Re: Really understanding the Rattleback
- From: Stephen Riley <steve@xxxxxxxxxxxxxxxxxxx>
- Date: Mon, 30 Jan 2006 15:04:11 +0000
In message <ko4st1pbefajcoabu0as8ev2f6ep86pe34@xxxxxxx>, John Bailey <john_bailey@xxxxxxxxxxxxxxxx> writes
The Rattleback aka wobblestone aka Celt is roughly a twisted kayak shaped object. When resting on a flat surface, if it is given a push to make it rotate around its point of surface contact, it has the characteristic of moving smoothly in that direction of rotation but if given a push to rotate in the other direction, it will start to turn but then, with a rocking motion, come to a stop and begin rotating in the direction it somehow prefers.
<Snip>
It might help build intuition on something simpler [than an asymmetric object with (possibly) friction added to the works]. An everyday thing that anyone could do right now and is easily explained by Eulers equations, but difficult to explain without mathematics.
Take something rectangular like a pack of cards or cigarette packet, ideally something with uniform mass distribution and the 3 axes different lengths. Now flip it on each of its (principle, you'll know) axes one at a time. For axes with the smallest and greatest moments of inertia it spins stably, but on the intermediate axis it tumbles. Doing it here, even one tumble on the intermediate axis is enough to have it coming down rotated partly on another axis.
It would be interesting to see how even this simple object would behave if a rocking motion were applied to the intermediate axis. Unfortunately since this is a rectangle it would need to be pivoted and attached to pivot with a couple of springs, or a curved surface added and rocked on the ground. Friction may not be as much of a complication here due to symmetry and rounded bottom, but better would be a pivot and springs. Would that try to 'flip' onto one the other axes? If so would the result be a wobble, spin, or what?
Something more complex like the rattleback might well start spinning or wobbling for the same reason, trying to flip onto another principle axis. (The long axis that's wobbled probably is the one with the intermediate moment of inertia). Except more difficult to explain because of asymmetry, principle axes not obvious and passing through the pivot point (if indeed the pivot point is fixed) and friction. A nice extra test would be to see how much of an affect friction is playing here, by rocking the rattleback on a smooth surface. Maybe some of the affects disappear, like reversing direction, but some remain.
-- Stephen Riley .
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