Think about it.
Sitting trot seems easier without stirrups because the rider is utilising gravity and the full weight of the body against the upward thrust from the horse's movement. Ie the rider's full weight is heavier than the force of the thrust. However without stirrups all the rider can do to absorb thrust is to "crumple" at the waist and perhaps take some of the thrust in the fatty tissue of the butt because the upper skeleton of the human is pretty rigid.
With the aid of the stirrup irons there are additional shock absorbers for use ie the toes, the ankles, the knees and the hips. These joints which are kept under tension by ligaments can bend under the force of the thrust and can thereby absorb the thrust.
It is all bit like skiing downhill - the skis go up and down but the hips stay at the same height.
To sit the trot starts with the correct "seat". Toes up, heels down, stirrups adjusted correctly, toes turned parallel to horse's body,body weight on the three seat bones , sat up straight 90 degrees whilst retaining natural curve in lower back , head upright and looking straight ahead, hands held either side of horse's wither. Stomach muscles held in. Rider in perfect balance and shoulders relaxed yet without slumping. When in this position the rider should feel the horse through the saddle via the under thigh muscles.
When practising first the rider has to sense the rythym of the horse and the slower the jog the better at the beginning. Up down, up down. A horse with a nice long stride makes it easier - ponies move their legs too fast and too short. The faster the horse moves - the more difficult it becomes. Careful selection of a suitable patient horse is important - because having a learner human bouncing up and down on its back is not every horse's idea of fun.
With practise eventually the silent part of the brain which controls our instinctive reactions starts to learn what to do. That bit of the brain certainly doesn't want to fall off. But it is very important that the rider starts from the correct "seat" - otherwise the silent brain may learn to respond incorrectly.
A shoe lace across the front of the saddle will act as a balancing aid for use by the thumb - but the rider must not tip forwards.
It also helps if the learner rider is sitting on a horse on the lunge - so that the responsibility for keeping the horse steady is with the person in the centre of the arena.
The big enemy of learning the sitting trot is tension in the rider. The brain sends out the message "this is dangerous" and as a result the body stiffens up at a time when relaxation is the key requirement. Keep the work light hearted. Try some music. Wiggle the toes. And work on it for short periods only and steadily build up. Use the same horse every time.
But don't get too fussed about it, unless you want to go in for dressage competitions. It is far more important that you master the rising trot.
Sitting trot will come naturally with time and for some high stepping short legged horses (fancy trotting welsh cobs for example) it is a pace with little use. Big heavy Shires with nice broad backs can be a doddle.