Abstract
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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References
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Whittaker, E. T.: 1927,Analytical Dynamics of Particles and Rigid Bodies, Cambridge University Press, pp. 109–111.
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Molnár, S. Applications of Szebehely's equation. Celestial Mechanics 25, 81–88 (1981). https://doi.org/10.1007/BF01301809
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DOI: https://doi.org/10.1007/BF01301809