Aerodynamic question for you engineers

Tina wrote:
[ Elided since this doesn't directly deal with any specifics of Tina's
posts, but rather the whole context of this thread. ]

(1) Yes, an aircraft can be made to appear to rotate around any point in
space. The center of gravity is (obviously) not a constraint per se to
those rotations.

(2) But for the purposes of predicting an aircraft's motion due to external
forces, engineers must deal with an extended rigid body. The center of
gravity is almost essential to successfully determining how it rotates
_and_ translates in response to those forces.

So when a pilot makes an aircraft do turns around, say, a pylon, the
engineer says that the aircraft is _rotating_ around its c.g. at the same
time that the c.g. of the aircraft is _translating_ around the pylon. But
why? Well:

(a) The reason why the engineer says the aircraft is _rotating_ around its
c.g. is because the aircraft is a single solid extended body.

(b) The reason why the engineer says the aircraft is _translating_ around
the pylon is because the pylon and aircraft are independent objects.

Hmmm. There is more I could say on the subject to clarify the above points,
but I'm not sure that investment of time would accomplish much.