Abstract In this paper, the methodology of Desoyer and Slibar, for an approximate analytical solution of the nonlinear differential equations governing the dynamics of a circular centrifugal pendulum, has been herein extended to the case of cycloidal and epicycloidal pendula paths. Another distinctive feature treatment of this investigation is the use of parametric cartesian equations of the mass pendulum for the cycloidal and epicycloidal paths. The tuning conditions for the three cases of circular, cycloidal and epicycloidal centrifugal pendula have been deduced. These are consistent with the findings of Denman. Due to the tautochronism associated with these paths, the centrifugal pendula with such paths demonstrated a damping capabilities also under large oscillations. The numerical examples discussed confirm such features.

中文翻译：

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圆形、摆线和外摆线离心摆的调谐条件：统一的笛卡尔方法

摘要 在本文中，Desoyer 和 Slibar 的方法用于控制圆形离心摆动力学的非线性微分方程的近似解析解，已在此扩展到摆线和外摆线摆路径的情况。这项研究的另一个显着特征处理是使用质量摆的参数笛卡尔方程来处理摆线和外摆线路径。推导出圆形、摆线和外摆线离心摆三种情况的调谐条件。这些与 Denman 的发现一致。由于与这些路径相关的同时性，具有此类路径的离心摆在大振荡下也表现出阻尼能力。讨论的数值例子证实了这些特征。