Stability of spin top (tippy top)

[GRQC]

Stability of "spin top" (tippy top)

I'm looking for a decent discussion of the stability of a spin top (sometimes called the tippy top), which shows that the stable configuration when spinning is the "inverted" one (spinning on the stick).

Any help would be appreciated.

 

[Andre]

You picked the right season for that question, Easter. spin an egg.

Tip or Egg, the physics are not that different I guess.

The Science of Spin
Here’s a trick to try on a leftover Easter egg-or any hard-boiled egg. Spin it on its tip. Last week, Yutaka Shimomura of Japan’s Keio University and Keith Moffatt of Cambridge University said in Nature that they had figured out why. The details are mathematical, but the basic reason is that an egg spinning on its side always wobbles and starts precessing-moving its angle of lean in a circle like a tilted top. Its contact point with the surface slides around, creating friction that slows the precession while some energy turns into spin on the long axis. These two effects push the egg into a more stable state-spinning on end. It won’t work a with a raw egg, though-its innards slosh and dissipate energy.

Here is the abstract:

Nature 416, 385 - 386 (28 March 2002); doi:10.1038/416385a

Classical dynamics: Spinning eggs — a paradox resolved

H. K. MOFFATT* AND Y. SHIMOMURA†

* Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge CB3 9EW, UK
e-mail: hkm2@damtp.cam.ac.uk
† Department of Physics, Keio University, Hiyoshi, Yokohama 223-8521, Japan
e-mail: yutaka@phys-h.keio.ac.jp
If a hard-boiled egg is spun sufficiently rapidly on a table with its axis of symmetry horizontal, this axis will rise from the horizontal to the vertical. (A raw egg, by contrast, when similarly spun, will not rise.) Conversely, if an oblate spheroid is spun sufficiently rapidly with its axis of symmetry vertical, it will rise and spin about the vertical on its rounded edge with its axis of symmetry now rotating in a horizontal plane. In both cases, the centre of gravity rises; here we provide an explanation for this paradoxical behaviour, through derivation of a first-order differential equation for the inclination of the axis of symmetry.

 

[Chen]

I have a little dreidel, I made it out of clay
And when it's dry and ready, with dreidel I shall play.
Oh, Dreidel, Dreidel, Dreidel, I made you out of clay
Dreidel, Dreidel, Dreidel, with Dreidel I shall play.