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Cover 1 Stability and Chaos in Celestial Mechanics 4 Copyright 5 Dedication 6 Table of Contents 8 Preface 12 Acknowledgments 15 1 Order and chaos 18 1.1 Continuous and discrete systems 18 1.2 Linear stability 21 1.3 Conservative and dissipative systems 23 1.4 The attractors and basins of attraction 24 1.5 The logistic map 26 1.6 The standard map 29 1.7 The dissipative standard map 32 1.8 Hénon’s mapping 34 2 Numerical dynamical methods 38 2.1 Poincaré map 38 2.2 Lyapunov exponents 40 2.3 The attractor’s dimension 42 2.4 Time series analysis 43 2.5 Fourier analysis 48 2.6 Frequency analysis 49 2.7 Hénon’s method 50 2.8 Fast Lyapunov Indicators 52 3 Kepler’s problem 56 3.1 The motion of the barycenter 57 3.2 The solution of Kepler’s problem 58 3.3 \hat{f} and \hat{g} series 61 3.4 Elliptic motion 61 3.4.1 Mean and eccentric anomaly 63 3.4.2 Solution of Kepler’s equation 65 3.5 Parabolic motion 66 3.6 Hyperbolic motion 67 3.7 Classification of the orbits 68 3.8 Spacecraft transfers 70 3.9 Delaunay variables 70 3.10 The two–body problem with variable mass 74 3.10.1 The rocket equation 74 3.10.2 Gylden’s problem 75 4 The three–body problem and the Lagrangian solutions 80 4.1 The restric

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