 | | 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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| << Previous article | Volume 58, Issue 6 / 2023 | Next article >> |
| V.N. Tkhai, "A Family of Oscillations Connecting Stable and Unstable Permanent Rotations of a Heavy Solid with a Fixed Point," Mech. Solids. 58 (6), 2067-2079 (2023) |
| Year |
2023 |
Volume |
58 |
Number |
6 |
Pages |
2067-2079 |
| DOI |
10.3103/S0025654423600800 |
| Title |
A Family of Oscillations Connecting Stable and Unstable Permanent Rotations of a Heavy Solid with a Fixed Point |
| Author(s) |
V.N. Tkhai (V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow, 117997 Russia, tkhaivn@yandex.ru) |
| Abstract |
The rotation of a heavy rigid body around a fixed point is investigated if the center of gravity belongs to the main plane of the ellipsoid of inertia. A reduction of the system of Euler-Poisson equations to a reversible conservative system with two degrees of freedom is given, and a bifurcation analysis of permanent rotations is carried out. Global families of periodic motions are found that connect stable and unstable permanent rotations of the same frequency. It is proved that non-degenerate symmetric periodic motion in a reversible mechanical system always continues to the global family. |
| Keywords |
heavy rigid body with a fixed point, reversibility, permanent rotations, reduction, bifurcation, Lyapunov family, global continuation, oscillations of a rotating body |
| Received |
28 February 2023 | Revised |
18 March 2023 | Accepted |
10 May 2023 |
| Link to Fulltext |
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