- Bayly, P.V. and Virgin, L.N., Experimental evidence of diffusive dynamics and `random walking' in a simple deterministic mechanical system: the shaken pendulum,
Int. J. Bifurcation Chaos Appl. Sci. Eng. (Singapore), vol. 2 no. 4
pp. 983 - 8 .
(last updated on 2007/03/23)
An experimental model of a simple pendulum, harmonically shaken, displays chaotic dynamics. Moreover, in strongly excited chaotic regimes the time series of total angular displacement, which is rarely examined, wanders unboundedly, displaying a power spectrum which falls off as 1/fα over several decades. This behavior corresponds to deterministic diffusion, which has been found in simulations of nonlinear maps with periodic translational symmetry. The displacement time series obtained by sampling the pendulum displacement once per cycle is self-affine and quantitatively similar to Brownian motion
Brownian motion;chaos;diffusion;dynamics;pendulums;random processes;time series;