 | | Journal of Applied
Mathematics and Mechanics
Russian Academy of Sciences | | Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
(print version) |
Archive of Issues
| Total articles in the database: | | 10512 |
| In Russian (ΟΜΜ): | | 9713
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| In English (J. Appl. Math. Mech.): | | 799 |
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| << Previous article | Volume 79, Issue 1 / 2015 | Next article >> |
| Yu.P. Bychkov, "The rolling of a body with a rotor on a moving supporting sphere," J. Appl. Math. Mech. 79 (1), 71-80 (2015) |
| Year |
2015 |
Volume |
79 |
Issue |
1 |
Pages |
71-80 |
| DOI |
10.1016/j.jappmathmech.2015.04.020 |
| Title |
The rolling of a body with a rotor on a moving supporting sphere |
| Author(s) |
Yu.P. Bychkov (Moscow, Russia) |
| Abstract |
The rolling without slipping of a body with a rotor on a mobile supporting sphere in a uniform gravitational field is considered. The boundary of the body in the contact area with the support is part of a spherical surface. The central ellipsoid of inertia of the system (body + rotor) is an ellipsoid of revolution, the axis of which passes through the geometrical centre of the sphere, not, generally speaking, coinciding with the system mass centre. The supporting sphere is displaced translationally in an arbitrary way and is rotated around a vertical axis. The complete system of equations of motion of the supporting body and the rotor is obtained. Two integral equations of motion are obtained in the case of a solid of revolution. In the case when the body is a homogeneous sphere, four integral equations of motion are obtained, where the coordinates of the point of contact of the sphere and the supporting sphere are determined by quadratures, and all possible trajectories of the point of contact of the sphere and the body are indicated. |
| Received |
15 September 2014 |
| Link to Fulltext |
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