In skiing, efficiency is the magic word. Everything we can do to reduce the energy and movement we have to expend to go where we want to go and do what we want to do as we make our way down the slope is a good thing. This striving for efficiency goes hand in hand with elevating our skiing prowess. We know a great skier when we see them, because they make it look effortless.
Well executed transitions are an example of that employment of efficiency. Great skiers don't have to make aggressive movements or devote big muscular efforts to move from one turn into the next, They have a little secret they use to make it happen virtually automatically, requiring them to expend almost no effort at all.
That little secret is "Imbalance". As we ski through a turn we are balanced. What does that mean? It means all the forces acting on our Center of Mass (CM) are in equilibrium, and we are able to stand on top of our skis without tipping to the left or right. We just stand in balance and ride our skis right around the turn.
As the end of the turn approaches, something needs to be done to disrupt that state of balance. If left alone we'll just keep right on turning. I'll use two common turn transitions to describe how that disruption of balance is done. OLR, and ILE.
OLR is the acronym for "Outside Leg Relaxation". It works like this. For this hypothetical, as you go through a turn you are balanced entirely on your outside leg. The combined effect of all the external forces acting you, those being gravity and centrifugal/centripetal force, are acting on your CM along a vector path that points right at your outside foot. If as you approach the end of that turn you relax your outside leg, your mechanism for resisting those forces goes away, those forces are now free to have their way with you, and your CM begins to pummel down towards your outside foot.
To avoid hitting the ground you tension your other leg, your uphill leg, and use that leg to catch your falling body. It works, but not perfectly, because you're not in balance anymore. The forces are still pushing your CM towards your old outside (downhill) foot, but you're standing on your uphill foot. It's as though you're a table, and someone just cut off two of your legs. You're suddenly out of balance, and begin to topple over, towards your cut off legs.
That's what happens in skiing. OLR instantly creates a state of imbalance, and you immediately begin to topple downhill, across your skis, and into the new turn. You've done nothing more than relax your old outside (downhill) leg, and allow your weight to passively transfer to your old inside (uphill) leg. At that point the external forces take over and power the transition for you. You've just exploited the external forces, and made them do the bulk of the work of transitioning for you. All you had to do to open their cage and put them to work was create a state of imbalance.
I'll leave it there for now, let you digest that and ask any questions you may have, then go into ILE later.