@Owain Glyndwr
Dutch roll is certainly an oscillation, but it doesn't have to be one of increasing bank; in fact it would be a lousy aircraft for which that were true - very probably unflyable. Increasing bank as a result of suitably (mis)timed pilot inputs is quite another thing.
Sure the rolling motion is usually the most obvious sign of a dutch roll, but the motion is a combination of two oscillations -one around the roll axis and the other around the yaw - linked together by a common driver - sideslip.
Way back in the 1950s Ashkenas and McRuer established the importance of the roll/sideslip ratio as a parameter to describe the goodness/badness of dutch roll. The larger the number the worse the aircraft basically. So dutch roll can be triggered by rudder application, but as you say it is best controlled by aileron.
So far as I know, the A300 was not noted as having poor dutch roll characteristics.
I am holding that resonance definition of "dutch roll" from my automation teacher, an engineer working at the last French projects.
Iself had read conventional things about dutch roll in ATPL books but was interested by real dutch roll since 1979 from a Learjet Captain who feared it during any approach. I read and listening again.
And it happened that I decided to study automation after a background of pure and applied math, scientific informatik, and aeronautics.
One day (1985) the teacher resumed about stable/unstable systems : You know, phase planes, Lyapounov, Nyquist, Bode, sign of real part of poles, aso. And suddenly he had a thought, stopped one second, and said "Dutch roll is resonance tween the first degree system of roll of the aircraft, and action of pilot....
He ignored that at least one student from around 30 was concerned by dutch roll!
He came back to the class concerns, but the sentence was printed in my brain. I had not seen the learjet's or books' "dutch roll" in these terms. So I did nothing more during years with that declaration, despite all the respect I had for my teacher.
In my airline a MD 83 had in 1992 a dutch roll approaching NICE 05. They were very mute about it (well finished over the sea, the Captain leaved controls as he had learned as Cadet in USA. But the Airline head decided to let us discover the pleasures of dutch roll during the next off-line sim test. Nobody said they had all failed before me and I was the last one. The instructor was a former business pilot on Learjet! The first pilot started and lost 11000', we went on the back right and left... At the end the instructor said him very sad "You have seen it".
It was now to me. Suddenly I reminded to my automation teacher, and I thought that if "dutch roll" accorded to HIS definition, I could perhaps try to get it. I showed the animal,his position, speed, acceleration, counted seconds in my head, reckoned two easy differential equations in my head and piloted the result (nothing to do with the above B727 rolls described method).
And five times ago I was able to stop the "dutch roll" (in the sense of my former learjet instructor and the books) with a bank which was never more than 30°, in less than 30seconds, and never lost more than 1000 ft.
In my airline nobody asked me my method, included the instructor and the second pilot... Very sad,
I wrote it only in 1997 after I discovered that one of my former private pilot student had been killed as passenger from the Learjet which killed Baroin Sr perhaps in a dutch roll degenerating in a deepstall.Sad again.
I phoned to Leadair (LFPB) and finaly Learjet in Geneve (1998) . I told my story to the Chief Pilot, who answered they had finaly found a methodcagainst Leajet's dutch roll : ...sharing quickly the pedals... I asked me how it was possible to imagine that sequence.
On PPRuNe more recently I discovered that dutch roll was considered as a unworthy situation.
Machinbird who had written about PIO in the AF447 thread suggested me to read Mc Ruer's book about PIO and other APC.
I found there a world I had not found in aviation until that day : scientific methods and true solutions in the continuous and discontinuous domains of FBW and classical flights including the often missed rate limitations, omnipresent in FBW systems leading to oscillation (I don't remember mention in the FBW thread).
So I stay with my teacher's definition of dutch roll. I don't deny the roll and yaw reciprocity which conduced to the yaw damper conception, present on all airliners of course.
The failure of the yaw damper is the first cause of dutch roll or aggravated roll and yaw oscillations. If the pilot is not able to stop them quickly which is the most frequent case, the bank will really increase, also in the case where we still are in a first degree system in resonance with pilot's "normal" inputs...
About the stability of the "A300", the APA document refered by misd-agin is not so optimistic with the "FBW" technology version of the A300-600R. In any case iit needs its yaw-damper is functionning.
To mention too the sudden impulsion of yaw damper failure, and once again any brutality in piloting like quick reversals on rudder...
For the defense of some aircrafts major manufacturors I would like to remind that oscillation computation means are relatively recent.