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 Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz.: Year: Volume: Issue: Page: Find

 Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 2017, Volume 137, Pages 104–117 (Mi into208)

New cases of integrable systems with dissipation on tangent bundles of multidimensional spheres

M. V. Shamolin

Lomonosov Moscow State University, Institute of Mechanics

Abstract: In many problems of multidimensional dynamics, systems appear whose state spaces are spheres of finite dimension. Clearly, phase spaces of such systems are tangent bundles of these spheres. In this paper, we examine nonconservative force field in the dynamics of a multidimensional rigid body in which the system possesses a complete set of first integrals that can be expressed as finite combinations of elementary transcendental functions. We consider the case where the moment of nonconservative forces depends on the tensor of angular velocity.

Keywords: dynamical system, dissipation, transcendental first integral, integrability.

 Funding Agency Grant Number Russian Foundation for Basic Research 15-01-00848-a This work was supported by the Russian Foundation for Basic Research (project No. 15-01-00848-a).

Full text: PDF file (231 kB)

Document Type: Article
UDC: 517, 531.01
MSC: 34Cxx, 37E10, 37N05

Citation: M. V. Shamolin, “New cases of integrable systems with dissipation on tangent bundles of multidimensional spheres”, Differential equations. Mathematical physics, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 137, VINITI, Moscow, 2017, 104–117

Citation in format AMSBIB
\Bibitem{Sha17} \by M.~V.~Shamolin \paper New cases of integrable systems with dissipation on tangent bundles of multidimensional spheres \inbook Differential equations. Mathematical physics \serial Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz. \yr 2017 \vol 137 \pages 104--117 \publ VINITI \publaddr Moscow \mathnet{http://mi.mathnet.ru/into208}