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Diffusion in Phase Space as a Tool to Assess Variability of Vertical Centre-of-Mass Motion during Long-Range Walking
06 février 2023,
- CeREF Santé
- CeREF Technique
,
- Article scientifique
Article scientifique
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 ...
Motor strategies and adiabatic invariants: The case of rhythmic motion in parabolic flights
05 août 2021,
- CeREF Technique
,
- Article scientifique
Article scientifique
The role of gravity in human motor control is at the same time obvious and difficult to isolate. It can be
assessed by performing experiments in variable gravity. We propose that adiabatic invariant theory may be used
to reveal nearly conserved quantities in human voluntary rhythmic motion, an individual being seen as a complex
time-dependent dynamical system with bounded motion in phase space. ...
Adiabatic invariants drive rhythmic human motion in variable gravity
01 décembre 2020,
- CeREF Technique
,
- Article scientifique
Article scientifique
Voluntary human movements are stereotyped. When modeled in the framework of classical mechanics they are expected to minimize cost functions that may include energy, a natural candidate from a physiological point of view also. In time-changing environments, however, energy is no longer conserved—regardless of frictional energy dissipation—and it is therefore not the preferred candidate for any cost ...
Higher-derivative harmonic oscillators: stability of classical dynamics and adiabatic invariants
06 janvier 2019,
- CERISIC
,
- Article scientifique
Article scientifique
he status of classical stability in higher-deriv- ative systems is still subject to discussions. In this note, we argue that, contrary to general belief, many higher-derivative systems are classically stable. The main tool to see this prop- erty are Nekhoroshev’s estimates relying on the action-angle formulation of classical mechanics. The latter formulation can be reached provided the Hamiltonian ...