OK, I found this thread:
https://www.rocketryforum.com/threads/rocket-guidance.30537
It was about guidance overall, but drifted to pendulum guidnance in message #19.
And here is a reply I made, after others made good posts pointing out the problems with gravity based guidance. This looks at what would really be happening onboard, totally ignoring gravity, but totally focusing on any system that would respond to any horizontal force. (that is, perpendicular to the rocket's body, not the Earth, no matter which way the rocket was pointed).
(from:
https://www.rocketryforum.com/threads/rocket-guidance.30537/#post-328689)
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"A lot of good explanations of why a pendulum system won't work for rockets.
Here's another bug, that does not involve why gravity won't make it work.
It's lateral acceleration, or "sideways" G-forces relative to a rocket that for the sake of this beginning properly, at the launch is (was) pointed vertical.
Assuming a perfectly smooth vertical launch, the flight acceleration G force is perfectly straight down the length of the rocket, a line from the nose tip thru the center of the engine nozzle.
But then, a little bit of wind causes the rocket to have a very tiny angle of attack to the airflow, and therefore a tiny little lateral (sideways) G-force.
It's now doomed to rapidly force itself off-vertical and either hit the ground or do loops in the sky.
Note that the little lateral G-force in this case is not gravity-related, it's due to the airflow at a very slight angle of attack and therefore a slight lateral g-force. The rocket could be perfectly vertical but a wind gust could cause this lateral G-force.
The Pendulum guidance responds to this by producing a small corrective deflection to make it "turn" the other way to counter it the presumed off-vertical tilt, but that very corrective force causes its own G-load..... in the same direction as the original disturbance.
The Pendulum system then responds to its own self-generated lateral G-load by moving the control surfaces even more, causing even more of a lateral G- force, and in response to that more corrective "control" which feeds on itself rapidly until the Pendulum system reaches maximum control surface deflection and locks up completely, making the rocket do loops around and around until burnout (and then a few more loops till it slows down enough).
Actually what I described in the above paragraph would happen in a fraction of a second, from first tiny control response attempt to maximum lock-up.
So, if anyone does not quite believe that gravity won't make a free-flying pendulum work, then ignore the gravity part and note the above as to why it won't work for vertical guidance for rockets, it's own control response forces would lock itself up into a loop (if it did not hit the ground first)."
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I hope linking to that 2011 thread does NOT bring about yet another round of "guidance is not legal" crap. It is, long as it's unable to target anything (using guidance to fly "up" is fine).
- George Gassaway