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Existence of the solution of Szebehely's equation in three dimensions using a two-parametric family of orbits

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Abstract

The three-dimensional inverse problem is investigated. A quasi-linear system of partial differential equations is derived for the determination of the potential. The solution of this system is studied by a method of differential geometry. A necessary condition for the solution is derived and the determination of the potential is reduced to algebraic equations written in vectorial form. A few examples are also given.

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Authors and Affiliations

  1. Department of Astronomy, Eötvös University, Budapest, Hungary

    F. Váradi & B. Érdi

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  1. F. Váradi
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  2. B. Érdi
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Váradi, F., Érdi, B. Existence of the solution of Szebehely's equation in three dimensions using a two-parametric family of orbits. Celestial Mechanics 30, 395–405 (1983). https://doi.org/10.1007/BF01375509

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  • DOI: https://doi.org/10.1007/BF01375509

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