This model illustrates the chaotic dynamics associated with the movement of a metallic "bob" in the presence of two or more magnets. The motivation for the model is that of a pendulum bob, which is attracted by two magnets as is oscillates. The simulation shows an overhead view. The magnets are placed in a plane with the pendulum at particular height above the plane. With suitably light damping the system exhibits sensitive dependence on initial conditions.
created with NetLogo
view/download model file: Chaotic_Pendulum.nlogo
There are two types of turtles in this model: magnets and pendulum bobs. The magnets are fixed and the bobs are free to move. The bobs are attracted to magnets according to an inverse square law. The bobs also oscillate under the influence of gravity and are subject to damping. The damping, magnetic force and gravity can all be adjusted or turned off.
Press setup to position two magnets symmetrically on the screen. Press go and then press add-bobs. Now click somewhere on the world view to release the first bob. See if you can predict which magnet it will be attracted to. Place another bob close to where you released the first bob. Does it go to the same bob? Adjust the various parameters using the sliders or the buttons.
The create-map button can be used to create a map showing, with color, which magnet the pendulum bobs released at different locations are attracted to. The maps typically are fractal. Three preset maps can be loaded.
Experiment with different damping factors. You should see that the system behaves in a more chaotic way with lower damping. If the magnet strength is weak you will see that that neither magnet is a fixed point, but instead the only fixed point is the pendulum equilibrium position. You can also see chaotic behavior with no gravity when there are three or more magnets.
The model could be improved by using Runge Kutte for the numerical simulation rather than Euler's method.
See the other Chaos Models in this series
Copyright 2006 David McAvity
This model was created at the Evergreen State College, in Olympia Washington
is part of a series of applets to illustrate principles in physics and biology.
Funding was provided by the Plato Royalty Grant.
The model may be freely used, modified and redistributed provided this copyright is included and it not used for profit.
Contact David McAvity at mcavityd@evergreen.edu if you have questions about its use.