Inter-orbital transfer to the neighborhood of a collinear libration point

A two impulse transfer of a space body from its initial heliocentrical orbit to the collinear libration point L₁ is examined. The boundary conditions for the endpoint of the transfer trajectory are somewhat loosened. The loosening of the boundary conditions is based on the idea that the body is transferred to a five-dimensional invariant manifold, filled with bounded trajectories in the neighborhood of the L₁. The linear and quadratic approximations of the analytic representation of the mentioned invariant manifold are given. It is shown that the expenditure of energy in this case can be decreased by several percent.