Geodesic
Phase portraits of dynamical equations of motion of a rigid body in a resistive medium
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Dynamical systems, Tome 135 (2017), pp. 94-122.

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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.
Mots-clés : phase portrait
Keywords: quasi-stationarity, integrable system, transcendent first integral. 
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     author = {M. V. Shamolin},
     title = {Phase portraits of dynamical equations of motion of a rigid body in a resistive medium},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {94--122},
     publisher = {mathdoc},
     volume = {135},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2017_135_a1/}
}
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M. V. Shamolin. Phase portraits of dynamical equations of motion of a rigid body in a resistive medium. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Dynamical systems, Tome 135 (2017), pp. 94-122. http://geodesic.mathdoc.fr/item/INTO_2017_135_a1/