 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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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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