Chaotic Behaviour of Nonlinear Pendulum
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
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.