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		<citationkey>MacauCarnCast:2009:InBoBa</citationkey>
		<title>Interaction of a bouncing ball with a sinusoidally vi-brating table</title>
		<year>2009</year>
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		<author>Macau, Elbert Einstein Nehrer,</author>
		<author>Carneiro, Marcus V.,</author>
		<author>Castro, Joaquim José Barroso de,</author>
		<group>LAC-CTE-INPE-MCT-BR</group>
		<group>LAC-CTE-INPE-MCT-BR</group>
		<group>LAC-CTE-INPE-MCT-BR</group>
		<affiliation>Instituto Nacional de Pesquisas Espaciais (INPE)</affiliation>
		<affiliation>Instituto Nacional de Pesquisas Espaciais (INPE)</affiliation>
		<affiliation>Instituto Nacional de Pesquisas Espaciais (INPE)</affiliation>
		<conferencename>Latin American Workshop on Nonlinear Phenomena.</conferencename>
		<conferencelocation>Búzios, RJ</conferencelocation>
		<date>05-09 Oct.</date>
		<secondarytype>PRE CI</secondarytype>
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		<contenttype>External Contribution</contenttype>
		<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.</abstract>
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		<targetfile>macau_interaction.pdf</targetfile>
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		<url>http://mtc-m16c.sid.inpe.br/rep-/sid.inpe.br/mtc-m18@80/2009/09.22.14.48</url>
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