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On Oscillations of Connected Pendulums with Cavities Filled by Homogeneous Fluids

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Abstract

We consider the problem and normal oscillations (eigenoscillations) of the system of three connected (coupled to each other) pendulums with cavities filled with one or several immiscible homogeneous fluids. We study the case of partially dissipative system where the cavity of the first pendulum is completely filled with two ideal fluids, the cavity of the second one is filled with three viscous fluids, and the cavity third one is filled with one ideal fluid. We use methods of functional analysis. We prove the theorem on correct solvability of the initial-boundary value problem on any interval of time. We study the case of eigenoscillations of conservative system where all fluids in cavities of pendulums are ideal and the friction in joints (points of suspension) is not taken into account. We consider in detail three auxiliary problems on small oscillations of single pendulums with three above variants of fluids in cavities.

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Authors and Affiliations

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

    N. D. Kopachevsky & V. I. Voytitsky

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  1. N. D. Kopachevsky
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  2. V. I. Voytitsky
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Correspondence to N. D. Kopachevsky.

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Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 65, No. 3, Proceedings of the Crimean Autumn Mathematical School-Symposium, 2019.

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Kopachevsky, N.D., Voytitsky, V.I. On Oscillations of Connected Pendulums with Cavities Filled by Homogeneous Fluids. J Math Sci 265, 236–312 (2022). https://doi.org/10.1007/s10958-022-06053-x

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