  Stokes parameter formalism is applied to show the analogies between the
motion of an asymmetric Foucault pendulum and several phenomena known from
optics and atomic physics. Nonlinearity-induced precession of elliptical orbits
of the pendulum is shown to correspond to twisting transformations used for
spin squeezing of atomic systems. Transitions between regimes of predominant
nonlinearity and regimes where the Coriolis force or the asymmetry of the
pendulum are dominant correspond to quantum phase transitions in the
Lipkin-Meshkov-Glick model. A Foucault pendulum with highly anisotropic damping
can emulate an optical Zeno effect where a sequence of polarizing filters
inhibits polarization rotation of light in an optically active medium.
