Abstract:
This paper is concerned with the dynamics of a wheel with sharp edges moving on a horizontal plane without slipping and rotation about the vertical (nonholonomic rubber model). The wheel is a body of revolution and has the form of a ball symmetrically truncated on both sides. This problem is described by a system of differential equations with a discontinuous right-hand side. It is shown that this system is integrable and reduces to quadratures. Partial solutions are found which correspond to fixed points of the reduced system. A bifurcation analysis and a classification of possible types of the wheel’s motion depending on the system parameters are presented.
Keywords:
integrable system, system with a discontinuous right-hand side, nonholonomic constraint, bifurcation diagram, body of revolution, sharp edge, wheel, rubber model.
This research was carried out at the Steklov Mathematical Institute of the Russian Academy of Sciences and was supported by the Russian Science Foundation (project 14-50-00005).
Citation:
Alexander A. Kilin, Elena N. Pivovarova, “Integrable Nonsmooth Nonholonomic Dynamics of a Rubber Wheel with Sharp Edges”, Regul. Chaotic Dyn., 23:7-8 (2018), 887–907
\Bibitem{KilPiv18}
\by Alexander A. Kilin, Elena N. Pivovarova
\paper Integrable Nonsmooth Nonholonomic Dynamics of a Rubber Wheel with Sharp Edges
\jour Regul. Chaotic Dyn.
\yr 2018
\vol 23
\issue 7-8
\pages 887--907
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Linking options:
https://www.mathnet.ru/eng/rcd373
https://www.mathnet.ru/eng/rcd/v23/i7/p887
This publication is cited in the following 4 articles:
Ivan A. Bizyaev, Ivan S. Mamaev, “Permanent Rotations in Nonholonomic Mechanics.
Omnirotational Ellipsoid”, Regul. Chaotic Dyn., 27:6 (2022), 587–612
Elizaveta M. Artemova, Yury L. Karavaev, Ivan S. Mamaev, Evgeny V. Vetchanin, “Dynamics of a Spherical Robot with Variable Moments of Inertia and a Displaced Center of Mass”, Regul. Chaotic Dyn., 25:6 (2020), 689–706
Alexander A. Kilin, Elena N. Pivovarova, “Qualitative Analysis of the Nonholonomic Rolling of a Rubber Wheel with Sharp Edges”, Regul. Chaotic Dyn., 24:2 (2019), 212–233
A. V. Borisov, A. V. Tsyganov, “Vliyanie effektov Barnetta-Londona i Einshteina-de Gaaza na dvizhenie negolonomnoi sfery Rausa”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 29:4 (2019), 583–598
Citation in format AMSBIB
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