Periodic solutions of the restricted problem that are analytic continuations of periodic solutions of Hill's problem for small ?>0

DOI10.1007/BF01234301zbMath0545.70011MaRDI QIDQ3335038

Lawrence M. Perko

Publication date: 1983

Published in: Celestial Mechanics (Search for Journal in Brave)

zbMATH Keywords

Fourier seriesbifurcation pointsinitial conditionsexistence theoremanalytic continuations of symmetric periodic solutions of Hill's problemexistence and first-order perturbation approximationinfinite number of one-parameter families of symmetric periodic solutionsplanar, circular, restrictedretrograde and direct periodic orbits about the originsmall values of the mass ratiosolutions of the third species

Mathematics Subject Classification ID

Three-body problems (70F07) Celestial mechanics (70F15) Orbital mechanics (70M20)

Related Items (6)

Multiobjective routing problems ⋮ Multipliers of periodic Hill solutions in the theory of Moon motion and an averaging method ⋮ A general timing condition for consecutive collision orbits in the limiting case \(\mu{}=0\) of the elliptic restricted problem ⋮ A note on the elliptic restricted three-body problem ⋮ Periodic solutions of the restricted three-body problem for a small mass ratio ⋮ Periodic orbits

Cites Work

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• Über eine Schar periodischer Lösungen des ebenen Vierkörperproblems
• Second species solutions with an 0(? v ), 0<v<1, near-Moon passage
• Periodic Orbits in the Restricted Problem: An Analysis in the Neighborhood of a 1st Species-2nd Species Bifurcation
• Families of Symmetric Periodic Solutions of Hill's Problem I: First Species Periodic Solutions for C ≪-1
• Families of Symmetric Periodic Solutions of Hill's Problem II: Second Species Periodic Solutions for C ≪-1
• Periodic Orbits in the Restricted Three-Body Problem: Existence and Asymptotic Approximation
• Second species periodic solutions with an 0(?) near-moon passage
• Periodic Solutions of the Restricted Three Body Problem Representing Analytic Continuations of Keplerian Elliptic Motions

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