In 1911, A.E.H. Love formulated and solved equations governing the linear elastic deformation of planetary bodies due to tidal forces. In this talk, we show how modern computing capabilities reveal unstable behavior in Love's tidal model. We also extend his tidal model to include bodies of radially varying density and elastic properties.

Within the linear elastic framework, one cannot adequately explore the singular solutions. A nonlinear elastic model of the self gravitational deformation of a spherical body is posed. Analyzing spherical harmonic perturbations to this model allows us to explore the stability of the tidal problem. Solving the nonlinear elastic model requires a numerical method for a system of two nonlinear, integro-differential equations with highly nonlocal sixth integral term.