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Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya, 2013, Issue 9/1(110), Pages 35–41 (Mi vsgu397)  

This article is cited in 7 scientific papers (total in 7 papers)

Mathematics

Certain conditions of integrability of dynamical systems in transcendental functions

N. V. Pokhodnyaa, M. V. Shamolinb

a The Dept. of Mathematics and Physics, Sholokhov Moscow State University for the Humanities, Moscow, 109240, Russian Federation
b Institute of Mechanics, Moscow State University, Moscow, 119899, Russian Federation

Abstract: Certain general conditions of integrability in elementary functions for the systems on the tangent bundle of two-dimensional sphere are studied. At that an interesting example of three-dimensional phase pattern of pendulum-like system which describes the motion of spherical pendulum, placed in an over-run medium flow. Sufficient conditions of existence of the first integrals expressed through the finite combination of elementary functions, for multi-parametric third order systems are presented.

Keywords: variable dissipation dynamic system, integrability, transcendental first integral.

Full text: PDF file (311 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: 18.11.2013
Revised: 19.12.2013

Citation: N. V. Pokhodnya, M. V. Shamolin, “Certain conditions of integrability of dynamical systems in transcendental functions”, Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya, 2013, no. 9/1(110), 35–41

Citation in format AMSBIB
\Bibitem{PokSha13}
\by N.~V.~Pokhodnya, M.~V.~Shamolin
\paper Certain conditions of integrability of dynamical systems in transcendental functions
\jour Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya
\yr 2013
\issue 9/1(110)
\pages 35--41
\mathnet{http://mi.mathnet.ru/vsgu397}


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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, “Integriruemye sistemy na kasatelnom rassloenii k mnogomernoi sfere”, Vestn. SamGU. Estestvennonauchn. ser., 2014, no. 7(118), 60–69  mathnet
    2. 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
    3. M. V. Shamolin, “Sluchai integriruemosti, sootvetstvuyuschie dvizheniyu mayatnika v trekhmernom prostranstve”, Vestn. SamU. Estestvennonauchn. ser., 2016, no. 3-4, 75–97  mathnet  elib
    4. M. V. Shamolin, “Sluchai integriruemosti, sootvetstvuyuschie dvizheniyu mayatnika v chetyrekhmernom prostranstve”, Vestn. SamU. Estestvennonauchn. ser., 2017, no. 1, 41–58  mathnet  elib
    5. 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
    6. 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
    7. 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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