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Vestnik SamU. Estestvenno-Nauchnaya Ser., 2017, Issue 3, Pages 41–64 (Mi vsgu554)  

Mathematics

On a pendulum motion in multi-dimensional space. Part 1. Dynamical systems

M. V. Shamolin

Institute of Mechanics, Lomonosov Moscow State University, 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 thit work, we derive the general multi-dimensional dynamic equations of the systems under study.

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_а
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/10.18287/2541-7525-2017-23-3-41-64

Full text: PDF file (318 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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UDC: 517+531.01
Received: 18.06.2017

Citation: M. V. Shamolin, “On a pendulum motion in multi-dimensional space. Part 1. Dynamical systems”, Vestnik SamU. Estestvenno-Nauchnaya Ser., 2017, no. 3, 41–64

Citation in format AMSBIB
\Bibitem{Sha17}
\by M.~V.~Shamolin
\paper On a pendulum motion in multi-dimensional space. Part 1. Dynamical systems
\jour Vestnik SamU. Estestvenno-Nauchnaya Ser.
\yr 2017
\issue 3
\pages 41--64
\mathnet{http://mi.mathnet.ru/vsgu554}
\crossref{https://doi.org/10.18287/2541-7525-2017-23-3-41-64}
\elib{https://elibrary.ru/item.asp?id=32274172}


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