For monoparametric familiesf(x,y)=c of planar orbits, created by a planar potentialV(x,y), we introduce the notion of the family boundary curves (FBC). All members of the familyf(x,y)=c are traced in an allowable region of thexy plane, defined by the corresponding FBC, with total energyE=E(c) varying along the family. Family boundary curves are also found for two-parametric familiesf(x,y,b)=c. The relation of equilibrium points and asymptotic orbits, possibly possessed by the potentialV(x,y), to be FBC is studied.
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Bozis, G., Ichtiaroglou, S. Boundary curves for families of planar orbits. Celestial Mech Dyn Astr 58, 371–385 (1994). https://doi.org/10.1007/BF00692011
- Inverse problem
- family boundary curves