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See below gif image taken from here.

enter image description here

Or see this Youtube video about 30 sec in.

  1. Is this a real effect?

  2. Why does it seem to turn periodically?

  3. Can it be explained by classical mechanics alone?

  4. Is there a simple equation that models this behaviour?

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Related post Dzhanibekov Effect on MO – Pratik Deoghare Nov 27 '11 at 10:34
Wow, this is awesome. And just in Chapter 2 in my undergrad physic's book :-) – Martin Ueding Nov 27 '11 at 15:27
L. D. LANDAU and E. M. LIFSHITZ, "MECHANICS": The asymmetrical top – Martin Gales Nov 28 '11 at 8:06
The answer! – Dale Jun 20 '13 at 19:06

1 Answer 1

up vote 32 down vote accepted

It's a classical mechanics effect for sure although a really interesting one. Following links on "Dzhanibekov effect" one gets at Marsden and Ratiu's "Introduction to Mechanics and Symmetry" Chapter 15 Section 15.9 "Rigid Body Stability" treating this with use of the Casimir functions.

From remark 1: A rigid body tossed about its middle axis will undergo an interesting half twist when the opposite saddle point is reached.

Here is another and more profound example under weightless conditions.

This seems to be a home experiment where a guy throws the spinning object upwards.

And this seems to be a computer simulation.

There is a related unstable orbit effect which you can try out easily yourself with a tennis racket. A treatment due to Ashbauch Chicone and Cushman is here:

Mark S. Ashbaugh, Carmen C. Chicone and Richard H. Cushman, The Twisting Tennis Racket, Journal of Dynamics and Differential Equations, Volume 3, Number 1, 67-85 (1991). (One time found at which is no longer a working link.)

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This seems more like a list of references than an answer. It would be nice to have the important points explained here. – DanielSank Jul 19 at 22:51

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