Analytical Techniques of Celestial Mechanics

1. Front Matter

   Pages I-VIII

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2. Introduction

   • Victor A. Brumberg

   Pages 1-6

3. The Poisson-Series Processor

   • Victor A. Brumberg

   Pages 7-24

4. The Keplerian Processor

   • Victor A. Brumberg

   Pages 25-62

5. Quasi-polynomial Systems

   • Victor A. Brumberg

   Pages 63-74

6. Algorithms to Solve Polynomial Systems

   • Victor A. Brumberg

   Pages 75-82

7. The Satellite Disturbing Function

   • Victor A. Brumberg

   Pages 83-98

8. The Planetary Disturbing Function

   • Victor A. Brumberg

   Pages 99-119

9. Iteration Techniques of Perturbation Theory

   • Victor A. Brumberg

   Pages 121-140

10. Separation of Variables in Elements

    • Victor A. Brumberg

    Pages 141-156

11. Separation of Variables in Rectangular Coordinates

    • Victor A. Brumberg

    Pages 157-170

12. The General Planetary Theory

    • Victor A. Brumberg

    Pages 171-206

13. GPT Techniques in Minor-Planet and Lunar Problems

    • Victor A. Brumberg

    Pages 207-226

14. Back Matter

    Pages 227-236

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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.

• Computeralgebra
• Himmelsmechanik
• Planetary Systems
• Planetensystem
• algebraic computation
• algorithms
• celestial mechanics
• mechanics

• Russian Academy of Sciences, Institute of Applied Astronomy, St. Petersburg, Russia

  Victor A. Brumberg

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