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On the determination of potential function. (English) Zbl 0830.70009

Summary: Szebehely’s renowned equation given in [E. Proverbio (ed.), Proc. Intern. Meeting on Earth’s Rotation by Satellite Observations, Bologna (1973), 31], allowing for potential determination from a given orbit or family of orbits, is proved to be equivalent to an equation deduced by C. Drâmbă [Stud. Cerc. Astron. 8, 7 (1963)]. This basic equation in the inverse problem of dynamics, for which the denomination of Drâmbă-Szebehely equation is proposed, is generalized for the motion in the \(n\)-dimensional Euclidean space. A method for the determination of the potential function from equations of motion is extended to this space.

MSC:

70F15 Celestial mechanics
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References:

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[12] : 1992, Thesis, University of Cluj-Napoca
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