This article is cited in 1 scientific paper (total in 1 paper)
Dynamics of the Suslov problem in a gravitational field: reversal and strange attractors
I. A. Bizyaeva, A. V. Borisova, A. O. Kazakovbcd
a Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
b Udmurt State University, Universitetskaya 1, Izhevsk, 426034 Russia
c Lobachevsky State University of Nizhny Novgorod, 23 Prospekt Gagarina, Nizhny Novgorod, 603950, Russia
d Higher School of Economics National Research University, 25/12 Bolshaya Pecherskaya St., Nizhny Novgorod, 603155, Russia
In this paper, we present some results on chaotic dynamics in the Suslov problem which describe the motion of a heavy rigid body with a fixed point, subject to a nonholonomic constraint, which is expressed by the condition that the projection of angular velocity onto the body-fixed axis is equal to zero. Depending on the system parameters, we find cases of regular (in particular, integrable) behavior and detect various attracting sets (including strange attractors) that are typical of dissipative systems.We construct a chart of regimes with regions characterizing chaotic and regular regimes depending on the degree of conservativeness. We examine in detail the effect of reversal, which was observed previously in the motion of rattlebacks.
Suslov problem, nonholonomic constraint, reversal, strange attractor
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Regul. Chaotic Dyn., 2015, 20:5, 605–626
517.925 + 517.93
MSC: 37J60, 37N15, 37G35, 70E18, 70F25, 70H45
I. A. Bizyaev, A. V. Borisov, A. O. Kazakov, “Dynamics of the Suslov problem in a gravitational field: reversal and strange attractors”, Nelin. Dinam., 12:2 (2016), 263–287; Regul. Chaotic Dyn., 20:5 (2015), 605–626
Citation in format AMSBIB
\by I.~A.~Bizyaev, A.~V.~Borisov, A.~O.~Kazakov
\paper Dynamics of the Suslov problem in a gravitational field: reversal and strange attractors
\jour Nelin. Dinam.
\jour Regul. Chaotic Dyn.
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This publication is cited in the following articles:
A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, “Dynamical systems with non-integrable constraints, vakonomic mechanics, sub-Riemannian geometry, and non-holonomic mechanics”, Russian Math. Surveys, 72:5 (2017), 783–840
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