Physical pendulum model: Fractional differential equation and memory effects

TL;DR

This paper develops a fractional differential equation model for a physical pendulum that incorporates memory effects, inertia variations, and damping, providing a comprehensive explanation of complex oscillatory behaviors observed in experiments.

Contribution

It introduces a novel fractional differential equation model that effectively captures memory effects and other complex dynamics in pendular motion, outperforming previous models.

Findings

Fractional differential equation model fits experimental data well.

Memory effects are crucial for accurate pendulum modeling.

High initial amplitudes and friction significantly influence oscillations.

Abstract

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.