Continuous hitting movements modeled from the perspective of dynamical systems with temporal input

The kinematics of continuously repeated forehand and backhand tennis strokes were measured and analyzed in terms of a dynamical system with temporal input. The tennis strokes were performed under two conditions: when the same input pattern was repeated and when two different input patterns were switched stochastically. The condition with the two periodic inputs revealed that there were two different trajectories in cylindrical space, while the condition with switching input induced transitions between these two trajectories, which were considered as excited attractors. The transitions between the two excited attractors were characterized by a fractal-like feature that could be described by a simple Cantor set with rotation. This result suggests that continuous hitting movements have a hierarchical fractal structure, as was expected from the theory of dynamical systems with external temporal input.