Am 03.10.2018 um 02:34 schrieb Kenneth:
> To take a break from my other POV-ray chores, I made a simple animated demo of
> what an object looks like when it rotates (in POV-ray), as if free-falling under
> gravity-- but discounting wind resistance or any other extra force. Its a
> comparison between applying the rotations in two axes vs. three. I made the
> animation my own purposes (to easily refer to later), but it might be of
> interest to others as well.

If free-fall without air resistance is what you want to model, you
should use a /single/ rotation about an arbitrary axis.

This is because without external forces, angular momentum is conserved,
i.e. the axis of rotation doesn't change.


When you combine it with a second rotation, two things can happen:

(A) If both rotational axes remain stable in space and you apply the
rotations simultaneously, the result is just a single constant rotation
about a different axis.

A real-life equivalent would be a ball set in motion by two rollers
touching it on non-opposing points.

(B) If you apply the second rotation after or before the first, the
result is a precessing motion.

A real-life equivalent would be a rotating object mounted in a gimbal,
which in turn is also rotating.


Thing you get if you specify a two-axis rotation in POV-Ray is (B): The
rotation around the X axis is applied first, then the rotation around y
is applied, effectively changing the axis around which the first
rotation is applied.

This violates conservation of angular momentum, and thus is only
realistic when external forces are present, such as due to air
resistance. In that context, a precessing motion would happen if the
(asymmetric) wind resistance remained constant, which may be close to
realistic for some comparatively symmetric objects.

A rotation about a third axis adds yet another layer of complexity,
turning the precessing motion into a tumbling motion. This should be the
closest to realism at least for highly asymmetric objects.

In either case - precessing or tumbling motion - the motion will only be
a rough approximation of real physical behaviour.

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