In a time-independent model of the magnetosphere including a dipole magnetic field, a convection electric field (deduced from polar orbit observations), and an electric field due to the earth's rotation the motion of a proton in the equatorial plane is analyzed. By means of the Hamiltonian W of the motion, three regimes of motion are identified. A method is then developed for determining for any given observation point which arrival energies correspond to trapped particles and which represent 'open' trajectories.