This article considers the motion of a celestial body within the restricted three-body problem of the Sun-Earth system. The equations of controlled coupled attitude-orbit motion in the neighborhood of collinear libration point L₁ are investigated. The translational orbital motion of a celestial body is described using Hill's equations of circular restricted three-body problem of the Sun-Earth system. Rotational orbital motion is described using Euler's dynamic equations and quaternion kinematic equation. We investigate the problem of stability of celestial body rotational orbital motion in relative equilibrium positions and stabilization of celestial body rotational orbital motion with proposed control laws in the neighborhood of collinear libration point L₁. To study stabilization problem, Lyapunov function is constructed in the form of the sum of the kinetic energy and special "kinematic function" of the Rodriguez-Hamiltonian parameters. Numerical modeling of the controlled rotational motion of a celestial body at libration point L₁ is carried out. The numerical characteristics of the control parameters and rotational motion are given.