Mathematics – Differential Geometry
Scientific paper
Aug 1983
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983cemec..30..395v&link_type=abstract
Celestial Mechanics (ISSN 0008-8714), vol. 30, Aug. 1983, p. 395-405.
Mathematics
Differential Geometry
11
Differential Geometry, Orbital Elements, Orbital Mechanics, Potential Fields, Circular Orbits, Elliptical Orbits, Existence Theorems, Harmonic Oscillators, Kepler Laws, Partial Differential Equations
Scientific paper
Consideration is given to the three-dimensional inverse problem. For determining the potential, a quasi-linear system of partial differential equations is derived. The method of differential geometry is used in investigating the solution of this system. After deriving a necessary condition for the solution, the determination of the potential is reduced to algebraic equations written in vectorial form. Examples are also presented. Attention is also given to a two-parametric family of space curves. This is done in order to give a more general treatment than Erdi (1982) to the determination of the potential in the three-dimensional case.
Erdi Bálint
Varadi Ferenc
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