Modeling of controlled coupled attitude-orbit motion in the neighborhood of collinear libration point $L_1$

This paper considers the motion of a celestial body (as a rigid 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 $L_1$ are investigated. The translational orbital motion of a celestial body is described using Hill's equations of a circular restricted three-body problem of the Sun–Earth system. Rotational orbital motion is described using Euler's dynamic equations and quaternion kinematic equation. As an important result, we investigate the problems of celestial body motion stability in relative equilibrium positions and stabilization of a celestial body motion with proposed control laws in collinear libration point $L_1$. To study stabilization problems, Lyapunov function is constructed in the form of the sum of the kinetic energy of a celestial body and special “kinematics” function of the Rodriguez–Hamiltonian parameters. The numerical modeling of the controlled rotational motion of a celestial body at libration point $L_1$ is carried out. The numerical characteristics of the control parameters and rotational motion of the celestial body are given. Results of numerical integration are presented graphically. Refs 14. Figs 10.