  We provide some details about the recently discovered integrable systems
implied by commutativity of $W$ operators along the rays on the plane of roots
of $w_\infty$-algebra. The simplest system of this type is the rational
Calogero model, other systems escaped attention in the past. Existence of these
systems is intimately tied to the very interesting WLZZ matrix models, which
are now under intensive study.
