Dynamical quasi-symmetry of the classical Kepler-Coulomb problem and the conservation of the Laplace-Runge-Lenz vector

The paper studies a classical non-relativistic particle moving in $\mathbb{R}^{N}$, $(N\geqslant2)$, in the presence of the Kepler-Coulomb force $\boldsymbol{F}(\boldsymbol{r})=α\boldsymbol{r}/r^{3}$, $(α\neq0)$. It is shown that the extended-configuration-space transformation involving the projecti