Version 1
: Received: 13 September 2024 / Approved: 14 September 2024 / Online: 16 September 2024 (12:15:27 CEST)
How to cite:
Boulanger, N.; Buisseret, F.; Dierick, F.; White, O. The Two-Thirds Power Law Derived from an Higher-Derivative Action. Preprints2024, 2024091149. https://doi.org/10.20944/preprints202409.1149.v1
Boulanger, N.; Buisseret, F.; Dierick, F.; White, O. The Two-Thirds Power Law Derived from an Higher-Derivative Action. Preprints 2024, 2024091149. https://doi.org/10.20944/preprints202409.1149.v1
Boulanger, N.; Buisseret, F.; Dierick, F.; White, O. The Two-Thirds Power Law Derived from an Higher-Derivative Action. Preprints2024, 2024091149. https://doi.org/10.20944/preprints202409.1149.v1
APA Style
Boulanger, N., Buisseret, F., Dierick, F., & White, O. (2024). The Two-Thirds Power Law Derived from an Higher-Derivative Action. Preprints. https://doi.org/10.20944/preprints202409.1149.v1
Chicago/Turabian Style
Boulanger, N., Frederic Dierick and Olivier White. 2024 "The Two-Thirds Power Law Derived from an Higher-Derivative Action" Preprints. https://doi.org/10.20944/preprints202409.1149.v1
Abstract
The two-thirds power law is a link between angular speed $\omega$ and curvature $\kappa$ observed in voluntary human movements: $\omega$ is proportional to $\kappa^{2/3}$. Squared jerk is known to be a Lagrangian leading to the latter law. However, it leads to unbounded movements and is therefore incompatible with a quasi-periodic dynamics, such as the movement of the tip of a pen drawing ellipses.
To solve this drawback, we give a class of higher-derivative Lagrangians that allow for both quasi-periodic and unbounded movements, and at the same time leading to the two-thirds power law.
We then perform the Hamiltonian analysis leading to action-angle variables through Ostrogradski's procedure. In this framework, squared jerk is recovered as an action variable, and its minimization may be related to power expenditure minimization during motion. The identified higher-derivative Lagrangians are therefore natural candidates for cost functions, i.e. movement functions that are targeted to be minimal when an individual performs a voluntary movement.
Keywords
Higher-derivative actions; Phase-space; Motor control; Biomechanics; Adiabatic invariant
Subject
Physical Sciences, Mathematical Physics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
