The behavior of bouncing disks and pizza tossingK.-C. Liu, J. Friend and L. Yeo
MicroNanophysics Research Laboratory, Department of Mechanical Engineering, Monash University Melbourne, Victoria 3800, Australia
received 26 January 2009; accepted in final form 20 February 2009; published March 2009
published online 26 March 2009
We investigate the dynamics of a disk bouncing on a vibrating platform – a variation of the classic bouncing ball problem – that captures the physics of pizza tossing and the operation of certain standing-wave ultrasonic motors (SWUMs). The system's dynamics explains why certain tossing motions are used by dough-toss performers for different tricks: a helical trajectory is used in single tosses because it maximizes energy efficiency and the dough's airborne rotational speed, a semi-elliptical motion is used in multiple tosses because it is easier for maintaining dough rotation at the maximum rotational speed. The system's bifurcation diagram and basins of attraction also informs SWUM designers about the optimal design for high speed and minimal sensitivity to perturbation.
05.45.-a - Nonlinear dynamics and chaos.
84.60.-h - Direct energy conversion and storage.
43.38.Fx - Piezoelectric and ferroelectric transducers.
© EPLA 2009