Instability of long cylinders

>
> To which I responded:
>
> "Eh, you're referring to a real-life aspect of physics, but needlessly
> hyperbolizing it. It's more like if civilization fell in an O'Neill
> cylinder, and the stabilization systems failed, and if you went away and
>
> came back after a few decades, it would be tumbling end-for-end rather
> than
> on its long axis.

If I remember my physics correctly a cyclindrical gyroscope has a
magic length (I believe its 4.5 diameters but its been fifteen years
since I had to do that problem set) where the precision vector (the
thing that makes it want to go end-over end) is still has a component
pointing towards the axis (making the spin want to stay along the long
axis).

Now if a large force (say a substantial meteor) were to collide with
the cylinder, then the precision vector may be go past the circular
tangent and thus destablizing a such a cylinder momentarily but enough.

If the length is beyond the magic length the precision vector has a
component point away from the axis and will destablize.

>
> "Frankly, I consider the mirror design of Island 3 to come closer to
> making
> it impractical than the simple fact that it's longer than it is wide.
>
> "But the point relevant to Knobby's point was that cylinders 4 miles in
> diameter are possible with present materials."
>
Actually the mirror design is completely impractical, but it is
possible to decouple the mirror completely and have a non-rotating
conical section instead. The mirror would still need to be strong
enough to allow the precision needed to track the sun, and the actual
mirror would have to be designed not to completely fry the interior
(for example having strips of mirror panels followed by non-reflecting
or empty strips) since such a cone would be focusing light in the
interior.

> He came back to say that "It would tumbling be end for end in about ten
> minutes or half an hour" and further went on to say that an above-ground
> swimming pool breaking and dumping its water would be sufficient to
> destabilize the cylinder.
>

Again that depends on how long you make the cyclinder. If it is
substanially less than the magic length (which I claim is about 4.5
multiples of the diameter) then no this would never happen.

> So what say you guys? A problem if the automatic stabilization system
> remains off-line for weeks or months, or a catastrophic flip within the
> hour, killing millions?
>
> But ultimately, it occurs that my very first response should have been
> that an O'Neill Cylinder(s) habitat would actually have 0 net angular
> momentum because it's actually two counter-rotating cylinders. In The
> High Frontier, O'Neill only mentioned this as a solution to the problem
> of turning the axis of the habitat so as to track the sun, but could it
> be that this design solution was also proposed for the second reason of
> the instability of long cylinders?

Yes and no, the net angular moment is zero but the individual
cylinders have angular momentum and there is no reason why they can
fail individually.

Consider that a bridge has a net force on it of zero all the time (or
it would accelerate away) but that does mean the forces on the bridge
is zero. It means the sum of all the forces are zero. It can still
fail catastrophically (accelerate away from its position) if those
forces reach some critical point in a section of the bridge. This is
the same with the two cylinders. Together there is no net force on
them, but each has a large net force on them.

Bill