Generalization of Szebehely's equation

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.