[en] We investigate the motion of protons of arbitrary energy (below and above transition energy) in a storage ring. The motion is described both in terms of the fully six-dimensional formalism with the canonical variables x, p_x, z, p_z, σ = s - v₀ . t, η = ΔE/E₀ = p_σ and in terms of a dispersion formalism with new variables x, p_x, z, p_z, σ, p_σ. Since the dispersion function is introduced into the equations of motion via a canonical transformation the symplectic structure of these equations is completely preserved. In this formulation it is then possible to define three uncoupled linear (unperturbed) oscillation modes which are described by phase ellipses. Perturbations manifest themselves as deviations from these ellipses. The equations of motion are solved within the framework of the fully six-dimensional formalism. (orig.)