Non-linear model-based estimation of quadratic and cubic damping mechanisms governing the dynamics of a chaotic spherical pendulum

Abstract

We investigate the non-linear damping mechanisms that govern the dynamics of a chaotic spherical pendulum. We reproduce the conditions of the celebrated chaotic experiment of Tritton (1986), and identify the bifurcation regions that correspond to periodic, quasi-periodic and chaotic-like response. Construction of the pendulum frequency and damping backbone curves from free vibration decay data reveal the existence of non-negligible non-linear damping. A non-linear model-based estimation procedure enables extraction of both quadratic and cubic damping coefficients which are deduced from a non-linear Rayleigh-type gradient dissipation function. Comparison of experimental results with solutions obtained via numerical analysis of the strongly non-linear pendulum model, augmented by the estimated damping mechanisms, sheds light on the possible cause of documented discrepancies in similar whirling systems between measurements and theoretical predictions obtained from models with only linear damping.