On oscillatiions of a physical pendulum in a multilayer liquid

Abstract

Planar oscillations of a physical pendulum with a cavity partially filled
by a heavy multilayer ideal incompressible fluid is considered in a linear
statement. When assuming the hydrostatic stratification, the structure of
the spectrum is studied, the necessary and sufficient conditions for stability
are discussed, the stratification effect on the stability of the rigid body
equilibrium is evaluated. It is shown that the stratification reduces the
stability margin.