# Inverted pendulum kinematics?

## Main Question or Discussion Point

I'm trying to come up with a mechanics project idea and I'd like some suggestions. I have a mass that is oscillating back and forth and it can be thought of as an inverted pendulum. I also took a video of the moving mass and found its x and y coordinates and velocity as its moving back and forth. I took a second video and data set of the mass moving at a much faster speed. Using this data set, what would be an interesting problem to work out? Any ideas? Thanks!

Jim

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The biggest uncertainty in the inverted pendulum problem is the uncertainty principle itself; If the pendulum is standing exactly upside down, how long does it take [what is maximum time] to fall over? Is there any interesting physics here? Newtonian physics could answer what the period is for any starting position [other than exactly upside down].

You could perhaps do some studies on kinematic losses [e.g., air drag] vs. time for different amplitudes and pendulum lengths for a standard shape pendulum weight of different diameters, and compare to theory:
http://en.wikipedia.org/wiki/Drag_(physics [Broken])
At what point does the drag force change from linear (Stokes) to quadratic (turbulent)?

Bob S

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Here's a link to a 6 page engineering paper with some useful concepts:

http://www.sps.ele.tue.nl/members/m.j.bastiaans/spc/bugeja.pdf [Broken]

I recall there may be fuzzy logic research into problems such as the inverted pendulum, but other than these comments, I can't visualize an interesting project. I think a fuzzy processor works similar to the human brain and can be kept a trade secret once the fuzzy associative memory (FAM) is discovered to work in a given problem.

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