Wasn't the guidance computer on Eagle programmed so that when Armstrong wanted to rotate the LM he moved the stick and the LM started to rotate, but when he centered the stick, computer ordered the RCS to fire to the opposite direction stopping the rotation...
Close enough. In Apollo 11 and prior, manual mode inherited its attitude from the autopilot at the instant of changeover. If, for example, you are very slightly rolled to the right, you will begin to drift to the right faster and faster. You must correct the attitude manually and cancel the drift manually. This was likely why Armstrong had so much difficulty nulling drift rates in the last moments before touchdown. Eagle was drifting at more than 2 fps leftward at touchdown.
A mode was added where centering the ACA commanded "null all lateral drift rates."
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