A generalization of Szebehely's equation for three dimensions

Mathematics

Scientific paper

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Equations Of Motion, Orbital Elements, Orbital Mechanics, Kepler Laws, Linear Equations, Partial Differential Equations, Potential Theory

Scientific paper

Szebehely's equation for the potential generating a prescribed family of orbits in two dimensions is generalized for three-dimensional orbits. A simultaneous system of first-order linear partial differential equations is derived for the determination of the potential in the three-dimensional case. Solutions of this system are found in several cases including Kepler's problem.

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