Direct Lyapunov Method in the Problem of Ensuring the Stability of a Compact Minimum Set of a Dynamic System and the Formation of a Halo-Orbit Near the Lagrange Point L2

The efficiency of using the direct Lyapunov method for ensuring the stability of motion in compact invariant sets of finite-dimensional dynamical systems is shown. In the linear model of the restricted three-body problem, the possibility of ensuring the asymptotic stability of the periodic motion of a spacecraft (SC) in the vicinity of the collinear Lagrange point L2 using light pressure forces without the consumption of the working fluid is considered. The required area of control surfaces is estimated depending on the mass of the SC.