 | | 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: | | 11262 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
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| In English (Mech. Solids): | | 3251 |
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| A.P. Markeev, "On the Nonlinear Oscillations of a Triaxial Ellipsoid on a Smooth Horizontal Plane," Mech. Solids. 57 (8), 1805-1818 (2022) |
| Year |
2022 |
Volume |
57 |
Number |
8 |
Pages |
1805-1818 |
| DOI |
10.3103/S0025654422080209 |
| Title |
On the Nonlinear Oscillations of a Triaxial Ellipsoid on a Smooth Horizontal Plane |
| Author(s) |
A.P. Markeev (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, 119526 Russia; Moscow Aviation Institute (National Research University), Moscow, 125993 Russia, anat-markeev@mail.ru) |
| Abstract |
The motion of a homogeneous ellipsoid on a fixed horizontal plane in a uniform gravity
field is considered. The plane is considered to be perfectly smooth and the semiaxes of the ellipsoid
are different. There is a position of stable equilibrium, when the ellipsoid rests on the plane with the
lowest point of its surface. The nonlinear oscillations of the ellipsoid in the vicinity of this equilibrium
are studied. Analysis is performed using the methods of the classical perturbation theory, the Kolmogorov–Arnold–Moser (KAM) theory, and computer algebra algorithms. The normal form of the
Hamiltonian function of the perturbed motion is obtained including the terms of the sixth degree relative to deviations from the equilibrium position. An approximate analytical representation of the
Kolmogorov set of conditionally periodic oscillations and an estimate of the measure of this set are
presented. The problem of the existence and orbital stability of periodic motions occurring from the
stable equilibrium in the resonant and nonresonant cases is studied. |
| Keywords |
rigid body, conditionally periodic and periodic oscillations, stability |
| Received |
30 May 2022 | Revised |
20 July 2022 | Accepted |
20 July 2022 |
| Link to Fulltext |
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