An equation for the characteristic curve of a family of symmetric periodic orbits |
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Authors: | George Bozis Bálint Érdi |
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Affiliation: | (1) Department of Theoretical Mechanics, University of Thessaloniki, GR-540 06 Thessaloniki, Greece;(2) Department of Astronomy, Eötvös University, Budapest, Hungary |
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Abstract: | Szebehely's equation for the inverse problem of Dynamics is used to obtain the equation of the characteristic curve of a familyf(x,y)=c of planar periodic orbits (crossing perpendicularly thex-axis) created by a certain potentialV(x,y). Analytic expressions for the characteristic curves are found both in sideral and synodic systems. Examples are offered for both cases. It is shown also that from a given characteristic curve, associated with a given potential, one can obtain an analytic expression for the slope of the orbit at any point. |
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Keywords: | inverse problem characteristic curve |
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