Methods of Celestial Mechanics

G. Beutler's Methods of Celestial Mechanics is a coherent textbook for students in physics, mathematics and engineering as well as an excellent reference for practitioners. This Volume I gives a thorough treatment of celestial mechanics and presents all the necessary mathematical details that a professional would need. After a brief review of the history of celestial mechanics, the equations of motion (Newtonian and relativistic versions) are developed for planetary systems (N-body-problem), for artificial Earth satellites, and for extended bodies (which includes the problem of Earth and lunar rotation).

G. Beutler's Methods of Celestial Mechanics is a coherent textbook for students as well as an excellent reference for practitioners. Volume II is devoted to the applications and to the presentation of the program system CelestialMechanics. Three major areas of applications are covered: (1) Orbital and rotational motion of extended celestial bodies.

G. Beutler's Methods of Celestial Mechanics is a coherent textbook for students as well as an excellent reference for practitioners. Volume II is devoted to the applications and to the presentation of the program system CelestialMechanics. Three major areas of applications are covered: (1) Orbital and rotational motion of extended celestial bodies.

G. Beutler's Methods of Celestial Mechanics is a coherent textbook for students as well as an excellent reference for practitioners. Volume II is devoted to the applications and to the presentation of the program system CelestialMechanics. Three major areas of applications are covered: (1) Orbital and rotational motion of extended celestial bodies.

G. Beutler's Methods of Celestial Mechanics is a coherent textbook for students as well as an excellent reference for practitioners. Volume II is devoted to the applications and to the presentation of the program system CelestialMechanics. Three major areas of applications are covered: (1) Orbital and rotational motion of extended celestial bodies.

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.

Half a century ago, S. Chandrasekhar wrote these words in the preface to his 1 celebrated and successful book: In this monograph an attempt has been made to present the theory of stellar dy­ namics as a branch of classical dynamics - a discipline in the same general category as celestial mechanics. [ … ] Indeed, several of the problems of modern stellar dy­ namical theory are so severely classical that it is difficult to believe that they are not already discussed, for example, in Jacobi's Vorlesungen. Since then, stellar dynamics has developed in several directions and at var­ ious levels, basically three viewpoints remaining from which to look at the problems encountered in the interpretation of the phenomenology. Roughly speaking, we can say that a stellar system (cluster, galaxy, etc.) can be con­ sidered from the point of view of celestial mechanics (the N-body problem with N» 1), fluid mechanics (the system is represented by a material con­ tinuum), or statistical mechanics (one defines a distribution function for the positions and the states of motion of the components of the system).