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arXiv · 2301.02298

Diffusion in Phase Space as a Tool to Assess Variability of Vertical Centre-of-Mass Motion During Long-Range Walking

N. Boulanger·F. Buisseret·V. Dehouck·F. Dierick·O. White
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Abstract

When a Hamiltonian system undergoes a stochastic, time-dependent anharmonic perturbation, the values of its adiabatic invariants as a function of time follow a distribution whose shape obeys a Fokker-Planck equation. The effective dynamics of the body's centre-of-mass during human walking is expected to represent such a stochastically perturbed dynamical system. By studying, in phase space, the vertical motion of the body's centre-of-mass of 25 healthy participants walking for 10-minutes at spontaneous speed, we show that the distribution of the adiabatic invariant is compatible with the solution of a Fokker-Planck equation with constant diffusion coefficient. The latter distribution appears to be a promising new tool for studying the long-range kinematic variability of walking.

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N. Boulanger, F. Buisseret, V. Dehouck, F. Dierick, O. White. 2023-01-05. Diffusion in Phase Space as a Tool to Assess Variability of Vertical Centre-of-Mass Motion During Long-Range Walking. https://doi.org/10.3390/physics5010013

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