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In 2010: Odyssey Two, the Russian spacecraft Cosmonaut Alexei Leonov finds the derelict spacecraft Discovery rotating around its pitch axis (end-over-end). In the book, I believe this is explained as angular momentum which has transferred over the years from the centrifuge room to the rest of the spaceship. I don't think they bother to explain it in the film.

enter image description here

I'm not sure if there's a canonical layout of the interior of the Discovery, but all of the fan art on the Internet places the centrifuge at the back of the globe structure, with the centrifuge's central axis in line with the ship's long axis. And in fact, there's kind of a "cap" on the back of the globe that might help accomodate the centrifuge:

enter image description here enter image description here

But if the centrifuge's axis is along the Discovery's roll axis, then transferring that momentum to the rest of the ship would cause it to spin along its roll axis, not its pitch axis. So why is it found to be spinning the way it is?

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Rotation around the roll axis of a long thin object isn't stable; a mathematical explanation of why can be found in this Physics StackExchange question. Even if Discovery was initially tumbling on its roll axis the instability would cause conversion to end-over-end rotation over time.

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    Reading through the physics SE page leads to this book which cites a real-world example of the phenomenon. The torpedo-shaped 1958 satellite Explorer 1 was supposed to spin on its long axis, but precessed to end-over-end while in orbit.
    – Kenster
    Sep 1, 2015 at 21:34
  • @KyleJones Could you clarify why you believe the roll axis should be unstable? It is the minimum-moment-of-inertia axis, and so it seems that by the intermediate-axis theorem it should be a stable axis.
    – RLH
    Oct 22, 2019 at 22:33
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    @Kenster: My understanding of the Explorer 1 precession is that it was an effect of the satellite behaving as a deformable body with dissipation instead of the rigid body it was initially modeled as. This could actually provide a good explanation for how to get from axial to tumbling spin, but is a separate mechanism from the inherent instability of rotation about the intermediate axis (which, as I mentioned in my other comment, should not apply to rotation around the long axis).
    – RLH
    Oct 23, 2019 at 1:16
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    @KyleJones From Polhode: Rotation about the axis of minimum inertia (also called the minor principal axis) is also stable, but given enough time, any perturbations due to energy dissipation or torques would cause the polhode path to expand, in larger and larger ellipses or circles, and eventually migrate through the separatrix and its axis of intermediate inertia to its axis of maximum inertia. Real Discovery 1 would eventually (how much?) drop to (a/the) third axis. Maybe due to energy dissipated in vibrations of the main parabolic antenna. Oct 23, 2019 at 15:19
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    This explanation makes complete sense, but I just learned that in the book they correct the rotation by turning the centrifuge back on, which wouldn't work if this were the case - it would just end up tumbling all over the place.
    – N. Virgo
    Mar 25, 2022 at 4:03
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In the book, the Discovery's centrifuge (carrousel) spins on the yaw (vertical) axis of the sphere.

from chapter 17 of 2001:

The equatorial region of the pressure sphere - the slice, as it were, from Capricorn to Cancer - enclosed a slowly rotating drum, thirty-five feet in diameter. As it made one revolution every ten seconds, this carrousel or centrifuge produced an artificial gravity equal to that of the Moon. This was enough to prevent the physical atrophy which would result from the complete absence of weight, and it also allowed the routine functions of living to be carried out under normal - or nearly normal - conditions.

So it should be tumbling on that axis - sideways rather than bow-up/stern-down. It looks like this got lost or confused somewhere between the first book, first movie, second book, and second movie. The pod bay scenes in particular seem to indicate the centrifuge is on the yaw axis (the same as in the book), but other scenes seem to show it on the roll axis.

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    The original production blueprints of the Discovery interior reprinted on p. 49 of 2001: The Lost Science show the centrifuge hub at the back of the sphere, just as in the cutaway diagram Kenster posted (which according to this page comes from this book.) And Clarke's 2010 book was more a sequel to the movie than the first book.
    – Hypnosifl
    May 11, 2015 at 15:26
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If the ship had a torque applied to it perpendicular to the axis of rotation, conservation of angular momentum would cause the centrifuge to start to precess, inducing an end-over-end flipping.

Such a torque could happen from the air slowly leaking out through the airlock doors (HAL was not online to make corrections).

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For an out of universe explanation, the bone thrown in the air by the cave man in the beginning of 2001 is spinning around the same axis.

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    This is nice to know, but the question isn't looking for an out-of-universe explanation.
    – F1Krazy
    Jul 8, 2019 at 18:01
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During diving or tumbling a back layout somersault (end over end) with a double full twist (centrifuge rotation) we end up with the flipping to land on our feet.

At the 41 minute 30 second point in the movie (41:30) where we see the Discovery tumbling, approximately once revolution every 30 seconds, same rate as the Russian Leanov's.

Links to movie: www.AmericanMoon.org/2001/2010 enter image description here

At a rate of 2 rotations per minute, 120 per hour, 2880 per day, 1051920 per year, Discovery did 9.4 million flips during the 9 years from 2001 - 2010.

Discovery would have still been twisting somewhat along the longitudinal axis. But that would be harder for the movie model makers to do, and for Maxim Brailovsky and Walter Curnow to make the initial trip from the Leanov trying to grab the Discovery turning both horizontally and vertically.

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