We explore a set of differential equations for a binary system describing the tidal evolution of its orbital elements, rotational dynamics, and deformation (flattening), under the assumption that one body remains spherical while the other is slightly aspherical. The additional hypothesis that the system is in the viscous regime allows us to apply methods of singular perturbation theory to show how the dynamics of the entire system can be approximated by the evolution of its secular equations. We also use singular perturbation theory to provide a geometrical description of the evolution of the system observed in numerical simulations, as well the stability and bifurcations of their equilibria.
Organized by: Catarina Cosme