Simple model of bouncing ball dynamics: displacement of the table assumed as quadratic function of time
arXiv:1010.2886 · doi:10.1007/s11071-011-0055-x
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.
11 pages, 6 figures