Solvable cases of Szebehely's equation

Details Solvable cases of Szebehely's equation Solvable cases of Szebehely's equation

Jul 1999

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999cemda..74..211g&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, v. 74, Issue 3, p. 211-221 (1999).

Astronomy and Astrophysics

Astronomy

3

Szebehely'S Equation, Inverse Problem, Szebehely'S Equation, Inverse Problem

Scientific paper

Szebehely’s equation is a first order partial differential equation relating a given family of orbits f (x, y) = q traced by a unit mass material point, the total energy E=E(f), and the unknown potential V=V (x, y) which produces the family. Although linear in V, this equation cannot generally be solved. In this paper we develop the reasoning for finding several cases for which Szebehely’s equation can be solved by quadratures.

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