For such a fascinating shape you'd think that there would be at least one video, picture, or even illustration of it sitting on its unstable equilibrium point.
It is also interesting how this particular shape seems to have strong marketing campaign behind it. It is not everyday you see mathematical concepts perk up commercial interest.
An object can move through an equilibrium position due to momentum, no? Being an stable equilibrium position just means that slight perturbations from that position will be reduced by the forces acting on it. An unstable equilibrium means any perturbation away from the position will be increased-- thus the object may pass close to this point, but will never stay at because even the smallest deviation would cause it to leave.
The unstable point is at the top of the crest. You would need a vacuum chamber with dampened vibrations to have any chance of it standing there, as any small deviation from a perfectly balanced position would make it fall.
In practice, friction and material deformation will probably give the top of the crest some degree of stability, possibly enough for a demonstration. At the very least it will probably be much slower to roll from such a metastable orientation.
Edit: also, based on the following gif someone else posted, I don't think the top of the crest is the metastable point. You can see the object linger at that point before seemingly spontaneously finding true equilibrium - illustrating my point rather well.
You could also just build a version of the object with an internal accelerometer and motor milled into it, that work together against torque. This would make the point of unstable equilibrium into a point of dynamic equilibrium, like a modern jet fighter, or a human being using their core to support their weight, or a hoverboard (but in more dimensions.)
There was a lecture on the long science night fest here about the Gömböc.¹ A very interesting observation accompanying the idea of the Gömböc is, that the number of stable and unstable equilibrium points decreases, the more a stone travels along a river.
> Each Gömböc comes with a booklet containing every necessary information about the product, as well as a unique product ID to identify the Gömböc and prove its authenticity.
Sandblasted Al: 239 Euro
Porcelain: 606 Euro
Steel: 499 Euro
Bronze: 599 Euro
Plexiglass: 199 Euro
Polished Al: 269 Euro
Al (rough polish): 199 Euro
Black (polyoxymethylene): 249 Euro
I'm guessing it costs an order of magnitude less than those published prices to machine an aluminum one, given an accurate model? The product page says the Al one is 500g, so the machining cost is probably the most significant factor?
But apparently their only shipping method that ships outside Hungary is "currently unavailable".
Well, there is also the option "SZEMÉLYES ÁTVÉTEL GLS CSOMAGPONTON" but Google is not very concrete when translating it. It sounds to me like picking up in a "something-point" though, which also looks like it's not international shipping.
If anyone keeps investigating and finds a gömböc that wouldn't make me broke and can ship without shenanigans outside of Hungary, I'd be grateful.
OK, I now see that the problem is that for some reason they do not ship to my work address's postcode... if I enter that code, they say that DHL delivery is temporarily unavailable. With my home address postcode, it works (a pity I'm almost never home).
> The shape of those bodies is very sensitive to small variation, outside which it is no longer mono-monostatic. For example, the first solution of Domokos and Várkonyi closely resembled a sphere, with a shape deviation of only 10−5. It was dismissed, as it was extremely hard to test experimentally. Their published solution was less sensitive; yet it has a shape tolerance of 10−3, that is 0.1 mm for a 10 cm size.
19 comments
[ 5.2 ms ] story [ 52.8 ms ] threadIt is also interesting how this particular shape seems to have strong marketing campaign behind it. It is not everyday you see mathematical concepts perk up commercial interest.
https://en.m.wikipedia.org/wiki/File:G%C3%B6mb%C3%B6c.gif
It would be interesting to see what the GP is describing.
In practice, friction and material deformation will probably give the top of the crest some degree of stability, possibly enough for a demonstration. At the very least it will probably be much slower to roll from such a metastable orientation.
Edit: also, based on the following gif someone else posted, I don't think the top of the crest is the metastable point. You can see the object linger at that point before seemingly spontaneously finding true equilibrium - illustrating my point rather well.
https://en.m.wikipedia.org/wiki/File:Gömböc.gif
¹ https://www.mis.mpg.de/wissenschaftsnacht2016/programm-im-vo...
If anyone would like to have their own gömböc, there is a web shop here: https://gomboc-shop.com
I'm guessing it costs an order of magnitude less than those published prices to machine an aluminum one, given an accurate model? The product page says the Al one is 500g, so the machining cost is probably the most significant factor?
I found this website which has much cheaper gömböcs (42 €):
http://gomboc-online.com/index.php/gomboc.html
But apparently their only shipping method that ships outside Hungary is "currently unavailable".
Well, there is also the option "SZEMÉLYES ÁTVÉTEL GLS CSOMAGPONTON" but Google is not very concrete when translating it. It sounds to me like picking up in a "something-point" though, which also looks like it's not international shipping.
If anyone keeps investigating and finds a gömböc that wouldn't make me broke and can ship without shenanigans outside of Hungary, I'd be grateful.
Means that you can pick it up personally at a GLS (like FedEx) point.
The checkout page does say it ships internationally: "DHL EXPRESS WORLDWIDE"