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Russia Nizhni Novgorod
Section  Mechanics 
Title  On stability of the Chaplygin ball motion on a plane with an arbitrary friction law 
Author(s)  Ovsyannikov I.I.^{a} 
Affiliations  Research Institute for Applied Mathematics and Cybernetics, Nizhni Novgorod State University^{a} 
Abstract  The Chaplygin ball on a plane is considered under the action of the friction force which satisfies the following condition: $({\bf F}, {\bf u}) < 0$ as ${\bf u} \neq 0$ and ${\bf F} = 0$ as ${\bf u} = 0$, where ${\bf u}$ is the gliding velocity. The ball is supposed to have a point contact with the supporting plane (this means that the contact spot is absent and also there is no rotation friction torque). The main task of the paper is to determine a set of possible stationary (or final) motions and their stability. In the current paper it is shown that exactly three stationary motions are possible; these motions represent straightline uniform rolling motions of the ball without sliding, at that the ball is rotating around one of the primary axes of the inertia tensor. Rotation around the axis of the greatest moment of inertia is stable, around the middle one and the lowest one it is unstable. 
Keywords  Chaplygin ball, stationary motions, stability 
UDC  531.011 
MSC  37N15, 70E18, 70K20 
DOI  10.20537/vm120411 
Received  24 September 2012 
Language  Russian 
Citation  Ovsyannikov I.I. On stability of the Chaplygin ball motion on a plane with an arbitrary friction law, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2012, issue 4, pp. 140145. 
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