On the Integrability Cases of the Equation of Motion for a Satellite in an Axially Symmetric Gravitational Field

Details On the Integrability Cases of the Equation of Motion for a Satellite in an Axially Symmetric Gravitational Field On the Integrability Cases of the Equation of Motion for a Satellite in an Axially Symmetric Gravitational Field

Sep 1971

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1971cemec...4...49g&link_type=abstract

Celestial Mechanics, Volume 4, Issue 1, pp.49-53

Physics

Optics

Scientific paper

The projection of an axially symmetric satellite's orbit on a plane perpendicular to the rotation axis (z=const.) is given by the second-order differential equation. {y''}/{1 + y'^2 } = bar Ψ _y - y'bar Ψ _{x,} where the prime denotes the derivative with respect tox andbar Ψ (x,y) is a known function. Two integrability cases have been investigated and it has been shown that for these two cases the integration can be carried out either by quadratures or reduced to a first-order differential equation. Analytical and physical properties are expressed, and it is shown that the equation can be derived from the calssical plane eikonal equation of geometric optics.

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