Open AccessOn Oscillations of Two Connected Pendulums Containing Cavities Partially Filled with Incompressible Fluid
Author(s) -
Nikolay D. Kopachevsky,
N. D. Kopachevskiĭ,
V. I. Voytitsky,
В И Войтицкий,
Z. Z. Sitshaeva,
Z. Z. Sitshaeva
Publication year - 2017
Publication title -
sovremennaâ matematika. fundamentalʹnye napravleniâ
Language(s) - English
Resource type - Journals
eISSN - 2949-0618
pISSN - 2413-3639
DOI - 10.22363/2413-3639-2017-63-4-627-677
Subject(s) - compressibility , physics , hinge , boundary value problem , classical mechanics , interval (graph theory) , pendulum , boundary (topology) , mathematical analysis , initial value problem , ideal (ethics) , mechanics , mathematics , philosophy , epistemology , combinatorics , quantum mechanics
We consider the linearized problem on small oscillations of two pendulums connected to each other with a spherical hinge. Each pendulum has a cavity partially lled with incompressible uid. We study the initial-boundary value problem as well as the corresponding spectral problem on normal motions of the hydromechanic system. We prove theorems on correct solvability of the problem on an arbitrary interval of time both in the case of ideal and viscous uids in the cavities, and we study the corresponding spectral problems as well.