Computation of libration point orbits and manifolds using collocation methods

This thesis contains a methodology whose aim is to compute trajectories describing natural motion of the phase space in a neighborhood of Libtation points and stable/unstable manifolds which correspond to these orbits in the Restricted Three Body Problem. There are two models the Circular Restricted Three Body Problem and Elliptic Restricted Three Body Problem which are special cases of RTBP . In this paper we pay attention to CRTBP which is autonomous (depending on time). The CRTBP is the most easily understood and well-analysed in a coordinate system rotating with two large bodies. The method is based on the collocation method implemented in AUTO - 07p software and must provide an isolated periodic solution. The paper includes explanation of the collocation method, its application in case of CRTBP, numerical and graphical results of its implementation