I’ve been trying to answer this, but the Board hasn’t let me yet. Maybe this time…

It’s true that you expect that , if the centrifuge stops rotating because of the bearing seizxing up (lubrication fails, or the lubricant freezes, or something) that the whole Discovery will start rotating about the long axis, and you’d think that would be the end of it.

But even in the absence of outside torques, the object can shift in interesting ways. The equations describing the motion of rotating objects are the Euler Equations* for Rotations. One of the classic examples of these equations is the rotation of a rectangular solid with differemnt dimensions along the three axes. When they demonstrate this, they use a cardboard box taped shut, or a hardcover book with a rubber band around it to keep it from opening.

You can throw the book up in the air, rotating around the axis that runs vertically through the cover, and it will simply rotate about that axis. You can also throw it into the air rotating about the axis that runs perpendicular to the cover (and the pages within), and it’ll simply rotate. But if you try to throw it up rotating about the axis that runs horizontally through the cover, it’ll flip over iin the air.

For the first two cases, if you combine the Euler equations and do a bit of algebra you get a second order differential equation that has sines and cosines as its solutions, showing that small perturbations from a simple rotation about those axes result in little oscillations with no big changes – the rotation is pretty stable. But the third equation has the sign reversed, and the solutions are hyberpoluic sines and cosines (or expoential functions, if you prefer). Small perturbations from simple spin about that one axis rapidly blow up until the small angle approximation isn’t valid anymore, and the object departs from its spin about that one axis.

The Discovery isn’t a book-shaped object. If it were really more cylindrical, like a pencil, then it would have a pretty stable rotation about that long axis, until something big perturbed it. But it’s got that wonking big AE-35 communication dish (with its two side dishes) sticking out of the center, and that’s probably throw things off and make rotation about the long axis unstable. Even absent outside perturbations, any slight wobble would quickly be magnified until it started rotating about one of the other axes. Ahnd I’d expect it to be the one running perpendicular to the plane with the antenna – which is the one they do show it flopping over.

I can’t find a webpage with the book example, but I don’t doubt it’s out there on the web. Look in a good upper-level book on mechanics.

Leonard Euler was one heavy hitter, with several sets of equations to his name. You have to specify “Euler’s Equations of Rotation” so people don’t tyhink you’re referring to Thermo, or something.