@ Machinbird, Owain Glyndwr,
With your's teacher definition of dutch roll, Owain Glyndwr, the pilot does never need to do something to stop it. The yaw damper or the raw stability of the frame does the work. Once more "do nothing"...
With my teacher's definition of dutch roll (which has been more a flag in my brain than a complete definition -I told the context to emphasize that fact) , it works only if there is a dutch roll problem, not only a dutch roll...
1 vs 1.
The first order - surely more complex for the total plane- has already an oscillating output after an oscillating input - turbulence, yawcdamper failure, etc. -, and the pilot gives a second oscillation to try to stop the dutch roll "problem", starting resonance.
Semantics? Agreed.
Now we all know that after the AA587 we do not need to redefine Va. We need Va for what it isx not more, not less.
What we need is a new point of view that does not exist in our regulations of certification concerning RESONANCE. It could be builded on Machinbird's post and enhanced from his first text and his experience of PIO and high level flight experience. His post with Bode figure with numbers is a good beginning of what we have to think about the dynamic system.
In any case what is missing in our certification and knowledge is a quantified reference to dynamics of the transient parts of the plane's oscillation, Pio and other APC.
Resolving easy differential equations when flying (as I did) or reckoning dutch roll characteristics before computers (as you did 50 years ago) needs notthing more that what Richard Feynmann taughted to all his student : have no hesitation on basics calculations, integrals, aso.
