Periodic orbits around the collinear libration points

The locations for the collinear libration points in the framework of the restricted three-body problem are determined when the bigger primary is a triaxial rigid body. The analysis of the periodic motion around these points is performed and given up to second order in the case that the initial state of the motion gives rise to periodic orbits. Moreover, some numerical results for the locations of collinear points are provided and the graphical investigations for the periodic motion are plotted, as well. It is worth mentioning that the collinear libration points and associated periodic orbits are considered the optimal placement to transfer a spacecraft to the nominal periodic orbits or to an associated stable manifold.