Conversion of Rotational Angular Momentum in Cislunar Skyhooks: System Architecture and Ground-Traction Overspin Dynamics

We present a formal classical mechanics formulation for transforming internal rotational kinetic energy into linear center-of-mass orbital momentum via planetary surface interaction. While internal momentum management in free space is strictly bounded by closed-system conservation ($\Delta \vec{v}_{\text{CM}} = 0$), establishing an instantaneous boundary condition against an airless celestial surface allows the planetary body to act as an effectively infinite reaction mass. In contrast to classical non-synchronous skyhook designs operating at zero surface relative velocity, we mandate a retrograde overspin condition ($v_{\text{spin}} > v_{\text{CM}}$) to generate a prograde external reaction drag force ($\vec{F}_{\text{drag}}$). We demonstrate that the total center-of-mass velocity boost ($\Delta \vec{v}_{\text{CM}}$) is governed by the time-integrated reaction impulse $\int \vec{F}_{\text{drag}} \, dt$, where the instantaneous force is bounded by the inertial deceleration of the effective tip mass ($F_{\text{drag}} = m_{\text{eff}} \cdot a_{\text{decel}}$). A numerical case study for a low lunar orbit skyhook operating over the equatorial highlands is provided.