The problem of determining the orbits of energetic ions in the confining magnetic field of a tokamak plasma and their phase space characteristics is considered analytically. First, starting from the orbit invariants in the simplified magnetic field of a tokamak plasma, a quartic equation describing the trajectories in configuration space is derived. Then from an examination of the coefficients of the orbit equation, the orbit types and their classification are deduced. Analytic solutions of the orbit equation are given and the partition of phase space into regions of trapped (passing) particles and loss cones is determined. Finally, as a specific application, the trajectories and phase space characteristics of 3.5 MeV α particles in the magnetic field of the JET tokamak are calculated.