The motion of two pendulums with a spherical cavity filled with a viscous liquid (Q1358359)

The title problem is analysed by using action-angle coordinates and an asymptotic method. First, the author considers the decay of oscillations of the second pendulum with a speed proportional to the parameter \(\varepsilon= \nu^{-1}\), where \(\nu\) is the viscosity of the fluid. Then he investigates the case when the first pendulum exhibits the oscillation decay proportional to \(\varepsilon^3\), and the approaching of the system to the stable equilibrium position.