 | | 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: | | 12882 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8071
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| In English (Mech. Solids): | | 4811 |
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| G.M. Rosenblat, "On the Equilibrium of a Solid Supported by a Single Point on a Rigid Plane," Mech. Solids. 58 (6), 1929-1945 (2023) |
| Year |
2023 |
Volume |
58 |
Number |
6 |
Pages |
1929-1945 |
| DOI |
10.3103/S0025654422601525 |
| Title |
On the Equilibrium of a Solid Supported by a Single Point on a Rigid Plane |
| Author(s) |
G.M. Rosenblat (Moscow Automobile and Road State Technical University (MADI), Moscow, 125319 Russia, gr51@mail.ru) |
| Abstract |
The problem of possible and obligatory (in the sense of Jellett) equilibria of a rigid body, which is in contact with one of its points with a rigid plane and is under the action of an arbitrary system of forces, is considered. Mass distributions in the body (i.e., the central inertia tensor and the position of the body's center of mass relative to the fulcrum) are assumed to be arbitrary. At the point of contact of the body with the support, a one-way connection is realized and a dry friction force acts, obeying the classical Coulomb–Euler law. Necessary and sufficient conditions for mandatory equilibrium are obtained. These conditions are expressed by simple analytical formulas. A comparison is made with the corresponding results obtained earlier for a similar problem. The problem of possible and obligatory equilibria of a heavy ellipsoid on a rigid inclined plane is considered. All possible equilibrium positions of the ellipsoid are found, as well as conditions on the angle of inclination of the plane under which such equilibria are possible and mandatory. |
| Keywords |
dry friction, static equilibrium, point contact, mandatory equilibrium, one-way connection, ellipsoid |
| Received |
19 September 2022 | Revised |
19 October 2022 | Accepted |
20 October 2022 |
| Link to Fulltext |
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