Abstract
The chapter discusses the basic ideas of the theory of oscillations of a liquid and the liquid-containing body. It gives an account of the numerical methods and results of the calculation of free oscillations of a liquid in a motionless container. This is the simplest problem that appears in the investigation of the general dynamics of a body containing liquid masses with a free surface. Despite the simplicity of the mathematical formulation, it is not a t all easy to obtain accurate numerical results in this problem of free oscillations of a heavy liquid. Only in the simplest cases, one can manage to solve it analytically by the Fourier method. In this respect, the chapter describes the importance of the Ritz method and its application to the calculation of natural oscillations of a liquid in containers of various shapes. The chapter discusses free oscillations in an inclined circular cylinder, a conical container, a spherical container, and in a container formed by two horizontal coaxial cylinders.
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