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Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya, 2012, Issue 9(100), Pages 136–150 (Mi vsgu107)  

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

Mathematic Modeling

New case of integrability in dynamics of multi-dimensional body

N. V. Pokhodnyaa, M. V. Shamolinb

a Dept. of Mathematics, Moscow Pedagogical State University, Moscow, 107140, Russian Federation
b Institute of Mechanics, Moscow State University, Moscow, 119899, Russian Federation

Abstract: In this chapter the new results are systematized on study of the equations of motion of dynamically symmetrical four-dimensional ($4D-$) rigid body which residing in a certain nonconservative field of forces in case of special dynamical symmetry. Its type is unoriginal from dynamics of the real smaller-dimensional rigid bodies of interacting with a resisting medium on the laws of a jet flow, under which the nonconservative tracing force acts onto the body and forces both the value of velocity of a certain typical point of the rigid body and the certain phase variable to remain as constant in all time, that means the presence in system nonintegrable servo-constraints.

Keywords: multi-dimensional rigid body, integrability, transcendental first integral.

Full text: PDF file (150 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
References: PDF file   HTML file

Document Type: Article
UDC: 517.925+531.01
Received: 18.09.2012
Revised: 18.09.2012

Citation: N. V. Pokhodnya, M. V. Shamolin, “New case of integrability in dynamics of multi-dimensional body”, Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya, 2012, no. 9(100), 136–150

Citation in format AMSBIB
\Bibitem{PokSha12}
\by N.~V.~Pokhodnya, M.~V.~Shamolin
\paper New case of integrability in dynamics of multi-dimensional body
\jour Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya
\yr 2012
\issue 9(100)
\pages 136--150
\mathnet{http://mi.mathnet.ru/vsgu107}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. N. V. Pokhodnya, M. V. Shamolin, “Nekotorye usloviya integriruemosti dinamicheskikh sistem v transtsendentnykh funktsiyakh”, Vestn. SamGU. Estestvennonauchn. ser., 2013, no. 9/1(110), 35–41  mathnet
    2. N. V. Pokhodnya, M. V. Shamolin, “Integriruemye sistemy na kasatelnom rassloenii k mnogomernoi sfere”, Vestn. SamGU. Estestvennonauchn. ser., 2014, no. 7(118), 60–69  mathnet
    3. M. V. Shamolin, “Integrable variable dissipation systems on the tangent bundle of a multi-dimensional sphere and some applications”, J. Math. Sci., 230:2 (2018), 185–353  mathnet  crossref  elib
  • Вестник Самарского государственного университета. Естественнонаучная серия
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