Dynamics and mission design near libration points. Vol. 4: Advanced methods for triangular points (Q2710188)

The book deals with the analysis of motion in the vicinity of triangular equilibrium points of Sun-Earth-Moon system for restricted three-body problem (RTBP), for the elliptic problem, and for the bicircular problem. The results are then used for the determination of possible nominal orbits in future space missions. The book consists of an introduction, six chapters, four appendices, and bibliography list.NEWLINENEWLINENEWLINEThe introduction summarizes known facts and difficulties related to RTBP. In chapter 1, the authors describe the equations of motion and the values of parameters for the numerical integration, which is carried out using the RKF78 method with local threshold \(10^{-13}\). This numerical procedure provides stable zones in an extended neighbourhood of triangular equilibrium points of Earth-Moon system. In chapter 2, the authors obtain the normal form of Hamiltonian in the three-dimensional RTBP for Earth-Moon system around equilibrium points \(L_4\) and \(L_5\). This gives a possibility to determine periodic and quasi-periodic orbits in an easy way. Chapter 3 is concerned with the normal form of bicircular model, which is a simplified version of the four-body problem. The potentials of Earth, Moon and Sun are expanded in Legendre polynomials, and invariant two- and three-dimensional unstable tori are found by the implementation of a version of Lindstedt-Poincaré method. In chapter 4, the authors consider the motion with Hamiltonians corresponding to the motions near the points \(L_4\) and \(L_5\) to establish dominant terms of the Hamiltonian for the full Solar system with radiation pressure taken into account. Chapter 5 deals with computations of some quasi-periodic orbits near Lagrangian points \(L_4\) and \(L_5\) of the real Earth-Moon system. Using analytical solutions constructed in chapter 4, the solutions are refined numerically for JPL model. Then the stability of these orbits is investigated by means of a variational study. Finally, in chapter 6 the authors study the transfer of a satellite in a vicinity of Lagrangian points. The transfer strategy is selected taking into account the cost and time of the transfer.NEWLINENEWLINENEWLINEThe results obtained in the book are presented in figures and tables. Appendices contain extra information on the considered problems, and summarize the achievements.