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Technical Brief

An improved mathematical model of Galton board with velocity dependent restitution

[+] Author and Article Information
Auni Aslah Mat Daud

The University of Western Australia 35 Stirling Highway Crawley Perth Western Australia 6009, AustraliaSchool of Informatics and Applied Mathematics, Universiti Malaysia Terengganu, 21030 Kuala Nerus, Malaysia
auni_aslah@yahoo.com

1Corresponding author.

ASME doi:10.1115/1.4036418 History: Received April 04, 2016; Revised March 25, 2017

Abstract

A Galton board, also referred to as quincunx, 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. This study also confirms that the details of the of the deterministic models of Galton board are not essential for demonstrating deviations from the statistical models.

Copyright (c) 2017 by ASME
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