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Comments. Discussion. Critique
Comparative analysis of friction models in dynamics of a ball on a plane
A. P. Ivanov^{} ^{} Moscow Institute of Physics and Technology
Abstract:
Comparative analysis of the dynamics of a homogeneous ball on a plane with dry friction is conducted for two conjectures: 1) single contact point (nonholonomic statement); 2) the normal load is distributed in the circle spot of contact with radius $\varepsilon$. It is assumed that for given active forces and coefficient of friction the nonslip motion is possible. The expression for load distribution function $\phi$ at the contact spot (second statement) is arbitrary, with general mild restrictions, which ensure correctness of the passage to the limit. It is shown that for $\varepsilon\to 0$ the trajectory of the ball with contact spot approaches the trajectory of the ball with single contact point. Previously similar result was obtained by Fufaev [1] in the case $\phi=\mathrm{const}$. The possibility of approximation of reactions of nonholonomic constraints by means of forces of viscous friction was proved [2], [3], as well as by means of forces of dry friction with infinitely large coefficient of friction [4].
Keywords:
systems with rolling motion, dry friction.
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UDC:
531.01
MSC: 70Е18 Received: 22.12.2010
Citation:
A. P. Ivanov, “Comparative analysis of friction models in dynamics of a ball on a plane”, Nelin. Dinam., 6:4 (2010), 907–912
Citation in format AMSBIB
\Bibitem{Iva10}
\by A.~P.~Ivanov
\paper Comparative analysis of friction models in dynamics of a ball on a plane
\jour Nelin. Dinam.
\yr 2010
\vol 6
\issue 4
\pages 907912
\mathnet{http://mi.mathnet.ru/nd15}
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http://mi.mathnet.ru/eng/nd15 http://mi.mathnet.ru/eng/nd/v6/i4/p907
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V. F. Zhuravlev, “Ponyatie svyazi v analiticheskoi mekhanike”, Nelineinaya dinam., 8:4 (2012), 853–860

A. V. Borisov, I. S. Mamaev, “Notes on new friction models and nonholonomic mechanics”, Phys. Usp., 58:12 (2015), 1220–1222

Alexey V. Borisov, Yury L. Karavaev, Ivan S. Mamaev, Nadezhda N. Erdakova, Tatyana B. Ivanova, Valery V. Tarasov, “Experimental Investigation of the Motion of a Body with an Axisymmetric Base Sliding on a Rough Plane”, Regul. Chaotic Dyn., 20:5 (2015), 518–541

Alexander P. Ivanov, “On Final Motions of a Chaplygin Ball on a Rough Plane”, Regul. Chaotic Dyn., 21:78 (2016), 804–810

Zobova A.A., “A Review of Models of Distributed Dry Friction”, PmmJ. Appl. Math. Mech., 80:2 (2016), 141–148

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