There is very little out there (or in this thread) that is helpful for teaching this to people who haven't already learned it via V2 in alpine skiing or in some other way, usually when very young. Vitrually all instruction I've seen - and I'm PSIA - has a problem presenting the matter dynamically. Learning as an adult, I had the same problem. Here's the approach that I happened upon that worked for me, and one that I've used repeatedly with students are having a problem (note: this method assumes a skier's ability to use visual imagery, which is not something that is in everyone's cognitive wheel house - learning styles and all that):
- assume correct posture with or w/o skis on
- find center of gravity/center of balance. For our purposes, that will be the halfway between the heads of the femurs horizontally and halfway between the navel and pubic bone vertically. For practical purposes, that means go directly below the belly button to the bottom of that roll of fat, and then mentally take that inside to the middle.
- Imagine there's a fist-size shape or ball at that center point with a 3-foot arrow coming out.
- Then move or ski the arrow down the track mentally, i.e., moving it in the direction of the next ski, stride after stride or skate after skate. Hence, it's like you're moving from this center point (core, center of gravity/balance, etc.), guiding the arrow ahead. N.B. This is *not* sticking out the stomach but rather imagining an extension ("arrow") coming out of the center, which one is mentally using to guide their body ahead.
What this does is 1) cause the hips to rotate slightly up and forward very subtly (N.B. just imagining it causes that before even moving); and 2) leads one to move oneself from the center or core instead from the periphery (arms, legs/feet).
Note: This is a drill, which must be practiced a lot, continuously, and usually through a few sessions until the new body position becomes a matter of habit. It creates the basis for using other, more advanced, keys of movement to be used (driving hips, knees, etc.). It also serves as a fall-back technique thought for steeper hills, especially in skating, when continuity sometimes breaks down, and in general, for technique self-checks.
I have a single page PDF cheat sheet showing it graphically and with text that I put together from a Silent Sports series by John Burns several years ago (the series was way too long and complicated). If you'd like to see it, write me at genegold**[at]**fastmail *dot* net (get rid of the extraneous).