Orbital and celestial mechanics [[electronic resource] /] / John P. Vinti ; edited by Gim J. Der, Nino L. Bonavito

• Record Nr.: UNINA9910825537503321
• Autore: Vinti John P (John Pascal), <1907->
• Pubbl/distr/stampa: Reston, Va., : American Institute of Aeronautics and Astronautics, c1998
• ISBN: 1-60086-648-4; 1-60086-429-5
• Descrizione fisica: 1 online resource (415 p.)
• Collana: Progress in astronautics and aeronautics ; ; v. 177
• Altri autori (Persone): DerGim J; BonavitoNino L
• Disciplina: 629.4/113
• Soggetti: Orbital mechanics; Celestial mechanics; Astrodynamics
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: 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. VariationsII. 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 ProblemIV. 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 QuarticsX. 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 ElementsReferences; 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 > 0