Open AccessMany authors have considered a problem of small fluctuations of an incompressible ideal fluid, partially filled a movable arbitrarily shaped tank. Long list of references in the field concerned proves it. The article presents a solution to the problem of natural oscillations of the axisymmetric pendulum with a spherical cavity, partially filled with fluid, with the boundary conditions at the free surface and resistance surface - fluid draining surface. The relevance of the problems is stipulated by finding the eigenvalues and frequency of oscillation equations of perturbed motion of axisymmetric pendulum and fluid with dissipation available on the boundary surfaces.
The paper also considers a variational adjustment of the auxiliary boundary value problems. Associated Legendre functions are used in solving the variational problems, as the coordinate functions. Next, after substituting solutions of variational problems in the boundary conditions and upon the following mathematical operations based on the equations of the pendulum motion was obtained a characteristic equation. The validity of numerical results is confirmed by proximity when comparing with the result of calculating frequencies of natural fluctuations of the "solidified" fluid and frequencies obtained from the solution to the problem of natural fluid fluctuations in a spherical tank with the constant depth of fluid. All numerical calculations were performed using the Matlab computing environment.