Small oscillations of a liquid in a rotating container with an elastic bottom in zero gravity

In this paper, the author studies the problem of the small oscillations of an inviscid liquid in an rigid container of revolution, the bottom of which is an elastic membrane or a plate, under zero gravity, a problem in which the surface tension determines the character of motion. Using the variational formulation of the problem, he gives sufficient conditions of stability of the equilibrum position of the system and proves the existence of the eigenfrequencies of its motion.