On perturbed two-body problems and harmonic oscillators.

Details On perturbed two-body problems and harmonic oscillators. On perturbed two-body problems and harmonic oscillators.

Jul 1996

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996crasb.323...71a&link_type=abstract

Comptes Rendus de l'Academie des Sciences, Sér. II, Fasc. b, Tome 323, No. 1, p. 71 - 76

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Two-Body Problem: Perturbations

Scientific paper

The possibility of achieving linearization (i.e. reduction of the equations of motion to second-order differential equations corresponding to harmonic oscillators) of a class of r-n-perturbed Kepler problems is investigated by using BF focal-type canonical variables. The authors show that the only r-n-perturbation of the considered class which admits exact linearization is that corresponding to the Deprit-type potentials (say, for n = 2) constructed within the framework of artificial satellite theory. Approximate linearization is also obtained for perturbations involving other powers of the radial distance. In any case, this process requires the use of a fictitious time of the true anomaly type.

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