Two body problem
Springer Online Journal Archives 1860-2000
Abstract We present here a group theoretical analysis of the structure of the space Ω of orbits in the classical (plane) Kepler problem, and relate it to the description of the Kepler orbits as curves in configuration and in velocity spaces. A Minkowskian parametrization in Ω is introduced which allows us a clear description of many aspects of this problem. In particular, this parametrization suggests us the introduction in Ω of a Lorentzian metric, whose conformal group SO(3, 2) contains a seven-dimensional subgroup which is induced by point transformations in the configuration space X. A SO(2, 1) subgroup of this group still acts transitively on X, which is thus identified as a homogeneous space for SO(2,1); each regular Kepler orbit is the trace of a one-dimensional subgroup whose canonical parameter automatically equals to the classical anomalies. These results are somehow a configuration space analogous of the geometrical structure of the Kepler problem in the velocity space previously known.
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