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IssuesArchive of Issues2003-4pp.59-63

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A. P. Ivanov, "On the motion of planar bodies in the presence of static friction," Mech. Solids. 38 (4), 59-63 (2003)
Year 2003 Volume 38 Number 4 Pages 59-63
Title On the motion of planar bodies in the presence of static friction
Author(s) A. P. Ivanov (Moscow)
Abstract A planar body in a state of rest on a rough plane is considered. When acted upon by external forces, the body can start sliding along the plain or preserve equilibrium owing to friction. The problem is to determine the distribution of accelerations in the body for a prescribed system of forces. The solution of this problem is shown to be uniquely defined. An example of a rod with lumped masses at the endpoints is considered. Dynamics of systems with dry friction has been studied previously in [1-5]. Equilibrium conditions for the body have been obtained for a number of specific cases [6-8].
References
1.  P. Painlevé, Lectures on Friction [Russian translation]. Gostekhizdat, Moscow, 1954.
2.  G. K. Pozharitskii, "Vanishing slips of mechanical systems with dry friction," PMM [Applied Mathematics and Mechanics], Vol. 29, No. 3, pp. 558-563, 1965.
3.  P. Contensou, "Relation between sliding friction and spinning friction as applied to the theory of a top," in Problems of Gyro Engineering [Russian translation], pp. 60-67, Mir, Moscow, 1967.
4.  A. Yu. Ishlinskii, B. N. Sokolov, and F. L. Chernousko, "On the motion of planar bodies in the presence of dry friction," Izv. AN SSSR. MTT [Mechanics of Solids], No. 4, pp. 17-28, 1980.
5.  V. Ph. Zhuravlev, "On the model of dry friction in the problem of rolling of rigid bodies," PMM [Applied Mathematics and Mechanics], Vol. 62, No. 5, pp. 762-767, 1998.
6.  N. E. Zhukovskii, "Equilibrium conditions for a rigid body based on a fixed plane with a certain area and able to move along this plane with friction," in N. E. Zhukovskii, Collected Works. Volume 1 [in Russian], pp. 339-354, Gostekhteorizdat, Moscow, Leningrad, 1949.
7.  F. L. Chernousko, "Equilibrium conditions for a body on a rough plane," Izv. AN SSSR. MTT [Mechanics of Solids], No. 6, pp. 6-17, 1988.
8.  A. S. Smyshlyaev and F. L. Chernousko, "Equilibrium conditions for a rod on a rough plane," PMM [Applied Mathematics and Mechanics], Vol. 66, No. 2, pp. 177-182, 2002.
Received 24 April 2003
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