# Classical mechanics in coadjoint orbits

We know that coadjoint orbits are symplectic manifolds, and they can be used to find unitary representations of Lie groups and stuff, and it's also related to quantization. However, is it true that given a classical mechanics system, you could always realize this as a coadjoint orbit of some Lie group? And would finding its corresponding representation be be equivalent with finding its corresponding quantization?