Well let's see now. It seems to me the pivot point for the gun is going to be at its point of contact with the shoulder. Assuming no cast & the but fitting the shoulder squarely (Neither of which is a universal given) then this pivot point could be extended forward down the center of the gun. As the axis of the bore for the right barrel would lie in its entirety to the right of this line then the natural tendency would seem to be for it to swing to the right on firing. Vice/versa of course for the left barrel. Due to the fact that on all doubles I am even remotely aware of the barrels converge toward the muzzle it would appear the major movement at least follows this general theory as they still shoot essentially to point of aim. There are of course other minor movements occurring due to barrel flexibility etc, but this would seem to be the major one. This would tend to move the stock away from the cheek in firing the right barrel & toward it when firing the left. It will of course rise when either is fired & to a greater extent than the side movement. There is of course the matter of barrel Whip to consider. This occurs as the gun starts to move in one direction the flexibility of the barrels will cause the muzzle to lag or even move in the opposite direction. This can be easily visualized by holding a fly rod out in front of you. With a good grip ion it flip your wrist to one side while watching the tip. You will not it move at first opposite of the way you moved the butt. It would seem to me that the barrels would be stiffer, thus less whip, in the sideways direction than vertical & also there would be more impetus given in the vertical direction. As said though there is a lot going on that cannot truly be seen..
