This article is cited in 1 scientific paper (total in 1 paper)
Regular and chaotic attractors in the nonholonomic model of Chapygin’s ball
Alexey V. Borisova, Alexey O. Kazakovb, Igor R. Sataevc
a Udmurt State University, Universitetskaya 1, Izhevsk, 426034, Russia
b Lobachevsky State University of Nizhny Novgorod, 23 Prospekt Gagarina, Nizhny Novgorod, 603950, Russia
c Saratov Branch of Kotelnikov’s Institute of Radio-Engineering and Electronics of RAS, Zelenaya st. 38, Saratov, 410019, Russia
We study both analytically and numerically the dynamics of an inhomogeneous ball on a rough horizontal plane under the infuence of gravity. A nonholonomic constraint of zero velocity at the point of contact of the ball with the plane is imposed. In the case of an arbitrary displacement of the center of mass of the ball, the system is nonintegrable without the property of phase volume conservation. We show that at certain parameter values the unbalanced ball exhibits the effect of reversal (the direction of the ball rotation reverses). Charts of dynamical regimes on the parameter plane are presented. The system under consideration exhibits diverse chaotic dynamics, in particular, the figure-eight chaotic attractor, which is a special type of pseudohyperbolic chaos.
Chaplygin’s top, rolling without slipping, reversibility, involution, integrability, reverse, chart of dynamical regimes, strange attractor.
PDF file (1334 kB)
MSC: 37J60, 37N15, 37G35, 70E18, 70F25, 70H45
Alexey V. Borisov, Alexey O. Kazakov, Igor R. Sataev, “Regular and chaotic attractors in the nonholonomic model of Chapygin’s ball”, Nelin. Dinam., 10:3 (2014), 361–380
Citation in format AMSBIB
\by Alexey~V.~Borisov, Alexey~O.~Kazakov, Igor~R.~Sataev
\paper Regular and chaotic attractors in the nonholonomic model of Chapygin’s ball
\jour Nelin. Dinam.
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This publication is cited in the following articles:
I. R. Sataev, A. O. Kazakov, “Stsenarii perekhoda k khaosu v negolonomnoi modeli volchka Chaplygina”, Nelineinaya dinam., 12:2 (2016), 235–250
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