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 Vestnik SamU. Estestvenno-Nauchnaya Ser., 2017, Issue 4, Pages 40–67 (Mi vsgu561)

Mathematics

On a pendulum motion in multi-dimensional space. Part 2. Independence of force fields on the tensor of angular velocity

M. V. Shamolin

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

Abstract: In the proposed cycle of work, we study the equations of the motion of dynamically symmetric fixed $n$-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 $n$-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. In this work, we study the case of independence of force fields on the tensor of angular velocity.

Keywords: multi-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 The work is carried out at the financial support of the grant of the Russian Foundation for Basic Research 15-01-00848-a.

DOI: https://doi.org/10.18287/2541-7525-2017-23-4-40-67

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Document Type: Article
UDC: 517+531.01

Citation: M. V. Shamolin, “On a pendulum motion in multi-dimensional space. Part 2. Independence of force fields on the tensor of angular velocity”, Vestnik SamU. Estestvenno-Nauchnaya Ser., 2017, no. 4, 40–67

Citation in format AMSBIB
\Bibitem{Sha17} \by M.~V.~Shamolin \paper On a pendulum motion in multi-dimensional space. Part 2. Independence of force fields on the tensor of angular velocity \jour Vestnik SamU. Estestvenno-Nauchnaya Ser. \yr 2017 \issue 4 \pages 40--67 \mathnet{http://mi.mathnet.ru/vsgu561} \crossref{https://doi.org/10.18287/2541-7525-2017-23-4-40-67} \elib{http://elibrary.ru/item.asp?id=32274179}