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## Archive of Issues

Russia Moscow
Year
2012
Issue
4
Pages
125-139
 Section Mechanics Title On free movement of puck on horizontal plane Author(-s) Burlakov D.S.a, Seslavina A.A.a Affiliations Lomonosov Moscow State Universitya Abstract We consider the problem of a homogeneous direct cylinder of an arbitrary form (a puck) sliding on a horizontal surface under the action of dry friction forces. The surface contact spot of the cylinder coincides with its base. One of the central hypotheses in the work is the choice of a mathematical model of interaction between a small surface element of a puck and a plane. It is assumed, that the current effect is described by the Amonton-Coulomb's law of friction. In the present work the basic attention is given to the qualitative analysis of the equations of motion for systems, the one which allow to describe dynamics at small values of the system's kinetic energy (final dynamics). Qualitative properties of dynamics for arbitrary pucks are formulated and proved. We present examples illustrating the difference in final dynamics for pucks with round, centrosymmetrical and arbitrary bases on a rough surface. Keywords dry friction, Amontons-Coulomb law, puck, final dynamics, stability UDC 539.3 MSC 70F40, 70F35, 70E18 DOI 10.20537/vm120410 Received 15 September 2012 Language Russian Citation Burlakov D.S., Seslavina A.A. On free movement of puck on horizontal plane, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2012, issue 4, pp. 125-139. References Sal’nikova T.V., Treschev D.V., Gallyamov S.R. On the motion of free disc on the rough horizontal plane, Nelineinaya Dinamika, 2012, vol. 8, no. 1, pp. 83–101. Farkas Z., Bartels G., Unger T., Wolf D. Frictional coupling between sliding and spinning motion, Phys. Rev. Letters, 2003, vol. 90, no. 24, pp. 248–302. Ivanov A.P. Dynamic collaborative model of contact stress at the plane motion of a rigid body, Prikl. Mat. Mekh., 2009, vol. 73, no. 2, pp. 189–203. Rosenblat G.M. On the integration of the equation of motion of the body, based on a rough plane by three points, Doklady Akademii Nauk, Mekhanika, 2010, vol. 435, no. 4, pp. 475–478. Field P. On the motion of a disk with three supports on a rough plane, Phys. Rev. (Series I), 1912, vol. 35, pp. 177–184. Treschev D.V., Erdakova N.N., Ivanova T.B. On the final movement of cylindrical bodies on a rough plane, Nelineinaya Dinamika, 2012, vol. 8, no. 3, pp. 585–603. Full text