2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/57872In 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.latex2e, 28 pages; misprints correctedMathematical PhysicsHigh Energy Physics - Theorytext