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Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 2017, Volume 135, Pages 3–93 (Mi into195)  

Low-dimensional and multi-dimensional pendulums in nonconservative fields. Part 2

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 (730 kB)

English version:
Journal of Mathematical Sciences (New York), 2018, 233:3, 301–397

Bibliographic databases:

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

Citation: M. V. Shamolin, “Low-dimensional and multi-dimensional pendulums in nonconservative fields. Part 2”, Dynamical systems, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 135, VINITI, Moscow, 2017, 3–93; J. Math. Sci. (N. Y.), 233:3 (2018), 301–397

Citation in format AMSBIB
\Bibitem{Sha17}
\by M.~V.~Shamolin
\paper Low-dimensional and multi-dimensional pendulums in nonconservative fields. Part~2
\inbook Dynamical systems
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz.
\yr 2017
\vol 135
\pages 3--93
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into195}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3805813}
\zmath{https://zbmath.org/?q=an:06945090}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2018
\vol 233
\issue 3
\pages 301--397
\crossref{https://doi.org/10.1007/s10958-018-3934-6}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85049999336}


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