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R. Karim, P. Bauer, B. Heinzl, M. Rößler, G. Schneckenreither, A. Körner, F. Breitenecker, G. Zauner, N. Popper:
"Hybrid State Chart Modelling For Nonlinear Bouncing Ball Dynamics";
Talk: EUROSIM 2010 - 7th Congress on Modelling and Simulation, Prague, Czech Republic; 2010-09-06 - 2010-09-10; in: "Proceedings of the 7th Congress on Modelling and Simulation", M. Snorek, Z. Buk, J. Drchal, M. Cepek (ed.); Vol.2 Full Papers (2010), ISBN: 978-80-01-04589-3; 893 - 898.

This contribution highlights two aspects of the classical bouncing ball modeling and simulation. On modelling level, the ball characterises more a big bubble than a ball, so that drag forces cannot be neglected and impacts must be modelled by distortion, and additionally the implication of the big-sized ball for different atmospheres (comparing Earth and Mars). What looks like fun - may be used for education in modelling and simulation, and may become serious science once. On implementation level, the presented MATLAB/Stateflow version is a purely discrete approach: fly and distortion are modelled by state charts, updated by triggered stepsize events which drive an ODE solver. Switching between impact, distortion, and fly is triggered by state events following a predictive event finding strategy: as the event function is the state ball height, also first and second derivative of event function are known. Thus allows approximating the event function by a polynomial of first order or second order near the impact, the known zero of which may be used for adjusting a smaller step size, and in last consequence, to give the impact time. The idea may be generalized for contact problems in mechanical systems.

Bouncing Ball, State Flow, State Charts, Hybrid Modelling