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IssuesArchive of Issues2005-2pp.11-20

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Total articles in the database: 9121
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I. I. Argatov, "Equilibrium conditions for a rigid body on a rough plane in the case of axially symmetric distribution of normal pressures," Mech. Solids. 40 (2), 11-20 (2005)
Year 2005 Volume 40 Number 2 Pages 11-20
Title Equilibrium conditions for a rigid body on a rough plane in the case of axially symmetric distribution of normal pressures
Author(s) I. I. Argatov (St. Petersburg)
Abstract The issue of determining the conditions for limiting equilibrium of a rigid body based on a rough surface is studied. The distribution of the normal pressures is assumed to be axially symmetric. Friction forces obey the Amonton-Coulomb law. The solution is obtained within the framework of Zhukovskii's theory. The concept of the limiting equilibrium curve is introduced and the convexity of this curve is proved. A sufficient equilibrium condition is established. The deceleration of a disk moving along a rough surface is considered under the assumption that the distributions of mass and normal pressures over the body are axially symmetric. It is shown that the linear and angular velocities of the disk vanish simultaneously.
References
1.  N. N. Shiller, "Note on the equilibrium of a rigid body under the action of friction on a part of its surface," Trudy Otdeleniya Fizicheskikh Nauk Obshschestva Lyubitelei Estestvoznaniya," Vol. 5, No. 1, pp. 1-5, 1892.
2.  N. E. Zhukovskii, "An equilibrium condition for a rigid body based on a fixed plane by an area and able to move along this plane with friction," in N. E. Zhukovskii, Collected Works [in Russian], Vol. 1, pp. 339-354, Fizmatgiz, Moscow, Leningrad, 1949.
3.  A. I. Lur'e, Analytical Mechanics [in Russian], Fizmatgiz, Moscow, 1961.
4.  I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Series, Sums, and Products [in Russian], Fizmatgiz, Moscow, 1961.
5.  A. L. Mozhevitinov, S. A. Kuz'min, and A. F. Popov, "Analysis of the resistance of structures to shift by an eccentric force," Izv. VNIIG, Vol. 95, pp. 70-76, 1971.
6.  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.
7.  A. Yu. Ishlinskii, B. N. Sokolov, and F. L. Chernousko, "On the motion of flat bodies under the action of dry friction," Izv. AN SSSR. MTT [Mechanics of Solids], No. 4, pp. 17-28, 1981.
8.  V. F. Zhuravlev, "On the model of dry friction for rolling of rigid bodies," PMM [Applied Mathematics and Mechanics], Vol. 62, No. 5, pp. 762-767, 1998.
9.  A. A. Kireenkov, "On the motion of a homogeneous rotating disk along a plane in the case of combined friction," Izv. AN. MTT [Mechanics of Solids], No. 1, pp. 65-67, 2002.
10.  N. P. Erugin, A Book for Reading on the General Course in Differential Equations [in Russian], Nauka i Tekhnika, Minsk, 1970.
11.  N. N. Dmitriev, "On the motion of flat bodies along a surface under the action of anisotropic dry friction," No. 8143-B88, VINITI, Moscow, 1988.
Received 22 May 2003
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