  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. We propose that a broader class of higher-derivative
Lagrangians leads to the two-thirds power law and we perform the Hamiltonian
analysis leading to action-angle variables through Ostrogradski's procedure. In
this framework, squared jerk appears 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 one
individual performs a voluntary movement.
