Chaos (Non-Linear Dynamics) Driven Damped Pendulum

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1. Jul 15, 2015

H-S-D

I want to investigate the phenomenon of Chaos in the form of how its driving amplitude affects _____, in a driven, damped pendulum, using a computer simulation given.

Initially I was looking at 'degree of chaos' for the dependent variable - to measure this I wanted to use the Lyapunov exponent, however I do not know how to calculate this.

1) Is there a simple way to calculate this? If not,
2) Are there any other ways I can measure the 'degree of chaos' of this driven damped pendulum? If not,
3) Are there any other possible things I can set as a dependent variable? With the system being chaotic, I do not know if I can measure any sort of correlation between two variables....

Thank you SO MUCH for your help!!

2. Jul 15, 2015

Dr. Courtney

For most pendulum type problems, you need two degrees of freedom (coordinates) to have chaos.

3. Jul 15, 2015

H-S-D

Yes, the driven damped pendulum is the addition of a torque, or force, to a simple pendulum with gravity and damping - there are 3 forces acting on it which makes it chaotic.

4. Jul 16, 2015