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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2017, Volume 27, Issue 4, Pages 590–607 (Mi vuu611)  

This article is cited in 1 scientific paper (total in 1 paper)

MECHANICS

A study of permanent rotations of a heavy dynamically symmetric rigid body with a vibrating suspension point

E. A. Vishenkovaa, O. V. Kholostovabc

a Research and Production Company "Infosystem-35", ul. Tret'ya Mytishchinskaya, 16, bld. 37, Moscow, 129626, Russia
b Moscow Aviation Institute (National Research University), Volokolamskoe shosse, 4, Moscow, 125080, Russia
c Moscow Institute of Physics and Technology (State University), Institutskii per., 9, Dolgoprudnyi, Moscow oblast, 141700, Russia

Abstract: The motion of a dynamically symmetric rigid body in a uniform gravity field is considered for the case of vertical high-frequency harmonic oscillations of small amplitude of one of its points (the suspension point). The investigation is carried out within the framework of an approximate autonomous system of differential equations of motion written in the canonical Hamiltonian form. A detailed description of admissible arcs of permanent rotations of the body about vertical axes is given. Special cases of motions of the body are found which are caused by fast vibrations of the suspension point. One of these cases is studied when the rotation axis lies in the principal plane of inertia which does not contain the center of mass of the body and does not coincide with the equatorial plane of inertia. A complete nonlinear stability analysis of the corresponding equilibrium position of the two-degree-of-freedom system is carried out. For all admissible values of the three-dimensional parameter space, regions of linear stability are found. Cases of resonances of the third and fourth orders, as well as degeneration cases, are considered.

Keywords: Staude's permanent rotations, high-frequency oscillations, rigid body, dynamic symmetry, stability, resonance.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 3.3858.2017/4.6


DOI: https://doi.org/10.20537/vm170409

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Bibliographic databases:

UDC: 531.36, 531.38
MSC: 53A17, 70E20, 70E50
Received: 28.09.2017

Citation: E. A. Vishenkova, O. V. Kholostova, “A study of permanent rotations of a heavy dynamically symmetric rigid body with a vibrating suspension point”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 27:4 (2017), 590–607

Citation in format AMSBIB
\Bibitem{VisKho17}
\by E.~A.~Vishenkova, O.~V.~Kholostova
\paper A study of permanent rotations of a heavy dynamically symmetric rigid body with a vibrating suspension point
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2017
\vol 27
\issue 4
\pages 590--607
\mathnet{http://mi.mathnet.ru/vuu611}
\crossref{https://doi.org/10.20537/vm170409}
\elib{http://elibrary.ru/item.asp?id=32248460}


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    This publication is cited in the following articles:
    1. A. P. Markeev, D. A. Sukhoruchkin, “K dinamike mayatnika, ustanovlennogo na podvizhnoi platforme”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 28:2 (2018), 240–251  mathnet  crossref  elib
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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