Lagrangian equilibrium point, linear quadratic regulator, L2 point, Halo orbit, control law, control simulation, 3 body problem, equation of motion, linearization, Lissajous figure, trajectory control, orbit calculation, simulation
A Lagrange point of Sun-Earth system, L1 or L2 is conceived one of the best point for astronomy and connection ports for outer planets. This paper describes a new useful control method for realizing and keeping small circular Halo orbits around the L2 point. First, a control law is mathematically derived from the restricted three body problem formulation and the associated properties are discussed. And next, some useful cases for the space mission are verified numerically using real ephemeris. The resulted Halo orbit is compact and circular realized with satisfactorily small thrust. The paper concludes the strategy is applied to many kinds of missions.
Design of small circular Halo orbit around L2
