# The Kepler Problem

## Group Theoretical Aspects, Regularization and Quantization, with Application to the Study of Perturbations

- 32 Citations
- 7 Mentions
- 6.3k Downloads

Part of the Progress in Mathematical Physics book series (PMP, volume 29)

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- 32 Citations
- 7 Mentions
- 6.3k Downloads

Part of the Progress in Mathematical Physics book series (PMP, volume 29)

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.

Boundary value problem Mathematical physics Minkowski space Potential astrophysics differential geometry theory

- DOI https://doi.org/10.1007/978-3-0348-8051-0
- Copyright Information Birkhäuser Basel 2003
- Publisher Name Birkhäuser, Basel
- eBook Packages Springer Book Archive
- Print ISBN 978-3-0348-9421-0
- Online ISBN 978-3-0348-8051-0
- Buy this book on publisher's site