Well, as I said before you are very confused because you do not understand the terminology nor its definition.
For example:
When a vessel is moving against the wave propagation direction, and a wave lifts the bow to cause pitching, I would have described that as excitation moment, not restoring moment, ….
That’s because you are unware of how seakeeping is defined and derived. As you are mixing and matching, as noted here:
… to achieve the same pitch resisting lift force with same induced drag but less viscous drag.
So….is it a force or is it a moment? Hmmm…YOU decide!
Yet you seem to not like this statement:
..An active system will also provide a ‘counter’ restoring force in real time to the response. ...
By your reply:
..You seem to mix force (left hand side) and moment(right hand side) in the same equation…
A foil providing a force, is a restoring force. Thus, it is no different to the shape of the hull that provides reserve buoyancy when a vessel rolls or pitches. The “force” is the buoyancy force. This is the “c” component in the equation of motion. The restoring moment.
Thus further understanding and definition which axis of motion you are referring to, when it is heave for example, it is just a force. When it is pitching/rolling it is a moment…thus which are YOU talking about as you cannot lump sway, heave etc with roll/pitching all into one. But for now, I put that down to your lack of knowledge in seakeeping. But, it doesn’t alter the fact that there is a “force”, whether it comes from the hull (its shape providing the reserve buoyancy) or via lifting device that is added as an appendage matters nowt – it is a restoring force.
You also seem not to like that fact that some equations show F as the excitement. When you think it should be M – exciting moment. So, your bone of connection is merely semantics of how the equation is written, or rather the letter of the alphabet that is used. The fact that F is used rather than M…. oh my, then you better tell Professor Molland not to use “d” then as he does here:
And others like::
and
They like 'F'..
And so, just for clarity if you start to read any of the text you will find this:
I assume this will please you because this author uses M rather than F or D...!!!
If you don’t like the fact that each author uses different letters for the terms that do not sit well with you, I would suggest you take it up with them.