Instability of long cylinders

From: Bill

> 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).

If true, it means that this particular single-cylinder habitat design is
probably OK:
http://ssi.org/assets/images/Ch06p086.gif
http://ssi.org/assets/images/Ch06p088.gif

> 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.

I've had similar thoughts, but we would have to give up the appearance
of a normal sun in the sky, especially as you moved closer to the
sunward end of the cylinder. Another thing I've though about was a
continuous mirror with a kind of bugle flare on it. Now we'd get a
continuous, single sun, but it's shape would depart markedly from a disc
shape. But that might be acceptable to many.

> 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.

Yeah, but I was thinking that the linking structures (one tower under
compression at one end, and one cable under tension at the other) would
restrain the cylinders, preventing the spin axis from departing from the
structural axis. In other words they would keep the wobble from getting
started.

Regards,

Mike Combs