Double Square Pendulum

The SoP double square pendulum
The SoP double square pendulum
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...

Animated gif Animated gif
In 2007 a student in the School of Physics (Mohammad Rafat) did a Senior physics project on the dynamics of the double square pendulum, supervised by Mike Wheatland and Tim Bedding. Some of the results of that investigation are summarised on three pages describing the behaviour of the pendulum for low, intermediate, and high energy. A paper on the work appeared in the American Journal of Physics (Rafat, Wheatland and Bedding 2009). The AJP preprint is available here. (Please see this copyright notice.)

Modelling and numerical solution
Dynamics 1: Poincare sections and animations for low energy
Dynamics 2: Poincare sections and animations for intermediate energy
Dynamics 3: Poincare sections and animations for high energy
Images and videos of the device
The simple double pendulum
Mike Wheatland's home page

Page maintained by m.wheatland (at) Page last updated Monday, 5-Aug-2008