|
This article is cited in 12 scientific papers (total in 12 papers)
Regular and Chaotic Dynamics in the Rubber Model of a Chaplygin Top
Alexey V. Borisova, Alexey O. Kazakovb, Elena N. Pivovarovaa a Udmurt State University,
ul. Universitetskaya 1, Izhevsk, 426034 Russia
b National Research University Higher School of Economics,
ul. Bolshaya Pecherskaya 25/12, Nizhny Novgorod, 603155 Russia
Abstract:
This paper is concerned with the rolling motion of a dynamically asymmetric unbalanced ball (Chaplygin top) in a gravitational field on a plane under the assumption that there is no slipping and spinning at the point of contact. We give a description of strange attractors existing in the system and discuss in detail the scenario of how one of them arises via a sequence of period-doubling bifurcations. In addition, we analyze the dynamics of the system in absolute space and show that in the presence of strange attractors in the system the behavior of the point of contact considerably depends on the characteristics of the attractor and can be both chaotic and nearly quasi-periodic.
Keywords:
Chaplygin top, nonholonomic constraint, rubber model, strange attractor, bifurcation, trajectory of the point of contact.
Received: 21.11.2016 Accepted: 06.12.2016
Citation:
Alexey V. Borisov, Alexey O. Kazakov, Elena N. Pivovarova, “Regular and Chaotic Dynamics in the Rubber Model of a Chaplygin Top”, Regul. Chaotic Dyn., 21:7-8 (2016), 885–901
Linking options:
https://www.mathnet.ru/eng/rcd234 https://www.mathnet.ru/eng/rcd/v21/i7/p885
|
|