Abstract

This work investigates stability and the maintenance of balance using tools from dynamical systems. In particular we investigate the application of such tools to the study of the ground reaction forces resulting from an athlete being perturbed from quiet stance. For the modelling of the re-stabilization process, a set of coupled vector fields is used. When examining the phase space of the dynamical system governing the angles between resultant ground reaction force and the vertical in the mediolateral and the anteroposterior directions, one can see that there exists a region where the subject is able to maintain balance without falling. We considered this region to be a basin of attraction, bound by a closed curve which we call the critical curve. It is only inside this curve that perturbations can be corrected, with the orbit spiralling onto an attractor corresponding to quiet stance. We investigate the linear stability of the features of the model and show how the critical curve and also the strength of the attractor found in the basin of attraction can be fit to model the experimental data for an individual. We also discuss how our model can be used to identify non-symmetric behaviour caused by muscle imbalances and differences in the ranges of motion on either side of the body.

J.R.Stirling and M. S. Zakynthinaki, Stability and the maintenance of balance following a perturbation from quiet stance, Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 14, 1, pp. 96-105, 2004.