Satellite pitch dynamics in the elliptic problem of three bodies

An extension of the restricted elliptic three-bodies problem to include the gravity gradient is presented. The nonlinear pitch dynamics of a satellite located at an equilibrium point is investigated. A closed-form solution for the circular case Is presented. Small perturbations solutions, periodic solutions, and global dynamics via Poincare maps and bifurcation diagrams are studied. The pitch is most stable and has the largest liberation manifold and the smallest chaotic region at L(2). A numerical example of pitch in the Earth-moon system is presented.