Double
Pendulum
Visualizing Airflow, Heat Gradients, and Acoustic Fields with Light
In Short
Schlieren imaging is a powerful optical technique that reveals refractive index gradients in transparent media — such as air — by making otherwise invisible phenomena visible. Temperature differences, gas flows, shock waves, and even sound fields can be observed in real time. Our setup demonstrates this principle using a point light source, a precision spherical mirror, and an aperture in front of a camera. Subtle changes in the air — from warm breath to standing acoustic waves — appear as striking patterns of light and shadow.
Details and Theory
The line describing the motion of a pendulum’s centre of mass is called its trajectory. The theoretical description of the trajectory of a double pendulum leads to coupled nonlinear equations. Nonlinear systems generally have the property that a small change in initial conditions causes a large change in its dynamics.
Therefore, if you release the pendulum several times from almost the same position, you will get a completely different pattern each time. If all initial parameters were exactly adjustable (which is impossible in reality), the ‘chaos’ of the double pendulum could be controlled – hence we specifically call it ‘deterministic chaos’.
In our installation, an ultraviolet laser mounted on the tip of the pendulum creates an afterglow on a phosphorescent film that illuminates the path of the pendulum.