On relative periodic solutions of the planar general three-body problem

DOI10.1007/BF01595390zbMath0322.70012MaRDI QIDQ4085311

Roger A. Broucke

Publication date: 1975

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

Mathematics Subject Classification ID

Celestial mechanics (70F15) (n)-body problems (70F10)

Related Items (21)

Periodic orbits of the general three-body problem for the Sun-Jupiter-Saturn system ⋮ Linear stability of the criss-cross orbit in the equal-mass three-body problem ⋮ Equivariant degree method for analysis of Hopf bifurcation of relative periodic solutions: case study of a ring of oscillators ⋮ Geometric properties of minimizers in the planar three-body problem with two equal masses ⋮ On the co-orbital motion in the planar restricted three-body problem: the quasi-satellite motion revisited ⋮ Continuous symmetry reduction and return maps for high-dimensional flows ⋮ Angular Momentum and Topological Dependence of Kepler’s Third Law in the Broucke-Hadjidemetriou-Hénon Family of Periodic Three-Body Orbits ⋮ On ``generalized Kepler's third law and mass dependence of periods of three-body orbits ⋮ A guide to hunting periodic three-body orbits with non-vanishing angular momentum ⋮ Unnamed Item ⋮ The rectilinear three-body problem ⋮ The three-dimensional general three-body problem: Determination of periodic orbits ⋮ The family of planar periodic orbits generated by the equal-mass four-body Schubart interplay orbit ⋮ Linear stability of periodic three-body orbits with zero angular momentum and topological dependence of Kepler’s third law: a numerical test ⋮ A family of periodic solutions of the planar three-body problem, and their stability ⋮ The present status of periodic orbits ⋮ Properties of linearized mappings associated with periodic orbits in the three-body problem ⋮ The Broucke–Hénon orbit and the Schubart orbit in the planar three-body problem with two equal masses ⋮ On action-minimizing retrograde and prograde orbits of the three-body problem ⋮ Bifurcations of planar to three-dimensional periodic orbits in the general three-body problem ⋮ Periodic orbits

Cites Work

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• New periodic solutions of the plane three-body problem corresponding to elliptic motion in the lunar theory
• Families of periodic orbits in the three-body problem
• Periodic orbits in the Planar General Three-Body Problem
• The stability of periodic orbits in the three-body problem
• Classification of the motions of three bodies in a plane
• Solution of theN-body problem with recurrent power series
• A note on relative motion in the general three-body problem
• A Symmetric Reduction of the Planar Three-Body Problem
• On a Symmetrical Canonical Reduction of the Problem of Three Bodies

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