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Rotorblade Tektite:
 

Tektites are generally splash drops or amorphous shapes that tumbled about. One perfectly oriented tektite managed to spin in what resembles a flight state, possibly generating lift as the surface behind the leading edges to either tip point apparently experienced spalling.  All we really seem to know is that the tektite was spinning, and that there May have been an aerothermodynamic effect (a transient shock) that led to mechanical failure (i.e. spalling) of the presumably-trailing edges.  Uncertain plasticity and structural strength in a regime of rarified gasdynamics need to be resolved.  We need a good simulation to determine what this tektite represents.  It's just a loose hypothesis that lift was generated.  For the moment, this is the most mysterious tektite I've encountered among thousands of tektites.

We just don't know the wonder of it all.

Consider two conditions: 1) symmetric airfoil and 2) zero angle of attack.

An auto-rotator, even symmetric, can generate lift with zero cyclic pitch because the vector sum of its angular velocity plus its descent velocity results in an angle of attack.  But if the axis of spin is orthogonal to the net velocity vector (i.e. relative to the freestream), angle of attack is zero and there is no lift, thus no auto-rotation.  To put it more simply, if the object spins in the same plane as its trajectory (think discus, not
frisbee), and the body is symmetric, lift is zero.

OK, now you May ask, what about a boomerang?  After all, that spins in the same plane as its trajectory.  Fair enough, but examine a boomerang closely. It's flat on the bottom, curved on the top.  Not a symmetric airfoil, so it generates lift.

Is discus-spinning stable?  Gyroscopic force provides a restoring moment. With a sufficiently high moment of inertia, divergent aerodynamic forces (especially in a rarified atmosphere) will be inconsequential.  With a lower moment of inertia, (think flying saucer), aerodynamic instability results.  All well-designed flying saucers must either have tails or spin like...ahem, excuse me. This is supposed to be science.*

So there are some fairly strong constraints on the dynamic modeling of our little tektite weirdity.

There are probably other such tektites.  There is probably not an enormous number of such oddities.  This exceeds even the stable oriented buttons and more generally flanged Australites for aerodynamic weirdness.