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

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

3. 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

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

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

6. Pendulum Nonlinear Double pendulum

7. Power Spectrum Chaos Nonlinear

8. 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.