This applet shows how very small changes in initial conditions can cause large differences very quickly in chaotic systems.
To try this
simulation:
Click with the right mouse button to place the pendulums in an initial location.
Click the up and down arrows to change the difference in degrees between the two pendulums. The initial value of 0.010 indicates that the two pendulums are 0.010 degrees from each other when the system is started. Changes to this difference will only be visible after you restart the pendulums. Once the system starts, the difference is no longer used.
Click and drag with the left mouse button to look at the pendulum from other angles.
What's Going On?
Nobody really knows! The motion you see is called chaotic because it is not predictable.
This pendulum is not a normal pendulum. This is called a compound pendulum. Two pendulums are hooked together, one attached to another. A simple pendulum swings back and forth - its motion is predictable and regular. With a compound pendulum, as one pendulum swings the other one is swinging as well. As one pendulum swings, its accelerations and motions are coupled to the other pendulum. Subsequent motions are dependent on previous motions. Given the complex interactivity between the two pendulums, it is impossible to derive simple mathematical formulas which describe the resultant motions.
There's More!
Chaotic motions are not limited just to compound pendulums. The earth's weather is another example of a chaotic system. The atmosphere is a single entity, but conditions are different around the world. Temperatures, air pressure and humidity are affected by local situations. Since all parts of the atmosphere are connected, higher temperatures here will eventually affect the weather somewhere else.
For example, the weather report for Italy is clear skies with high humidity for several days.. Here in Georgia, warm coastal weather causes increased evaporation from the ocean. The moist air moves eastward and forms clouds over Spain. The cloud cover cools Spain and causes high winds to blow over North Africa. The winds lift dust into the air. The dust scatters over Italy and induces rainfall! So much for sunny skies!
