دانلود کتاب Gravitational Few-Body Dynamics: A Numerical Approach

فهرست مطالب :

Contents Preface Introduction 1 The Problems 1.1 Introductory Presentation of the Problems 1.2 Historical (a Point of View of the Author) 2 Two-Body Motion 2.1 Solution of Equations of Motion 2.2 Orbital Elements 2.3 Solving the Basic Kepler’s Equation 2.4 Two-Body Motion in Short Steps 2.5 Evaluation of c-Functions 2.6 General Algorithms for c-Functions 3 Analytical Tools 3.1 The Lagrangian 3.2 The Hamiltonian 3.3 Canonical Transformations 3.4 Time-Dependent Hamiltonian 3.5 Time-Dependent Point Transformation 3.6 Poincaré’s Time Transformation 3.7 Hamilton–Jacobi Equation 4 Variation of Parameters 4.1 Lagrange’s Formulation 4.2 Poisson’s Equations 4.3 Herrick’s Perturbative Variation 4.4 Perturbations of Orbital Elements 5 Numerical Integration 5.1 Difference Methods 5.2 Runge–Kutta and Power Series Methods 5.3 Extrapolation Methods and Substep Algorithms 5.4 High-Order Leapfrogs 6 Symplectic Integration 6.1 Basic Theory 6.2 Composite Symplectic Methods 6.3 Non-Canonical Forces 6.4 Alternative Formulations 6.5 Near-Integrable Systems 6.6 Time Transformations 6.7 The Logarithmic Hamiltonian 6.8 Functional Time Transformation 7 KS-Regularization 7.1 Extended Phase Space and Time Transformations 7.2 KS-Transformation 7.3 Binaries as Perturbed Harmonic Oscillators 7.4 Multiparticle Regularization 7.5 Slow-Down 8 Algorithmic Regularization 8.1 The Basic Leapfrog Algorithms 8.2 Generalized Composite Leapfrog 8.3 Algorithmic Regularization 8.4 Logarithmic Hamiltonian Derivations 8.5 Logarithmic Leapfrog 8.6 Time-Transformed Leapfrog 8.7 Velocity-Dependent Perturbations 8.8 Special Cases 8.9 Tidal Friction and Spin of Stars 8.10 An Efficient Three-Body Algorithm 8.11 Formulation with Relative Coordinates 8.12 Algorithms 9 Motion in the Field of a Black Hole 9.1 Post-Newtonian Terms 10 Artificial Satellite Orbits 10.1 Logarithmic Hamiltonian 10.2 The Exact Two-Body Leapfrog 10.3 Perturbed Two-Body Motion 10.4 Application to Artificial Satellites 10.5 Methods and Functions References Index