The 'critical inclination' - Another look

Details The 'critical inclination' - Another look The 'critical inclination' - Another look

Nov 1981

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981cemec..25..235h&link_type=abstract

Celestial Mechanics, vol. 25, Nov. 1981, p. 235-266.

Mathematics

8

Artificial Satellites, Astrodynamics, Inclination, Satellite Orbits, Satellite Orientation, Satellite Perturbation, Canonical Forms, Eccentricity, Equations Of Motion, Geopotential, Hill Method, Numerical Integration, Singularity (Mathematics), Transformations (Mathematics)

Scientific paper

The occurrence and uniqueness of the critical inclination in satellite theory are discussed. It is shown that an infinite set of canonical transformations in Hill variables exists whereby the first order secular part of the disturbing function can be changed into an alternative form. As a consequence of such a transformation, the critical inclination can become (1) any other real or complex inclination or a function independent of the satellite's orbital inclination and (2) a function dependent on the semi-major axis, eccentricity, and inclination of the satellite's orbit. In addition, it is shown that all transformations of types (1) and (2) are valid only for short intervals of time of the order of a few satellite revolutions. Moreover, if such transformations are modified so that they become valid for greater intervals of time, then the resulting solutions in all cases contain no singular divisor other than the critical inclination. It is concluded that the singularity at the critical inclination is unique and that it represents an actual physical resonance rather than something resulting from the method of solution or the type of variable employed in the analysis.

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