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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2020, Volume 495, Pages 26–30
DOI: https://doi.org/10.31857/S2686954320060077 (Mi danma12) 		 
This article is cited in 4 scientific papers (total in 5 papers)

MATHEMATICS

On the existence of focus singularities in one model of a Lagrange top with a vibrating suspension point

A. V. Borisovabc, P. E. Ryabovabd, S. V. Sokolovab

a A. A. Blagonravov Mechanical Engineering Institute RAS, Moscow
b Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow Region
c Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
d Financial University under the Government of the Russian Federation, Moscow
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DOI: https://doi.org/10.31857/S2686954320060077
Abstract: We consider a completely integrable Hamiltonian system with two degrees of freedom that describes the dynamics of a Lagrange top with a vibrating suspension point. The results of a stability analysis of equilibrium positions are clearly presented. It turns out that, in the case of a vibrating suspension point, both equilibrium positions can be unstable, which corresponds to the existence of focus singularities in the considered model.
Keywords: completely integrable Hamiltonian systems, Lagrange top, focus singularities.
Funding agency Grant number
Russian Science Foundation 19–71–30012
Ministry of Education and Science of the Russian Federation
Russian Foundation for Basic Research 18–29–10051-мк
Borisov's research (Section 1) was supported by the Russian Science Foundation, grant no. 19-71-30012. Sokolov's research was performed at the Moscow Institute of Physics and Technology within the framework of the state support of leading universities of the Russian Federation (project no. 5-100) and was supported by the Russian Foundation for Basic Research, grant no. 18-29-10051-mk.
Presented: V. V. Kozlov
Received: 10.09.2020
Revised: 30.10.2020
Accepted: 01.11.2020
English version:
Doklady Mathematics, 2020, Volume 102, Issue 3, Pages 468–471
DOI: https://doi.org/10.1134/S1064562420060095
Bibliographic databases:
Document Type: Article
UDC: 532.5.031, 517.938.5
Language: Russian
Citation: A. V. Borisov, P. E. Ryabov, S. V. Sokolov, “On the existence of focus singularities in one model of a Lagrange top with a vibrating suspension point”, Dokl. RAN. Math. Inf. Proc. Upr., 495 (2020), 26–30; Dokl. Math., 102:3 (2020), 468–471
Citation in format AMSBIB
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