Bouncing ball with a finite restitution: Chattering, locking, and chaos.

摘要: We study the dynamic evolution of a bouncing ball on vibrating platform, such as membrane loudspeaker, function its coefficient restitution \ensuremath{\alpha} and demonstrate primarily that presence chaos in this system is by no means inevitable development obvious. Indeed, we show generic trajectories starting under experimental conditions terminate region ``chattering'' (where memory earlier dynamics lost), before repeating themselves periodic way. As consequence, except possibly for strictly elastic case (\ensuremath{\alpha}=1), to via period-doubling route will not be observed. Our arguments are corroborated numerical studies, concerning especially divergence mean period limit approached (\ensuremath{\alpha}\ensuremath{\rightarrow}1).