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Pion elastic, charge exchange scattering and induced eta production on thetrinucleon systems are investigated in a coupled-channels approach in momentumspace with Fadeev wave functions. The channel $\pi N \rightarrow \eta N$ isincluded using an isobar model with S-, P-, and D-wave resonances. While thecoherent reactions like $^3$He($\pi,\pi)^3$He can be reasonably well reproducedup to $T_{\pi}$=500 MeV, large discrepancies appear for the incoherentprocesses, $^3$He($\pi^-,\pi^0)^3$H and $^3$He($\pi^-,\eta)^3$H at backwardangles and energies above $\Delta$-resonance. In the forward direction the$(\pi,\eta)$ calculations underestimate the experimental measurements veryclose to threshold but agreement with the data improves with increasing pionenergy. Predictions are made for the asymmetries of the various reactions onpolarized $^3$He.Comment: 40 pages, 12 figures (available from the authors), Mainz preprint  MKPH-T-92-1

Pion interaction with the trinucleon up to the eta production threshold