Complex representation of planar motions and conserved quantities of the Kepler and hooke problems

Abstract

Using a complex representation of planar motions, we show that the dynamical conserved quantities associated to the isotropic harmonic oscillator (Fradkin-Jauch-Hill tensor) and to the Kepler's problem (Laplace-Runge-Lenz vector) find a very simple and natural interpretation. In this frame we also establish in an elementary way the relation which connects them. © 2010 The Author(s).