The three-dimensional dynamics of the die throw

Marcin Kapitaniak, Jaroslaw Strzalko, Juliusz Grabski, Tomasz Kapitaniak

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)


A three-dimensional model of a die throw which considers the die bounces with dissipation on the fixed and oscillating table has been formulated. It allows simulations of the trajectories for dice with different shapes. Numerical results have been compared with the experimental observation using high speed camera. It is shown that for the realistic values of the initial energy the probabilities of the die landing on the face which is the lowest one at the beginning is larger than the probabilities of landing on any other face. We argue that non-smoothness of the system plays a key role in the occurrence of dynamical uncertainties and gives the explanation why for practically small uncertainties in the initial conditions a mechanical randomizer approximates the random process.
Original languageEnglish
Article number047504
Number of pages8
Issue number4
Publication statusPublished - Dec 2012


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