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Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 2020, Volume 174, Pages 83–108 (Mi into570)  

Motion of a rigid body with frontal cone in a resistive medium: Qualitative analysis and integrability

M. V. Shamolin

Lomonosov Moscow State University

Abstract: We consider a mathematical model of the plane-parallel action of a medium on a rigid body whose surface contains a cone-shaped being part. A complete system of equations of motion under in the quasi-stationary case is presented. A new family of phase portraits on the phase cylinder of quasi-velocity is obtained. Also, we consider a mathematical model of the influence of the medium on an axisymmetric body whose surface contains a cone-shaped part. We examine the stability with respect to a part of variables of the key mode, namely, the spatial rectilinear translational deceleration of the body. The problem of integrability is discussed.

Keywords: rigid body, resistive medium, spatial motion, stability, phase portrait

DOI: https://doi.org/10.36535/0233-6723-2020-174-83-108

Full text: PDF file (546 kB)
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Bibliographic databases:

UDC: 517.933
MSC: 70G60

Citation: M. V. Shamolin, “Motion of a rigid body with frontal cone in a resistive medium: Qualitative analysis and integrability”, Geometry and Mechanics, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 174, VINITI, Moscow, 2020, 83–108

Citation in format AMSBIB
\Bibitem{Sha20}
\by M.~V.~Shamolin
\paper Motion of a rigid body with frontal cone in a resistive medium: Qualitative analysis and integrability
\inbook Geometry and Mechanics
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz.
\yr 2020
\vol 174
\pages 83--108
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into570}
\crossref{https://doi.org/10.36535/0233-6723-2020-174-83-108}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=4150663}


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