  A dynamical model based on effective Lagrangians is proposed to describe the
bremsstrahlung reaction $ \pi N \to \pi N \gamma$ at low energies. The
$\Delta(1232)$ degrees of freedom are incorporated in a way consistent with
both, electromagnetic gauge invariance and invariance under contact
transformations. The model also includes the initial and final state
rescattering of hadrons via a T-matrix with off the momentum-shell effects. The
double differential distribution of photons is computed for three different
T-matrix models and the results are compared with the soft photon
approximation, and with experimental data. The aim of this analysis is to test
the off-shell behaviour of the different T-matrices under consideration.
Finally an alternative simpler dynamical model that incorporates the unstable
character of the isobar-$\Delta(1232)$ through a complex mass, is presented. As
we will see it is suitable for the study of the magnetic moment of the
resonance.
