Abstract
The two-dimensional problem of determining the frequencies and modes of small natural osciliations of an ideal fluid in a rectangular channel under near-weightless conditions is considered. It is assumed that a weak gravitational field acts parallel to the vertical walls of the channel. The Ritz method is employed for the variational problem, which is equivalent to the problem of oscillations of a fluid under weightless conditions [1, 2].
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Literature Cited
M. Ya. Barnyak and A. N. Komarenko, “Finding the Eigenvalues of a Problem of the Oscillations of a Fluid in a Weak Gravitational Field,” Proceedings of the Seminar on Differential Equations, Kiev (1969).
N. D. Kopachevskii, A. D. Myshkis, and A. D. Tyuptsov, “Oscillations of a Fluid under Conditions of Total and Partial Weightlessness,” in: Mathematical Physics and Functional Analysis [in Russian], Khar'kov (1969), No. 1.
N. D. Kopachevskii, “Small Oscillations of an Ideal Fluid in a Vessel under Near-Weightless Conditions,” in: Introduction to the Dynamics of a Body with a Fluid under Weightless Conditions [in Russian], VTs Akad. Nauk SSSR, Moscow (1968).
N. N. Moiseev and F. L. Chernous'ko, “Problem of the Oscillations of a Fluid Subjected to Surface Stresses,” Zh. Vychisl. Mat. Mat. Fiz.,5, No. 6 (1965).
N. N. Moiseev and V. V. Rumyantsev, Dynamics of a Body with Cavities Containing a, Fluid [in Russian], Nauka, Moscow (1965).
N. D. Kopachevskii and N. N. Morozovskaya, “Determination of the First Frequency of an Ideal Fluid in a Cylindrical Vessel in a Weak Gravitational Field” in: Introduction to the Dynamics of a Body with a Fluid under Weightless Conditions [in Russian], VTs Akad. Nauk SSSR, Moscow (1968).
S. G. Mikhlin, Variational Methods of Mathematical Physics [in Russian], Nauka, Moscow (1970).
A. D. Tyuptsov, “Hydrostatics in Weak Force Fields. Stability of Equilibrium Forms of a Fluid Surface,” Izv. Akad. Nauk SSSR Mekh. Zhidk. i Gaza, No. 2 (1966).
M. A. Belyaeva, L. A. Slobozhanin, A. D. Tyuptsov, “Hydrostatics in Weak Force Fields,” in: Introduction to the Dynamics of a Body with a Fluid under Weightless Conditions [in Russian], VTs Akad. Nauk SSSR, Moscow (1968).
Konkus, “Capillary Stability of the Free Surface of a Fluid in an Inverted Rectangular Channel with a Curvature of Variable Sign,” Raket. Tekh. Kosmonavt., No. 2 (1964).
N. N. Moiseev and A. A. Petrov, Numerical Methods for Calculating the Natural Frequencies of the Oscillations of a Finite Volume of a Fluid [in Russian], VTs Akad. Nauk SSSR, Moscow (1966).
S. G. Mikhlin, Numerical Realization of Variational Methods [in Russian], Nauka, Moscow (1966).
Additional information
Khar'kov. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 3–13, September–October, 1972.
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Kopachevskii, N.D. Hydrodynamics in weak gravitational fields two-dimensional oscillations of an ideal fluid in a rectangular channel. Fluid Dyn 7, 705–714 (1972). https://doi.org/10.1007/BF01205747
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DOI: https://doi.org/10.1007/BF01205747