`%0 Conference Proceedings`

`%4 sid.inpe.br/mtc-m18@80/2009/09.22.14.48`

`%2 sid.inpe.br/mtc-m18@80/2009/09.22.14.48.41`

`%T Interaction of a bouncing ball with a sinusoidally vi-brating table`

`%D 2009`

`%A Macau, Elbert Einstein Nehrer,`

`%A Carneiro, Marcus V.,`

`%A Castro, Joaquim José Barroso de,`

`%@affiliation Instituto Nacional de Pesquisas Espaciais (INPE)`

`%@affiliation Instituto Nacional de Pesquisas Espaciais (INPE)`

`%@affiliation Instituto Nacional de Pesquisas Espaciais (INPE)`

`%B Latin American Workshop on Nonlinear Phenomena.`

`%C Búzios, RJ`

`%8 05-09 Oct.`

`%X Exploring all its rami¯cations, this presentation gives an overview of the fundamental bouncing ball problem, which consists of a ball bouncing vertically on a sinusoidally vi-brating table under the action of gravity. The dynamics is modeled on the basis of a discrete map of di®erence equations, which numerically solved fully reveals a rich variety of nonlinear behaviors, encompassing irregular non-periodic orbits, subharmonic and chaotic motions, chattering mechanisms, and also unbounded non-periodic orbits. For periodic motions, the corresponding conditions for stability and bifurcation are determined from analytical considerations of a re- duced map. Through numerical examples, it is shown that a slight change in the initial conditions makes the ball motion switch from periodic to chaotic orbits bounded by a velocity strip v = §s=(1 ¡ r), where s; is the non-dimensionalized shaking acceleration and r the coe±cient of restitution which quantities the amount of energy lost in the ball-table collision. Moreover, a detailed numerical discussion of the excitation of the unstable 1-periodic mode and the ensuing transition to its stable counterpart mode is also given.`

`%3 macau_interaction.pdf`