The attitude motion of a rigid spacecraft in fully nonlinear reference orbits is explored in this investigation, within the context of the planar circular restricted three-body problem. The reference trajectories originate from the Lyapunov families about the Lagrangian points L1 and L2 in the Earth–Moon system. Kane’s method is employed to derive the equations of motion, which are numerically solved. The capability to reproduce the dynamic response is leveraged to understand the attitude behavior across the Lyapunov families. The problem formulation and the simulation environment are detailed. The inertia properties of the spacecraft are varied across the periodic family of orbits. Finally, attitude maps are introduced to summarize the results and identify the regions, in terms of the orbit size and inertia properties, where the spacecraft maintains the initial orientation with respect to the rotating frame in the circular restricted three-body problem