The mathematics involved in the theory of tides are formidable. Even in homogeneous, tidally locked systems things can get complicated very quickly.
But tides are nevertheless very important. One two objects pass very close to each other, tidal effects are substantial and can actual destroy one of the objects: https://en.wikipedia.org/wiki/Tidal_disruption_event
https://en.wikipedia.org/wiki/Roche_limit
https://en.wikipedia.org/wiki/Roche_lobe
Indeed given that we now think most of the heavy elements in the universe were created in type 1a mass-transfer supernovae, we can ultimately thank tidal phenomena for the existence of things like rocky planets and humans.