Year: 2024
Type: article
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.
Source: Physics
Language: English
Topic: Motor Control and Adaptation
Subfield: Cognitive Neuroscience
Field: Neuroscience
Domain: Life Sciences
Open Access status: gold
Estimated APC paid: $1,591
OpenAlex ID: W4404262302