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Sibirskii Zhurnal Industrial'noi Matematiki, 2023, Volume 26, Number 3, Pages 56–72
DOI: https://doi.org/10.33048/SIBJIM.2023.26.305 (Mi sjim1247) 		 
On the integrability and stability of stationary solutions of the Goryachev—Sretensky gyrostat

A. A. Kosov, E. I. Semenov

Matrosov Institute for System Dynamics and Control Theory SB RAS, ul. Lermontova 134, Irkutsk 664033, Russia
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DOI: https://doi.org/10.33048/SIBJIM.2023.26.305
Abstract: The equations of motion of the Goryachev-Sretensky gyrostat are studied. All stationary solutions are found on the invariant set of the zero level of the area integral and their stability is analyzed. For the case where the suspension point coincides with the center of mass and the action of a gyroscopic moment of a special type, integration in quadratures is performed.
Keywords: Goryachev—Sretensky gyrostat, stationary solutions, stability, quadrature integration.
Funding agency Grant number
Russian Science Foundation 22-29-00819
Received: 16.08.2022
Revised: 05.06.2023
Accepted: 07.06.2023
English version:
Journal of Applied and Industrial Mathematics, 2023, Volume 17, Issue 3, Pages 557–570
DOI: https://doi.org/10.1134/S1990478923030092
Document Type: Article
UDC: 531.36
Language: Russian
Citation: A. A. Kosov, E. I. Semenov, “On the integrability and stability of stationary solutions of the Goryachev—Sretensky gyrostat”, Sib. Zh. Ind. Mat., 26:3 (2023), 56–72; J. Appl. Industr. Math., 17:3 (2023), 557–570
Citation in format AMSBIB
\Bibitem{KosSem23}
\by A.~A.~Kosov, E.~I.~Semenov
\paper On~the~integrability and~stability of~stationary solutions of~the~Goryachev---Sretensky gyrostat
\jour Sib. Zh. Ind. Mat.
\yr 2023
\vol 26
\issue 3
\pages 56--72
\mathnet{http://mi.mathnet.ru/sjim1247}
\crossref{https://doi.org/10.33048/SIBJIM.2023.26.305}
\transl
\jour J. Appl. Industr. Math.
\yr 2023
\vol 17
\issue 3
\pages 557--570
\crossref{https://doi.org/10.1134/S1990478923030092}
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    		Сибирский журнал индустриальной математики
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