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We show asymptotic, exponential stability of the equilibrium configuration,$\smallL$, of a hollow physical pendulum with its inner part entirely filledwith a viscous liquid, corresponding to the center of mass being in the lowestposition. Moreover, we prove that every weak solution with initial datapossessing finite total initial energy and belonging to a "large" open set,becomes eventually smooth and decays exponentially fast to the equilibrium$\smallL$. These results are obtained also as byproduct of a "generalizedlinearization principle" that we show for evolution equations with non-empty"slow" center manifold.

Stability and Long-Time Behavior of a Pendulum with an Interior Cavity Filled with a Viscous Liquid