Stability of motion in the Sitnikov 3-body problem

DOI10.1007/s10569-007-9093-6zbMath1162.70312OpenAlexW1967324405MaRDI QIDQ2458486

Yanyan Li

Publication date: 1 November 2007

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

Full work available at URL: https://doi.org/10.1007/s10569-007-9093-6

zbMATH Keywords

``Islands of bounded motionExtended and general Sitnikov problemRestricted 3-body Sitnikov problemStability intervals

Mathematics Subject Classification ID

Three-body problems (70F07) Stability for nonlinear problems in mechanics (70K20)

Related Items (13)

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 ⋮ Chaotic dynamics of string around charged black brane with hyperscaling violation ⋮ Periodic orbits and bifurcations in the Sitnikov four-body problem ⋮ Stability and bifurcations of even periodic orbits in the Sitnikov problem ⋮ Matched asymptotic expansions to the circular Sitnikov problem with long period ⋮ Transient chaos in the Sitnikov problem ⋮ Straight-line oscillations generating three-dimensional motions in the photogravitational restricted three-body problem ⋮ Spatial restricted rhomboidal five-body problem and horizontal stability of its periodic solutions ⋮ An analytical approach to small amplitude solutions of the extended nearly circular Sitnikov problem ⋮ Effects of manifold correction methods on chaos indicators

Cites Work

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• A global analysis of the generalized Sitnikov problem
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• Stable and Random Motions in Dynamical Systems
• Alignment indices: a new, simple method for determining the ordered or chaotic nature of orbits
• QUASIRANDOM DYNAMICAL SYSTEMS. I. QUASIRANDOM DIFFEOMORPHISMS

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