I find thinking about the Center of Mass (also called the Center of Gravity) is useful in helping me breakdown my skating
First, what is the center of mass? In layman's language, it's the average position of all the mass in your body. If you're standing up straight, the center of mass is a little bit below your navel. But it isn't there all the time. If you bend over far enough the center of mass can actually move outside of your body. The picture below (Fig. 1) shows some examples. If the arms are down, the center of mass is lower because the arms are close to the body. If the arms are up, the center of mass is higher because the raised mass of the arms has raised the average height of all the mass in the body. If the man bends over, he moves his upper body at an angle from his legs and the center of mass is averaged to a different place.
If the man in Figure 1 had weights in his hands while they were over his head, the center of mass would move even higher than shown in the picture. What would happen if he had weights on his legs in the picture on the far left? The center of gravity would be lower down, maybe even below hip level.
Is the man on the diving board (Fig. 2) ready to jump off? If he doesn't want to jump off, what can he do? He can lean back and bring his center of mass back, and the line of gravity will be closer to his feet, making it easier to stand.
It's easy to understand why we don't fall when the center of mass is over our feet, but why don't we fall when it's outside our body as in the man on the far right in Fig.1? Well, when we're standing we have big flat feet, and we have a superb feedback system in our brain keeping us from falling over. We maintain our balance by moving forward and back at the ankle so subtly we don't even recognize it. But if you lean forward with your arms over your head and weights in your hands, eventually you will swamp your body's ability to respond and you'll fall.
Once we get on the rocker in skates the added bit of stability from our big feet disappears. If you stood on your skates like the man on the right, in Figure 1, you probably would feel a bit of instability. But your body would make automatic adjustments to keep you from falling over. Unconsciously your body could do any or all of several things; e.g. bend the knees to move your rump back and pull the center of mass over the skates, or raise one leg behind you to move the center of mass backwards over the skate, even easing one leg back and moving the arms back might be enough. (But skating with your arms to your side brings in problems of a different sort.)
How does this help me in figuring out my skating fixes? Well, barring any math at all, this simple model of human balance is very helpful. Let's look at a couple of drawings of skaters and see if you can use the center of mass method on them.
In Figure 4 we see a young man doing back crossovers. Where's the center of mass? What about the line of gravity? Want to bet the line of gravity goes through the ball of his skating foot? What if the line of gravity is too far back? How do I think about correcting that? I admit back crossovers are a curse to me. Even though I understand them, I don't feel I've mastered them, but thinking this through has helped me improve them.
So how do I use this in understanding my skating flaws? Well, coaches have told me 'Hold those arms up!', 'Bend that knee!', 'Don't look down!', 'Don't hunch!', 'Sit down on that crossover!'. Once I started analyzing this from a center of mass and line of gravity process (no math, just thinking about it), I began to realize that stabilizing my skating had to do with keeping the line of gravity in the right place. And thinking about my skating as a physics problem motivated me to follow the rules. Coach wants me over the ball of the foot, I do exactly what he tells me to do to get there. And sometimes, I can figure out little tricks to help myself that he's never mentioned. Those little techniques of arm position, head position, and upper body etc. aren't just the arbitrary 'pretty skating' rules I used to think they were; they're newtonian physics in action. And I love physics.
I'm post on these skating techniques (Don't.Look.Down, Don't.Hunch, Bend.The.Knee, Keep. Your. Legs. Close) from the perspective of the center of mass. Then at some point, I'll get into moment of inertia (Hold.Those.Arms.Up), jerk (Move.Smooth), and Independence of Movement.