On oscillations of connected pendulums with cavities filled with homogeneous fluids

We consider the problem and normal (eigen) oscillations of the system of three connected (coupled to each other) pendulums with cavities filled with one or several immiscible homogeneous fluids. We study the case of partially dissipative system when the cavity of the first pendulum is completely filled with two ideal fluids, the cavity of the second one is filled with three viscous fluids, and the cavity third one is filled with one ideal fluid. We use methods of functional analysis. We prove the theorem on correct solvability of the initial-boundary value problem on any interval of time. We study the case of eigen oscillations of conservative system where all fluids in cavities of pendulums are ideal and the friction in joints (points of suspension) is not taken into account. We consider in detail three auxiliary problems on small oscillations of single pendulums with three above variants of fluids in cavities.