Geodesic
Motion of a rigid body with frontal cone in a resistive medium: Qualitative analysis and integrability
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry and Mechanics, Tome 174 (2020), pp. 83-108

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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, stability
Mots-clés : spatial motion, phase portrait. 
@article{INTO_2020_174_a7,
     author = {M. V. Shamolin},
     title = {Motion of a rigid body with frontal cone in a resistive medium: {Qualitative} analysis and integrability},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {83--108},
     publisher = {mathdoc},
     volume = {174},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2020_174_a7/}
}
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M. V. Shamolin. Motion of a rigid body with frontal cone in a resistive medium: Qualitative analysis and integrability. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry and Mechanics, Tome 174 (2020), pp. 83-108. http://geodesic.mathdoc.fr/item/INTO_2020_174_a7/