Abstract
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.
| Original language | English |
|---|---|
| Article number | 060901 |
| Number of pages | 3 |
| Journal | Journal of Computational and Nonlinear Dynamics |
| Volume | 12 |
| Issue number | 6 |
| DOIs | |
| Publication status | Published - 1 Nov 2017 |
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An Improved Mathematical Model of Galton Board with Velocity-Dependent Restitution. / Mat Daud, Auni Aslah.
In: Journal of Computational and Nonlinear Dynamics, Vol. 12, No. 6, 060901, 01.11.2017.Research output: Contribution to journal › Article
TY - JOUR
T1 - An Improved Mathematical Model of Galton Board with Velocity-Dependent Restitution
AU - Mat Daud, Auni Aslah
PY - 2017/11/1
Y1 - 2017/11/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85029141952&partnerID=8YFLogxK
U2 - 10.1115/1.4036418
DO - 10.1115/1.4036418
M3 - Article
VL - 12
JO - Journal of Computational and Nonlinear Dynamics
JF - Journal of Computational and Nonlinear Dynamics
SN - 1555-1415
IS - 6
M1 - 060901
ER -