  A solvable many-body problem in the plane is exhibited. It is characterized
by rotation-invariant Newtonian (``acceleration equal force'') equations of
motion, featuring one-body (``external'') and pair (``interparticle'') forces.
The former depend quadratically on the velocity, and nonlinearly on the
coordinate, of the moving particle. The latter depend linearly on the
coordinate of the moving particle, and linearly respectively nonlinearly on the
velocity respectively the coordinate of the other particle. The model contains
$2n^2$ arbitrary coupling constants, $n$ being the number of particles. The
behaviour of the solutions is outlined; special cases in which the motion is
confined (multiply periodic), or even completely periodic, are identified.
