The Research of Motion in a Neighborhood of Collinear Libration Point by Conservative Methods

In this paper we research the orbital motion described by equations in hamiltonian form. The shift mapping along a trajectory of motion is canonical one and it makes possible to apply conservative methods. The examples of application of such methods in problems of celestial mechanics are given. The first order approximation of generating function of shift mapping along the trajectory is constructed for uncontrolled motion in a neighborhood of collinear libration point of Sun-Earth system. Also this approach is applied to controllable motion with special kind of control, which ensuring the preservation of hamiltonian form of the equations of motion. The form of iterative schemes for numerical modeling of motion is given. For fixed number of iterations the accuracy of presented numerical method is estimated in comparison with Runge-Kutta method of the fourth order. The analytical representation of the generating function up to second-order terms with respect to time increment is given.