Special families of orbits for the Hénon-Heiles type potential

For a Henon-Heiles type potential, with undetermined coefficients, the possibility for a material point to describe a family of curves of the form \(x\symbol{94}(-p)y=q\) is studied. Two admissible cases, \(p=4\) and \(p=-2\), are found; for these the potential and the family boundary curves are specified, and the regions in which the curves of the given family can be traced are determined.

Mira-Cristiana Anisiu
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, Romania

Arpad Pal
Babes-Bolyai University, Cluj-Napoca

words: inverse problem – family boundary curves – Henon-Heiles potential.

M.-C. Anisiu, Á. Pál, Special families of orbits for the Hénon-Heiles type potential, Rom. Astron. J. 9 (2) (1999), 179-185

Book of abstracts: https://www.astro.ro/~roaj/volume/abs9_2.html#Special%20Families%20Of%20Orbits%20For%20The%20Henon-Heiles

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