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

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

2010-10-14

arxiv.org/abs/1010.2886v1

Nonlinear Dyn (2012) 67:1115-1122

Nonlinear Sciences

Chaotic Dynamics

11 pages, 6 figures

Scientific paper

10.1007/s11071-011-0055-x

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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