Abstract:
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 filled with incompressible fluid. 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 fluids in the cavities, and we study the corresponding spectral problems as well.
Citation:
N. D. Kopachevsky, V. I. Voytitsky, Z. Z. Sitshaeva, “On oscillations of two connected pendulums containing cavities partially filled with incompressible fluid”, Differential and functional differential equations, CMFD, 63, no. 4, Peoples' Friendship University of Russia, M., 2017, 627–677
\Bibitem{KopVoySit17}
\by N.~D.~Kopachevsky, V.~I.~Voytitsky, Z.~Z.~Sitshaeva
\paper On oscillations of two connected pendulums containing cavities partially filled with incompressible fluid
\inbook Differential and functional differential equations
\serial CMFD
\yr 2017
\vol 63
\issue 4
\pages 627--677
\publ Peoples' Friendship University of Russia
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd340}
\crossref{https://doi.org/10.22363/2413-3639-2017-63-4-627-677}
Linking options:
https://www.mathnet.ru/eng/cmfd340
https://www.mathnet.ru/eng/cmfd/v63/i4/p627
This publication is cited in the following 6 articles:
V. I. Voytitsky, “Weakly dissipative linear dynamical systems and a quadratic Keldysh pencil”, Math. Notes, 116:2 (2024), 209–222
V. I. Voititskii, M. A. Muratov, Yu. S. Pashkova, P. A. Starkov, T. A. Suslina, D. O. Tsvetkov, “Pamyati Nikolaya Dmitrievicha Kopachevskogo, matematika i cheloveka”, Posvyaschaetsya pamyati professora N.D. Kopachevskogo, SMFN, 67, no. 2, Rossiiskii universitet druzhby narodov, M., 2021, 193–207
D. A. Zakora, K. V. Forduk, “A problem of normal oscillations of a system of bodies partially filled with ideal fluids under the action of an elastic damping device”, Sib. elektron. matem. izv., 18:2 (2021), 997–1014
V. I. Voititskii, N. D. Kopachevskii, “O normalnykh kolebaniyakh mayatnika s polostyu, chastichno zapolnennoi idealnoi neszhimaemoi zhidkostyu”, Materialy Voronezhskoi vesennei matematicheskoi shkoly
«Sovremennye metody teorii kraevykh zadach. Pontryaginskie chteniya–XXX». Voronezh, 3–9 maya 2019 g. Chast 1, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 190, VINITI RAN, M., 2021, 34–49
N. D. Kopachevskii, V. I. Voytitsky, “on Small Oscillations of Three Joined Pendulums With Cavities Filled With Homogeneous Ideal Fluids”, Sib. Electron. Math. Rep., 17 (2020), 260–299
N. D. Kopachevskii, V. I. Voititskii, “O kolebaniyakh sochlenennykh mayatnikov s polostyami, zapolnennymi odnorodnymi zhidkostyami”, Trudy Krymskoi osennei matematicheskoi shkoly-simpoziuma, SMFN, 65, no. 3, Rossiiskii universitet druzhby narodov, M., 2019, 434–512
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