  In this study, we formulate a set of differential equations for a binary
system to describe the secular-tidal evolution of orbital elements, rotational
dynamics, and deformation (flattening), under the assumption that one body
remains spherical while the other is slightly aspherical throughout the
analysis. By applying singular perturbation theory, we analyze the dynamics of
both the original and secular equations. Our findings indicate that the secular
equations serve as a robust approximation for the entire system, often
representing a slow-fast dynamical system. Additionally, we explore the
geometric aspects of spin-orbit resonance capture, interpreting it as a
manifestation of relaxation oscillations within singularly perturbed systems.
