Spin Motion at and Near Orbital Resonance in Storage Rings with Siberian Snakes I: at Orbital Resonance

In this paper, and in a sequel, we invoke the invariant spin field to provide an in-depth study of spin motion at and near low order orbital resonances in a simple model for the effects of vertical betatron motion in a storage ring with Siberian Snakes. This leads to a clear understanding, within the model, of the behaviour of the beam polarization at and near so-called snake resonances in proton storage rings.