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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2017, Volume 134, Pages 6–128 (Mi into194)  
This article is cited in 7 scientific papers (total in 7 papers)

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

M. V. Shamolin

Lomonosov Moscow State University, Institute of Mechanics
Full-text PDF (1207 kB) Citations (7)
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.
English version:
Journal of Mathematical Sciences (New York), 2018, Volume 233, Issue 2, Pages 173–299
DOI: https://doi.org/10.1007/s10958-018-3933-7
Bibliographic databases:
Document Type: Article
UDC: 517.9+531.01
MSC: 34Cxx, 37E10, 37N05
Language: Russian
Citation: M. V. Shamolin, “Low-dimensional and multi-dimensional pendulums in nonconservative fields. Part 1”, Dynamical systems, Itogi Nauki i Tekhniki. 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. Sovrem. Mat. Pril. Temat. Obz.
\yr 2017
\vol 134
\pages 6--128
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into194}
\mathscinet{http://mathscinet.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}
Linking options:
  • https://www.mathnet.ru/eng/into194
  • https://www.mathnet.ru/eng/into/v134/p6
    Cycle of papers
    This publication is cited in the following 7 articles:
    1. M. V. Shamolin, “Examples of Integrable Equations of Motion of a Five-Dimensional Rigid Body in the Presence of Internal and External Force Fields”, J Math Sci, 2025  crossref
    2. Maxim V. Shamolin, “Spatial motion of a pendulum in a jet flow: qualitative aspects and integrability”, Proc Appl Math and Mech, 20:1 (2021)  crossref
    3. M. V. Shamolin, “Sluchai integriruemosti uravnenii dvizheniya pyatimernogo tverdogo tela pri nalichii vnutrennego i vneshnego silovykh polei”, Geometriya i mekhanika, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 187, VINITI RAN, M., 2020, 82–118  mathnet  crossref  mathscinet
    4. 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
    5. M. V. Shamolin, “Integrable systems with many degrees of freedom and with dissipation”, Moscow University Mechanics Bulletin, 74:6 (2019), 137–146  mathnet  crossref  zmath  isi
    6. M. V. Shamolin, “Dissipative Integrable Systems on the Tangent Bundles of 2- and 3-Dimensional Spheres”, Journal of Mathematical Sciences, 245:4 (2020), 498–507  mathnet  crossref  mathscinet
    7. M. V. Shamolin, “Examples of Integrable Systems with Dissipation on the Tangent Bundles of Multidimensional Spheres”, J. Math. Sci. (N. Y.), 250:6 (2020), 932–941  mathnet  crossref  mathscinet
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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