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This is the most interesting part of the pivot slip to me - the release:
From watching Bob Barnes and Jerry Berg's pivot slip drill video, it seems to me that there should be no edge release.....
Well, that's an interesting point. I think you're right.
You are saying that if you don't set an edge, you don't need a release. And not setting an edge in a pivot slip is a goal. Sure, why not?
To avoid setting that edge as the skis come around, one needs to do something specific.
We normally call it a release in a real turn, because in a turn we want grip and as the turn ends we need to let go of that grip. But not in a pivot slip - we need constant lack of grip. If a skier does that specific thing early enough in a pivot slip, and progressively enough, there will be no release.
The way to do a pivot slip to avoid setting that edge is to keep the CoM in the right place the whole time. When the skis are pointing downhill the CoM needs to be centered downhill, over the skis. When they pivot to point across the hill, the CoM needs to be between the feet, not uphill of both feet as often happens. Also one needs to keep the skis flat enough so they don't grip when they point across the slope. Keeping the CoM between the feet when the skis are pointing across the slope accomplishes both of these.
Letting the CoM get uphill of the feet as they point across the hill sets the edge and requires an extension release, or a flexion release, to get the CoM to cross over the skis. So not letting the CoM get uphill of the feet is the trick. So how does one do that?
Notice that as the skis point across the hill, there is tip lead because of the separation, and one foot is uphill of the other foot. When they point the other direction, there is tip lead again, but the opposite foot will have moved uphill. When pivoting the skis, if one pulls that downhill foot back uphill of the CoM as the skis rotate, the CoM will remain between the feet uphill-downhill-wise, and the task will be accomplished without a release. This is the magic move, the specific thing that will delete the need for a release - pull the downhill foot back uphill, so the CoM stays between the feet.
Pivot slips done this way can be very smooth and even quick. There will be no sticking point and no need to extend or flex to move the CoM downhill. The feet will have done all the moving.