  We find and solve a large class of integrable dynamical systems which
includes Calogero-Sutherland models and various novel generalizations thereof.
In general they describe $N$ interacting particles moving on a circle and
coupled to an arbitrary number, $m$, of $su(N)$ spin degrees of freedom with
interactions which depend on arbitrary real parameters $x_j$, $j=1,2,...,m$. We
derive these models from SU(N) Yang-Mills gauge theory coupled to non-dynamic
matter and on spacetime which is a cylinder. This relation to gauge theories is
used to prove integrability, to construct conservation laws, and solve these
models.
