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

Format:

Book

Author/Creator:

Vinti, John P. (John Pascal), 1907-

Contributor:

Der, Gim J.

Bonavito, Nino L.

Series:

Progress in astronautics and aeronautics ; v. 177.

Progress in astronautics and aeronautics ; v. 177

Language:

English

Subjects (All):

Orbital mechanics.

Celestial mechanics.

Astrodynamics.

Physical Description:

1 online resource (415 p.)

Edition:

1st ed.

Place of Publication:

Reston, Va. : American Institute of Aeronautics and Astronautics, c1998.

Language Note:

English

Summary:

Orbital and Celestial Mechanics affords engineering students, professors and researchers alike an opportunity to cultivate the mathematical techniques necessary for this discipline - as well as physics and trajectory mechanics - using the familiar and universal concepts of classical physics. For nonspecialists and students unfamiliar with some of the underlying maths principles, the Vinti Spheroidal Method demonstrates computer routines for accurately calculating satellite orbit and ballistic trajectory. More than 20 years ago, Dr. Vinti's revolutionary method was used aboard a ballistic missile targeting programme with great success. His work continues to enable both students and professionals to predict position and velocity vectors for satellites and ballistic missiles almost as accurately as numerical integration. Now the best Vinti algorithms and companion computer source codes are available.

Contents:

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

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

1-60086-648-4

1-60086-429-5

OCLC:

922978817