A detailed analysis of three pendular motion models is presented. Inertial effects, self-oscillation, and memory, together with non-constant moment of inertia, hysteresis and negative damping are shown to be required for the comprehensive description of the free pendulum oscillatory regime. The effects of very high initial amplitudes, friction in the roller bearing axle, drag, and pendulum geometry are also analysed and discussed. The model that consists of a fractional differential equation provides both the best explanation of, and the best fits to, experimental high resolution and long-time data gathered from standard action-camera videos.

中文翻译：

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物理钟摆模型：分数微分方程和记忆效应

介绍了三种摆动运动模型的详细分析。惯性效应、自振荡和记忆，以及非恒定惯性矩、滞后和负阻尼被证明是自由摆振荡机制的综合描述所必需的。还分析和讨论了非常高的初始振幅、滚子轴承轴中的摩擦、阻力和摆几何的影响。由分数阶微分方程组成的模型提供了对从标准动作相机视频收集的实验高分辨率和长时间数据的最佳解释和最佳拟合。