Regular and Chaotic Dynamics in Bouncing Ball Models

One of the prime paradigms for complex temporal dynamics, the motion of an inelastic ball bouncing on a sinusoidally oscillating table, is revisited. Using extensive numerical simulations, we addre...

[1]  A. Bernstein Listening to the coefficient of restitution , 1977 .

[2]  Kowalik,et al.  Self-reanimating chaos in the bouncing-ball system. , 1988, Physical review. A, General physics.

[3]  D. Tabor A simple theory of static and dynamic hardness , 1948, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[4]  G. Zaslavsky The simplest case of a strange attractor , 1978 .

[5]  C. Oliveira,et al.  Bifurcations and chaos for the quasiperiodic bouncing ball , 1997 .

[6]  R. H. Cohen,et al.  Fermi acceleration revisited , 1980 .

[7]  Hamid El hor,et al.  Model for transport of granular matter on an annular vibratory conveyor , 2005 .

[8]  C. V. Raman The photographic study of impact at minimal velocities , 1918 .

[9]  J. Reed Energy losses due to elastic wave propagation during an elastic impact , 1985 .

[10]  Luna-Acosta Regular and chaotic dynamics of the damped Fermi accelerator. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[11]  N. P. Kruyt,et al.  Theoretical and experimental study of the transport of granular materials by inclined vibratory conveyors , 1996 .

[12]  Enrico Fermi,et al.  On the Origin of the Cosmic Radiation , 1949 .

[13]  W. Goldsmith,et al.  Impact: the theory and physical behaviour of colliding solids. , 1960 .

[14]  C. V. Raman,et al.  On some applications of Hertz's theory of impact , 1920 .

[15]  N. Tufillaro,et al.  Strange attractors of a bouncing ball , 1987 .

[16]  D. Gugan Inelastic collision and the Hertz theory of impact , 2000 .

[17]  Sergio Celaschi,et al.  The electronic bouncing ball , 1992 .

[18]  Mehta,et al.  Bouncing ball with a finite restitution: Chattering, locking, and chaos. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[19]  A. B. Pippard The physics of vibration: THE SIMPLE CLASSICAL VIBRATOR , 1989 .

[20]  Z. Kowalik,et al.  Jumping particle model. A study of the phase space of a non-linear dynamical system below its transition to chaos , 1985 .

[21]  Erik Mosekilde,et al.  Deterministic analysis of the probability machine , 1995 .

[22]  H. Isomäki,et al.  Fractal Properties of the Bouncing-Ball Dynamics , 1990 .

[23]  I. Stensgaard,et al.  Listening to the coefficient of restitution - revisited , 2001 .

[24]  Yves Garrabos,et al.  Inelastic ball-plane impact: An accurate way to measure the normal restitution coefficient , 2006 .

[25]  S. Fauve,et al.  Behavior of one inelastic ball bouncing repeatedly off the ground , 1998 .

[26]  Pieranski Direct evidence for the suppression of period doubling in the bouncing-ball model. , 1988, Physical review. A, General physics.

[27]  Tufillaro Braid analysis of a bouncing ball. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[28]  Nicholas B. Tufillaro Comment on "Bouncing ball with finite restitution ..." , 1994 .

[29]  A. B. Pippard The physics of vibration: Index , 1989 .

[30]  H. Stöckmann,et al.  Quantum Chaos: An Introduction , 1999 .

[31]  Richard M. Everson,et al.  Chaotic dynamics of a bouncing ball , 1986 .

[32]  M. Hénon,et al.  A two-dimensional mapping with a strange attractor , 1976 .

[33]  Mehta,et al.  Novel temporal behavior of a nonlinear dynamical system: The completely inelastic bouncing ball. , 1990, Physical review letters.

[34]  Nicholas B. Tufillaro,et al.  Period doubling boundaries of a bouncing ball , 1986 .

[35]  Philip A. Maurone Time of flight for the bouncing ball experiment , 1979 .

[36]  Lambertus Ter Borg,et al.  On the theoretical and experimental conveying speed of granular bulk solids on vibratory conveyors , 1994 .

[37]  P. A. Smith,et al.  Microcomputer listens to the coefficient of restitution , 1981 .

[38]  H. Brody,et al.  Physics of the tennis racket , 1979 .

[39]  Pieranski,et al.  Noisy precursors and resonant properties of the period-doubling modes in a nonlinear dynamical system. , 1986, Physical review. A, General physics.

[40]  Philip A. Maurone,et al.  Bouncing ball experiment , 1978 .

[41]  Sergio Celaschi,et al.  Evolution of a two-parameter chaotic dynamics from universal attractors , 1987 .

[42]  Peter Walzel,et al.  Partikeltransport unter verschiedenen Stoßbedingungen auf vibrierten Unterlagen , 1997 .

[43]  Paul Sánchez,et al.  Chaotic dynamics of an air-damped bouncing ball. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[44]  Victor Sosa,et al.  Chaos control: The problem of a bouncing ball revisited , 2009 .

[45]  Nicholas B. Tufillaro,et al.  Experimental approach to nonlinear dynamics and chaos , 1992, Studies in nonlinearity.