General relativity derivation of beam rest-frame Hamiltonian

Analysis of particle interaction in the laboratory frame of storage rings is often complicated by the fact that particle, motion is relativistic, and that reference particle trajectory is curved. Rest frame of the reference particle is a convenient coordinate system to work with, within which particle motion is non-relativistic. We have derived the equations of motion in the beam rest frame from the general relativity formalism, and have successfully applied them to the analysis of crystalline beams