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Analytical Techniques of Celestial Mechanics
     

Analytical Techniques of Celestial Mechanics

by Victor Brumberg, V. A. Brumberg
 

ISBN-10: 3540587829

ISBN-13: 9783540587828

Pub. Date: 03/17/1995

Publisher: Springer Berlin Heidelberg

The aim of this book is to describe contemporary analytical and semi­ analytical techniques for solving typical celestial-mechanics problems. The word "techniques" is used here as a term intermediate between "methods" and "recipes". One often conceives some method of solution of a problem as a general mathematical tool, while not taking much care with its

Overview

The aim of this book is to describe contemporary analytical and semi­ analytical techniques for solving typical celestial-mechanics problems. The word "techniques" is used here as a term intermediate between "methods" and "recipes". One often conceives some method of solution of a problem as a general mathematical tool, while not taking much care with its computa­ tional realization. On the other hand, the word "recipes" may nowadays be understood in the sense of the well-known book Numerical Recipes (Press et al. , 1992), where it means both algorithms and their specific program realiza­ tion in Fortran, C or Pascal. Analytical recipes imply the use of some general or specialized computer algebra system (CAS). The number of different CAS currently employed in celestial mechanics is too large to specify just a few of the most preferable systems. Besides, it seems reasonable not to mix the essence of any algorithm with its particular program implementation. For these reasons, the analytical techniques of this book are to be regarded as algorithms to be implemented in different ways depending on the hardware and software available. The book was preceded by Analytical Algorithms of Celestial Mechanics by the same author, published in Russian in 1980. In spite of there being much common between these books, the present one is in fact a new mono­ graph.

Product Details

ISBN-13:
9783540587828
Publisher:
Springer Berlin Heidelberg
Publication date:
03/17/1995
Series:
Astronomy and Astrophysics Library
Pages:
236
Product dimensions:
6.10(w) x 9.25(h) x 0.03(d)

Table of Contents

1 The Poisson-Series Processor.- 1.1 Universal CAS and Poisson-Series Processors.- 1.2 Operations with Poisson Series.- 1.3 Location of Poisson Series.- 2 The Keplerian Processor.- 2.1 The Keplerian Processor in Closed Form.- 2.2 The Keplerian Processor in Poisson-Series Form.- 2.3 General Terms of the Elliptic-Motion Expansions.- 2.4 The Keplerian Processor in Taylor-Series Form.- 2.5 The Keplerian Processor with the Aid of Elliptic Functions.- 2.6 Functions Involving the Coordinates of Two Bodies.- 3 Quasi-polynomial Systems.- 3.1 The N-Planet Problem in Polynomial Form.- 3.2 Kustaanheimo-Stiefel (KS) Variables.- 3.3 Hansen Coordinates and Euler Parameters.- 4 Algorithms to Solve Polynomial Systems.- 4.1 Taylor Expansions.- 4.2 Normalization and Trigonometric Expansions.- 5 The Satellite Disturbing Function.- 5.1 Expansions in Spherical Functions.- 5.2 The Recurrence Determination of Solid Spherical Harmonics.- 5.3 The Disturbing Function and Its Derivatives.- 5.4 Equations of Motion in Rotating Systems.- 6 The Planetary Disturbing Function.- 6.1 General Structure.- 6.2 Expansion Algorithms.- 6.3 Expansion with the Aid of Elliptic Functions.- 7 Iteration Techniques of Perturbation Theory.- 7.1 Iteration Versions of the Classical Methods.- 7.2 Intermediate Orbits in the N-Planet Problem.- 7.3 Iterations in the Two-Body Problem.- 8 Separation of Variables in Elements.- 8.1 The Krylov-Bogoljubov Method.- 8.2 The von Zeipel Method and Its Modifications.- 8.3 The von Zeipel Method as a “Coordinate” Method.- 8.4 The Kolmogorov-Arnold Method Using Howland’s Technique.- 9 Separation of Variables in Rectangular Coordinates.- 9.1 Reducibility of the Equations of Variations.- 9.2 The Perturbed Two-Body Problem.- 9.3 Solution Techniques.- 10 The General Planetary Theory.- 10.1 The Basic Theory.- 10.2 Right-Hand Members.- 10.3 The Intermediary.- 10.4 Linear Eccentricity and Inclination Terms.- 10.5 Non-linear Terms.- 10.6 The Secular System.- 11 GPT Techniques in Minor-Planet and Lunar Problems.- 11.1 Right-Hand Members.- 11.2 The Intermediary.- 11.3 Solution Techniques.- 11.4 The Secular System.- 11.5 The Lunar Problem.- References.

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