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ЖУРНАЛЫ // Regular and Chaotic Dynamics // Архив

Regul. Chaotic Dyn., 2018, том 23, выпуск 7-8, страницы 887–907 (Mi rcd373)

Эта публикация цитируется в 4 статьях

Integrable Nonsmooth Nonholonomic Dynamics of a Rubber Wheel with Sharp Edges

Alexander A. Kilin, Elena N. Pivovarova

Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia

Аннотация: This paper is concerned with the dynamics of a wheel with sharp edges moving on a horizontal plane without slipping and rotation about the vertical (nonholonomic rubber model). The wheel is a body of revolution and has the form of a ball symmetrically truncated on both sides. This problem is described by a system of differential equations with a discontinuous right-hand side. It is shown that this system is integrable and reduces to quadratures. Partial solutions are found which correspond to fixed points of the reduced system. A bifurcation analysis and a classification of possible types of the wheel’s motion depending on the system parameters are presented.

Ключевые слова: integrable system, system with a discontinuous right-hand side, nonholonomic constraint, bifurcation diagram, body of revolution, sharp edge, wheel, rubber model.

MSC: 70E15, 70E18, 70E40, 37Jxx

Поступила в редакцию: 12.10.2018
Принята в печать: 03.12.2018

Язык публикации: английский

DOI: 10.1134/S1560354718070067



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