Applications of Szebehely's equation

Details Applications of Szebehely's equation Applications of Szebehely's equation

Sep 1981

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981cemec..25...81m&link_type=abstract

Celestial Mechanics, vol. 25, Sept. 1981, p.81-88.

Physics

19

Celestial Mechanics, Differential Equations, Orbit Calculation, Potential Theory, Ellipses, Kepler Laws, Polar Coordinates

Scientific paper

It is shown that the potential obtained from Joukovsky's formula, corresponding to a given family of orbits, is a general solution of Szebehely's equation. Then it is shown how a general solution of Szebehely's equation can be obtained from its particular solution. This method is applied to several examples. Potentials generating families of concentric elliptic orbits and families of orbits of conic sections are determined. Finally, the inverse Keplerian problem is solved using Szebehely's equation in polar coordinates.

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