Orbital and Celestial Mechanics.

Cover -- Title -- Copyright -- Foreword -- Table of Contents -- Preface -- Introduction -- Chapter 1 Newton's Laws -- I. Newton's Laws of Motion -- II. Newton's Law of Gravitation -- III. The Gravitational Potential -- IV. Gravitational Flux and Gauss' Theorem -- V. Gravitational Properties of a True Sphere -- Chapter 2 The Two-Body Problem -- I. Reduction to the One-Center Problem -- II. The One-Center Problem -- III. The Laplace Vector -- IV. The Conic Section Solutions -- V. Elliptic Orbits -- VI. Spherical Trigonometry -- VII. Orbit in Space -- VIII. Orbit Determination from Initial Values -- Chapter 3 Lagrangian Dynamics -- I. Variations -- II. D'Alembert's Principle -- III. Hamilton's Principle -- IV. Lagrange's Equations -- Reference -- Chapter 4 The Hamiltonian Equations -- I. An Important Theorem -- II. Ignorable Variables -- Chapter 5 Canonical Transformations -- I. The Condition of Exact Differentials -- II. Canonical Generating Functions -- III. Extended Point Transformation -- IV. Transformation from Plane Rectangular to Plane Polar Coordinates -- V. The Jacobi Integral -- References -- Chapter 6 Hamilton-Jacobi Theory -- I. The Hamilton-Jacobi Equation -- II. An Important Special Case -- III. The Hamilton-Jacobi Equation for the Kepler Problem -- IV. The Integrals for the Kepler Problem -- V. Relations Connecting β[sub(2)] and β[sub(3)] with ω and Ω -- VI. Summary -- Bibliography -- Chapter 7 Hamilton-Jacobi Perturbation Theory -- Bibliography -- Chapter 8 The Vinti Spheroidal Method for Satellite Orbits and Ballistic Trajectories -- I. Introduction -- II. The Coordinates and the Hamiltonian -- III. The Hamilton-Jacobi Equation -- IV. Laplace's Equation -- V. Expansion of Potential in Spherical Harmonics -- VI. Return to the HJ Equation -- VII. The Kinematic Equations -- VIII. Orbital Elements -- IX. Factoring the Quartics.

X. The ρ Integrals -- XI. The η Integrals -- XII. The Mean Frequencies -- XIII. Assembly of the Kinematic Equations -- XIV. Solution of the Kinematic Equations -- XV. The Periodic Terms -- XVI. The Right Ascension Φ -- XVII. Further Developments -- References -- Chapter 9 Delaunay Variables -- Reference -- Chapter 10 The Lagrange Planetary Equations -- I. Semi-Major Axis -- II. Eccentricity -- III. Inclination -- IV. Mean Anomaly -- V. The Argument of Pericenter -- VI. The Longitude of the Node -- VII. Summary -- Reference -- Chapter 11 The Planetary Disturbing Function -- Bibliography -- Chapter 12 Gaussian Variational Equations for the Jacobi Elements -- References -- Chapter 13 Gaussian Variational Equations for the Keplerian Elements -- I. Preliminaries -- II. Equations for α[sub(1)] and a -- III. Equations for α[sub(2)] and e -- IV. Equations for α[sub(3)] and I -- V. Equations for β[sub(3)] = Ω -- VI. Equations for β[sub(2)] = ω -- VII. Equations for β[sub(1)] and l -- VIII. Summary -- Chapter 14 Potential Theory -- I. Introduction -- II. Laplace's Equation -- III. The Eigenvalue Problem -- IV. The R(r) Equation -- V. The Assembled Solution -- VI. Legendre Polynomials -- VII. The Results for P[sub(n)](x) -- VIII. The 0 Solution for m &gt -- 0 -- References -- Chapter 15 The Gravitational Potential of a Planet -- I. The Addition Theorem for Spherical Harmonics -- II. The Standard Series -- III. Orthogonality of Spherical Harmonics -- IV. The Normalized Coefficients and Harmonics -- V. The Figure of the Earth -- VI. Geoid as an Oblate Spheroid -- References -- Chapter 16 Elementary Theory of Satellite Orbits with Use of the Mean Anomaly -- I. A Few Numbers -- II. The Disturbing Function -- III. Elliptic Expansions -- IV. Solution of the Lagrange Variational Equations -- V. Motion of Perigee, First Approximation.

VI. Motion of the Node, First Approximation -- VII. The Semi-Major Axis -- VIII. The Inclination -- IX. The Eccentricity -- X. Variation of the Mean Motion -- XI. Variation of the Mean Anomaly -- References -- Chapter 17 Elementary Theory of Satellite Orbits with Use of the True Anomaly -- I. Introduction -- II. Derivatives with Respect to e -- III. The Semi-Major Axis a -- IV. The Eccentricity e -- V. The Inclination I -- VI. The Motion of the Node -- VII. The Motion of Perigee -- VIII. Variation of the Mean Anomaly -- Reference -- Chapter 18 The Effects of Drag on Satellite Orbits -- I. Introduction -- II. Components of the Drag in Terms of the Anomalies E and f -- III. Equations for a and e in Terms of the True Anomaly -- IV. Secular Behavior of a, e, ω, and l -- V. Equations for a and e in Terms of the Eccentric Anomaly -- VI. An Equation for E -- VII. Equations for the Integration -- References -- Chapter 19 The Brouwer-von Zeipel Method I -- I. Introduction -- II. Splitting F[sub(1)] into Two Parts -- III. Elimination of l -- IV. Short Periodic Terms of Order J[sub(2)] -- V. Second-Order Terms, General -- VI. A Second Canonical Transformation -- VII. Results to This Point -- VIII. Secular Terms -- IX. Algorithm -- References -- Chapter 20 The Brouwer-von Zeipel Method II -- I. Introduction -- II. The Effects of J[sub(3)] -- III. The Effects of J[sub(4)] -- IV. The Average Δ[sub(4)]F -- Reference -- Chapter 21 Lagrange and Poisson Brackets -- I. Introduction -- II. Lagrange Brackets -- III. The Jacobi Relations -- IV. Poisson Brackets -- V. Invariance of a Poisson Bracket to a Contact Transformation -- VI. Other Relations for Poisson Brackets -- References -- Chapter 22 Lie Series -- I. Introduction -- II. Hori's Section 1 -- III. Theorems -- References -- Chapter 23 Perturbations by Lie Series -- I. Introduction -- II. Lie Transformations.

III. Application to Satellite Orbits -- IV. Elimination of the Mean Anomaly -- V. Comparison with Brouwer's Theory -- VI. A Second Lie Transformation -- References -- Chapter 24 The General Three-Body Problem -- I. Introduction -- II. Formulation of the General Three-Body Problem -- III. Momentum Integrals -- IV. Angular Momentum -- V. Energy -- VI. Stationary Solutions -- VII. The Triangular Stationary Solution -- VIII. The Collinear Stationary Solution -- Reference -- Chapter 25 The Restricted Three-Body Problem -- I. Introduction -- II. Zero-Velocity Curves -- III. Equilibrium Points -- IV. Motion near the Equilibrium Points -- V. Motion in the Plane of the Primarics -- VI. Further Considerations About L[sub(4)] and L[sub(5)] -- VII. Further Considerations About the Collinear Points -- References -- Chapter 26 Staeckel Systems -- I. Staeckel's Theorem -- II. Staeckel Systems -- III. The Staeckel Integrals -- IV. An Example: The Kepler Problem -- V. General Remarks About Separable Systems -- VI. Motion According to x[sub(2)] = F(x) -- VII. Conditionally Periodic Staeckel Systems -- VIII. Action and Angle Variables -- IX. Keplerian Action Variables -- X. Conditionally Periodic Staeckel Systems, Continued -- References -- Appendix A Coordinate Systems and Coordinate Transformations -- I. Coordinate Systems -- II. Coordinate Transformations -- References -- Appendix B Vinti Spheroidal Method Computational Procedure and Trajectory Propagators -- I. The Kepler Problem -- II. Given Constants -- III. The vinti3 Computation Procedure -- IV. The vinti6 Computation Procedure -- V. Summary of the Vinti Trajectory Propagators -- References -- Appendix C Examples -- I. Low-Earth Orbit -- II. High-Earth Orbit -- III. Molniya Orbit -- IV. Geosynchronous Orbit -- V. Parabolic Orbit of 0° Inclination.

VI. "Parabolic Orbit" of 0° Inclination in the Oblate Spheroidal System -- VII. Hyperbolic Orbit of 0° Inclination -- VIII. Hyperbolic Orbit of 90° Inclination -- IX. Long-Range Ballistic Missile Trajectory -- X. Exo-Atmospheric Interceptor Trajectory -- Appendix D How to Use the Vinti Routines -- I. The Source Folder -- II. The Examples Folder -- III. The Users -- IV. Some Editing Problems -- Appendix E Bibliography -- I. Papers Published by the Author -- II. Papers Acknowledging Vinti's Work -- III. Books Acknowledging Vinti's Work -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- J -- K -- L -- M -- N -- O -- P -- S -- T -- V -- Z.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.