Chaotic Behaviour of Nonlinear Pendulum

Cuthbert Nyack
One of the effects which can occur in nonlinear systems is chaos. One of the simplest systems which can display this behaviour is the simple pendulum in which the sine term is retained as the restoring force instead of being linearised as x of approximated as a cubic.

The applet shows the response of the pendulum to a driving force with amplitude g, angular frequency K/wd and phase q. The definition of these terms can be seen in the book Chaotic Dynamics by G.L. Baker and J.P. Gollub, published by Cambridge University Press.

For the eg parameters (2.0, 2.0, 3.0, g 500 4.0 0.9) variation of the parameter will reveal "islands" of chaos. Some of the values of g at which non chaotic behaviour can be seen are 0.7, 0.79, 0.9, 1.02, 1.03, 1.06, 1.08, 1.11, 1.29, 1.42, 1.44 double, 1.47 another double, 1.51, 1.54, 1.57 to 1.67, 1.82, 2.13.

Chaootic behaviour can be seen at values of g = 1.1, 1.15 to 1.27, 1.5, 1.87 to 2.1.

Gif image below shows how applet should appear.

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COPYRIGHT 2006 Cuthbert Nyack.