ANSWER:
You can't do lateral movements at the double longe line, because the horse is going in a circle around you. This may be a terminological issue. Double longeing means that the rider stays in the center of a circle that the horse describes around him. You can go straight down the long side and make another circle. You can even do a figure 8 at the double longe line, but that's more or less it. So you are limited to transitions and flexions and turns.
If you want to do lateral movements, you have to long rein the horse. That means you have to be right next to the croup, so that your hand or elbow can touch the croup. This is usually done with just a long rein and snaffle bridle, no surcingle or side reins. With this setup you can do all dressage movements. We have photos of myself long reining a variety of horses in the trot and canter, as well as piaffe and passage on our website.
Another setup that is often confused with long reining is ground driving. In ground driving, the driver is behind the horse and quite far away from the hind legs. Here, people usually use a surcingle to guide the driving lines, and sometimes even side reins. This is usually done in the walk and jog, and on a single track, whereas long reining is done mostly at the trot and canter. Since the driver is very far away from the horse in ground driving, you can't do lateral movements or pirouettes.
Ground driving is derived from driving, whereas long reining is derived from riding.
As a general rule of thumb, the farther you are away from the horse, the less precise the timing and feel of the aids becomes, because they have to travel a long way through the reins before they reach the horse. And you can't frame the horse's hips and shoulders very precisely when you are too far away. The closer you are, the more precisely you can align the hips and shoulders. And better alignment means better access to the poll and hips of the horse.
- Thomas Ritter
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