Challenge Team Abstract
Team Number: 072 School Name: Sandia Preparatory School Area of Science: Mathematics Project Title: Examination of Chaos and NonLinearity Through Modeling of the Levitron 



With the discoveries of Newton, a form of thought emerged that said the universe was like a clock wound up at the beginning of time. One could describe the past and future with the right combination of variables. This ideal clockwork universe was reexamined with the discovery that natural processes exhibit chaotic behavior. When developing the equations for such systems, we often discover nonlinearity. Nonlinear systems fail to behave like everyday systems in that the solution can change each time we solve the equation. Such dynamic systems lend themselves to the use of supercomputers by presenting a situation in which the results constantly vary. By modeling the solutions to these equations, patterns often emerge allowing one to predict the behavior of typically chaotic systems. The system we chose to model was that of the levitron. Our model involves the suspension of a small magnet over a larger one, with the two fields interacting in such a way as to allow the smaller body to be suspended in free space. Earnshaw's theorem states that stability cannot be achieved in a static system, however by spinning the smaller magnet and precisely controlling its weight, suspension is possible by the creation of a gyroscopic moment. We can examine nonlinearity based on the stability of the system at a given time.
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