8 ms·
Explain mathematically a video from a space station (2011)
- bootload 9y agoA good example: https://twitter.com/fermatslibrary/status/853236042966552576 https://twitter.com/fermatslibrary/status/853236042966552576
- avenoir 9y agoThanks for the link. What a goldmine of cool stuff!
- jeffwass 9y agoYou can see the effect with a tennis racket. https://en.m.wikipedia.org/wiki/Tennis_racket_theorem https://en.m.wikipedia.org/wiki/Tennis_racket_theorem Basically the rotation of any 3D rigid object can be reduced to the rotation of an equivalent ellipsoid. The lengths of the three principle axes of the ellipsoid determine the moment of intertia around that axis. For the case where the three principle axes are different lengths, the rotation is only stable around the smallest and biggest axis. Ie, in a tennis racket you can easily spin the racket around the axis of the handle, and also the axis that is perpendicular to the plane of the netting. But the racket won't easily spin in the axis perpendicular to these two. We saw this as a demo in my undergrad classical mechanics class using a book (where the three axis are a bit easier to see since a book is more uniform).
- semi-extrinsic 9y agoI love how someone in one of the answers has an intuitive feeling that the phase space dimensionality can be reduced, and asks "does this hold generally", and then Terence Tao comes along in a comment and explains why it indeed does hold. Math Overflow must be one of the most extreme examples of successful communication on a narrow topic between people at widely different levels of fame/skill.
- Sharlin 9y agoTerry Tao is also the author of the top answer, mind.
- mirimir 9y agoWow, I could actually follow that explanation, and it's been decades since I thought much about mechanics. Very intuitive. However, I'm left a little confused at the end, by this: > The process then repeats itself (imagine a marble rolling frictionlessly between two equally tall hills, starting from a position very close to the peak of one of the hills). But it's not really just two hills, I think. It must be two hills in a closed space, because you can get from one peak to the other in either direction. Yes? Also, back in physical reality, I wonder whether the periodic axis rotation continues in the same direction, once a small perturbation gets it started. Or whether the direction of axis rotation randomly changes. Anyone know?
- ecma 9y agoThe Lagrangian answer covers this a bit more obviously by stating a solution which results in a closed curve of states around some equilibrium point(s) for certain initial variables. I think that matches your understanding of this as two peaks in a closed circuit.
- mirimir 9y agoThank you. When I saw this thread, I was sure that it would be something about orbital mechanics or the Coriolis effect. But no, it seems.
- Double_Cast 9y agoGiven Tao's rotating frame: * For each M-mass, the centrifugal-vector lies along the x-axis. * For each m-mass, the centrifugal-vector lies along the z-axis. * For each centrifugal-vector, the magnitude is proportional to "the point-mass's distance from the disk's axis-of-rotation (the y-axis)". Since the m-masses move along a unit circle in the yz-plane, their magnitudes vary. E.g. an m-mass which starts at (0, .9, .1) will accelerate towards (0, 0, 1) then deccelerate towards (0, -.9, .1). Then it will retrace its path. This results in oscillation between (0, .9, .1) and (0, -.9, .1) along a semi-circle in the yz-plane. N.b. no oscillation will occur if an m-mass starts at exactly (0, 1, 0).
- sidcool 9y agoDid Terry Tao, the great present day mathematician just answer that?
- BlackFingolfin 9y agoNo, he answered that in 2011 :-). And he and many other famous (and not so famous) mathematicians contribute to MathOverflow
- Sharlin 9y agoMath Overflow is probably one of the most hardcore SX sites there are. Even most of the easiest topics discussed are MS or PhD level math, and many (most?) of the regulars are career mathematicians. Then there's math.stackexchange.com for us mere mortals. But I believe that division did not yet exist in 2011, though.
- hackuser 9y agoWhat is generally the difference between X Overflow and x.stackexchange.com? Both are from Stack Exchange, AFAICT.
- dbaupp 9y agoI believe the X Overflow are the old format, and are now just grandfathered in. All new ones are in the latter style.
- hackuser 9y agoThanks. What I meant to ask was, given X is the same topic, what is the difference between X overflow and x.stackexchange.com? That is, if there is a general rule. Perhaps the answer is the same: It's just age. But then if X Overflow already existed, why create a redundant x.stackexchange.com?
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- david-given 9y agoI can't comment on the effect, other than that it looks really weird and I'd really appreciate a plain-English explanation, but Dzhanibekov is also famous for being part of the repair crew that flew to the defunct Salyut 7 space station in 1985. There's a good writeup here: https://arstechnica.com/science/2014/09/the-little-known-soviet-mission-to-rescue-a-dead-space-station/ https://arstechnica.com/science/2014/09/the-little-known-sov... ...but the tl;dr is: no power, no automated docking system, no life support, no onboard computers, and it was so cold that all the station's water supplies had frozen. They got it working; Dzhanibekov ended up staying on the station for 110 days...
- saganus 9y agoWow. That's one hell of a story! It's like those hollywood space stories.... Only real. And then... A station-to-station transfer?!? That must be really hard. I mean, I'm no astronaut, but even in KSP it's a hard operation. Can't even begin to imagine what kind of skills and calculations that required. Both stations need to be on sinilar altitudes I guess? Otherwise the amount of fuel needed would be prohibitive, no? Could any one shed sone light on this manouver? I mean, if that's the only obe time this has been done it's probably because it' very hard and I'm guessing it's not something terribly useful. Or is it? Any write ups on this?
- pgtan 9y agoA russian film is just made on this topic. Here a link with trailers on the page: http://ctb.ru/en/films/salyut-7/ http://ctb.ru/en/films/salyut-7/
- david-given 9y agoThat looks really cool (although the free fall scenes are faked, sadly) --- do you know if it's getting an international release with English subtitles?
- pgtan 9y ago
- seanwasere 9y agoyou can simulate it using the blender game engine. this video shows you how. https://www.youtube.com/watch?v=kXwS-3Uy3WI&t=107s https://www.youtube.com/watch?v=kXwS-3Uy3WI&t=107s
- philipov 9y agoI like how in the second youtube link, they go on to speculate this effect is responsible for the flipping of the magnetic poles because the earth's axis changes directions. Does anyone know more about where the current state of research is on that?
- platz 9y agoit only happens if the rotation is along an unstable axis
- deleted 9y ago[deleted]
- Y_Y 9y agoWho keeps changing the titles on HN threads? This is about the Dzhanibekov Effect (as the title used to say), not space stations!
- bootload 9y agoI take care on the titles. I even forget the exact title but I did put ^Dzhanibekov^ in there. There is an army of little helpers trying to make it easier. I'd prefer the ones I assign 'cause I take care to stay within the 80char limit, be technically descriptive and true to the article.
- andrenotgiant 9y agoThis was discussed on reddit three weeks ago, here's the post https://www.reddit.com/r/gifs/comments/61fbyr/the_dzhanibekov_effect/ https://www.reddit.com/r/gifs/comments/61fbyr/the_dzhanibeko... I think it's interesting to see the difference between stackoverflow and reddit explanations and content in general. On stackoverflow you have (purported) experts talking to experts, and the voting system seems to bias towards answers with lots of technical details and difficult terms. Reddit is exactly the opposite. SO is great for answers in your area of expertise, but when you just want to understand the basics, reddit bubbles up some really good explanations.