On the connection between the Kepler problem and the isotropic harmonic oscillator in classical mechanics.

Details On the connection between the Kepler problem and the isotropic harmonic oscillator in classical mechanics. On the connection between the Kepler problem and the isotropic harmonic oscillator in classical mechanics.

Aug 1998

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998rmxf...44..333t&link_type=abstract

Revista Mexicana de Fisica, Vol. 44, No. 4, p. 333 - 338

Physics

Two-Body Problem

Scientific paper

Using the relationship between cartesian and parabolic coordinates, it is shown that the Kepler problem in two dimensions can be related with the isotropic harmonic oscillator in two dimensions in such a way that the Hermann-Bernoulli-Laplace-Runge-Lenz vector and the angular momentum, as well as the dynamical symmetry group generated by them, are obtained from the constants of the motion of the oscillator and its symmetry group. All possible values of the energy are considered and it is shown that the orbits in the Kepler problem are easily obtained form those of the harmonic oscillator.

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