加部分将逐渐减小，并使解收敛于稳定运转周期解。由此得知，取前一个计算循环的末值作为下一个计算循环的初值将使解收敛得最快。

This article discusses the stability of numerical solution, in accordance with theory of numerical solution of differential equation and combined with the characteristic of machine motion.The result shows there is no instrinic instability for this equation. Hence, it is practicable,under the condition of initial motion given approximately,for solving the equation of machine motion by numerical method.The solution is stable or unstablc which is only related to the calculated step-length selected under the condition of the step-length is less than emaximum permitted one, the error of initial value will be corrected automatically with error reduced gradually and converged to the steady motion Thus, to regard the end value of the former cycle as the initial value of the latter cycle it causes solution convergent most rapidly