A snack of classical mechanics

April 6, 2012 8:16 AM

What is the Dzhanibekov effect? Known as the Tennis Racket theorem in English and documented by Vladimir Dzhanibekov in 1985 space, it is the result of unstable rotation about a principle axis.
posted by Algebra (21 comments total)

Machine translation (so lazy) of first two YouTube comments on the first video:

Learn the mechanics. The rotation of the body around one of the three axes of inertia (with the intermediate moment of inertia) is not stable. The effect has long been known.
npast1 9 months ago 29

What is surprising - the effect is described more Tsiolkovsky, but then no one took for granted that theory ... And noticed this effect after more than 80 years.
Pashtet495 1 year ago 18

It's like some sort of horrible parallel universe!
posted by griphus at 8:20 AM on April 6, 2012 [1 favorite]

yet, what's strange is this seems like, from a reflex point of view, something we intuitively know.

I never knew (or thought about) this effect. But the second video with the ping-pong paddle reminded me how "intuitively" we know if something will flip over as it rotates when thrown. Or at least after the first fumble, you know how to toss with the right momentum so that it will rotate back around so you can catch it where you want to.

(That said, the first video, in space, is, well. WOW neat..)
posted by k5.user at 8:22 AM on April 6, 2012

What a bunch of wing nuts.
posted by The 10th Regiment of Foot at 8:36 AM on April 6, 2012 [1 favorite]

We learned about this in sophomore physics - it follows directly from the Euler equations describing a rigid rotor. You can demonstrate this by tossing a brick in the air repeatedly, spinning it about each of the 3 axes - the rotation about the middle-length axis is the unstable one. I never heard it referred to as the "Dzhanibekov effect", that seems like a bit of a stretch for something that's been understood for hundreds of years.

And, despite what the titles in the video linked as "Tennis Racket Theorem" read, the correct terminology is "principal" not "principle" axes. (Sadly, it seems that lots of physicists aren't so great with their English ...)
posted by crazy_yeti at 8:39 AM on April 6, 2012 [2 favorites]

The top answer was written by Terry Tao who is a disgraced Fields Medalist now redeemed.

Also, MathOverflow needs a way to make diagrams.
posted by DU at 8:40 AM on April 6, 2012 [1 favorite]

This video is a nice illustration of the aforementioned instability.
posted by RichardP at 8:42 AM on April 6, 2012

Very neat, but...

Principal axis! Principal axis, not "principle axis"! Unless you're rotating around your credo!
posted by languagehat at 8:45 AM on April 6, 2012 [3 favorites]

In Soviet Russia, tennis racket destabilizes you!
posted by blue_beetle at 8:50 AM on April 6, 2012 [1 favorite]

'Principle axis" is the one that U.S. politics revolves around, and it's unstable in a far more fundamentally wacky way than that tennis racket thingy they're showing in the videos . . .
posted by flug at 8:56 AM on April 6, 2012

That looks more bistable than unstable but looking closer at the video RichardP linked, the object doesn't trace the same path which makes it seem closer to chaotic motion than anything else. Terence Tao describes it as bi-instability which I didn't know was a thing but its been awhile since I swam in the waves of control theory.

Actually, it is more of a bi-instability than a bistability; the object is oscillating between two unstable equilibria, with no stable equilibrium in between.
posted by euphorb at 8:59 AM on April 6, 2012

I wouldn't depend on that RichardP video too much. The whole effect requires some initial instability which isn't present there.
posted by DU at 9:20 AM on April 6, 2012

Yay! I've always wanted to see the Magellenic clouds!
posted by sexyrobot at 9:26 AM on April 6, 2012

DU: MathOverflow allows for uploading of images. It doesn't need a way to make the diagrams itself. And RichardP's video has instability, it's just initially small enough that it takes a few seconds to manifest. It's really an excellent video because it shows how the trajectories are different after each flip, which is the essence of the "bi-instability".
posted by grog at 9:36 AM on April 6, 2012

...rotating around his credo...heh...(objection sustained, but get on with it.)

[I may have to use that in another venue; shall I cite you?]
posted by mule98J at 9:48 AM on April 6, 2012

disgraced Fields Medalist

There's a gallium joke in there somewhere.
posted by The 10th Regiment of Foot at 10:14 AM on April 6, 2012 [1 favorite]

Very interesting. Thank you.

I stared at the math talk on MO for a while and realized that there are people who are much better at math than me.

Now that I know about it, this effect is something I had observed from tossing things in the air, but I had always attributed it to my lack of ability to throw properly.
posted by grubby at 11:42 AM on April 6, 2012

Heh, heh, heh. One of my favorite parts of teaching dynamics is watching the students try to make a paperback book, rubber-banded shut, rotate around and each principal axis. They all think they can do it until they try it. :)

I will make use of the Russian wingnut space video in the future. Thanks!
posted by BrashTech at 11:52 AM on April 6, 2012

> [I may have to use that in another venue; shall I cite you?

You shall. As per Chicago:

languagehat [Stephen Dodson], April 6, 2012 (11:45 a.m.), comment on Algebra, "A Snack of Classical Mechanics," MetaFilter (blog), April 6, 2012, http://www.metafilter.com/114594/A-snack-of-classical-mechanics.
posted by languagehat at 12:22 PM on April 6, 2012 [2 favorites]

This video illustrates the bistable / choatic nature of the motion pretty well.
posted by intermod at 12:23 PM on April 6, 2012

The Simpsons had it right: all that time, they really were up there studying the effects of zero gravity on tiny metal screws.
posted by ShutterBun at 5:23 PM on April 6, 2012

Posted by Algebra! Shurely...
posted by marienbad at 4:09 AM on April 7, 2012