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AuthorCordani, Bruno. author
TitleThe Kepler Problem [electronic resource] : Group Theoretical Aspects, Regularization and Quantization, with Application to the Study of Perturbations / by Bruno Cordani
ImprintBasel : Birkhรคuser Basel : Imprint: Birkhรคuser, 2003
Connect tohttp://dx.doi.org/10.1007/978-3-0348-8051-0
Descript XVII, 442 p. online resource

SUMMARY

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


CONTENT

Preface -- List of Figures -- 1 Introductory Survey -- 1.1 Part I - Elementary Theory -- 1.2 Part II - Group-Geometric Theory -- 1.3 Part III - Perturbation Theory -- 1.4 Part IV - Appendices -- I Elementary Theory 17 -- 2 Basic Facts -- 3 Separation of Variables and Action-Angle Coordinates -- 4 Quantization of the Kepler Problem -- 5 Regularization and Symmetry -- II Group-Geometric Theory 109 -- 6 Conformal Regularization -- 7 Spinorial Regularization -- 8 Return to Separation of Variables -- 9 Geometric Quantization -- 10 Kepler Problem with Magnetic Monopole -- III Perturbation Theory 235 -- 11 General Perturbation Theory -- 12 Perturbations of the Kepler Problem -- 13 Perturbations with Axial Symmetry -- IV Appendices 321 -- A Differential Geometry -- B Lie Groups and Lie Algebras -- C Lagrangian Dynamics -- D Hamiltonian Dynamics


Mathematics Topological groups Lie groups Applied mathematics Engineering mathematics Physics Astrophysics Mathematics Applications of Mathematics Mathematical Methods in Physics Topological Groups Lie Groups Astrophysics and Astroparticles



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