 | | 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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| Markeev A.P., "Evolution of motion of a solid suspended on a thread in a homogeneous gravity field," Mech. Solids. 56 (3), 320-325 (2021) |
| Year |
2021 |
Volume |
56 |
Number |
3 |
Pages |
320-325 |
| DOI |
10.3103/S0025654421030080 |
| Title |
Evolution of motion of a solid suspended on a thread in a homogeneous gravity field |
| Author(s) |
Markeev A.P. (Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow, 119526 Russia; Moscow Aviation Institute (National Research University), Moscow, 125993 Russia, anat-markeev@mail.ru) |
| Abstract |
The plane motion of a solid in a uniform gravity field is studied. The solid is suspended on
a weightless inextensible thread, which remains stretched during the motion. It is assumed that the length of the thread is large (~ε−1/2) and the distance from the point of solid suspension to its center of gravity is small (~ε). The equations of motion are presented as equations of a system with one rapidly rotating phase. This system is analyzed using classical perturbation theory and KAM theory. It is shown that for all values of time, the movement differs little (by ~ε) from the slow oscillations of the thread in the vicinity of the descending vertical and the solid rotation relative to the suspension point with an almost constant angular velocity. The measure of the set of motions, different from the above motions, is estimated from above by the value of the order of exp(−c/ε) (c>0=const). |
| Keywords |
Hamilton system, pendulum, oscillations, rotations, stability |
| Received |
25 April 2020 | Revised |
25 July 2020 | Accepted |
07 August 2020 |
| Link to Fulltext |
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