This paper reports and investigates paradoxical simulation results of the bouncing ball system. Chaos-like motion of the bouncing ball system with intermittent chattering (Zeno behavior) is observed in simulations if the relative acceleration of the table exceeds a critical value. However, one can show that this is theoretically impossible. A detailed analysis is given by looking at the backward and forward dynamics of grazing solutions. It is shown in detail that a self-similar structure appears if the relative acceleration of the table exceeds the critical value.
%0 Journal Article
%1 Schindler&Leine2021
%A Schindler, K.
%A Leine, R. I.
%D 2021
%J Physica D: Nonlinear Phenomena
%K from:rleine inm journal leine project_schindler
%R https://doi.org/10.1016/j.physd.2021.132854
%T Paradoxical simulation results of chaos-like chattering in the bouncing ball system
%V 419
%X This paper reports and investigates paradoxical simulation results of the bouncing ball system. Chaos-like motion of the bouncing ball system with intermittent chattering (Zeno behavior) is observed in simulations if the relative acceleration of the table exceeds a critical value. However, one can show that this is theoretically impossible. A detailed analysis is given by looking at the backward and forward dynamics of grazing solutions. It is shown in detail that a self-similar structure appears if the relative acceleration of the table exceeds the critical value.
@article{Schindler&Leine2021,
abstract = {This paper reports and investigates paradoxical simulation results of the bouncing ball system. Chaos-like motion of the bouncing ball system with intermittent chattering (Zeno behavior) is observed in simulations if the relative acceleration of the table exceeds a critical value. However, one can show that this is theoretically impossible. A detailed analysis is given by looking at the backward and forward dynamics of grazing solutions. It is shown in detail that a self-similar structure appears if the relative acceleration of the table exceeds the critical value.},
added-at = {2022-03-22T14:39:07.000+0100},
author = {Schindler, K. and Leine, R. I.},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2c324d4d1c54c291d86ffa4a296cb77eb/inm},
doi = {https://doi.org/10.1016/j.physd.2021.132854},
interhash = {d319c1479775c509636a1ffd480848fb},
intrahash = {c324d4d1c54c291d86ffa4a296cb77eb},
journal = {Physica D: Nonlinear Phenomena},
keywords = {from:rleine inm journal leine project_schindler},
timestamp = {2022-06-13T12:40:31.000+0200},
title = {Paradoxical simulation results of chaos-like chattering in the bouncing ball system},
volume = 419,
year = 2021
}
