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Sib. Zh. Ind. Mat., 2019, Volume 22, Number 2, Pages 118–131 (Mi sjim1048)  

Family of phase portraits in the spatial dynamics of a rigid body interacting with a resisting medium

M. V. Shamolin

Institute of Mechanics Lomonosov Moscow State University, pr. Michurinskii 1, 119192 Moscow

Abstract: Under study is the problem of spatial free deceleration of a rigid body in a resisting medium. It is assumed that a axisymmetric homogeneous body interacts with the medium only through the front part of its outer surface that has the shape of flat circular disk. Under the simplest assumptions about the impact forces from the medium, it is demonstrated that any oscillations of bounded amplitude are impossible. In this case, any precise analytical description of the force-momentum characteristics of the medium impact on the disk is missing. For this reason, we use the method of "embedding" the problem into a wider class of problems. This allows us to obtain some relatively complete qualitative description of the body motion. For the dynamical systems under consideration, it is possible to obtain particular solutions as well as the families of phase portraits in the three-dimensional space of quasi-velocities which consist of a countable set of the phase portraits that are trajectory-nonequivalent and have different nonlinear qualitative properties.

Keywords: rigid body, resisting medium, qualitative and numerical analysis.

DOI: https://doi.org/10.33048/sibjim.2019.22.211

Full text: PDF file (532 kB)
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Document Type: Article
UDC: 531.01:531.552
Received: 08.09.2018
Revised: 18.12.2018
Accepted:27.12.2018

Citation: M. V. Shamolin, “Family of phase portraits in the spatial dynamics of a rigid body interacting with a resisting medium”, Sib. Zh. Ind. Mat., 22:2 (2019), 118–131

Citation in format AMSBIB
\Bibitem{Sha19}
\by M.~V.~Shamolin
\paper Family of phase portraits in the spatial dynamics of a rigid body interacting with a resisting medium
\jour Sib. Zh. Ind. Mat.
\yr 2019
\vol 22
\issue 2
\pages 118--131
\mathnet{http://mi.mathnet.ru/sjim1048}
\crossref{https://doi.org/10.33048/sibjim.2019.22.211}


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