 | | 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
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| V.Yu.Ol'shanskii, "Semi-Regular Precession of an Asymmetrical Rigid Solid Body Filled with a Liquid," Mech. Solids. 56 (8), 1500-1513 (2021) |
| Year |
2021 |
Volume |
56 |
Number |
8 |
Pages |
1500-1513 |
| DOI |
10.3103/S0025654421080148 |
| Title |
Semi-Regular Precession of an Asymmetrical Rigid Solid Body Filled with a Liquid |
| Author(s) |
V.Yu.Ol'shanskii (Institute of Precision Mechanics and Control, Russian Academy of Sciences, Saratov, Russia, olshanskiy_vlad@mail.ru) |
| Abstract |
The Poincaré–Zhukovsky equations are used to describe the rotation of a rigid body with an
ellipsoidal cavity filled with an ideal incompressible liquid. We obtain the relationships (called configurational conditions) between the inertia moments of a solid and a cavity with a liquid, at which the
solid can perform semi-regular precession when the precession rate is constant and the rate of its
proper rotation changes with time. When the axis of its proper rotation coincides with the principal
inertia axis, one condition is sufficient, but if the axes do not coincide, then there appear two configuration conditions. It is shown that, under the configuration conditions of semiregular precession, the
Poincaré–Zhukovsky equations have an invariant system of three linear functions. Analysis of the
configuration conditions for systems close to spherically symmetric is carried out. |
| Keywords |
liquid-filled rigid body, Poincaré–Zhukovsky equations, semiregular precession |
| Received |
10 January 2021 | Revised |
16 February 2021 | Accepted |
05 March 2021 |
| Link to Fulltext |
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