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The Kepler Problem: Group Theoretical Aspects, Regularization and Quantization, with Application to the Study of Perturbations: 29 (Progress in Mathematical Physics, 29) - Tapa blanda

Bruno Cordani

 
9783034894210: The Kepler Problem: Group Theoretical Aspects, Regularization and Quantization, with Application to the Study of Perturbations: 29 (Progress in Mathematical Physics, 29)
Tapa blanda
ISBN 10: 303489421X ISBN 13: 9783034894210
Editorial: Springer Nature B.V., 2013

Sinopsis

Because of the correspondences existing among all levels of reality, truths pertaining to a lower level can be considered as symbols of truths at a higher level and can therefore be the "foundation" or support leading by analogy to a knowledge of the latter. This confers to every science a superior or "elevating" meaning, far deeper than its own original one. - R. GUENON, The Crisis of Modern World Having been interested in the Kepler Problem for a long time, I have al ways found it astonishing that no book has been written yet that would address all aspects of the problem. Besides hundreds of articles, at least three books (to my knowledge) have indeed been published al ready on the subject, namely Englefield (1972), Stiefel & Scheifele (1971) and Guillemin & Sternberg (1990). Each of these three books deals only with one or another aspect of the problem, though. For example, En glefield (1972) treats only the quantum aspects, and that in a local way. Similarly, Stiefel & Scheifele (1971) only considers the linearization of the equations of motion with application to the perturbations of celes tial mechanics. Finally, Guillemin & Sternberg (1990) is devoted to the group theoretical and geometrical structure.

"Sinopsis" puede pertenecer a otra edición de este libro.

De la contraportada

This book contains a comprehensive treatment of the Kepler problem, i.e., the two body problem. It is divided into four parts. In the first part, written at an undergraduate student level, the arguments are presented in an elementary fashion, and the properties of the problem are demonstrated in a purely computational manner. In the second part a unifying point of view, original to the author, is presented which centers the exposition on the intrinsic group-geometrical aspects. This part requires more mathematical background, which the reader will find in the fourth part, in particular, the basic tools of differential geometry and analytical mechanics used in the book. The third part exploits some results of the second part to give a geometrical description of the perturbation theory of the Kepler problem.

Each of the four parts, which are to some extent independent, could itself form the basis for a one-semester course. The accompanying CD contains mainly the Microsoft Windows program KEPLER developed by the author. This program calculates the effects of any perturbation of the Kepler problem and plots the resulting trajectories.

"Sobre este título" puede pertenecer a otra edición de este libro.

Editorial
Springer Nature B.V.
Año de publicación
2013
Idioma
Inglés
ISBN 10 
303489421X
ISBN 13 
9783034894210
Encuadernación
Tapa blanda
Número de páginas
464
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