Mathematics
Scientific paper
Dec 1974
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1974cemec..10..437h&link_type=abstract
Celestial Mechanics, vol. 10, Dec. 1974, p. 437-449.
Mathematics
16
Coordinate Transformations, Orbit Calculation, Perturbation Theory, Satellite Orbits, Singularity (Mathematics), Artificial Satellites, Canonical Forms, Celestial Mechanics, Eccentric Orbits, Lie Groups, Polar Coordinates
Scientific paper
When the coordinate system used in perturbation theory presents a geometrical singularity and when the perturbation technique fails to take account of this, the solution developed may present singularities which are no longer easily explained by purely geometrical means. These singularities have been called virtual singularities by Deprit and Rom (1970). It is demonstrated that virtual singularities can generally be avoided by the use of Lie transforms. In general, it is sufficient to recognize that the original Hamiltonian function presents the d'Alembert characteristic with respect to pairs of action-angle variables and that the averaging operations preserve this characteristic. This criterion is then applied to the artificial satellite theory (for small to moderate eccentricity), showing that all of three possible virtual singularities can be avoided at the same time. A new set of elliptic elements, well suited to the problem at hand, is introduced.
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