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Russian Academy of Sciences
in January 1936
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IssuesArchive of Issues2009-6pp.623-630

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Total articles in the database: 1813
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A.A. Zobova and A.V. Karapetyan, "Analysis of the steady motions of the tippe top," J. Appl. Math. Mech. 73 (6), 623-630 (2009)
Year 2009 Volume 73 Issue 6 Pages 623-630
Title Analysis of the steady motions of the tippe top
Author(s) A.A. Zobova (Moscow, Russia,
A.V. Karapetyan (Moscow, Russia)
Abstract The motion of the tippe top on a horizontal plane is considered taking into account sliding friction within the Contensou model. The tippe top is modelled by two spherical segments rigidly joined by a rod directed along the common axis of symmetry of the segments. The dimensions of the spherical segments and the rod are chosen so that, as the axis of symmetry deviates from the upward vertical, the tippe top is supported on the plane at a point on one segment up to a certain critical value and at a point on the other segment at larger deviations (at points on both segments at the critical value). The motion of the tippe top is described by different equations in different regions of configuration space, and the motion is accompanied by impacts on the boundary of these regions. An effective potential of the system is constructed, and the type of its critical points is investigated. Poincaré-Chetayev bifurcation diagrams and generalized Smale diagrams are constructed for steady motions. Plots of the steady-state precessional motions have a discontinuity on the boundary between the regions indicated.
Received 23 March 2009
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