This is the “tennis racket” problem, isn’t it? I “learned” it in college physics. To me, it is demonstrably true, but I just don’t understand it.
To be honest, I’m not entirely clear on why the smallest-moment axis is stable, either, but it is.
And we never said anything about tennis rackets when we studied it. It was always just bricks for us.
In simple terms, the highest moment principal axis has the highest resistance to change, while the lowest moment axis takes the least energy to change speed. The intermediate axis has nothing to recommend it, so any perturbations in rotation about it end up transferring momentum to P1 or P3. A more nuanced explanation requires delving into free gyroscopic motion, and that way madness (or at least, some seriously intensive mathematics) lies.
Stranger
Just to clarify, in Varley’s Titan novels, the upper surface of the torus was not open to space; there were large sections of the inner surface which were transparent so that sunlight could be reflected into the Titan.
Several sources mention the tumbling problem with longer cylinders, here for instance.
http://settlement.arc.nasa.gov/Kalpana/KalpanaOne2007.pdf
O’Neill’s Island Three design included two coupled cylinders, which could exchange momentum via their couplings and maintain any desired orientation. I would imagine that the same effect could be achieved by coupling the cylinder to a non-rotating light-gathering array (like the mirror in the Stanford Torus design) but this would require energy use.
The Dzhanibekov Effect. (You see why they call it the tennis racket effect, I guess.)
I don’t pretend to understand it, but this illustrates the concept pretty well.
(And gives me a headache.)
Strictly speaking, that just illustrates that the middle axis is unstable, and doesn’t say anything about the first or third axis.
But yes, that’s a really cool video.
I remember reading that NASA was considering installing a bar and lounge on the International Space Station but then decided against it.
The reason? No atmosphere.
How would a ball bounce in such a habitat? Suppose a spinning cylindrical or toroid habitat, very large, simulates 1 g just like Earth – would the ball in a sport like racketball, tennis, or basketball behave in the same way it would on Earth?
You would not need 1 atm of pressure at the surface level, but you would need the partial pressure of O2 to be approximately what is it here at 1 atm of pressure for life support.
So with lower pressure you could get away with lower walls. I don’t know how far you could push it, like if you could reduce the pressure to 1/5th of earth but have a nearly pure O2 environment. - however such a thing was proposed for mars if we can get enough pressure, apx 1/5th of earth through some unknown terraforming method then all one has to carry is a O2 pack to breath from, no sealed spacesuit required.
Over longer distances the curvature of the habitat and coriolis effects would be noticeable. Over short distances both effects become asymptotically small as the ratio of the rotation radius to the length of movement approaches infinity.
More about the Tennis Racket Theorem from this earlier thread:
See the video of the rotating handle repeatedly flipping for a mind-blower.
So the longer the ball is in the air, the greater the difference would be in terms of its movement with respect to how it would move on earth? Roughly how big would a habitat have to be (a radius in hundreds of meters, or kilometers, or hundreds of KMs, etc.) for, say, a tennis return the whole length of the court to not behave noticeably different than on Earth? Thanks for your input!
Theodore Hall has written extensively on this subject. This essay has some very interesting diagrams; for instance, running in one direction on a rotating habitat feels like running uphill, and in the other direction feels like running downhill.
Looking at his diagrams, it seems that a habitat needs to be considerably larger than 1km in radius before the Coriolis effects become imperceptible.
One point about the pressure at the top of the walls. It can’t just be low, like a 1/10 of an atmosphere, or a 1/100 for that matter. If you want an open top, its gotta be really low, otherwise your atmosphere is just gonna flow right on out of there.
For one G, you are probably talking 50 mile high sides and maybe closer to a 100 mile high. Maybe even more than that.