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The School of Physics at the
University of Sydney has a demonstration device in the main corridor,
which attracts student attention. The device is shown at left. (More
detailed images and movies are available here.)
The device was designed and built by J. Pasiut in the Workshop in the School
in 1998, based on a request by the then head of School, Dick Collins, who had
seen something similar at the Swiss Federal Institute of Technology
in Zurich. The device is a distributed mass double pendulum
consisting of two heavy square metal plates joined by an
axle near one corner and free to rotate about an axle near a corner of
the top plate. The plates are behind glass, presumably for the safety
of all involved, but they can be set into motion by rotating the wheel
on the back, which turns the top axle. Double pendulums such as this one
exhibit complex dynamical behaviour, including chaos.
The device may be modelled as two thin plates hinged together at two
corners and free to rotate/oscillate in the plane of the plates about two pivot
points (the axles). Friction is neglected. Details of the model are provided
here. The resulting equations of motion
may be solved numerically. The animated gifs below visualise two solutions
for different initial conditions. The example on the right illustrates
what happens when the system is given a very large amount of energy, e.g.
by an enthusiastic student...
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