Mn-1 Chaotic Double Pendulum Published: Thursday 09 March 2006 -
Updated: Thursday 24 March 2011 To demonstrate a double pendulum
with chaotic motion. Double pendulum as illustrated Click on
pictures to enlarge. Chaotic Pendulum 1 Chaotic Pendulum 2 The
double pendulum demonstrates the chaotic unpredictable behavour
that can occur in the motions of a pair of coupled nonlinear
oscillators. When the oscillations of the two physical pendula,
are of small enough angular amplitude for the linear
approximation Sin Ø ~ Ø to be well satisfied, there is no chaos
and the system can be treated as a pair of coupled linear
oscillators with the familiar in-phase and out of phase normal
modes (which can be demonstrated first). But for large
amplitudes- including motions that go "over the top", ie
rotations as well as oscillations- the non linearity results in
chaotic motion. Students can be encouraged to try this
demonstration for themselves after the lecture, but with the
warning to keep out of the way of the system once i