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Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2021, Volume 8, Issue 3, Pages 511–522
DOI: https://doi.org/10.21638/spbu01.2021.312
(Mi vspua100)
 

MECHANICS

Areas of attraction of the pendulum under the influence of oblique vibration of the suspension point

A. G. Petrov

St. Petersburg State University, 7-9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation
Abstract: The inverse problem of stabilizing a spherical pendulum in a given position by means of high-frequency vibration of the suspension point is posed. The position of the pendulum is determined by the angle between the pendulum rod and the vertical. For any given position of the pendulum, a one-parameter series of oblique vibration characteristics (the amplitude of the vibration velocity and the angle between the vibration velocity vector and the vertical) is found to stabilize the pendulum in this position. For the obtained series, the regions of attraction are determined (the initial points from which a given stable position of the pendulum will be established under the influence of vibration).
Keywords: spherical pendulum, stability, vibration of the suspension point, inverse problem, region of attraction.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation АААА-А20-120011690138-6
The work was carried out within the framework of the state task (state registration number AAAAA20-120011690138-6)
Received: 12.09.2020
Revised: 16.03.2020
Accepted: 19.03.2020
English version:
Vestnik St. Petersburg University, Mathematics, 2021, Volume 8, Issue 4, Pages 273–281
DOI: https://doi.org/10.1134/S1063454121030067
Document Type: Article
UDC: 517.93:531.391.3
MSC: 70J25, 70K40
Language: Russian
Citation: A. G. Petrov, “Areas of attraction of the pendulum under the influence of oblique vibration of the suspension point”, Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 8:3 (2021), 511–522; Vestn. St. Petersbg. Univ., Math., 8:4 (2021), 273–281
Citation in format AMSBIB
\Bibitem{Pet21}
\by A.~G.~Petrov
\paper Areas of attraction of the pendulum under the influence of oblique vibration of the suspension point
\jour Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy
\yr 2021
\vol 8
\issue 3
\pages 511--522
\mathnet{http://mi.mathnet.ru/vspua100}
\crossref{https://doi.org/10.21638/spbu01.2021.312}
\transl
\jour Vestn. St. Petersbg. Univ., Math.
\yr 2021
\vol 8
\issue 4
\pages 273--281
\crossref{https://doi.org/10.1134/S1063454121030067}
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