Spin motion at and near orbital resonance in storage rings with Siberian Snakes. Part I: at orbital resonance

Here, 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