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On the Existence of Focus Singularities in One Model of a Lagrange Top with a Vibrating Suspension Point

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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.

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Funding

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.

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Authors and Affiliations

  1. Blagonravov Institute of Machines Science, Russian Academy of Sciences, 101990, Moscow, Russia

    A. V. Borisov, P. E. Ryabov & S. V. Sokolov

  2. Moscow Institute of Physics and Technology (National Research University), 141701, Dolgoprudnyi, Moscow oblast, Russia

    A. V. Borisov, P. E. Ryabov & S. V. Sokolov

  3. Steklov Mathematical Institute, Russian Academy of Sciences, 119991, Moscow, Russia

    A. V. Borisov

  4. Financial University under the Government of the Russian Federation, 125993, Moscow, Russia

    P. E. Ryabov

Authors
  1. A. V. Borisov
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  2. P. E. Ryabov
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  3. S. V. Sokolov
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Corresponding authors

Correspondence to A. V. Borisov, P. E. Ryabov or S. V. Sokolov.

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Translated by I. Ruzanova

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Borisov, A.V., Ryabov, P.E. & Sokolov, S.V. On the Existence of Focus Singularities in One Model of a Lagrange Top with a Vibrating Suspension Point. Dokl. Math. 102, 468–471 (2020). https://doi.org/10.1134/S1064562420060095

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  • DOI: https://doi.org/10.1134/S1064562420060095

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