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Nelin. Dinam., 2015, Volume 11, Number 1, Pages 99–116 (Mi nd467)  

This article is cited in 3 scientific papers (total in 3 papers)

On the stability of the specific motions of a heavy rigid body due to fast vertical vibrations of one of its points

Olga V. Kholostova

Moscow Aviation Institute (National Research University), Volokolamskoe Shosse, 4, GSP-3, A-80, Moscow, 125993, Russia

Abstract: We consider the motion of a heavy rigid body with one point performing the specified high-frequency harmonic oscillations along the vertical. In the framework of an approximate autonomous system of differential equations of motion two new types of permanent rotations of the body about the vertical are found. These motions are affected by presence of fast vibrations and do not exist in the case of a body with a fixed point. The problem of stability of the motions is investigated.

Keywords: rigid body, fast vibrations, permanent rotations, stability, resonance.

Funding Agency Grant Number
Russian Science Foundation 14-21-00068


Full text: PDF file (363 kB)
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Document Type: Article
UDC: 531.36
MSC: 70E17, 70E20,70H14
Received: 22.10.2014
Revised: 16.12.2014

Citation: Olga V. Kholostova, “On the stability of the specific motions of a heavy rigid body due to fast vertical vibrations of one of its points”, Nelin. Dinam., 11:1 (2015), 99–116

Citation in format AMSBIB
\Bibitem{Kho15}
\by Olga~V.~Kholostova
\paper On the stability of the specific motions of a heavy rigid body due to fast vertical vibrations of one of its points
\jour Nelin. Dinam.
\yr 2015
\vol 11
\issue 1
\pages 99--116
\mathnet{http://mi.mathnet.ru/nd467}
\elib{http://elibrary.ru/item.asp?id=23051491}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. E. A. Vishenkova, “Ob ustoichivosti chastnykh reshenii priblizhennykh uravnenii dvizheniya tyazhelogo tverdogo tela s vibriruyuschei tochkoi podvesa”, Nelineinaya dinam., 11:3 (2015), 459–474  mathnet
    2. E. A. Vishenkova, O. V. Kholostova, “O vliyanii vertikalnykh vibratsii na ustoichivost permanentnykh vraschenii tverdogo tela vokrug osei, lezhaschikh v glavnoi ploskosti inertsii”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 27:1 (2017), 98–120  mathnet  crossref  elib
    3. E. A. Vishenkova, O. V. Kholostova, “Issledovanie permanentnykh vraschenii tyazhelogo dinamicheski simmetrichnogo tverdogo tela s vibriruyuschei tochkoi podvesa”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 27:4 (2017), 590–607  mathnet  crossref  elib
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