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Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2022, Volume 9, Issue 1, Pages 144–151
DOI: https://doi.org/10.21638/spbu01.2022.114
(Mi vspua49)
 

MECHANICS

Stability of a vertical descent of a heavy finned body in resisting medium

Yu. M. Okunev, O. G. Privalova, V. A. Samsonov

Institute of Mechanics of Lomonosov Moscow State University, 1, Michurinsky pr., Moscow, 119192, Russian Federation
References:
Abstract: A free descent of a finned body in resisting medium is studied. Fins are installed in such a way that there is a regime of a translational descent with a constant speed. Beforehand, a descent of a heavy body in an autorotation mode was studied. It exists when pitch angles of all fins are equal to each other. For a descent with autorotation, general properties and tendencies of motion were described depending on initial conditions and parameters. In the current paper, the descent of a body is discussed for the case when fins have equal absolute values of pitch angles, but signs of these angles alternate. Asymptotic stability of a translational descent with a constant speed is studied for such orientation of fins. Domains of stability are constructed in the plane of the following parameters: pitch angle of fins and displacement of the center of mass. Fins represented either by circle or rectangular blades are discussed. Domains of stability are compared with that for the autorotation mode descent. Trajectories of the center of mass are constructed. Varied types of such trajectories are obtained when parameters of the model correspond to the case of unstable translational descents with a constant speed.
Keywords: stability, finned body, autorotation mode, translational descent with a constant speed.
Funding agency
The research was carried out with the support of the Interdisciplinary scientific-educational school of the Moscow State University “Mathematical methods of analysis of complex systems”.
Received: 30.03.2021
Revised: 23.06.2021
Accepted: 02.09.2021
English version:
Vestnik St. Petersburg University, Mathematics, 2022, Volume 9, Issue 1, Pages 102–107
DOI: https://doi.org/10.1134/S1063454122010101
Document Type: Article
UDC: 531.36
MSC: 34D20
Language: Russian
Citation: Yu. M. Okunev, O. G. Privalova, V. A. Samsonov, “Stability of a vertical descent of a heavy finned body in resisting medium”, Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 9:1 (2022), 144–151; Vestn. St. Petersbg. Univ., Math., 9:1 (2022), 102–107
Citation in format AMSBIB
\Bibitem{OkuPriSam22}
\by Yu.~M.~Okunev, O.~G.~Privalova, V.~A.~Samsonov
\paper Stability of a vertical descent of a heavy finned body in resisting medium
\jour Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy
\yr 2022
\vol 9
\issue 1
\pages 144--151
\mathnet{http://mi.mathnet.ru/vspua49}
\crossref{https://doi.org/10.21638/spbu01.2022.114}
\transl
\jour Vestn. St. Petersbg. Univ., Math.
\yr 2022
\vol 9
\issue 1
\pages 102--107
\crossref{https://doi.org/10.1134/S1063454122010101}
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