 | | 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: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
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| In English (Mech. Solids): | | 3212 |
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| << Previous article | Volume 54, Issue 5 / 2019 | Next article >> |
| A.S. Sumbatov, "On Rolling of a Heavy Disk on a Surface of Revolution with Negative Curvature," Mech. Solids. 54 (5), 638-651 (2019) |
| Year |
2019 |
Volume |
54 |
Number |
5 |
Pages |
638-651 |
| DOI |
10.3103/S0025654419050182 |
| Title |
On Rolling of a Heavy Disk on a Surface of Revolution with Negative Curvature |
| Author(s) |
A.S. Sumbatov (Dorodnitsyn Computing Center, Informatics and Control Federal Research Center, Russian Academy of Sciences, Moscow, 119333 Russia, sumbatow@ccas.ru) |
| Abstract |
In the problem on rolling of a heavy round homogeneous disk on a surface of revolution
with a negative Gaussian curvature, the classical nonholonomic model is used in which, at each
moment, the instantaneous velocity of the current drive point of the disk touching the support is zero.
Stationary motions of the disk are found. We note that, within the nonholonomic model the tangential
component of the reacton for a stationary motion can be larger than the pressure force. This means
that such motion in practice cannot be implemented or observed if we assume that the force that provides the no-slip condition is the dry friction force with a coefficient between zero and unity. For stationary motions of the disk the conditions of the stability in the first approximation are obtained. The
results of the numerical simulation of the rolling motion of the disk without slip while the mechanical
energy dissipation occurs, are presented. The purpose of these studies was to verify the adequacy of the
assumed nonholonomic model of coin movements observed in practice in the entertaining coinboxes
of the plastic funnel type. |
| Keywords |
surface of revolution, Gaussian curvature, nonholonomic model, stationary motions, stability, energy dissipation |
| Received |
02 November 2018 | Revised |
06 December 2018 | Accepted |
25 December 2018 |
| Link to Fulltext |
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