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We consider the linearized problem of small oscillations of two pendulums connected to each other by a spherical hinge. Each pendulum has a cavity partially filled by an incompressible fluid. We study the initial-boundary value problem as well as the corresponding spectral problem on normal motions of the hydromechanical 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.

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.