Geodesic
Regular and chaotic dynamics in the rubber model of a Chaplygin top
Russian journal of nonlinear dynamics, Tome 13 (2017) no. 2, pp. 277-297

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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 perioddoubling 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, trajectory of the point of contact.
Mots-clés : bifurcation 
@article{ND_2017_13_2_a8,
     author = {A. V. Borisov and A. O. Kazakov and E. N. Pivovarova},
     title = {Regular and chaotic dynamics in the rubber model of a {Chaplygin} top},
     journal = {Russian journal of nonlinear dynamics},
     pages = {277--297},
     publisher = {mathdoc},
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     number = {2},
     year = {2017},
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     url = {http://geodesic.mathdoc.fr/item/ND_2017_13_2_a8/}
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A. V. Borisov; A. O. Kazakov; E. N. Pivovarova. Regular and chaotic dynamics in the rubber model of a Chaplygin top. Russian journal of nonlinear dynamics, Tome 13 (2017) no. 2, pp. 277-297. http://geodesic.mathdoc.fr/item/ND_2017_13_2_a8/