A new set of canonical variables for orbit calculation

Mathematics

Scientific paper

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Canonical Forms, Orbit Calculation, Orbital Mechanics, Transformations (Mathematics), Harmonic Oscillators, Orbit Perturbation, Polynomials, Two Body Problem

Scientific paper

A canonical transformation which is useful to describe the orbital motion of a particle, and involves redundant variables is presented. It is shown that it shares interesting properties with the KS transformation. When the perturbation comes from the oblateness of the primary body, it seems reasonable to use the canonical equations, because their right hand parts result in polynomial expressions. In any case, it can be used to reduce the two body problem to four harmonic oscillators. Their common frequency is equal to one if a new time coincident with the true anomaly is used. This transformation could be used as an alternative method for an efficient calculation of orbits.

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