Randomness in the bouncing ball dynamics |
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| Institution: | 1. Dipartimento di Fisica, Università di Camerino, I-62032 Camerino, Italy;2. Dipartimento di Fisica, and Istituto Nazionale di Fisica Nucleare, Università di Perugia, I-06123 Perugia, Italy;1. Lehrstuhl für Theoretische Physik I, Institut für Physik, Universität Augsburg, Universitätsstr. 1, 86135 Augsburg, Germany;2. Dpto. Física Atómica Molecular y Nuclear, Facultad de Física, Universidad de Sevilla, Av. Reina Mercedes s/n, 41012 Sevilla, Spain;1. LEMTA, Université de Lorraine 2, avenue de la Forêt de Haye, 54504 Vandoeuvre les Nancy Cedex, France;2. LEMTA, CNRS 2, avenue de la Forêt de Haye, 54504 Vandoeuvre les Nancy Cedex, France;3. Laboratório Nacional de Computação Científica LNCC/MCT, Av Getúlio Vargas 333, 25651–070 Petrópolis, RJ, Brazil;1. Department of Engineering, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran;2. Department of Mechanical Engineering, Isfahan University of Technology, Isfahan 84156-83111, Iran;3. Young Researches and Elites Club, North Tehran Branch, Islamic Azad University, Tehran, Iran;1. Department of Civil and Environmental Engineering, University of Ottawa, Canada;2. Department of Civil and Environmental Engineering, Hong Kong University of Science and Technology, Hong Kong;3. Western China Earthquake and Hazards Mitigation Research Centre, Sichuan University, Chengdu, China;1. MSC Software Corporation, 201 Depot Street, Suite 100, Ann Arbor, MI 48104, USA;2. Division of Dynamics and Control, School of Astronautics, Harbin Institute of Technology, Harbin 150001, China;3. Department of Mechanical Engineering, University of Maryland, Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250, USA |
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| Abstract: | The dynamics of a vibrated bouncing ball is studied numerically in the reduced impact representation, where the velocity of the bouncing ball is sampled at each impact with the plate (asynchronous sampling). Its random nature is thus fully revealed: (i) the chattering mechanism, through which the ball gets locked on the plate, is accomplished within a limited interval of the plate oscillation phase, and (ii) is well described in impact representation by a special structure of looped, nested bands and (iii) chattering trajectories and strange attractors may coexist for appropriate ranges of the parameter values. Structure and substructure of the chattering bands are well explained in terms of a simple impact map rule. These results are of potential application to the analysis of high-temperature vibrated granular gases. |
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