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Phase Portraits of Dynamical Equations of Motion of a Rigid Body in a Resistive Medium

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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 secondorder subsystem. We ovtain a new family of phase portraits on the phase cylinder of quasi-velocities, which differs from families obtained earlier.

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  1. Institute of Mechanics of the M. V. Lomonosov Moscow State University, Moscow, Russia

    M. V. Shamolin

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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 135, Geometry and Mechanics, 2017.

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Shamolin, M.V. Phase Portraits of Dynamical Equations of Motion of a Rigid Body in a Resistive Medium. J Math Sci 233, 398–425 (2018). https://doi.org/10.1007/s10958-018-3935-5

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