Analysis of gravity-gradient-perturbed rotational dynamics at the collinear Lagrange points

This paper studies the dynamics and stability of a rigid spacecraft subjected to gravity gradient torques exerted by the Sun and the Earth in the circular restricted three-body problem. We focus on the dynamics in a close vicinity to the Lagrangian collinear equilibrium points, and show that the linear stability domain predicted by the Beletskii-DeBra-Delp method in the two-body problem is modified due to the presence of an additional gravitating primary. The nonlinear differential equations are derived using a Hamiltonian formalism and are subsequently investigated using Poincare maps. The effect of the gravity gradient torque is accentuated using difference Poincare maps. The Melnikov integral method is utilized for studying the chaotic behavior of the gravity-gradient-perturbed system.