Hello,
not an expert, and i'm already warming up for a party, so I really hope for someone wiser to come and offer a better explanation.
Re trim - the case boils down to the location of centre of lift, which is an acting point of the lift force, as integrated from lift distribution over a wing area. The point is also called the aerodynamic centre and as it is normally (reasonable regimes, conventional aircraft) located well behind the centre of grafity (of the aircraft), the resulting moment forces the plane nose down. That's why we've got the stabilizer back there. The point is that this aerodynamic centre, unlike the C/G, is nt constant, but linearly shifts backwards with growing angle of attack. The AoA, in turn, is directly related to amount of lift generated and hence to the airspeed. All summed up, an increase in speed results in a relocation of the aerodynamic centre, pitching moment changes and a retrim is desirable.
A cool web with animations
here.
With the yaw-roll coupling, this is one of the more difficult bits in aerodynamics and further factors such as the dihedral and the sweep angle play a significant role here. Very much simplified, let's say an airplane yaws from a rudder input, to the right. Because of its dihedral, the underside area of the left wing is now exposed to the airflow in a relatively larger extent to that of the right wing, and also because of its sweep angle, more airflow now follows lengthwise along an airfoil section, than it does on the right wing. As a result of those two effects, the left wing now generates more lift than the right one and the plane banks to the right. The entire process is reversible and works the other way round just as well.
Anyway, if you guys manage to get even a glimpse of the concept from what i've just written, a great kudos to you. I would've never been able to understand the principle, even in the silliest version, from any amount of text. I did have, though, a set of pics drawn by a friend of mine (an Einstein reincarnation and a very hot babe
), that helped a lot. I'll search them up and post, as soon as I recover from the hangover, which now appears inevitable.