Reading the thread about all of this started me thinking about my own ideas concerning this. There are teachers who advocate a purely rotational turn (like in the barrel). John Redman comes to mind on this. Ben Hogan in his Five Lessons stated, "To begin the downswing, TURN YOUR HIPS BACK TO THE LEFT. THERE MUST BE ENOUGH LATERAL MOTION FORWARD TO TRANSFER THE WEIGHT TO THE LEFT FOOT. The path the hips take on the downswing is not the exact same path they traveled as they were turned on the backswing. On the downswing, their "arc" should be a trifle wider--both as regards the amount of lateral motion and the amount of eventual rotation around to the rear." There are proponents of both schools of though. Personally, I agree with Hogan. However, I prefer not to think about either lateral motion or rotation in my swing. I know they happen but if I focus on making them happen usually it will be overdone and a bad shot will result. (I am speaking of the swing and not drills designed to promote the proper sequence, such as the Bertholy drills). IMO, a purely rotational move of the hips will be much more likely to cause the trail shoulder to come around and over the top. With the lateral move made first it helps to get the trail shoulder dropping into the slot. Hogan demonstrated this quite well and I think Peter has posted Hogan illustrating this in the past. Anyway, just my thoughts.
All tour pro swings that I've analyzed on video including Moe have both a lateral move and rotation from top of swing to impact. All of these start with the lateral move before the rotation. Sequencing is important.