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Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 2018, Volume 150, Pages 130–142 (Mi into334)  

Problems of Qualitative Analysis in the Spatial Dynamics of Rigid Bodies Interacting with Media

M. V. Shamolin

Lomonosov Moscow State University, Institute of Mechanics

Abstract: In this paper, we examine the problem on the spatial free deceleration of a rigid body in a resistive medium under the assumption that the interaction of the homogeneous axisymmetric body with the medium is concentrated on the frontal part of the surface, which has the shape of a flat circular disk. In earlier works of the author, under the simplest assumptions on interaction forces, the impossibility of oscillations with bounded amplitude was proved. Note that exact analytic description of forces and moments of the body-medium interaction is unknown, so we use the method of “embedding” of the problem into a wider class of problems; this allows one to obtain a sufficiently complete qualitative description of the motion of the body. For dynamical systems considered, we obtain particular solutions and families of phase portraits of quasi-velocities in the three-dimensional space that consist of countable sets of nonequivalent portraits with different nonlinear qualitative properties.

Keywords: rigid body, resistive medium, qualitative analysis, numerical analysis

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-00848-a
This work was partially supported by the Russian Foundation for Basic Research (project No. 15-01-00848-a).


Full text: PDF file (311 kB)

Bibliographic databases:

Document Type: Article
UDC: 517.933
MSC: 70G60

Citation: M. V. Shamolin, “Problems of Qualitative Analysis in the Spatial Dynamics of Rigid Bodies Interacting with Media”, Geometry and Mechanics, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 150, VINITI, Moscow, 2018, 130–142

Citation in format AMSBIB
\Bibitem{Sha18}
\by M.~V.~Shamolin
\paper Problems of Qualitative Analysis in the Spatial Dynamics of Rigid Bodies Interacting with Media
\inbook Geometry and Mechanics
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz.
\yr 2018
\vol 150
\pages 130--142
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into334}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3847625}


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