Abstract :
It is shown in Leach PGL et al; J. Math. Phys., 44 (2003) 4090-4106, that the classical Kepler problem is reducible to a linear system consisting of two isotropic harmonic oscillators and a conservation law, the variables in which are related to the Ermanno-Bernouilli constants and the components of the angular momentum vector. We show that a reduction to such a linear system is also possible for all dynamical systems which (i) admit a Laplace-Runge-Lenz vector (ii) describe motion in a plane, and for which the equation of motion for the angular momentum admits a first integral. We show that a number of choices exist for the variables in the reduced system. We show also that this reduction is possible for all such dynamical systems which, instead of planar motion, describe conical motion associated with a Poincar{\ʹe} vector constant of motion.
