Types of quantum field thories
Many important special cases of classical mechanics involve physical systems whose configuration space is a Lie group, for instance rigid body dynamics but also (for infinite-dimensional Lie groups) fluid dynamics.
All these systems have special properties, notably they are formall integrable systems.
Choose a Riemannian metric
on which is left invariant?.
This is now also called the Euler-Arnold equation.
The original influential article is
A standard textbook reference is section 4.4 of