ABSTRACT
To Bat a ball with a paddle repeatedly up in the air is a skill which involves moving the multi-jointed effector system consisting of arm, hand, and paddle and thereby controlling the ball’s periodic flight trajectory. If movement coordination within given task constraints is viewed as a nonlinear dynamical system, it can be expected that attractive stable regimes exist which become evident as an intrinsic preference for particular movement patterns. Batting a ball with a paddle is modeled as a planar surface performing periodic vertical motions, hitting a ball rhythmically. Goal of the analysis is to identify the characteristics of the paddle’s movement that achieves ball trajectories with invariant amplitude. Assuming arbitrary periodic motion of the surface, ballistic flight, and elastic impact for the ball, an equation system for ball and paddle movements is obtained. To investigate whether humans attune to the dynamical properties of a task, a dynamical model for batting is proposed for which attractor states and their stability can be identified.
