Why is the Discovery spinning end-over-end in 2010?

Question

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.

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:

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?

Answer 1

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.

Answer 2

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.

Answer 3

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).

Answer 4

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.

Answer 5

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

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.