3 research outputs found
Simple model of bouncing ball dynamics: displacement of the table assumed as quadratic function of time
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.Comment: 11 pages, 6 figure
Simple model of bouncing ball dynamics. Displacement of the limiter assumed as a cubic function of time
Nonlinear dynamics of a bouncing ball moving vertically in a gravitational
field and colliding with a moving limiter is considered and the Poincare map,
describing evolution from an impact to the next impact, is described.
Displacement of the limiter is assumed as periodic, cubic function of time. Due
to simplicity of this function analytical computations are possible. Several
dynamical modes, such as fixed points, 2 - cycles and chaotic bands are studied
analytically and numerically. It is shown that chaotic bands are created from
fixed points after first period doubling in a corner-type bifurcation. Equation
for the time of the next impact is solved exactly for the case of two
subsequent impacts occurring in the same period of limiter's motion making
analysis of chattering possible.Comment: 8 pages, 1 figure, presented at the DSTA 2011 conference, Lodz,
Polan