The Classical Isotropic bi-Dimensional Oscilator in the Eisenhart Formulation of Classical Mechanics

Accordingly with the general theory of relativity, the motion of a particle by the only action of inertia and gravity is described by a space-time geodesic. We use the Eisenhart geometric formulation of classical mechanics to establish a correspondence between geodesics and paths in phase space of the classical bi-dimensional isotropic oscillator. The Killing vectors and its associated constants of motion are presented and compared with nonNoetherian motion constant calculated by S. Hojman and collaborators. Keywords:  Geometric Mechanics, Geometrical and tensorial methods, Formalisms in classical mechanics.