Methods of Celestial Mechanics

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).

This book on recent investigations of the dynamics of celestial bodies in the solar and extra-Solar System is based on the elaborated lecture notes of a thematic school on the topic, held as a result of cooperation between the SYRTE Department of Paris Observatory and the section of astronomy of the Vienna University. Each chapter corresponds to a lecture of several hours given by its author(s). The book therefore represents a necessary and very precious document for teachers, students, and researchers in the ?eld. The ?rst two chapters by A. Lemaˆ ?tre and H. Skokos deal with standard topics of celestial mechanics: the ?rst one explains the basic principles of resonances in mechanics and their studies in the case of the Solar System. The differences between the various cases of resonance (mean motion, secular, etc. ) are emphasized together with resonant effects on celestial bodies moving around the Sun. The second one deals with approximative methods of describing chaos. These methods, some of them being classical, as the Lyapounov exponents, other ones being developed in the very recent past, are explained in full detail. The second one explains the basic principles of resonances in mechanics and their studies in the case of the Solar System. The differences between the various cases of resonance (mean motion, s- ular, etc. ) are emphasized together with resonant effects on celestial bodies moving around the Sun. The following three chapters by A. Cellino, by P. Robutel and J.