@InProceedings{MacauCarnCast:2009:InBoBa,
author = "Macau, Elbert Einstein Nehrer and Carneiro, Marcus V. and Castro,
Joaquim Jos{\'e} Barroso de",
affiliation = "{Instituto Nacional de Pesquisas Espaciais (INPE)} and {Instituto
Nacional de Pesquisas Espaciais (INPE)} and {Instituto Nacional de
Pesquisas Espaciais (INPE)}",
title = "Interaction of a bouncing ball with a sinusoidally vi-brating
table",
year = "2009",
organization = "Latin American Workshop on Nonlinear Phenomena.",
abstract = "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.",
conference-location = "B{\'u}zios, RJ",
conference-year = "05-09 Oct.",
targetfile = "macau_interaction.pdf",
urlaccessdate = "24 jan. 2021"
}