On oscillations of two connected pendulums containing cavities partially filled with incompressible fluid

We consider the linearized problem on small oscillations of two pendulums connected to each other with a spherical hinge. Each pendulum has a cavity partially filled with incompressible fluid. We study the initial-boundary value problem as well as the corresponding spectral problem on normal motions of the hydromechanic system. We prove theorems on correct solvability of the problem on an arbitrary interval of time both in the case of ideal and viscous fluids in the cavities, and we study the corresponding spectral problems as well.