  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.
