Comment on ‘Conservative discretizations of the Kepler motion’

We show that the exact integrator for the classical Kepler motion, recently found by Kozlov (2007 J. Phys. A: Math. Theor. 40 4529–39), can be derived in a simple natural way, using a well-known exact discretization of the harmonic oscillator. We also draw attention to important earlier references, where the exact discretization of the four-dimensional isotropic harmonic oscillator has been applied to the perturbed Kepler problem.