Physical pendulum model: Fractional differential equation and memory effects

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.

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