Lu said, "[Matthew has] just expressed [his] opinion and it differs from mine."
Lu, our opinions differ in how helicopter theory should be taught, but the information I gave about gyroscopic precession is fact not opinion.
I'll restate my position for you. Gyroscopic precession is a good way of teaching helicopter theory, but it is not completely accurate. I believe that a more fundamental look into rotational dynamics is better. Use gyroscopic precession as an example but don't teach it as the be all end all theory that it is sometimes presented as.
The point I was trying to illustrate is that all these theories are actually snippets of the same theory. The math that Nick referred to that substantiates the blade flying to position theory is the same math I used to derive gyroscopic precession in a very simple rotating body (that's why I used a hockey puck rather than AI or gimballed gyro).
I would be careful in substantiating a theory in helicopter dynamics by stating that it is the way that it is taught in training schools. That, to me, is like saying an introduction to computer science gives you enough theory to design a workstation. Facts are often somewhat inaccurate on purpose when being presented to non-experts. This is because the full story is far too complicated for the scope of the crowd, and a close enough description creates better understanding in general. This is why I see teaching helicopter dynamics using gyroscopic precession to be valid. Doesn't mean it's right.
In a different post, Lu said, "One might be led to think that at point A the blades are at their lowest flapping point they would also be at their lowest pitch."
Even if you ignore all the rotationally related theories, it is still obvious that the blade is moving (descending) prior to arriving at it's lowest point of flapping. The blade doesn't just magically stop there, the "brakes" are put on prior to arriving there. This means that pitch must be increased from it's lowest value prior to arriving at the blade's lowest point of flapping.
Lu also said, "If there were only one theory to cover a given area of science we would still be trying to make gold from lead."
It can be done, it's just not economically feasible.
Matthew.