On the instability with probability one of equilibrium of ideal incompressible liquid situated in a vertical cylinder under its random coaxial vibration
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2022), pp. 32-38
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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.
[1] Moiseev N. N., Petrov A. A., Chislennye metody rascheta sobstvennykh chastot kolebanii ogranichennogo ob'ema zhidkosti, VTs AN SSSR, M., 1966
[2] Doob J. L., Stochastic Processes, J. Wiley, N.Y.; Chapman and Hall, London, 1953 ; Dub Dzh.L., Veroyatnostnye protsessy, IL, M., 1956 | MR
[3] Dwight H. B., Tables of Integrals and Other Mathematical Data, Macmillan, N.Y., 1961 ; Dvait G. B., Tablitsy integralov i drugie matematicheskie formuly, Nauka, M., 1964 | MR