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Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2012, Number 4, Pages 44–47 (Mi vmumm512)  

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

Mechanics

Complete list of first integrals for dynamic equations of motion of a solid body in a resisting medium with consideration of linear damping

M. V. Shamolin

Lomonosov Moscow State University, Institute of Mechanics

Abstract: A new case of integrability in the spatial problem of rigid body motion with consideration of the nonconservative moment of forces is discussed. A nonconservative force field of action of the medium on the body is constructed. Contrary to some previous author's works, a linear dependence of this field on the angular velocity is taken into account, although the introducing of this dependence into the components of such a field is not obvious.

Key words: rigid body, resisting medium, dynamic equations, phase space, transcendental first integral.

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English version:
Moscow University Mechanics Bulletin, 2012, 67:4, 92–95

Bibliographic databases:

Document Type: Article
UDC: 531.01+531.552+517.925
Received: 12.10.2011

Citation: M. V. Shamolin, “Complete list of first integrals for dynamic equations of motion of a solid body in a resisting medium with consideration of linear damping”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2012, no. 4, 44–47; Moscow University Mechanics Bulletin, 67:4 (2012), 92–95

Citation in format AMSBIB
\Bibitem{Sha12}
\by M.~V.~Shamolin
\paper Complete list of first integrals for dynamic equations of motion of a solid body in a resisting medium with consideration of linear damping
\jour Vestnik Moskov. Univ. Ser.~1. Mat. Mekh.
\yr 2012
\issue 4
\pages 44--47
\mathnet{http://mi.mathnet.ru/vmumm512}
\transl
\jour Moscow University Mechanics Bulletin
\yr 2012
\vol 67
\issue 4
\pages 92--95
\crossref{https://doi.org/10.3103/S0027133012040036}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84867192133}


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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, “Integrable cases in the dynamics of a multi-dimensional rigid body in a nonconservative field in the presence of a tracking force”, J. Math. Sci., 214:6 (2016), 865–891  mathnet  crossref  mathscinet
    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, “Integrable systems on the tangent bundle of a multi-dimensional sphere”, J. Math. Sci. (N. Y.), 234:4 (2018), 548–590  mathnet  crossref
    4. M. V. Shamolin, “Integrable nonconservative dynamical systems on the tangent bundle of the multidimensional sphere”, Differ. Equ., 52:6 (2016), 722–738  crossref  crossref  mathscinet  zmath  isi  elib  scopus
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