Physics
Scientific paper
Mar 1987
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987cemec..41..343f&link_type=abstract
Celestial Mechanics, Volume 41, Issue 1-4, pp. 343-357
Physics
Scientific paper
In this paper, we present a canonical transformation that extends the change of coordinates of Cartesian type into the associate homogeneous coordinates, and provides a redundant set of eight canonical variables to describe the orbital motion of a particle. The transformed problem has two additional integrals, since the transformation increases the number of variables. Using these variables and a time proportional to the true anomaly, the Kepler problem can be reduced to a 4-dimensional oscillator, whose frequency can be selected to be either the magnitude of the angular momentum or unity, depending on a suitable scaling. Perturbed problems are represented by perturbed harmonic oscillators, whatever the type of the orbit is, and in the special case of central force fields, the resulting equations can be linearized exactly.
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