Abstract
Szebehely's partial differential equation for the force functionU=U(x,y) which gives rise to a given family of planar orbitsf(x,y)=Constant is generalized to account for velocity-dependent potentials V*=V*(x,y,\(\dot x,\dot y\)). The new partial differential equation is quasi-linear and of the first order. An example is given and a comparison is made of the two equations.
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Bozis, G. Generalization of Szebehely's equation. Celestial Mechanics 29, 329–334 (1983). https://doi.org/10.1007/BF01228527
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DOI: https://doi.org/10.1007/BF01228527