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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Bozis, G., Érdi, B. An equation for the characteristic curve of a family of symmetric periodic orbits. Celestial Mech Dyn Astr 59, 301–311 (1994). https://doi.org/10.1007/BF00692099
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DOI: https://doi.org/10.1007/BF00692099