The Two-Thirds Power Law Derived from a Higher-Derivative Action - Nicolas Boulanger; Fabien Buisseret; Frédéric Dierick; Olivier White (Physics)
The two-thirds power law is a link between angular speed <semantics>ω</semantics> and curvature <semantics>κ</semantics> observed in voluntary human movements: <semantics>ω</semantics> is proportional to <semantics>κ2/3</semantics>. Squared jerk is known to be a Lagrangian leading to the latter law. However, it leads to unbounded movements and is therefore incompatible with 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 lead to the two-thirds power law. The current study extends this framework and investigates a wider class of Lagrangians admitting generalised conservation laws.