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Motion of a Rigid Body with Frontal Cone in a Resistive Medium: Qualitative Analysis and Integrability

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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.

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  1. M. V. Lomonosov Moscow State University, Moscow, Russia

    M. V. Shamolin

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Correspondence to M. V. Shamolin.

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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 174, Geometry and Mechanics, 2020.

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Shamolin, M.V. Motion of a Rigid Body with Frontal Cone in a Resistive Medium: Qualitative Analysis and Integrability. J Math Sci 272, 703–728 (2023). https://doi.org/10.1007/s10958-023-06466-2

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