Bouncing ball dynamics

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A bouncing ball on a sinusoidally vibrating table is an example of a chaotic system.^[1] In such a system, the motion of the ball is altered by a series of deflections as well as the other forces, such as gravity.

The study of the dynamics of a bouncing ball on a sinusoidally vibrating table is a useful teaching example about the behavior of chaotic systems. In addition to its pedagogical value, the system is also of practical interest in several engineering applications, as well as in basic research.^{[citation needed]}

Notes

↑ Nicholas B. Tufillaro, Tyler Abbott, and Jerermiah Reilly (1992). An Experimental Approach to Nonlinear Dynamics and Chaos. Addison–Wesley. ISBN 0-201-55441-0.

References

T. M. Mello and N. B. Tufillaro, "Strange attractors of a bouncing ball," American Journal of Physics 55 (4), 316 (1987).
N. B. Tufillaro, "Braid analysis of a bouncing ball," Physical Review E 50 (6), 4509–4522 (1994).
N. B. Tufillaro, T. M. Mello, Y. M. Choi, and A. M. Albano, "Period doubling boundaries of a bouncing ball," Journal de Physique 47, 1477 (1986).
N. B. Tufillaro and A. M. Albano, "Chaotic dynamics of a bouncing ball," American Journal of Physics 54 (10), 939 (1986).
K. Wiesenfeld and N. B. Tufillaro, "Suppression of period doubling in the dynamics of a bouncing ball," Physica 26D, 321 (1987).
S. K. Joseph, I. P. Mariño and Miguel A.F. Sanjuán, "Effect of the phase on the dynamics of a perturbed bouncing ball system ", Commun. Nonlinear. Sci. and Numer. Simul",17 (8) 3279 - 3286 (2012).

External links

J. Thomas Bouncing Ball Page

v t e Chaos theory

Chaos theory	Anosov diffeomorphism Bifurcation theory Butterfly effect Chaos theory in organizational development Complexity Control of chaos Dynamical system Edge of chaos Fractal Predictability Quantum chaos Santa Fe Institute Synchronization of chaos Unintended consequences

Chaotic maps (list)	Arnold tongue Arnold's cat map Baker's map Chua's circuit Complex quadratic map Complex squaring map Coupled map lattice Double pendulum Duffing equation Duffing map Dyadic transformation Dynamical billiards outer Exponential map Gauss map Gingerbreadman map Hénon map Horseshoe map Ikeda map Interval exchange map Kaplan–Yorke map Logistic map Lorenz system Rabinovich–Fabrikant equations Rössler attractor Standard map Swinging Atwood's machine Tent map Tinkerbell map Van der Pol oscillator Zaslavskii map

Chaos systems	Bouncing ball dynamics Economic bubble Tilt-A-Whirl

Chaos theorists	Michael Berry Leon O. Chua Mitchell Feigenbaum Martin Gutzwiller Brosl Hasslacher Michel Hénon Edward Norton Lorenz Aleksandr Lyapunov Benoît Mandelbrot Henri Poincaré Otto Rössler David Ruelle Oleksandr Mykolaiovych Sharkovsky Floris Takens James A. Yorke

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