Reduction and unfolding: the Kepler problem

2004/11/30 by Antonella D'Avanzo, Giuseppe Marmo
Physics and Astronomy · Mathematics · #math-ph #hep-th #math.MP

paper · pdf

published as Int.J.Geom.Meth.Mod.Phys. 2 (2005) 83-109 · latex2e, 28 pages; misprints corrected

arxiv created 2005/02/28 · arxiv updated 2009/12/01

Abstract

In this paper we show, in a systematic way, how to relate the Kepler problem to the isotropic harmonic oscillator. Unlike previous approaches, our constructions are carried over in the Lagrangian formalism dealing with second order vector fields. We therefore provide a tangent bundle version of the Kustaahneimo-Stiefel map.

Related

• The geometry of the Kustaanheimo-Stiefel mapping
• Quantization of the Linearized Kepler Problem
• Alternative Angle-Based Approach to the KS-Map. An Interpretation Through Symmetry and Reduction
• An introduction to the Kepler-Heisenberg problem
• Elementary Solution of Kepler Problem (and a few other problems)