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 Vestnik SamU. Estestvenno-Nauchnaya Ser., 2018, Issue 24, Issue 2, Pages 33–54 (Mi vsgu574)

Mathematics

On a pendulum motion in multi-dimensional space. Part 3. Dependence 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 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 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 that case when the force fields linearly depend on the tensor of angular velocity.

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

DOI: https://doi.org/10.18287/2541-7525-2018-24-2-33-54

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Document Type: Article
UDC: 517+531.01

Citation: M. V. Shamolin, “On a pendulum motion in multi-dimensional space. Part 3. Dependence of force fields on the tensor of angular velocity”, Vestnik SamU. Estestvenno-Nauchnaya Ser., 24:2 (2018), 33–54

Citation in format AMSBIB
\Bibitem{Sha18} \by M.~V.~Shamolin \paper On a pendulum motion in multi-dimensional space. Part 3. Dependence of force fields on the tensor of angular velocity \jour Vestnik SamU. Estestvenno-Nauchnaya Ser. \yr 2018 \vol 24 \issue 2 \pages 33--54 \mathnet{http://mi.mathnet.ru/vsgu574} \crossref{https://doi.org/10.18287/2541-7525-2018-24-2-33-54} \elib{http://elibrary.ru/item.asp?id=36731733}