Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2012-03-19
Nonlinear Sciences
Chaotic Dynamics
8 pages, 1 figure, presented at the DSTA 2011 conference, Lodz, Poland
Scientific paper
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.
Okninski Andrzej
Radziszewski Boguslaw
No associations
LandOfFree
Simple model of bouncing ball dynamics. Displacement of the limiter assumed as a cubic function of time does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Simple model of bouncing ball dynamics. Displacement of the limiter assumed as a cubic function of time, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Simple model of bouncing ball dynamics. Displacement of the limiter assumed as a cubic function of time will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-212472