  We consider the evolution of a binary system interacting due to tidal effects
without restriction on the orientation of the orbital, and where significant,
spin angular momenta, and orbital eccentricity. We work in the low tidal
forcing frequency regime in the equilibrium tide approximation. Internal
degrees of freedom are fully taken into account for one component, the primary.
In the case of the companion the spin angular momentum is assumed small enough
to be neglected but internal energy dissipation is allowed for as this can be
significant for orbital circularisation in the case of planetary companions. We
obtain a set of equations governing the evolution of the orbit resulting from
tidal effects. These depend on the masses and radii of the binary components,
the form and orientation of the orbit, and for each involved component, the
spin rate, the Coriolis force, the normalised rate of energy dissipation
associated with the equilibrium tide due to radiative processes and viscosity,
and the classical apsidal motion constant. These depend on stellar parameters
with no need of additional assumptions or a phenomenological approach as has
been invoked in the past. They can be used to determine the evolution of
systems with initial significant misalignment of spin and orbital angular
momenta as hypothesised for systems containing Hot Jupiters. The inclusion of
the Coriolis force may lead to evolution of the inclination between orbital and
spin angular momenta and precession of the orbital plane which may have
observational consequences.
