Abstract:
Consider an interval on a horizontal line with random roughness. With probability one it is supported at two points: one on the left, and another on the right from its center. We compute the probability distribution of the support points provided the roughness is fine grained. We also solve an analogous problem where a circle or a disk lies on a rough plane. Some applications in static are given.
Keywords:
rigid body, support with random roughness.
The research is supported by the grants NSh-2519.2012.1, RFBR grant 12-01-00441-a, the
program of Russian Academy of Science “Dynamical systems and Control theory”, and the OFI-m
grant 13-01-12462.
\Bibitem{BurTre14}
\by Daniil~Burlakov, Dmitry Treschev
\paper A Rigid Body on a Surface with Random Roughness
\jour Regul. Chaotic Dyn.
\yr 2014
\vol 19
\issue 3
\pages 296--309
\mathnet{http://mi.mathnet.ru/rcd148}
\crossref{https://doi.org/10.1134/S1560354714030034}
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\zmath{https://zbmath.org/?q=an:1309.70006}
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Linking options:
https://www.mathnet.ru/eng/rcd148
https://www.mathnet.ru/eng/rcd/v19/i3/p296
This publication is cited in the following 5 articles:
Alexey V. Borisov, Ivan S. Mamaev, Nadezhda N. Erdakova, “Dynamics of a body sliding on a rough plane and supported at three points”, Theor. Appl. Mech., 43:2 (2016), 169–190
A. A. Zobova, “A review of models of distributed dry friction”, J. Appl. Math. Mech., 80:2 (2016), 141–148
Yu. L. Karavaev, A. A. Kilin, “Dinamika sferorobota s vnutrennei omnikolesnoi platformoi”, Nelineinaya dinam., 11:1 (2015), 187–204
Yury L. Karavaev, Alexander A. Kilin, “The Dynamics and Control of a Spherical Robot with an Internal Omniwheel Platform”, Regul. Chaotic Dyn., 20:2 (2015), 134–152
Vladimir Dragović, Borislav Gajić, “Four-Dimensional Generalization of the Grioli Precession”, Regul. Chaotic Dyn., 19:6 (2014), 656–662
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