  We revisit the two body problem, where one body can be deformed under the
action of tides raised by the companion. Tidal deformation and consequent
dissipation result in spin and orbital evolution of the system. In general, the
equations of motion are derived from the tidal potential developed in Fourier
series expressed in terms of Keplerian elliptical elements, so that the
variation of dissipation with amplitude and frequency can be examined. However,
this method introduces multiple index summations and some orbital elements
depend on the chosen frame, which is prone to confusion and errors. Here, we
develop the quadrupole tidal potential solely in a series of Hansen
coefficients, which are widely used in celestial mechanics and depend just on
the eccentricity. We derive the secular equations of motion in a vectorial
formalism, which is frame independent and valid for any rheological model. We
provide expressions for a single average over the mean anomaly and for an
additional average over the argument of the pericentre. These equations are
suitable to model the long-term evolution of a large variety of systems and
configurations, from planet satellite to stellar binaries. We also compute the
tidal energy released inside the body for an arbitrary configuration of the
system.
