Newton方法在非线性振动理论中的推广与应用

Extension and Application of Newton’s Method in Nonlinear Oscillation Theory

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.
- Newton方法 /
- 共振 /
- 非共振 /
- 强非线性系统 /
- 截断方程组
Abstract: In this paper we suggest and prove that Newton's method may calculate the asymptotic analytic periodic solution 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 systems. The periodic solution of Duffing equation is calculated by means of our method.
- Newton’s method /
- resonance /
- nonresonance /
- strongly nonlinear systems /
- truncated equations

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