A Galton board is an instrument invented in 1873 by Francis Galton (1822–1911). It is a box with a glass front and many horizontal nails or pins embedded in the back and a funnel. Galton and many modern statisticians claimed that a lead ball descending to the bottom of the Galton board would display random walk. In this study, a new mathematical model of Galton board is developed, to further improve three very recently proposed models. The novel contribution of this paper is the introduction of the velocity-dependent coefficient of restitution. The developed model is then analyzed using symbolic dynamics. The results of the symbolic dynamics analysis prove that the developed Galton board model does not behave the way Galton envisaged.
An Improved Mathematical Model of Galton Board With Velocity-Dependent Restitution
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received April 4, 2016; final manuscript received March 25, 2017; published online September 7, 2017. Assoc. Editor: Tomasz Kapitaniak.
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Mat Daud, A. A. (September 7, 2017). "An Improved Mathematical Model of Galton Board With Velocity-Dependent Restitution." ASME. J. Comput. Nonlinear Dynam. November 2017; 12(6): 060901. https://doi.org/10.1115/1.4036418
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