Hydrodynamics in weak force fields. Small oscillations of an ideal liquid
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Several problems concerned with small oscillations of an ideal liquid, taking account of the surface-tension forces, have been considered in [1–3] (as a rule, these are cases when the equilibrium liquid surface is spherical, plane, or differs only slightly from plane). Below we formulate the problem of the natural frequencies of small oscillations of a liquid for the general case of an equilibrium liquid surface in a weak potential mass force field. It is shown that the natural frequencies and the corresponding eigenfunctions of this problem may be found by the Ritz method. We note that analogous results in a somewhat different formulation have been obtained in the recently published .
KeywordsForce Field Liquid Surface Analogous Result Equilibrium Liquid Small Oscillation
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- 1.H. Lamb, Hydrodynamics [Russian translation], 1947.Google Scholar
- 2.L. D. Landau and E. M. Lifshitz, Mechanics of Continuous Media [in Russian], Gostekhizdat, 1953.Google Scholar
- 3.N. N. Moiseev and F. L. Chernous'ko, “Problems of oscillations of a liquid subjected to surface-tension forces,” Zh. vychislit. matem. i matem. fiz., vol. 5, no. 6, 1965.Google Scholar
- 4.V. V. Rumyantsev, “On the stability of the motion of a solid body containing a liquid having surface tension,” PMM, vol. 28, no. 4, pp. 746–753, 1964.Google Scholar
- 5.W. Blaschke, Differential Geometry [Russian translation], ONTI, 1935.Google Scholar
- 6.A. D. Tyuptsov, “Hydrostatics in weak force fields. Stability of equilibrium forms of a liquid surface,” Izv. AN SSSR, Mekhanika zhidkosti i gaza [Fluid Dynamics], no. 2, 1966.Google Scholar
- 7.S. L. Sobolev, Some Applications of Functional Analysis to Mathematical Physics [in Russian], Izd. LGU, 1950.Google Scholar
- 8.A. J. McConnell, Introduction to Tensor Analysis with Applications to Geometry, Mechanics, and Physics [Russian translation], Fizmatgiz, 1963.Google Scholar
- 9.S. G. Mikhlin, Minimum Problem for a Quadratic Functional [in Russian], Gostekhizdat, 1952.Google Scholar