# Why does this object periodically turn itself?

See below gif image taken from 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?

• Related post Dzhanibekov Effect on MO Nov 27, 2011 at 10:34
• L. D. LANDAU and E. M. LIFSHITZ, "MECHANICS": The asymmetrical top Nov 28, 2011 at 8:06
• The answer!
– Dale
Jun 20, 2013 at 19:06
• Sep 20, 2019 at 12:22

## 1 Answer

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.

http://www.youtube.com/watch?v=L2o9eBl_Gzw

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

http://www.youtube.com/watch?v=3VwS5ykAUHI

And this seems to be a computer simulation.

http://www.youtube.com/watch?v=LR5hkgfRPno

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 http://math.ucalgary.ca/files/publications/cushman/tennis.pdf which is no longer a working link.)

http://www.youtube.com/watch?v=4dqCQqI-Gis

• This seems more like a list of references than an answer. It would be nice to have the important points explained here. Jul 19, 2015 at 22:51