New solvable many-body problems in the plane

We revisit anintegrable (indeed, superintegrable and solvable) many-body model introduced almost two decades ago by Gibbons and Hermsen and by Wojciechowski, and we modify it so that its generic solutions are all isochronous (namely, completely periodic with fixed period). We then show how this model (or rather the more basic dynamical system that underlies its solvable character, and other avatars of it) can be conveniently reinterpreted as(rotation-invariant) models in the plane; and we thereby present several new (solvable, isochronous and rotation-invariant) many-body problems in the plane.