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