RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Vestnik SamU. Estestvenno-Nauchnaya Ser.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Vestnik SamU. Estestvenno-Nauchnaya Ser., 2017, Issue 1, Pages 41–58 (Mi vsgu547)  

Mathematics

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

M. V. Shamolin

Institute of Mechanics, Lomonosov Moscow State University, 1, Leninskie Gory, Moscow, 119192, Russian Federation

Abstract: In this article, we systemize some results on the study of the equations of motion of dynamically symmetric fixed four-dimensional 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 the motion of a free four-dimensional 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. We also show the nontrivial topological and mechanical analogies.

Keywords: four-dimensional rigid body, non-conservative force field, dynamical system, case of integrability.

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


Full text: PDF file (279 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
References: PDF file   HTML file

Document Type: Article
UDC: 517+531.01
Received: 11.02.2017

Citation: M. V. Shamolin, “Cases of integrability corresponding to the pendulum motion in four-dimensional space”, Vestnik SamU. Estestvenno-Nauchnaya Ser., 2017, no. 1, 41–58

Citation in format AMSBIB
\Bibitem{Sha17}
\by M.~V.~Shamolin
\paper Cases of integrability corresponding to the pendulum motion in four-dimensional space
\jour Vestnik SamU. Estestvenno-Nauchnaya Ser.
\yr 2017
\issue 1
\pages 41--58
\mathnet{http://mi.mathnet.ru/vsgu547}
\elib{http://elibrary.ru/item.asp?id=29945521}


Linking options:
  • http://mi.mathnet.ru/eng/vsgu547
  • http://mi.mathnet.ru/eng/vsgu/y2017/i1/p41

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Вестник Самарского государственного университета. Естественнонаучная серия
    Number of views:
    This page:43
    Full text:7
    References:11

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019