Modelling human gait using a nonlinear differential equation
Schmalz, J., Paul, D., Shorter, K., Schmalz, X., Cooper, M., Murphy, A. “Modelling human gait using a nonlinear differential equation”, 16th Australasian Conference on Mathematics and Computers in Sport (Mathsport 2022), 2022.
Abstract
We introduce an innovative method for the investigation of human gait, which is based on the visualisation of the vertical component of the movement of the centre of mass during walking or running, in the space of the coordinates position, velocity, and acceleration of the centre of mass. Collected data has been numerically approximated by the best fitting curve for a non-linear model. The resulting equation for the best fitting plane or curve in this space is a differential equation of second order. The model that we suggest is a Duffing equation with coefficients that depend on the height of a walker or runner and on the angular frequency of the oscillation. Statistics about the distribution of the Duffing stiffness depending on the speed is presented.
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