MathOverflow will be down for maintenance for approximately 3 hours, starting Monday evening (06/24/2013) at approximately 9:00 PM Eastern time (UTC-4).

3 fixed title; edited title

# The "Dzhanibekov effect" - an exercise in mechanics or fiction? Explain this mathematically :http://www.youtube.com/watch?v=L2o9eBl_Gzw, a video from a space station

2 added 70 characters in body; edited title

# The "Dzhanibekov effect" - an exercise onin mechanics or a fiction ? Explain this mathematically: http://www.youtube.com/watch?v=L2o9eBl_Gzw,a video from space station

Question

The question briefly:

can

Can one explain the "Dzhanibekov effect" (see youtube videos from space-station space station or comments below) on the basis of the standard Euler's rigid body dynamics using Euler's equations? (Or respectively explain that this is impossible and this is that would be yet another focus ... )

More detailed

Here are more details.

See these curious videos from a space station:

Or in the original form which is more striking (~30 seconds after the start) start): http://www.youtube.com/watch?v=dL6Pt1O_gSE

So

A mathematical description of the model - is the standard rigid body motion in the empty space (since we are in the outer space). Which is , which (as is well-known) can be decomposed as into a center of mass motion and a rotation part described by Euler equationEuler's equations. (Euler's equation equations can be seen as a geodesic flow for some left-invariant metric on SO(3) - as V.I. Arnold taght). taught.) Let us forget about the center of mass motion.

The phenomena shown at in the videos is the following - a rigid body is rotating around the axis and then SUDDENLY the rotation axis CHANGES ITS POSITION by 180 graddegrees. And this happends happens periodically with some time period.

I am a little puzzled how to explain this?.

If we admit that the motion of this rigid body is EXACTLY the rotation around the axis this is for sure IMPOSSIBLE - Euler's equation equations predict that such a motion will continue forever. However in the real world there is nothing exact so it might be probably related to some instability effect - something that we are around an unstable equilibrium - and go out of away from it after some time...

Can it be so?

If it so, it is however non not clear why it happens so quickly and we get exactly the rotation axis changes changing its position by 180grads..180 degrees...

Vladimir Dzhanibekov who observed this in 1985 is a famous Russian spaceman cosmonaut http://en.wikipedia.org/wiki/Vladimir_Dzhanibekov He was in space 5 times (as far as I know he is the champion in this). In 1985 his "mission impossible" was saving the Soviet space station "Salut-7" which due to some problems had run out of control...

If explain this can be explained I think it can be a beautiful decoration for lectures illustration for students in lectures on rigid body mechanics... Also if one would want to add some humor in such a lecture one may add that our Earth is a this kind of this finger-nut finger nut so it might also do such things ... (May be Maybe it really can ?can?)

1

# "Dzhanibekov effect" - exercise on mechanics or a fiction ? Explain this: http://www.youtube.com/watch?v=L2o9eBl_Gzw video from space station

Question briefly:

can one explain the "Dzhanibekov effect" (see youtube videos from space-station or comments below) on the basis standard Euler's rigid body equations? (Or respectively explain that this is impossible and this is yet another focus ... )

More detailed.

See these curious videos from space station:

Or in the original form which is more striking (~30 seconds after the start) http://www.youtube.com/watch?v=dL6Pt1O_gSE

So mathematical description of the model - is the standard rigid body motion in the empty space (since we are in the space). Which is (as well-known) can be decomposed as center mass motion and rotation part described by Euler equation. (Euler's equation can be seen as geodesic flow for some left-invariant metric on SO(3) - as V.I. Arnold taght). Let us forget about center mass motion.

The phenomena shown at the videos is the following - rigid body is rotating around the axis and then SUDDENLY rotation axis CHANGES ITS POSITION by 180 grad. And this happends periodically with some time period.

I am a little puzzled how to explain this ?

If we admit that the motion of this rigid body is EXACTLY the rotation around the axis this is for sure IMPOSSIBLE - Euler's equation predict that such motion will continue forever. However in real world there is nothing exact so it might be probably related to some instability effect - something that we are around unstable equilibrium - and go out of it after some time...

Can it be so ?

If it so, it is however non clear why it happens so quickly and we get exactly the rotation axis changes its position by 180grads...

Vladimir Dzhanibekov who observed this in 1985 is famous Russian spaceman http://en.wikipedia.org/wiki/Vladimir_Dzhanibekov He was in space 5 times (as far as I know he is champion in this). In 1985 his "mission impossible" was saving Soviet space station "Salut-7" which due to some problems run out of control...

If explain this I think it can be beautiful decoration for lectures for students on rigid body mechanics... Also if one would want to add some humor in such a lecture one may add that our Earth is a kind of this finger-nut so it might also do such things ... (May be it really can ?)