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arXiv · 1010.2886

Simple model of bouncing ball dynamics: displacement of the table assumed as quadratic function of time

Andrzej Okninski·Boguslaw Radziszewski
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Abstract

Nonlinear dynamics of a bouncing ball moving in gravitational field and colliding with a moving limiter is considered. Displacement of the limiter is a quadratic function of time. Several dynamical modes, such as fixed points, 2 - cycles and chaotic bands are studied analytically and numerically. It is shown that chaotic bands appear due to homoclinic structures created from unstable 2 - cycles in a corner-type bifurcation.

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Andrzej Okninski, Boguslaw Radziszewski. 2010-10-14. Simple model of bouncing ball dynamics: displacement of the table assumed as quadratic function of time. https://doi.org/10.1007/s11071-011-0055-x

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