Analytical Techniques of Celestial Mechanics [E-Book] / by Victor A. Brumberg.
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 so...
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Full text |
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Personal Name(s): | Brumberg, Victor A., author |
Imprint: |
Berlin, Heidelberg :
Springer,
1995
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Physical Description: |
VIII, 236 p. online resource. |
Note: |
englisch |
ISBN: |
9783642794544 |
DOI: |
10.1007/978-3-642-79454-4 |
Subject (LOC): |
- 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.