Ch. 1. Bibliographical survey. 1.1. Equations. The triangular equilibrium points and their stability. 1.2. Numerical results for the motion around L4 and L5. 1.3. Analytical results for the motion around L4 and L5. 1.4. Miscellaneous results -- ch. 2. Periodic orbits of the bicircular problem and their stability. 2.1. Introduction. 2.2. The equations of the bicircular problem. 2.3. Periodic orbits with the period of the Sun. 2.4. The tools: numerical continuation of periodic orbits and analysis of bifurcations. 2.5. The periodic orbits obtained by triplication -- ch. 3. Numerical simulations of the motion in an extended. Neighborhood of the triangular libration points in the Earth-Mmoon system. 3.1. Introduction. 3.2. Simulations of motion starting at the instantaneous triangular points at a given epoch. 3.3. Simulations of motion starting near the planar periodic orbit of Kolenkiewicz and Carpenter -- ch. 4. The equations of motion. 4.1. Reference systems. 4.2. The Lagrangian. 4.3. The Hamiltonian and the related expansions. 4.4. Some useful expansions. 4.5. Fourier analysis: the relevant frequencies and the related coefficients. 4.6. Concrete expansions of the Hamiltonian and the functions. 4.7. Simplified normalized equations. Tests -- ch. 5. Periodic orbits of some intermediate equations. 5.1. Equations of motion for the computation of intermediate periodic orbits. 5.2. Obtaining the periodic orbits around the triangular libration points for the intermediate equations. 5.3. Results and comments -- ch. 6. Quasi-periodic solution of the global equations: semianalytic approach. 6.1. The objective. 6.2. The algorithm. 6.3. The adequate set of relevant frequencies. 6.4. Avoiding secular terms. 6.5. The coefficients related to the different frequencies. 6.6. Determination of the coefficients of quasi-periodic functions using FFT. 6.7. Results and conclusions -- ch. 7. Numerical determination of suitable orbits of the simplified system. 7.1. The objective. 7.2. Description of two families of algorithms. reduction of the linearized equations. 7.3. Description of the methods. Comments. 7.4. Results and discussion -- ch. 8. Relative motion of two nearby spacecrafts. 8.1. The selection of orbits for the two spacecrafts. 8.2. Variations of the relative distance and orientation. Results. 8.3. Comments on the applicability of the results -- ch. 9. Summary. 9.1. Objectives of the work. 9.2. Contribution to the solution of the problem. 9.3. Conclusions. 9.4. Outlook
