Thank you Keith
Now I start to understand better.
So we are substituting
Lift-acting-at-the-CP by
Lift-acting-at-the-AC-plus-a-pitching-moment (which is convenient because it is constant with AoA).
The net effect would be the same as they are equivalent concepts.
I have always accepted that demonstration of the existence of a point with such a property, graphically expressed in the sketch by LM.
hmmmmm
But Is this pitching moment the same as the aerodynamic moment? Or is the sum of the AM plus the moment of Lift about the AC?
To find the required tailplane lift to trim the airplane in steady flight, we need to know the value of the Lift, the location of the CP and the value of the aerodynamic moment (which should be independent of any point we consider, if we are talking about a couple of forces).
Or, alternatively, we can consider Lift as acting on the AC without forgetting to add the pitching moment with respect to AC.
Still don't understand how the effect of the AM "magically dissapears" in the stability equation.