A high order perturbation analysis of the Sitnikov problem

DOI10.1007/s10569-005-0521-1zbMath1129.70007OpenAlexW2026106349MaRDI QIDQ816897

Christoph Lhotka, Johannes Hagel

Publication date: 2 March 2006

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

Full work available at URL: https://doi.org/10.1007/s10569-005-0521-1

zbMATH Keywords

perturbation theoryFloquet theoryMathematicaSitnikov problemCourant and Snyder transformation

Mathematics Subject Classification ID

Three-body problems (70F07)

Related Items

High order normal form construction near the elliptic orbit of the Sitnikov problem, The stability of vertical motion in the \(N\)-body circular 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, Periodic orbits and bifurcations in the Sitnikov four-body problem, A new method to construct integrable approximations to nearly integrable systems in Celestial mechanics: application to the Sitnikov problem, Transient chaos in the Sitnikov 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, The structure of the extended phase space of the Sitnikov problem, The Sitnikov problem investigation with the method of multiple scales, An analytical approach to small amplitude solutions of the extended nearly circular Sitnikov problem

Uses Software

• Mathematica

Cites Work

• A new analytic approach to the Sitnikov problem
• Invariant rotational curves in Sitnikov's problem
• Solution of the Sitnikov problem
• On the Sitnikov problem
• The Strong-Focusing Synchroton—A New High Energy Accelerator