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On Oscillations of Two Connected Pendulums Containing Cavities Partially Filled by Incompressible Fluids

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Abstract

We consider the linearized problem of small oscillations of two pendulums connected to each other by a spherical hinge. Each pendulum has a cavity partially filled by an incompressible fluid. We study the initial-boundary value problem as well as the corresponding spectral problem on normal motions of the hydromechanical system. We prove theorems on correct solvability of the problem on an arbitrary interval of time both in the case of ideal and viscous fluids in the cavities and we study the corresponding spectral problems as well.

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Authors and Affiliations

  1. Taurida Academy, V. I. Vernadsky Crimea Federal University, Simferopol, Russia

    N. D. Kopachevsky & V. I. Voytitsky

  2. Crimean Engineering-Pedagogical University, Simferopol, Russia

    Z. Z. Sitshaeva

Authors
  1. N. D. Kopachevsky
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  2. V. I. Voytitsky
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  3. Z. Z. Sitshaeva
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Correspondence to N. D. Kopachevsky.

Additional information

Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 63, No. 4, Differential and Functional Differential Equations, 2017.

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Kopachevsky, N.D., Voytitsky, V.I. & Sitshaeva, Z.Z. On Oscillations of Two Connected Pendulums Containing Cavities Partially Filled by Incompressible Fluids. J Math Sci 259, 845–896 (2021). https://doi.org/10.1007/s10958-021-05666-y

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