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

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 expecte...

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Bibliographic Details
Published in:Physics (Online) 2023-03, Vol.5 (1), p.168-178
Main Authors: Boulanger, Nicolas, Buisseret, Fabien, Dehouck, Victor, Dierick, Frédéric, White, Olivier
Format: Article
Language:English
Subjects:
Adiabatic flow
adiabatic invariant
Anharmonicity
Biomechanics
Center of mass
Diffusion coefficient
Dynamical systems
Energy
Fokker-Planck equation
Gait
gait variability
Hamiltonian functions
Invariants
Kinematics
Perturbation
phase-space dynamics
Physiology
random noise
Time dependence
Variables
Vertical motion
Walking
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Summary: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.
ISSN:2624-8174
2624-8174
DOI:10.3390/physics5010013