Design of the stabilizing control of the orbital motion using the analytical representation of an invariant manifold in the vicinity of a collinear libration point

The article is devoted to the problem of stabilization of orbital motion in the vicinity of the collinear libration point $L_1$ of the Sun–Earth system. The key concept of the suggested approach is the so-called hazard function. The latter is a function of the phase variables of the Hill's approximation of the circular restricted three-body problem, which is defined as a nondegenerate solution of some partial differential equation. The hazard function can be used for the analytical representation of an invariant manifold in the vicinity of the libration point. Approximations of the hazard function of the first, second and the third order are obtained with the method of indefinite coefficients. These approximations are then used in the construction of three motion stabilizing control laws. Numerical modelling of the controlled motion is applied to compare these laws with respect to the energy consumptions. Refs 8. Figs 3. Table 1.