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Vestnik SamU. Estestvenno-Nauchnaya Ser., 2016, Issue 3-4, Pages 75–97 (Mi vsgu512)  

This article is cited in 4 scientific papers (total in 4 papers)

Mechanics

Cases of integrability corresponding to the pendulum motion in three-dimensional space

M. V. Shamolin

Institute of Mechanics, Lomonosov Moscow State University, Moscow, 119192, Russian Federation

Abstract: In this actitity, we systemize some results on the study of the equations of spatial motion of dynamically symmetric fixed rigid bodies-pendulums located in a nonconservative force fields. The form of these equations is taken from the dynamics of real fixed rigid bodies placed in a homogeneous flow of a medium. In parallel, we study the problem of a spatial motion of a free rigid body also located in a similar force fields. Herewith, this free rigid body is influenced by a nonconservative tracing force; under action of this force, either the magnitude of the velocity of some characteristic point of the body remains constant, which means that the system possesses a nonintegrable servo constraint. The obtained results are systematized and served in the invariant form. We also show the nontrivial topological and mechanical analogies.

Keywords: rigid body, resisting medium, dynamical system, three-dimensional phase pattern, case of integrability.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-00848-а


Full text: PDF file (750 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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Document Type: Article
UDC: 531.01+531.552
Received: 18.05.2016

Citation: M. V. Shamolin, “Cases of integrability corresponding to the pendulum motion in three-dimensional space”, Vestnik SamU. Estestvenno-Nauchnaya Ser., 2016, no. 3-4, 75–97

Citation in format AMSBIB
\Bibitem{Sha16}
\by M.~V.~Shamolin
\paper Cases of integrability corresponding to the pendulum motion in three-dimensional space
\jour Vestnik SamU. Estestvenno-Nauchnaya Ser.
\yr 2016
\issue 3-4
\pages 75--97
\mathnet{http://mi.mathnet.ru/vsgu512}
\elib{http://elibrary.ru/item.asp?id=29389327}


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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. M. V. Shamolin, “Sluchai integriruemosti, sootvetstvuyuschie dvizheniyu mayatnika v chetyrekhmernom prostranstve”, Vestn. SamU. Estestvennonauchn. ser., 2017, no. 1, 41–58  mathnet  elib
    2. M. V. Shamolin, “O dvizhenii mayatnika v mnogomernom prostranstve. Chast 1. Dinamicheskie sistemy”, Vestn. SamU. Estestvennonauchn. ser., 2017, no. 3, 41–64  mathnet  crossref  elib
    3. M. V. Shamolin, “O dvizhenii mayatnika v mnogomernom prostranstve. Chast 2. Nezavisimost polya sil ot tenzora uglovoi skorosti”, Vestn. SamU. Estestvennonauchn. ser., 2017, no. 4, 40–67  mathnet  crossref  elib
    4. M. V. Shamolin, “O dvizhenii mayatnika v mnogomernom prostranstve. Chast 3. Zavisimost polya sil ot tenzora uglovoi skorosti”, Vestn. SamU. Estestvennonauchn. ser., 24:2 (2018), 33–54  mathnet  crossref  elib
  • Вестник Самарского государственного университета. Естественнонаучная серия
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