A fold catastrophe potential illustrated with a pure mechanical apparatus

Abstract

We present an apparatus consisting of a bar tightly connected to a disc, that acts as a pulley, free to rotate around its axis. A body is suspended by means of a thread that is wrapped around the collar of the pulley. Depending on the values of the masses and also on the geometric parameters of the various parts of the apparatus, the system may, or may not, stay in static equilibrium. When it moves, the system may perform stable oscillations around stability positions, or the body continuously falls down, while the pulley executes a sequence of complete rotations. We analyse these very diverse behaviours, basing the discussion on the shape of the potential energy, plotted as a function of the angular position of the system, stressing that the experiment provides a very good example of a fold catastrophe potential, besides being funny and pedagogically very valuable.