The estimation of controllability area in the problem of controllable movement in a neighborhood of collinear libration point

We consider the controllable orbital motion of a spacecraft in a neighborhood of the unstable collinear libration point L₁ of the Earth-Sun system. We use Hill´s equations, which are the special approximation of the equations of the circular restricted three-body problem, as a mathematical model. The control accelerations in this paper are directed along the Earth-Sun line. For the special family of control laws, which provided Lyapunov stability for the orbital motion in a neighborhood of the collinear libration point L₁, we built the approximations of controllability areas with help of Hamiltonian of controllable system and we have presented examples of such areas. Also, the constructed control laws are investigated in circular three-body problem, which is more adequate model.