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Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 2020, Volume 174, Pages 83–108
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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
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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}
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http://mi.mathnet.ru/eng/into570 http://mi.mathnet.ru/eng/into/v174/p83
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