M.Sc Thesis

M.Sc StudentBrucker Eytan
SubjectAttitude Dynamics and Passive Stabilization on Libration
Point Orbits
DepartmentDepartment of Aerospace Engineering
Supervisor PROF. Pinchas Gurfil
Full Thesis textFull thesis text - English Version


This work studies the dynamics 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 domains predicted by the Euler-Delp theory in the two-body problem are modified due to the presence of an additional gravitating primary.

The Hamiltonian of the unperturbed system is first derived and then expressed using the canonical Serret-Andoyer variables. The resulting nonlinear equations are augmented by expressions that result from the consideration of the gravity gradient. The nonlinear differential equations are investigated using Poincaré maps and by comparing to the unperturbed motion. The investigation shows that the gravity gradient can be treated as a small disturbance and therefore difference Poincaré maps are evaluated. The linear least squares method was used as a mathematical optimization technique in order to ``simplectify'' the numerical integration.

Lyapunov exponents and the Melnikov integral methods are subsequently utilized for studying the chaotic behavior of the gravity-gradient disturbed system. The main conclusion is that the perturbation due to the combined gravity gradient torques is a dominant factor in the rotational dynamics of a spacecraft flying on a libration-point orbit. We further conclude that the rotational motion is chaotic, but can be passively stabilized in some situations.