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 (Δ v⃗CM = 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 (vₛₚᵢₙ > vCM) to generate a prograde external reaction drag force (F⃗drag). We demonstrate that the total center-of-mass velocity boost (Δ v⃗CM) is governed by the time-integrated reaction impulse ∫ F⃗drag \, dt, where the instantaneous force is bounded by the inertial deceleration of the effective tip mass (Fdrag = meff · adecel). A numerical case study for a low lunar orbit skyhook operating over the equatorial highlands is provided.