
Explain mathematically a video from a space station (2011) - bootload
https://mathoverflow.net/questions/81960/the-dzhanibekov-effect-an-exercise-in-mechanics-or-fiction-explain-mathemat
======
david-given
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...](https://arstechnica.com/science/2014/09/the-little-known-soviet-
mission-to-rescue-a-dead-space-station/)

...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
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?

~~~
pgtan
A 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
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?

~~~
pgtan
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](https://www.youtube.com/watch?v=Wxhv6GOLZqE)
[2]
[https://www.goodreads.com/book/show/20633100](https://www.goodreads.com/book/show/20633100)

------
semi-extrinsic
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.

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

~~~
mirimir
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?

~~~
ecma
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.

~~~
mirimir
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.

------
jeffwass
You 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).

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

~~~
bootload
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.

------
andrenotgiant
This was discussed on reddit three weeks ago, here's the post
[https://www.reddit.com/r/gifs/comments/61fbyr/the_dzhanibeko...](https://www.reddit.com/r/gifs/comments/61fbyr/the_dzhanibekov_effect/)

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.

------
philipov
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?

~~~
platz
it only happens if the rotation is along an unstable axis

------
bootload
A good example:
[https://twitter.com/fermatslibrary/status/853236042966552576](https://twitter.com/fermatslibrary/status/853236042966552576)

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

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

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

~~~
Sharlin
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.

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

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

~~~
hackuser
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?

~~~
dbaupp
For the specific case of X = Math,
[https://math.meta.stackexchange.com/questions/41/differences...](https://math.meta.stackexchange.com/questions/41/differences-
between-mathoverflow-and-math-stackexchange) .

~~~
drewmate
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?

~~~
allenz
Taking a look through
[https://stackexchange.com/sites](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

