  We give a comprehensive analysis of the Euler-Jacobi problem of motion in the
field of two fixed centers with arbitrary relative strength and for positive
values of the energy. These systems represent nontrivial examples of integrable
dynamics and are analysed from the point of view of the energy-momentum mapping
from the phase space to the space of the integration constants. In this setting
we describe the structure of the scattering trajectories in phase space and
derive an explicit description of the bifurcation diagram, i.e. the set of
critical value of the energy-momentum map.
