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
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.
integrable system, system with a discontinuous right-hand side, nonholonomic constraint, bifurcation diagram, body of revolution, sharp edge, wheel, rubber model
|Russian Science Foundation
|This research was carried out at the Steklov Mathematical Institute of the Russian Academy of Sciences and was supported by the Russian Science Foundation (project 14-50-00005).
MSC: 70E15, 70E18, 70E40, 37Jxx
Alexander A. Kilin, Elena N. Pivovarova, “Integrable Nonsmooth Nonholonomic Dynamics of a Rubber Wheel with Sharp Edges”, Regul. Chaotic Dyn., 23:7-8 (2018), 887–907
Citation in format AMSBIB
\by Alexander A. Kilin, Elena N. Pivovarova
\paper Integrable Nonsmooth Nonholonomic Dynamics of a Rubber Wheel with Sharp Edges
\jour Regul. Chaotic Dyn.
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