Chaos in Pendulum Power spectrum approach Deeder Aurongzeb Instructor: Dr. Charles Myles.

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Presentation transcript:

Chaos in Pendulum Power spectrum approach Deeder Aurongzeb Instructor: Dr. Charles Myles

Outline Chaos Power Spectrum Simple pendulum Simple pendulum with nonlinear perturbation Double Pendulum Signature of Chaos

What is Chaos? System evolution sensetive to intial condition Nonlinear,random and Chaos are not the same thing Example: Butterfly flapping can produce large change in atmosphere

Power spectrum Multiplying FFT with its complex conjugate The Exponents give information about most possible signals

Pendulum Most oscillations are not linear. Three category considering two different pendulum Simple with nonlinear Double pendulum with chaotic motion

Pendulum Nonlinear Double pendulum

Power Spectrum Chaos Nonlinear

Conclusion Double pendulum exibits chaos Corresponding equation can be found from power spectrum References: 1. F. Biscarini, P. Samori, O. Greco and R. Zamboni, Phys. Rev. Lett. 78,2389(1997). Lecture notes,Dr. Charles MylesThe Mathematics of Chaos,Ian Stewart.