2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/206843Here, 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 polarisation at and near so--called snake resonances in proton storage rings.Accelerator Physicstext