An educational machine for teaching bifurcations and chaos

We have developed a machine that enables us to learn bifurcations and chaos intuitively. An inverted pendulum, excited at its pivot, generates the above-mentioned phenomena. The equation of motion of the pendulum is assumed to be described by the following equation: J/spl Theta/ + C/spl Theta/ + K/spl Theta/ - mgh sin/spl Theta/ = mha/spl omega//sup 2/ cos/spl Theta/cos/spl omega/ t. The experimental result shows that the n period behavior (n=1,2,3) and chaos are clearly observed and the bifurcation characteristics agree well with the simulation result. According to the points of designing the machine, an analogous one or more extended ones can be manufactured.