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 Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 2020, Volume 187, Pages 82–118 (Mi into734)

Examples of integrable equations of motion of a five-dimensional rigid body in the presence of internal and external force fields

M. V. Shamolin

Lomonosov Moscow State University

Abstract: In the study of integrable systems that describe multidimensional rigid bodies in nonconservative force fields, two approaches are used. The first approach is concerned with systems in which the nonconservativity of force fields is related to additional coefficients in the cinematical relations; note that $n=5$ and $n=6$ are special cases. The second approach is based on the simultaneous influence of two force fields: internal (conservative) and external (nonconservative). This paper is devoted to the special case where $n=5$.

Keywords: multidimensional rigid body, equations of motion, conservative force field, integrability, transcendental first integral

DOI: https://doi.org/10.36535/0233-6723-2020-187-82-118

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UDC: 517, 531.01
MSC: 58-xx, 70-xx

Citation: M. V. Shamolin, “Examples of integrable equations of motion of a five-dimensional rigid body in the presence of internal and external force fields”, Geometry and Mechanics, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 187, VINITI, Moscow, 2020, 82–118

Citation in format AMSBIB
\Bibitem{Sha20} \by M.~V.~Shamolin \paper Examples of integrable equations of motion of a five-dimensional rigid body in the presence of internal and external force fields \inbook Geometry and Mechanics \serial Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz. \yr 2020 \vol 187 \pages 82--118 \publ VINITI \publaddr Moscow \mathnet{http://mi.mathnet.ru/into734} \crossref{https://doi.org/10.36535/0233-6723-2020-187-82-118}