In the present work, the nonlinear oscillations of a pendulum wrapping on two cylinders is studied by means of a new analytical technique, namely the Optimal Auxiliary Functions Method (OAFM). The equation of motion is derived from the Lagrange’s equation. Analytical solutions and natural frequency of the system are calculated. Our results obtained through this new procedure are compared with numerical ones and a very good agreement was found, which proves the accuracy of the method. The presented numerical examples show that the proposed approach is simple, easy to implement and very accurate.

中文翻译：

---

两缸摆的最优辅助函数方法

在当前的工作中，通过一种新的分析技术，即最优辅助函数法（OAFM），研究了摆在两个圆柱上的摆的非线性振动。运动方程式是从拉格朗日方程式导出的。计算了系统的解析解和固有频率。将我们通过该新程序获得的结果与数值结果进行比较，发现了很好的一致性，证明了该方法的准确性。数值例子表明，该方法简单，易于实现且非常准确。