Double Pendulum Demonstration
The double pendulum is an example of a chaotic system. It has two bobs: the first one connects the two rods and acts like a joint. The second bob is at the end of the second rod. It's very difficult to predict where the second bob will go. (Although we can say where it definitely won't go.) However, we can predict the long-term average (mean) position of the second bob. If you look at the plot of the average position, you'll see that it soon converges to a predictable point. The average will only shift away from that position when the conditions change. For example, if a magnet is switched on that attracts the bob.
This is just a fun example, but there are some chaotic systems that are of great interest to scientists. One of these systems is the weather. It's difficult to predict what the weather will be like in a few days time (just like it's difficult to predict where the second bob will be in a few minutes time) but it is possible to predict the long-term average weather, that is, the climate. So next time someone says, "How can scientists predict the climate when they can't predict next week's weather?" tell them about the double pendulum!
- Set the initial angles (anti-clockwise from the vertical) for each bob.
- Press "Start" to start the simulation.
- Click "Pause" to pause the simulation.
- To switch on the magnet select "Add Magnet".
- If "Auto Pause" is selected, the simulation will pause whenever the number of iterations is an integer multiple of the value in the "Frequency" field. This allows you to, say, increment the magnet force every 100,000 iterations. Uncheck "Pause" to resume.