摘要
本文提出和证明了,用Newton方法可以求解强(弱)非线性非自治系统的渐近解析周期解,为研究强(弱)非线性系统振动提供了一个新的解析方法.根据本文方法的需要,讨论了二阶线性非齐次周期系统周期解的存在与计算问题.此外,还讨论了Newton方法对于拟线性系统的应用.最后,应用本文方法计算了Duffing方程的周期解.
In this paper we suggest and prove that Newton's method may calculate the asymptotic analytic periodic solutions of strong and weak nonlinear nonautonomous systems, so that a new analytic method is offered for studying strong and weak nonlinear oscillation systems. On the strength of the need of our method, we discuss the existence and calculation of the periodic solution of the second order nonhomogeneous linear periodic system. Besides, we investigate the application of Newton's method to quasi-linear system. The periodic solution of Duffing equation is calculated by means of our method.
出处
《应用数学和力学》
EI
CSCD
北大核心
1992年第9期829-842,共14页
Applied Mathematics and Mechanics
关键词
共振
非线性
振动
牛顿法
Newton's method, resonance, nonresonance, strong nonlinear systems,truncated equations
