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Ligon, Thomas (10. January 2017): The Kepler problem from a differential geometry point of view. Translation of the original German Version: Das Keplerproblem differentialgeometrisch gesehen. Diploma Thesis, Ludwig-Maximilians-Universität München
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Abstract

This paper examines the Kepler 2-body problem as an example of the symplectic differential geometric formulation of Hamiltonian mechanics. First, the foundations of symplectic differential geometry and the conventional analysis of the Kepler problem are presented. Then, the SO(4) and SO(3,1) symmetry of the problem and the conserved angular momentum and Runge-Lenz vectors are discussed. The symmetry is also discussed globally, and the integral curves of the Runge-Lenz vector are found.