Chaos in a pendulum with forced horizontal support motion: a tutorial

This contribution presents a tutorial on chaos in forced pendulum motion. A pendulum system with its support forced along a horizontal line is considered. The bifurcation diagram in function of the amplitude of the forced periodic motion shows several period doubling subharmonic cascades, chaotic motions and windows of periodic motions. It is illustrated that the cascades are governed by Feigenbaumʹs number from Universality Theory. The chaotic attractors are investigated for their characteristics such as its evolution in the phase plane, the computation of the Liapounov exponents, the Liapounov dimension, the power spectrum and the winding number.