Diffusion in Phase Space as a Tool to Assess Variability of Vertical Centre-of-Mass Motion during Long-Range Walking-Reference-Cited by-同舟云学术

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

Published:2023-02-05 Issue:1 Volume:5 Page:168-178
ISSN:2624-8174
Container-title:Physics
language:en
Short-container-title:Physics

Author:

Boulanger Nicolas¹^ORCID,Buisseret Fabien²³⁴^ORCID,Dehouck Victor¹⁵^ORCID,Dierick Frédéric²⁶⁷^ORCID,White Olivier⁵

Affiliation:

1. Physique de l’Univers, Champs et Gravitation, Université de Mons—UMONS, 20 Place du Parc, 7000 Mons, Belgium

2. CeREF, Chaussée de Binche 159, 7000 Mons, Belgium

3. Forme and Fonctionnement Humain Lab, Department of Physical Therapy, Haute Ecole Louvain en Hainaut, Rue Trieu Kaisin 136, 6061 Montignies sur Sambre, Belgium

4. Service de Physique Nucléaire et Subnucléaire, UMONS Research Institute for Complex Systems, Université Mons, 20 Place du Parc, 7000 Mons, Belgium

5. INSERM-U1093 Cognition, Action, and Sensorimotor Plasticity, Université de Bourgogne, Campus Universitaire, BP 27877, 21078 Dijon, France

6. Laboratoire d’Analyse du Mouvement et de la Posture (LAMP), Centre National de Réécation Fonctionnelle et de Réadaptation—Rehazenter, Rue André Vésale 1, 2674 Luxembourg, Luxembourg

7. Faculté des Sciences de la Motricité, Univercité Catholique Louvain (UCLouvain), Place Pierre de Coubertin 1-2, 1348 Ottignies-Louvain-la-Neuve, Belgium

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 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.

Publisher

MDPI AG

Subject

General Physics and Astronomy

Link

https://www.mdpi.com/2624-8174/5/1/13/pdf

Reference45 articles.

1. Landau, L., and Lifchitz, E. (1988). Physique Théorique, Tome 1: Mécanique, Éditions MIR.

2. On conservation of conditionally periodic motions for a small change in Hamilton’s function;Kolmogorov;Dokl. Akad. Nauk SSSR,1954

3. Casati, G., and Ford, J. (1979). Stochastic Behavior in Classical and Quantum Hamiltonian Systems, Springer.

4. Proof of a theorem of A.N. Kolmogorov on the invariance of quadi-periodic motions under small perturbations of the hamiltonian;Russ. Math. Surv.,1963

5. On invariant curves of area-preserving mappings of an annulus;Nachr. Akad. Wiss. Göttingen II Math.-Phys. Kl.,1962