 | | 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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| A.A. Burov, V.I. Nikonov, and E.S. Shalimova, "On the Motion of a Point Particle on a Homogeneous Gravitating Ball with a Spherical Cavity in the Presence of Dry Friction," Mech. Solids. 56 (8), 1587-1598 (2021) |
| Year |
2021 |
Volume |
56 |
Number |
8 |
Pages |
1587-1598 |
| DOI |
10.3103/S0025654421080045 |
| Title |
On the Motion of a Point Particle on a Homogeneous Gravitating Ball with a Spherical Cavity in the Presence of Dry Friction |
| Author(s) |
A.A. Burov (Federal Research Center “Computer Science and Control,” Russian Academy of Sciences, Moscow, Russia; National Research University Higher School of Economics, Moscow, Russia, jtm@narod.ru)
V.I. Nikonov (Federal Research Center “Computer Science and Control,” Russian Academy of Sciences, Moscow, Russia; National Research University Higher School of Economics, Moscow, Russia, nikon_v@list.ru)
E.S. Shalimova (Moscow State University, Moscow, Russia, ekateryna-shalimova@yandex.ru) |
| Abstract |
The problem of motion of a point particle on the surface of a homogeneous gravitating ball with a spherical cavity is considered. It is assumed that the body rotates uniformly around its axis of symmetry. At the same time, it is assumed that a particle located on the outer or inner (inside the cavity) surface of the body, in addition to the force of gravity, is affected by dry friction. The gravitational properties inside the cavity and outside the ball are described. The dependence of the existence, bifurcations, and stability of the relative equilibria of a point particle on the outer or inner body surface on the parameters of the problem is studied. The results obtained both analytically and numerically are presented in the form of bifurcation diagrams. The research is motivated by the possible existence of cavities or mass concentrations (mascons) in large and small celestial bodies. |
| Keywords |
dynamics on the surfaces of celestial bodies, celestial bodies with cavities, relative equilibria, dry friction, motion of a point particle in a noncentral gravitational field, generalization of a gravitating dumbbell |
| Received |
31 December 2020 | Revised |
10 March 2021 | Accepted |
15 March 2021 |
| Link to Fulltext |
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