Trajectory Design Using the Center Manifold Theory in the Circular Restricted Three-Body Problem

<p>Lagrangian points are libration points in the circular restricted three-body problem. Three of them are collinear libration points, and known to have unstable periodic and quasi-periodic orbits in the vicinity of themselves. This study aims to design periodic and quasi-periodic orbits from the center manifold theory standpoint. In this paper, a new approach is proposed to design periodic and quasi-periodic orbits around the collinear libration points based upon the successive approximate method. First, the verification of the proposed approach is discussed by evaluating obtained orbits. Then the relation between the initial condition and the type of resulting orbits is investigated. In conclusion, this paper reveals that the proposed method significantly reduces the effort to obtain bounded orbits in the circular restricted three-body problem. The proposed method needs neither an initial guess for the periodic orbit nor the complex algebraic manipulation unlike the conventional methods designing periodic or quasi-periodic orbits. Moreover, a guide to choose the initial condition to obtain desired orbits is given.</p>