The posting trot is the centerpiece of saddle seat, at least as long as one is three-gaiting. In equitation, you wow the judge at the trot and then try not to lose the class at the canter.
However, it has been a red-headed stepchild in everything else I’ve done. In hunters & jumpers you trot to warm up. Then you canter. In dressage, the posting trot is a beginner’s gait. As soon as you require anything from the horse, you sit. Even in hunter equitation, posting comes behind canter position & sitting trot in terms of impressing the judge. The posting trot is a gait to be half-assed before you go onto something more interesting.
Therefore, my recent lessons have focused on posting trot mechanics: posting at a walk, posting without stirrups, lunge line work. At one point, I looked over to the other ring. One of the wee up-downers was doing the same exercises I was.
I’m having a blast. My technically-minded, detail-oriented self is all over this kind of work.
After three intensive trot lessons, we have the engine in pieces all over the shop floor. We will now attempt to reassemble it and get it running in the modified configuration.
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Gratuitous cat picture
Virtual Brush Box 
Back in the day when I rode Saddle seat, one of the key differences was that my trainer instructed me to ride from the knee, pinching it in at the knee flap. This resulted in your lower leg sticking out (heels! DOWN! keep it still!), creating a pivot from which the upper body then rose in rising trot, while keeping balance with the ball of your foot on the stirrup. This is thirty years ago, so who knows if that’s how it’s done (or even if it’s how it was properly done thirty years ago, I only had the one instructor), but if it’s the case, how on earth do you rise in the trot without the stirrup to balance you? Core strength?
Posting without stirrups is a key to building leg strength – and independent legs. Tightens the upper leg muscles like nobody’s business. Also develops balance. The kids I used to teach always called this “torture time” but it made them better riders. I always spent about ten minutes of each ride working without stirrups. Helped.
Sorry, K, that last sentence should have read: “without the leg to balance you.” The basic assumption I am making is that you are pivoting from your knee in Saddle seat, versus using the leg against the horse, as in hunter/dressage style.
Response tomorrow. I went on to such an extent that I converted it from a long comment to a short post.
Glad to be of service. 😉
Hurray! Recent discomfort aside, my horse is at his happiest and best when we’re trotting and I’m rising. I’m so glad that there is a discipline where this is championed.