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 
                 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 
  conference-location = "B{\'u}zios, RJ",
      conference-year = "05-09 Oct.",
           targetfile = "macau_interaction.pdf",
        urlaccessdate = "24 jan. 2021"