Modeling Halo Orbits and the Associated Manifolds in the Restricted Three Body Problem

Development of halo orbits and their associated invariant manifolds are investigated. Halo orbits play a fundamental role in complex space mission designs. In essence, halo orbits are periodic solutions of the restricted three body problem (R3BP) determined under specific initial conditions. In this paper, the symmetric property of the nonlinear R3BP governing differential equations is utilized in order to obtain the desired initial conditions. In this regard the differential correction technique and the state transition matrix are used to generate the halo orbits. The differential correction technique, based on the Newton method, is an effective tool for solving two point boundary value problems. In addition to generate the stable and unstable manifolds, the initial conditions are perturbed in the direction of Eigenvectors and the equations of motion are integrated for an arbitrary time interval.