Explain mathematically a video from a space station (2011) | Hacker News Reader

Explain mathematically a video from a space station (2011)

mathoverflow.net

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I 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-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...

Wow. 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?

A russian film is just made on this topic. Here a link with trailers on the page:

http://ctb.ru/en/films/salyut-7/

That looks really cool (although the free fall scenes are faked, sadly) --- do you know if it's getting an international release with English subtitles?

no idea, really. Apparently the film should be already out in the Russian cinemas. There is also a documentary from Roskosmos about the operation[1]. The beginning is boring, but then they claim, the Shuttle "Challenge" visited Saljut-7 as a preparation for taking the soviet station to the Earth. Still watching it, no subtitles (my Russian is rather intermediate). There is also a book from Victor Savinikh, the flight engineer called "diaries from a dead station"[2], but couldn't find any comments on that book.

[1] https://www.youtube.com/watch?v=Wxhv6GOLZqE [2] https://www.goodreads.com/book/show/20633100

I'm amazed it's not better known. (Of course, the USA had to send an emergency repair crew to their own Skylab station when a bit fell off during launch...)

Re station-to-station transfers: Mir and Salyut 7 both had the same orbital inclinations (probably deliberately) of 51.5°; Mir's apoapsis was about 360km, Salyut 7's was about 250km. So a transfer would be relatively cheap. The vehicle was a Soyuz T only had about 320m/s of delta-V, which was also needed for rendezvous and deorbit, so it would have to be.

I think this was the only station-to-station transfer ever done. It was probably only feasible because they were in the same orbital plane.

(Although I'm a little surprised they didn't build Mir using Salyut-7 as a core module. Even if they ditched the module later as it wore out, it'd provide power, attitude control and automated docking.)

Thanks for the extra info!

According to the article this was indeed the only station-to-station transfer, and although very cool I am not sure exactly why would you do it except for some emergency or for building up a new station out of parts from others like you suggested.

Do you have any idea what use would there be for a s-to-s transfer? I'm guessing it's more expensive and dangerous than launching a specific mission from Earth, so the use would be limited. Maybe to test some emergency procedure a-la Gravity (the movie)?

It would be really cool if there was some other big space station so that this would be something to think about... but oh well, I guess having the ISS will have to suffice for now.... It's not like I have the money to build my own unfortunately :(

I 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.

Terry Tao is also the author of the top answer, mind.

Wow, 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?

The 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.

Thank 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.

Given 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).

You can see the effect with a tennis racket. 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).

Who keeps changing the titles on HN threads? This is about the Dzhanibekov Effect (as the title used to say), not space stations!

I 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.

This was discussed on reddit three weeks ago, here's the post 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.

I 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?

it only happens if the rotation is along an unstable axis

A good example: https://twitter.com/fermatslibrary/status/853236042966552576

Thanks for the link. What a goldmine of cool stuff!

Did Terry Tao, the great present day mathematician just answer that?

No, he answered that in 2011 :-). And he and many other famous (and not so famous) mathematicians contribute to MathOverflow

Math 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.

What is generally the difference between X Overflow and x.stackexchange.com? Both are from Stack Exchange, AFAICT.

I believe the X Overflow are the old format, and are now just grandfathered in. All new ones are in the latter style.

Thanks. 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?

For the specific case of X = Math, https://math.meta.stackexchange.com/questions/41/differences... .

That is interesting. I can see the logic there, mostly I'm just impressed that both sites maintain a critical mass of activity, since (at least in recent years) SX seems to require a pretty high level of engagement to get out of perpetual beta.

Does anyone know of any other cases with two similar but distinct SX communities?

Taking a look through https://stackexchange.com/sites, I see several fairly specific programming communities:

askubuntu.com and unix.stackexchange.com

vi.stackexchange.com and emacs.stackexchange.com

stackoverflow.com and codereview.stackexchange.com

Math Overflow was created as a Stack Exchange 1.0 site, which means essentially that SE hosted the software, but everything else was done by the users that initiated the site.

A few years ago, SE stopped supporting the 1.0 sites, and Math Overflow decided to join the Stack Exchange network. They're still somewhat special, e.g. they have the right to leave the SE network again, if they would want to.

At least on the math side, MathOverflow is generally for research level questions, and math.stackexchange is for any level math, often easier, questions.

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