In this report we try to make estimates of both kinematic and field effects on the stability of a particle motion, by employing a truly Maxwellian representation of the magnetic field in exact equations of motion. For this purpose we adopt a simple FODO cell model, which repeats periodically to infinity. This model includes only quadrupoles and drifts, leaving out the bending magnets to avoid the problem of the trajectory curvature. We think this model is a physically consistent approximation of a storage ring. We derive several models with different levels of approximation and compare them by evaluating the importance of these effects. The relevance to long‐term stability is being investigated in the meantime by comparing the different models with extensive computer simulations. The results will be shown in a subsequent report. (AIP)