Ballet-derived, barre-assisted, and a good deal harder than it looks from the doorway.
The method is high repetition through a very small range of motion, holding muscles under tension until they have opinions about it. Legs, glutes, core, and the parts of the shoulder nobody trains. The heat means your hips and hamstrings are open from the first minute rather than the fifteenth, so the work starts immediately.
The shaking is not a sign that something’s wrong. It’s the class working. Stay in it.