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On the Instability with Probability One of Equilibrium of Ideal Incompressible Liquid Situated in a Vertical Cylinder under Its Random Coaxial Vibration

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Moscow University Mechanics Bulletin Aims and scope

Abstract

The paper concerns with the equilibrium of the ideal incompressible liquid situated in a moving cylindrical vertical vessel. It is proved that the equilibrium is unstable with probability one if the vessel movement is defined as the vertical random vibration. Random vibration is simulated by stationary Markov chain.

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REFERENCES

  1. N. N. Moiseev and A. A. Petrov, Numerical Methods for Eigenvalue Analysis of Oscillations of a Bounded Volume of Liquid (Vychislit. Tsentr Akad. Nauk SSSR, Moscow, 1966).

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  2. J. L. Doob, Stochastic Processes (Wiley, New York, 1953).

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Authors and Affiliations

  1. Chair of Theoretical Mechanics and Mechatronics, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia

    I. L. Antonov

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  1. I. L. Antonov
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Correspondence to I. L. Antonov.

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The author declares that he has no conflicts of interest.

Additional information

Translated by E. Oborin

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Cite this article

Antonov, I.L. On the Instability with Probability One of Equilibrium of Ideal Incompressible Liquid Situated in a Vertical Cylinder under Its Random Coaxial Vibration. Moscow Univ. Mech. Bull. 77, 155–161 (2022). https://doi.org/10.3103/S0027133022060024

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  • DOI: https://doi.org/10.3103/S0027133022060024

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