Oscillations of rotating bodies: A self-adjoint formalism applied to dynamic tides and tidal capture

We consider the excitation of the inertial modes of a uniformly rotating fully convective body due to a close encounter with another object. This could lead to a tidal capture or orbital circularisation depending on whether the initial orbit is unbound or highly eccentric. We develop a general self-adjoint formalism for the response problem and thus solve it taking into account the inertial modes with $m=2$ for a full polytrope with $n=1.5.$ We are accordingly able to show in this case that the excitation of inertial modes dominates the response for large impact parameters and thus cannot be neglected in calculations of tidal energy and angular momentum exchange or orbital circularisation from large eccentricity.