Tidal evolution for any rheological model using a vectorial approach expressed in Hansen coefficients

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