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Ligon, Thomas (Juni 1973): Das Keplerproblem differentialgeometrisch gesehen. Diplomarbeit, Fakultät für Physik, 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 S0(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.