An analytical approach to small amplitude solutions of the extended nearly circular Sitnikov problem

DOI10.1007/s10569-009-9187-4zbMath1157.70005OpenAlexW2021931147MaRDI QIDQ1008072

J. Martínez

Publication date: 24 March 2009

Published in: Celestial Mechanics and Dynamical Astronomy (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10569-009-9187-4

zbMATH Keywords

convergenceperturbation methodsfunction iteration

Mathematics Subject Classification ID

Three-body problems (70F07)

Related Items (6)

High order normal form construction near the elliptic orbit of the Sitnikov problem ⋮ Basins of Convergence in the Circular Sitnikov Four-Body Problem with Nonspherical Primaries ⋮ On the circular Sitnikov problem: the alternation of stability and instability in the family of vertical motions ⋮ A new method to construct integrable approximations to nearly integrable systems in Celestial mechanics: application to the Sitnikov problem ⋮ Matched asymptotic expansions to the circular Sitnikov problem with long period ⋮ The Sitnikov problem investigation with the method of multiple scales

Uses Software

• Mathematica

Cites Work

• A high order perturbation analysis of the Sitnikov problem
• A new analytic approach to the Sitnikov problem
• The phase space structure of the extended Sitnikov problem
• Solution of the Sitnikov problem
• Periodic orbits and bifurcations in the Sitnikov four-body problem
• The manifolds of families of 3D periodic orbits associated to Sitnikov motions in the restricted three-body problem
• Stability of motion in the Sitnikov 3-body problem
• On the Sitnikov problem

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