求解完全强非线性自治系统周期解及其稳定性的三变量迭代法

THREE VARIABLES ITERATION METHOD FOR OBTAINING THE PERIODIC SOLUTIONS AND THEIR STABILITY OF FULLY STRONG NONLINEAR AUTONOMOUS SYSTEMS

摘要: 本文提出用广义位移x,基波幅值变化率da/dt=A(a)和系统频率ω(a)进行迭代的一种解析方法——三变量迭代法,求解一般的二阶完全强非线性自治系统的周期解及其稳定性。通过若干实例计算,表明了该方法行之有效。

Abstract: In this paper the three variables iteration method is suggested to find the periodic solutions and determine their stability of fully strong nonlinear autonomous systems of 2nd order. The comparison between the results obtained by our method and those obtained by numerical method shows that the three variables iteration method is both effective and of high accuracy.