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How do three celestial bodies move under their mutual gravitational attraction? This problem has been studied by Isaac Newton and leading mathematicians over the last two centuries. Poincaré's conclusion, that the problem represents an example of chaos in nature, opens the new possibility of using a statistical approach. For the first time this book presents these methods in a systematic way, surveying statistical as well as more traditional methods. The book begins by providing an introduction to celestial mechanics, including Lagrangian and Hamiltonian methods, and both the two and restricted three body problems. It then surveys statistical and perturbation methods for the solution of the general three body problem, providing solutions based on combining orbit calculations with semi-analytic methods for the first time. This book should be essential reading for students in this rapidly expanding field and is suitable for students of celestial mechanics at advanced undergraduate and graduate level.

Three-body problem. --- Planetary theory. --- Planets, Theory of --- Celestial mechanics --- Problem of three bodies --- Mechanics, Analytic

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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.
Contents:

• Global Stability Zones Around the Triangular Libration Points
• The Normal Form Around L5 in the Three-dim

Three-body problem. --- Lagrangian points. --- Equilibrium points, Lagrangian --- Lagrangian equilibrium points --- Libration points --- Points, Lagrangian --- Orbits --- Problem of three bodies --- Mechanics, Analytic

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In this book the problem of station keeping is studied for orbits near libration points in the solar system. The main focus is on orbits near halo ones in the (Earth+Moon)-Sun system. Taking as starting point the restricted three-body problem, the motion in the full solar system is considered as a perturbation of this simplified model. All the study is done with enough generality to allow easy application to other primary-secondary systems as a simple extension of the analytical and numerical computations. Contents: Bibliographical Survey Halo Orbits. Analytical and

Three-body problem. --- Lagrangian points. --- Equilibrium points, Lagrangian --- Lagrangian equilibrium points --- Libration points --- Points, Lagrangian --- Orbits --- Problem of three bodies --- Mechanics, Analytic

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Differential geometry. Global analysis --- Celestial mechanics --- Hamiltonian systems --- Three-body problem --- Congresses --- 521.1 --- -Hamiltonian systems --- -Three-body problem --- -Problem of three bodies --- Mechanics, Analytic --- Hamiltonian dynamical systems --- Systems, Hamiltonian --- Differentiable dynamical systems --- Gravitational astronomy --- Mechanics, Celestial --- Astrophysics --- Mechanics --- Celestial mechanics. General principles of dynamical astronomy --- -Celestial mechanics. General principles of dynamical astronomy --- 521.1 Celestial mechanics. General principles of dynamical astronomy --- -521.1 Celestial mechanics. General principles of dynamical astronomy --- Problem of three bodies --- Celestial mechanics - Congresses --- Hamiltonian systems - Congresses --- Three-body problem - Congresses

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Three-body problem. --- Hamiltonian systems. --- Hamiltonian systems --- Three-body problem --- #TELE:SISTA --- Hamiltonian dynamical systems --- Systems, Hamiltonian --- Differentiable dynamical systems --- Problem of three bodies --- Mechanics, Analytic --- Poincare, Henri --- -Contributions in dynamics --- Poincaré, Henri, --- Poincaré, Henri, --- Poicaré, Henri, 1854-1912-contributions in dynami --- Dynamique différentiable --- Mécanique analytique --- Histoire des mathematiques --- Mecanique celeste --- 19e siecle --- Probleme des trois corps --- Poincaré, Henri