I think that there's a "look_at" type positioning of the object, and a "sky"
type twisting.

With regard to the "look" and "feel" of the motion, I do believe that Stephen
and TdG agree with me that 1 more thing is "too much".

Consider the external ballistics of a projectile.
Usually one imparts spin to stabilize it in flight, and this gives it a
rotational inertia that must be overcome to twist it perpendicular to the axis
of rotation.   The faster it spins, the less it nutates.

So I think that you may have a tumble with a bit of wobble, but adding a 3rd
element of motion just doesn't seem to "fit in" to the scheme of things.

https://www.google.com/search?q=projectile+stabilization+spin

Of tangential, somewhat related interest is how calculators do sin cos, etc,
which IIRC has it's origin in flight computers.

https://www.google.com/search?q=cordic
https://www.qc.cuny.edu/Academics/Degrees/DMNS/Faculty%20Documents/Sultan1.pdf

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