Keplerization of motion in any central force field

The paper introduces a unified methodology for the study of bounded motion in central force fields, which serves both for qualitative insights, as well as for the derivation of closed-form vectorial solutions for the equations of motion. The paper offers a full regularization of the equations of motion in a central force field, starting from the polar equations in the plane of motion. A time transformation, as well as a coordinate transformation, are performed together, and the motion is (i) reduced to a Kepler motion in a rotating frame, with respect to a new time variable (ii) regularized further to a harmonic oscillator. In addition, some new results pertaining to the existence of a Laplace-Runge- Lenz vector in a central-force motion are presented.