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Beek and van Santvoord [Beek, P. J., & van Santvoord, A. A. M. (1992). Journal of Motor Behavior, 24, 85-94] proposed a three-stage model of learning to juggle based on group analyses of temporal measures. Here, we examined in detail how the temporal and spatial features of juggling evolved in eight individual participants progressing from the second to the third stage of learning. During the second stage, the dwell ratio, defined as the ratio of the time that the juggler holds a ball between catch and toss and the hand cycle time (HCT), was stable when it was about 0.83. The subjects with a dwell ratio near this value and controlled throws exhibited stable juggling, whereas the subjects with a dwell ratio of 0.80 or smaller exhibited unstable juggling. Compared to the former group, the latter group had a longer time from the throw of a ball to the arrival at its zenith (TZ), and a shorter time between the arrival of an airborne ball at its zenith and the subsequent throw (IZR). The latter group also exhibited larger variability in the dwell ratio and IZR. With practice, the subjects appropriated, on average, the duration of TZ and IZR to the dwell ratio and improved the ability to accurately throw balls by changing the motions of the limb segments involved. Although these changes helped to stabilize the performance during the second stage, the variability problem was not sufficiently resolved. Only two out of eight subjects passed on to the third stage by the last (10th) Session. They achieved small variability in IZR, dwell ratio, and flight paths of the ball while juggling with short HCTs and small dwell ratios. These results suggest that the reduction of variability in these variables was essential to pass on to the third stage.[authors summary]

The circle map provides a general mathematical model for the mode-locking behavior observed in systems of coupled oscillators. From this theoretical perspective, multifrequency tapping was studied. Three experiments were conducted in which skilled drummers participated. The results were in qualitative agreement with the dynamical features of the circle map. The stability of behavior was affected by the movement frequency at which the multifrequency relations were performed. Attraction to lower order ratios (predominantly showing Farey relations) was observed. In some situations bistability and hysteresis occurred, implying that the system was situated in the supercritical domain of the circle map where resonance zones overlap. Furthermore, the results suggest that multifrequency tapping is characterized by an asymmetrical coupling in that the influence of the fast hand on the slow hand is the strongest. [authors summary]