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This book studies several problems related to the analysis of planned or possible spacecraft missions. It is divided into four chapters. The first chapter is devoted to the computation of quasiperiodic solutions for the motion of a spacecraft near the equilateral points of the Earth-Moon system. The second chapter gives a complete description of the orbits near the collinear point, L₁, between the Earth and the Sun in the restricted three-body problem (RTBP) model. In the third chapter, methods are developed to compute the nominal orbit and to design and test the control strategy...

It is well known that the restricted three-body problem has triangular equilibrium points. These points are linearly stable for values of the mass parameter, μ, below Routh's critical value, μ₁. It is also known that in the spatial case they are nonlinearly stable, not for all the initial conditions in a neighborhood of the equilibrium points L₄, L₅ but for a set of relatively large measures. This follows from the celebrated Kolmogorov-Arnold-Moser theorem. In fact there are neighborhoods of computable size for which one obtains “practical...

The aim of this book is to explain, analyze and compute the kinds of motions that appear in an extended vicinity of the geometrically defined equilateral points of the Earth-Moon system, as a source of possible nominal orbits for future space missions. The methodology developed here is not specific to astrodynamics problems. The techniques are developed in such a way that they can be used to study problems that can be modeled by dynamical systems.