Geodesic
Investigation of the influence of random perturbations on the dynamics of the system in the Suslov problem
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 73 (2021), pp. 17-29

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The paper considers the generalized Suslov problem with variable parameters and the influence of random perturbations on the dynamics of the system under consideration. The physical meaning of the Suslov problem is Chaplygin's sleigh, which moves along the inner side of the circle. In the case of a deterministic system, a brief review of the previously obtained results is made, the presence of chaotic dynamics in the system and such effects as the appearance of a strange attractor and noncompact (escaping) trajectories is shown. Moreover, the latter may indicate a possible acceleration in the system. The appearance of chaotic strange attractors occurs due to a cascade of bifurcations of doubling the period. We also consider the dynamics of a perturbed system which arises due to the addition of «white noise» modeled by the Wiener process to one of the equations. Changes in the dynamics of a perturbed system compared to an unperturbed one are studied: chaotization of periodic regimes, the appearance of noncompact trajectories, and the premature destruction of strange attractors. In this paper, phase portraits, maps for the period, graphs of system solutions, and a chart of dynamical regimes are constructed using the Maple software package and the software package «Computer Dynamics: Chaos» (/http://site4.ics.org.ru//chaos_pack).
Keywords: nonholonomic system, Suslov problem, strange attractor, stochastic differential equation.
Mots-clés : random perturbations 
@article{VTGU_2021_73_a1,
     author = {E. A. Mikishanina},
     title = {Investigation of the influence of random perturbations on the dynamics of the system in the {Suslov} problem},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {17--29},
     publisher = {mathdoc},
     number = {73},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2021_73_a1/}
}
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E. A. Mikishanina. Investigation of the influence of random perturbations on the dynamics of the system in the Suslov problem. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 73 (2021), pp. 17-29. http://geodesic.mathdoc.fr/item/VTGU_2021_73_a1/