The study revisits the dynamics of an oblate satellite subjected to the gravitational fields of two spherical primaries, a problem traditionally approached via the translational and rotational motion equations of Kondurar and Shinkarik (1972). While the translational equations adequately predict the conditions for libration points, the conventional rotational equations fail to provide a general framework for determining these equilibrium configurations. Motivated by earlier works (Choudhry, 1977; Kumar & Choudhry, 1986; Ahmad and Singh, 1995), this paper derives modified equations of rotational motion for an oblate satellite. By considering the satellite as an oblate spheroid with distinct moments of inertia about its equatorial and polar diameters, and employing Eulerian angles alongside a coordinate transformation that aligns the system with the primaries’ circular orbits, we reformulate the rotational dynamics. The derivation involves a detailed analysis of the potential function and kinetic energy, leading to a set of modified Lagrange equations that successfully generalize the conditions for libration points under rotational motion. The resultant equations not only address the limitations of the classical formulation but also provide deeper insights into the equilibrium configurations of satellites in multi-body gravitational fields. These advancements hold significant implications for celestial mechanics and the precise design of satellite orbits in complex gravitational environments.