[en] We describe atom--diatom collisions at hyperthermal energies within the theory of three-body scattering. We show how one can treat angular momentum coupling and rotational excitation to low order in a multiple-collision expansion. The emphasis here is in the use of accurate two-atom transition amplitudes and form factors, and on impulse and peaking approximations with simple interaction potentials. We present results for differential cross sections as functions of final rotational quantum numbers j/sub f/ for Li⁺--CO and Li⁺--N₂ at several center of mass angles in the eV region of collision energies. Form factors are also shown for varying j/sub f/, and are discussed in terms of simple overlap models in momentum space