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, grazing 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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Okniński, A., Radziszewski, B. Simple model of bouncing ball dynamics: displacement of the table assumed as quadratic function of time. Nonlinear Dyn 67, 1115–1122 (2012). https://doi.org/10.1007/s11071-011-0055-x
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DOI: https://doi.org/10.1007/s11071-011-0055-x