  We consider a large $N$ limit of the Hitchin type integrable systems.
  The first system is the elliptic rotator on $GL_N$ that corresponds to the
Higgs bundle of degree one over an elliptic curve with a marked point. This
system is gauge equivalent to the $N$-body elliptic Calogero-Moser system, that
is derived from the Higgs bundle of degree zero over the same curve. The large
$N$ limit of the former system is the integrable rotator on the group of the
non-commutative torus. Its classical limit leads to the integrable modification
of 2d hydrodynamics on the two-dimensional torus. We also consider the elliptic
Calogero-Moser system on the group of the non-commutative torus and consider
the systems that arise after the reduction to the loop group.
