Chaos (Non-Linear Dynamics) Driven Damped Pendulum

[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!

 

[Dr. Courtney]

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

 

[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.

 

[atyy]

How about thinking about the driven pendulum using the circle map, and calculating the topological entropy?

http://www.cmp.caltech.edu/~mcc/Chaos_Course/Lesson18/Demo6.html
http://astro.pas.rochester.edu/~aquillen/phy411/lectures.html