Re: Couple Old Style Space Opera questions...

James A. Donald
Imagine a cylinder where the rotation axis is
slightly misaligned to cylinder axis. Say the
cylinder is four kilometers wide and twenty
kilometers long, and at the ends the axis of
rotation is three kilometers off the cylinder axis.
It is immediately apparent that near the ends of the
cylinder, all loose objects will be smacked hard
from one side of the cylinder to the other every
rotation or so. This dissipates a significant
portion of the rotational energy of the cylinder in
every rotation, which means that the cylinder is
going to move a lot further off axis in every
rotation - that the growth of the instability is
going to be of the same order of magnitude as the
rotation time of the cylinder.

Alternatively, spin a raw egg about its axis and
see what happens. It flips in about one or two
rotations.

Michael Ash
So no math, then?

If the egg is insufficient, you will not be interested
in the math.

If w is the rotation vector, and I is inertia tensor,
then Iw is the angular momentum, and wIw is the kinetic
energy.

You will notice that for a given angular momentum, the
kinetic energy will me minimal when object is rotating
about the largest principal axis of inertia, and maximal
when it is rotating about the smallest principal axis of
inertia. A wheel rotates about the largest axis of
inertia, a cylinder about the smallest. So a cylinder
spinning about its axis is at an energy maximum, hence
unstable.

--
----------------------
We have the right to defend ourselves and our property, because
of the kind of animals that we are. True law derives from this
right, not from the arbitrary power of the omnipotent state.

http://www.jim.com/ James A. Donald
.

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  • Re: Couple Old Style Space Opera questions...
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    (rec.arts.sf.science)
  • Re: Couple Old Style Space Opera questions...
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    (rec.arts.sf.science)
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