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Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 2017, Volume 135, Pages 94–122 (Mi into196)  

Phase portraits of dynamical equations of motion of a rigid body in a resistive medium

M. V. Shamolin

Lomonosov Moscow State University, Institute of Mechanics

Abstract: We consider a mathematical model of the influence of a medium on a rigid body with a specific shape of its surface. In this model, we take into account the additional dependence of the moment of the interaction force on the angular velocity of the body. We present a complete system of equations of motion under the quasi-stationarity conditions. The dynamical part of equations of motion forms an independent third-order system, which contains, in its turn, an independent second-order subsystem. We obtain a new family of phase portraits on the phase cylinder of quasi-velocities, which differs from families obtained earlier.

Keywords: phase portrait, quasi-stationarity, integrable system, transcendent first integral.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-00848_


Full text: PDF file (2141 kB)

English version:
Journal of Mathematical Sciences (New York), 2018, 233:3, 398–425

Bibliographic databases:

Document Type: Article
UDC: 531.01+531.552
MSC: 34Cxx, 37E10, 37N05

Citation: M. V. Shamolin, “Phase portraits of dynamical equations of motion of a rigid body in a resistive medium”, Dynamical systems, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 135, VINITI, Moscow, 2017, 94–122; J. Math. Sci. (N. Y.), 233:3 (2018), 398–425

Citation in format AMSBIB
\Bibitem{Sha17}
\by M.~V.~Shamolin
\paper Phase portraits of dynamical equations of motion of a rigid body in a resistive medium
\inbook Dynamical systems
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz.
\yr 2017
\vol 135
\pages 94--122
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into196}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3805814}
\zmath{https://zbmath.org/?q=an:06945091}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2018
\vol 233
\issue 3
\pages 398--425
\crossref{https://doi.org/10.1007/s10958-018-3935-5}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85049918709}


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