论文标题
一类等方面和非等线性非线性振荡器
A Class of Isochronous and Non-Isochronous Nonlinear Oscillators
论文作者
论文摘要
在这项工作中，我们提出了一种生成一类非线性普通微分方程（ODE）的方法，代表适当的非线性振荡器的动力学，该动力学具有振动频率的振幅独立频率的特征或来自简单和谐振动器积分的振荡频率的振幅依赖性频率。为了实现这一目标，我们考虑了在任何情况下，对于线性和非线性振荡器的积分形式相同形式的情况。我们还讨论了两种类型以谐波形式得出相关积分和一般解决方案的方法。在两种情况下，我们证明了该方法的适用性，最高可达2N耦合一阶非线性ODE。此外，我们在每种情况下都用一个例子说明了理论。
In this work, we present a method of generating a class of nonlinear ordinary differential equations (ODEs), representing the dynamics of appropriate nonlinear oscillators, that have the characteristics of either amplitude independent frequency of oscillations or amplitude dependent frequency of oscillations from the integrals of the simple harmonic oscillator equation. To achieve this, we consider the case where the integrals are in the same form both for the linear and the nonlinear oscillators in either of the cases. We also discuss the method of deriving the associated integrals and the general solution in harmonic form for both the types. We demonstrate the applicability of this method up to 2N coupled first order nonlinear ODEs in both the cases. Further, we illustrate the theory with an example in each case.
