Analytical Techniques of Celestial Mechanics

The author develops specialized computer systems and perturbation algorithms to construct a general planetary theory, general relativistic lunar theory, etc., for solving typical celestial mechanics problems. The book develops specialized software, with particular attention paid to applying the elliptic functions expansions and treating otherwise intractable problems.

Klappentext

The book exposes contemporary analytical and semianalytical techniques for solving typical celestial mechanics problems by computer. It presents new algorithms of perturbation theory and helps to develop, on the basis of some general computer algebra systems, specialized software enabling one to construct analytical theories of the motion of celestial objects. Particular attention is paid to applying the elliptic functions expansions to economize on the number of terms in the resulting series in problems with large values of parameters. Even problems considered as intractable may now be treated efficiently. The author addresses not only astronomers but also amateurs interested in orbit calculations for celestial objects or satellites.

Inhalt
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.