Bifurcations of planar to three-dimensional periodic orbits in the general three-body problem

DOI10.1007/BF01301803zbMath0517.70012OpenAlexW3089767419MaRDI QIDQ3666304

V. V. Markellos

Publication date: 1981

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

Full work available at URL: https://doi.org/10.1007/bf01301803

zbMATH Keywords

bifurcation processvertical-critical orbitsorbits which allow continuationplanar problem continued directly to nonplanar

Mathematics Subject Classification ID

Three-body problems (70F07)

Related Items (8)

Nonlinear approximation of periodic three-body motions around collinear equilibrium configurations ⋮ The stability parameters of three-dimensional periodic three-body orbits ⋮ Mass ratios of three bodies for stable low-inclination three-dimensional periodic motion ⋮ On basic families of three-dimensional periodic orbits of three massive bodies and their stability ⋮ Computation of Periodic Solutions of Conservative Systems with Application to the 3-Body Problem ⋮ The use of vertical instability of \(L_1\) and \(L_2\) planar Lyapunov orbits for transfers from near rectilinear halo orbits to planar distant retrograde orbits in the Earth-Moon system ⋮ Three-dimensional periodic motion of three finite masses around collinear equilibrium configurations ⋮ Periodic orbits

Cites Work

• Restricted problem stability and the solar system
• Families of periodic orbits in the general three-body problem for the Sun-Jupiter-Saturn mass-ratio and their stability
• Numerical determination of three-dimensional periodic orbits generated from vertical self-resonant satellite orbits
• The three-dimensional general three-body problem: Determination of periodic orbits
• Bifurcations of plane with three-dimensional periodic orbits in the elliptic restricted problem
• Families of periodic orbits in the three-body problem
• The stability of periodic orbits in the three-body problem
• On relative periodic solutions of the planar general three-body problem
• On the continuation of periodic orbits from the planar to the three-dimensional general three-body problem

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