An analogy between a gravity modulated porous layer heated from below and the inverted pendulum with an oscillating pivot point

The governing equations for the inverted pendulum is developed and shown to be analogous to the gravity modulated porous layer heated from below. In particular the temperature in a gravity modulated porous layer heated from below (R>0-unstable) is likened to the motion of an inverted pendulum (unstable). As gravity modulation stabilizes convection, Transport Porous Med. 57 (2004), 113, it is found that oscillating the pivot point of an unstable, inverted pendulum stabilizes the motion.