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Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 2017, Volume 134, Pages 6–128 (Mi into194)  

This article is cited in 5 scientific papers (total in 5 papers)

Low-dimensional and multi-dimensional pendulums in nonconservative fields. Part 1

M. V. Shamolin

Lomonosov Moscow State University, Institute of Mechanics

Abstract: In this review, we discuss new cases of integrable systems on the tangent bundles of finite-dimensional spheres. Such systems appear in the dynamics of multidimensional rigid bodies in nonconservative fields. These problems are described by systems with variable dissipation with zero mean. We found several new cases of integrability of equations of motion in terms of transcendental functions (in the sense of the classification of singularities) that can be expressed as finite combinations of elementary functions.

Keywords: fixed rigid body, pendulum, multi-dimensional body, integrable system, variable dissipation system, transcendental first integral.

Full text: PDF file (1207 kB)

English version:
Journal of Mathematical Sciences (New York), 2018, 233:2, 173–299

Bibliographic databases:

UDC: 517.9+531.01
MSC: 34Cxx, 37E10, 37N05

Citation: M. V. Shamolin, “Low-dimensional and multi-dimensional pendulums in nonconservative fields. Part 1”, Dynamical systems, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 134, VINITI, Moscow, 2017, 6–128; J. Math. Sci. (N. Y.), 233:2 (2018), 173–299

Citation in format AMSBIB
\Bibitem{Sha17}
\by M.~V.~Shamolin
\paper Low-dimensional and multi-dimensional pendulums in nonconservative fields. Part~1
\inbook Dynamical systems
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz.
\yr 2017
\vol 134
\pages 6--128
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into194}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3799506}
\zmath{https://zbmath.org/?q=an:06945089}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2018
\vol 233
\issue 2
\pages 173--299
\crossref{https://doi.org/10.1007/s10958-018-3933-7}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85049677792}


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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, “Integriruemye sistemy s dissipatsiei na kasatelnykh rassloeniyakh k sferam razmernostei $2$$3$”, Geometriya i mekhanika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 145, VINITI RAN, M., 2018, 86–94  mathnet  mathscinet
    2. M. V. Shamolin, “Sluchai integriruemykh sistem s dissipatsiei na kasatelnom rassloenii mnogomernoi sfery”, Geometriya i mekhanika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 150, VINITI RAN, M., 2018, 78–87  mathnet  mathscinet
    3. M. V. Shamolin, “Integrable dynamical systems with dissipation on tangent bundles of 2D and 3D manifolds”, J. Math. Sci. (N. Y.), 244:2 (2020), 335–355  mathnet  crossref  elib
    4. M. V. Shamolin, “Integrable systems with many degrees of freedom and with dissipation”, Moscow University Mechanics Bulletin, 74:6 (2019), 137–146  mathnet  crossref  isi
    5. M. V. Shamolin, “Sluchai integriruemosti uravnenii dvizheniya pyatimernogo tverdogo tela pri nalichii vnutrennego i vneshnego silovykh polei”, Geometriya i mekhanika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 187, VINITI RAN, M., 2020, 82–118  mathnet  crossref
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