Nonlinear variability in human movement analysis
This paper provides an introduction to the calculation of the Lyapunov exponent as a measure of nonlinear variability in time series data, with application to human movement data. The Lyapunov exponent is defined mathematically, and a survey of the theoretical results that underpin its computation is given. Computational algorithms for reconstructing the state space of the movement process and calculating the Lyapunov exponent are then described and translated into the R programming language when necessary. These algorithms are then applied to data on cambered running provided by Dr. Michael Bird at Truman State University. Preliminary results indicate that the Lyapunov exponent may be able to distinguish between flat-surface running and running on a camber, but uncertainties remain concerning the degree to which parameters of the algorithms must be set "by hand" for each subject and each time series.