Physics (Feb 2023)

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

  • Nicolas Boulanger,
  • Fabien Buisseret,
  • Victor Dehouck,
  • Frédéric Dierick,
  • Olivier White

DOI
https://doi.org/10.3390/physics5010013
Journal volume & issue
Vol. 5, no. 1
pp. 168 – 178

Abstract

Read online

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 min at spontaneous speed, we show that the distribution of the adiabatic invariant is compatible with the solution of a Fokker–Planck equation with a constant diffusion coefficient. The latter distribution appears to be a promising new tool for studying the long-range kinematic variability of walking.

Keywords