Rott's Pendulum

Rott's pendulum is really two pendulums coupled together, one pivoted in the middle, the other connected at one end.  For small swings, the pendulums behave predictably.  Energy is exchanged from one pendulum to the other at a steady rate until friction makes them stop.  However, for large swings, the pendulums behave very erratically.  They still exchange energy, but swing, stop and whirl around in an unpredictable fashion.  The pair of pendulums are, in fact, a 'chaotic' system, whose motion cannot be mathematically predicted, even if you know the 'initial conditions' very precisely.  The tiniest change in the initial conditions results in an entirely different subsequent motion.  You can be certain that the way the pendulum behaves when you set it going with large swings will never be repeated, however long the exhibit may last.