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Drawing Movements as an Outcome of the Principle of Least Action.

According to the two-thirds power law the cube of the speed of a drawing movement is proportional to the radius of curvature of the trajectory, and the coefficient of proportionality has the meaning of mechanical power. We derive this empirical law from the variational principle known in physics as the principle of least action. It states that if a movement between two points of a given path obeys the two-thirds law, then the amount of work required to execute a trajectory in a fixed time is minimal. In this strict sense one may say that among infinitely many ways to execute a given path, the central nervous system chooses the most economical. We show that the kinematic equations for all drawing movements are solutions of a certain differential equation with a single (time-variable) coefficient. We consider several special cases of drawing movements corresponding to simplest forms of this coefficient. Copyright 2001 Academic Press.