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 Vestnik SamU. Estestvenno-Nauchnaya Ser., 2017, Issue 1, Pages 41–58 (Mi vsgu547)

Mathematics

Cases of integrability corresponding to the pendulum motion in four-dimensional space

M. V. Shamolin

Institute of Mechanics, Lomonosov Moscow State University, 1, Leninskie Gory, Moscow, 119192, Russian Federation

Abstract: In this article, we systemize some results on the study of the equations of motion of dynamically symmetric fixed four-dimensional rigid bodies–pendulums located in a nonconservative force fields. The form of these equations is taken from the dynamics of real fixed rigid bodies placed in a homogeneous flow of a medium. In parallel, we study the problem of the motion of a free four-dimensional rigid body also located in a similar force fields. Herewith, this free rigid body is influenced by a nonconservative tracing force; under action of this force, either the magnitude of the velocity of some characteristic point of the body remains constant, which means that the system possesses a nonintegrable servo constraint. We also show the nontrivial topological and mechanical analogies.

Keywords: four-dimensional rigid body, non-conservative force field, dynamical system, case of integrability.

 Funding Agency Grant Number Russian Foundation for Basic Research 15-01-00848_à

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Citation: M. V. Shamolin, “Cases of integrability corresponding to the pendulum motion in four-dimensional space”, Vestnik SamU. Estestvenno-Nauchnaya Ser., 2017, no. 1, 41–58

Citation in format AMSBIB
\Bibitem{Sha17} \by M.~V.~Shamolin \paper Cases of integrability corresponding to the pendulum motion in four-dimensional space \jour Vestnik SamU. Estestvenno-Nauchnaya Ser. \yr 2017 \issue 1 \pages 41--58 \mathnet{http://mi.mathnet.ru/vsgu547} \elib{https://elibrary.ru/item.asp?id=29945521}