# Equation of motion for a wobbling disc

While looking at a frisbee the other day, I suddenly had a question.

Suppose (in free space) you set a disc-shaped object spinning, and then you impart a sudden force perpendicular to the spinning surface near the edge.

This undoubtedly causes the disc to drift away in the direction of the force, but let's suppose we recalibrate our frame so that the center of the disc is stationary, but we are still left with the wobble induced by the impact.

What is the equation of motion for a fixed point on the edge of the disc?

Experimentally and intuitively I'm led to believe it's some sort of dampened sinusoidal path. If that's the case, that the wobble is fading and the disc is returning to a single plane of rotation, I'm curious to know if it has to be parallel to the original plane of rotation.

I won't be too picky: you can make whatever reasonable assumptions you feel are necessary.

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The original disc is originally spinning in the obvious way: like you throw a frisbee. – rschwieb Sep 20 '12 at 14:46
Unless you're considering air resistance, the motion of the frisbee will not be damped. It will perform what is known as torque-free precession. – Rahul Sep 20 '12 at 15:45
@RahulNarain I was hoping to understand the 'deep space' version, so thank you for the lead :) I had thought maybe the angular momentum would damp the wobble in an attempt to return to equillibrium. – rschwieb Sep 20 '12 at 15:55
Richard Feynman asked a similar question and his solution led to a Nobel Prize (not directly). Check out: stuleja.org/vscience/osp/contents/physicsClub/feynmanPlate.html – Korgan Rivera Sep 20 '12 at 17:14
@KorganRivera Dang, no Nobel Prize for frisbees huh... – rschwieb Sep 20 '12 at 17:32