  We consider classical three-body interactions on a Euclidean line depending
on the reciprocal distance of the particles and admitting four functionally
independent quadratic in the momenta first integrals. These systems are
superseparable (i.e. multiseparable), superintegrable and equivalent (up to
rescalings) to a one-particle system in the three-dimensional Euclidean space.
Common features of the dynamics are discussed. We show how to determine the
quantum symmetry operators associated with the first integrals considered here
but do not analyze the corresponding quantum dynamics. The conformal
superseparability is proved and examples of conformal first integrals are
given. The systems considered here in generality include the Calogero, Wolfes,
and other three-body interactions widely studied in mathematical physics.
