Abstract
Equilibrium forms of a liquid surface in weak gravitation fields have been studied in [1], As noted in [1], not all the equilibrium forms may be realized in practice, since they are not always stable. Below we consider the problem of the stability of the equilibrium state of an ideal, incompressible liquid under the influence of surface-tension forces and a potential mass force field. In solving this problem we use the principle of minimal system potential energy. The stability condition is formulated in terms of the eigenvalues of the linear boundary-value problem which arises in considering the question of the potential energy minimum. This general condition is applied to the axisymmetric problem, and, in particular, to the problem of the stability of a liquid suspended in a cylindrical vessel.
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M. A. Belyaeva, A. D. Myshkis, and A. D. Tyuptsov, “Hydrostatics in weak gravitational fields. I. Equilibrium forms of a liquid surface,” Izv. AN SSSR. Mekhanika i mashinostroenie, no. 5, 1964.
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In conclusion, the author wishes to thank M. A. Belyaeva for carrying out the calculations and N. D. Kopachevskii and A. D. Myshkis for their interest in the study and helpful suggestions.
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Tyuptsov, A.D. Hydrstatics in weak force fields. Fluid Dyn 1, 51–55 (1966). https://doi.org/10.1007/BF01013814
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DOI: https://doi.org/10.1007/BF01013814