COMPLEX REPRESENTATION OF PLANAR MOTIONS AND CONSERVED QUANTITIES OF THE KEPLER AND HOOKE PROBLEMS

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.