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An equation for the characteristic curve of a family of symmetric periodic orbits
Authors:George Bozis  Bálint Érdi
Institution:(1) Department of Theoretical Mechanics, University of Thessaloniki, GR-540 06 Thessaloniki, Greece;(2) Department of Astronomy, Eötvös University, Budapest, Hungary
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.
Keywords:inverse problem  characteristic curve
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