Mechanics of Solids (about journal) 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

Russian Russian English English About Journal | Issues | Guidelines | Editorial Board | Contact Us
 


IssuesArchive of Issues2022-8pp.1805-1818

Archive of Issues

Total articles in the database: 12854
In Russian (Èçâ. ÐÀÍ. ÌÒÒ): 8044
In English (Mech. Solids): 4810

<< Previous article | Volume 57, Issue 8 / 2022 | Next article >>
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 2022Revised 20 July 2022Accepted 20 July 2022
Link to Fulltext
<< Previous article | Volume 57, Issue 8 / 2022 | Next article >>
Orphus SystemIf you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter

101 Vernadsky Avenue, Bldg 1, Room 246, 119526 Moscow, Russia (+7 495) 434-3538 mechsol@ipmnet.ru https://mtt.ipmnet.ru
Founders: Russian Academy of Sciences, Ishlinsky Institute for Problems in Mechanics RAS
© Mechanics of Solids
webmaster
Rambler's Top100