On Szebehely's equation and its connection with Dainelli's-Whittaker's equations

Details On Szebehely's equation and its connection with Dainelli's-Whittaker's equations On Szebehely's equation and its connection with Dainelli's-Whittaker's equations

May 1984

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984cemec..33...85g&link_type=abstract

Celestial Mechanics (ISSN 0008-8714), vol. 33, May 1984, p. 85-97.

Physics

6

Celestial Mechanics, Orbit Calculation, Trajectory Analysis, Whittaker Functions, Orbital Mechanics, Partial Differential Equations, Potential Theory

Scientific paper

The authors prove that Szebehely's equation is not only a necessary condition to be satisfied by the potential U(x→) but that it is also a sufficient condition. This was shown by Broucke and Lass (1977) using a different procedure. The authors obtain also a first order partial differential equation for the function g2(x→) appearing in the paper of Broucke and Lass. This equation, being of a quite simple structure, is quite adequate for its integration, and this is shown by examples.

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