Hydrodynamics in weak force fields. Small oscillations of an ideal liquid

Abstract

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 [3].