# Ever play with a rattleback

1. Jul 15, 2009

### Creator

The real question here is what is the determining factor to have a nonholonomic system?

A rattleback shape is symmetrical (at least in one direction)....is there a shape asymmetry that causes it to preferentially rotate clockwise and avoid the counter-clockwise direction.
Spin it counter clockwise and it will reverse directions and spin the opposite. Even if you tip the edge of it it will always rotate counterclock.

More theoretically, since it doesn't conserve angular momentum, (but does conserve energy) could it be said that the classical Hamiltonian that describes it is incomplete.
Pragmatically, Is a shape anisoptrophy neccessary for anholonomic behavior.??
I think it also must have a velocity dependent constraint that is not positionally related.

Someone help me fill in the blanks for such amazing behavior. Give it to me in the dumbed down version.

...

2. Jul 15, 2009

### Fenn

I once had a wireless mouse that did this very nicely. I never really gave it much thought, but my guess was that it had something to do with the fact that the axis of lowest moment of inertia did not pass through the center of mass. Because of this, when the object is rotated, the pivot point would not want to sit vertically in line with the center of mass, and it would start to precess due to the torque exerted on the system due to gravity.

In one rotation sense, the precession effect would compliment the asymmetric shape of the object, bringing the center of mass closer to be vertically above the pivot point. The system would tilt a little and stabilize on a slightly different pivot point. In the opposite rotation sense, the effect would be reversed where the center of mass is pushed further from the pivot point. Rotation is lost due to the object tilting quite far off axis and making additional off-axis contacts with the surface.

This isn't really a good scientific guess, but as I said, it's the best I had come up with when I was pondering it years ago, while idly spinning my upside-down mouse, waiting for a file to download or a page to load or whatever.

Last edited: Jul 15, 2009
3. Jul 15, 2009

### Creator

WOW!; that's a very good phenomenological analysis. I never considered an inverted mouse as a rattleback, but it definitely is very close to the typical shape.
I think you may be getting close with the idea of center of mass and pivot point changing with rotation, but....

.... do you really think 'the rotation is lost" in the opposite direction due to greater friction with the surface? because I think counter rotation is still depressed even on a frcitionless surface. maybe try it on a block of ice.

And besides, I think a typical rattleback may not even have enough shape asymmetry to change the pivot point with rotational direction (I could be wrong).

here : check this out .... great rattleback video which is worth a thousand...er, something...

http://www.metacafe.com/watch/1055021/discrepant_event_the_rattleback/

(He claims the counter rotation is due to the shape....I dunno, how can angular momentum non-conservation be due to shape? I guess the 'bottom' is not exactly a smooth curvature and like you say, one rotational sense changes the pivot point relative to center of mass.) .

Last edited: Jul 15, 2009
4. Jul 16, 2009

### Fenn

Well, I never saw my mouse reverse rotation direction when I played with it. But I can agree that friction may not be the full reason for the poor performance in one rotation sense. Perhaps the fact that it rocks so violently.

When I think about it, as the object rocks around, the orientation of the center of mass with respect to the rotation axis changes considerably. Also, as the object tilts, the pivot point changes. The axis of rotation is not constant in all this, and so I don't think concepts like conservation of angular momentum can apply.

Perhaps in the erratic motion, torque from gravity acting on the center of mass about the pivot point causes some net tangential acceleration about this axis, causing it to accelerate and begin spinning in the opposite direction. Since the opposite direction allows for smooth rotation, the system randomly rattles toward this condition.

I wish I still had that mouse that did this well! The one I have now (Logitech G7) has a large, protruding, rubber scroll wheel, which prevents an appreciable amount of rotation.

5. Jul 16, 2009

### Creator

Yes, Just so others can realize what we are talking about here: It is amazing to see that if you spin the object in one direction that it slows down so quickly (and apparently not due to friction), then it stops, and begins to wobble violently, and then REGAINS its speed IN THE OPPOSITE direction! Sheesh! How can it transfer its momentum in the opoosite direction with no external forces?

Well that is exactly what I was wondering; what is neccessary to CREATE this 'nonholonomic behavior, as it is called. In general, Does it require two sets of pivot points, etc.?

Secondarily, the initial angular momentum has to go somewhere; so where does it go? Into linear momentum of the wobble? and then into the opposite angular momentum?
Surely, no matter what the path, or even if it changes pivot points, this implies breaking of a long standing physical principle of momentum conservation, no?
And thus ...If there are cases where angular momentum conservation doesn't 'apply' then how can we ever PREDICT any behavior with assurance.?

Which begs my initial question as to what exactly are the requirements of the (anholonomic)system which would make momentum conservation inapplicable.?

If true, then surely, classical Hamiltonian/ Lagrangian analysis is incomplete. Yikes, I'm gonna hear it from the 'equation of motion' guys now.

This behavior reminds me of the concept of trying to convert angular momentum to linear momentum , (Laithwaite and crew).

I wish i could bring it to the moon; maybe changing the amount of gravity would test that hypothesis, resulting in less torque and affecting the rotation rate.
The thing that is really freaky is why it would always "chose" to prefer one direction of spin (counterclockwise) over the other?; where is the asymmetry that would always guarantee one direction over the other.

Here's another video for those interested.:

Here they changed the weight distribution on the 'top', but notice that the 'bottom' is perfectly symmetrical. But this one seems to prefer 'clockwise " spin direction. (maybe they are south of the equator, ()
..
.Creator

Last edited by a moderator: Sep 25, 2014