Geometric characterizations for variational minimization solutions of the 3-body problem

DOI10.1007/PL00011566zbMath0980.70009OpenAlexW3148603735MaRDI QIDQ5925952

Long, Yiming, Zhang, Shiqing

Publication date: 4 March 2002

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/pl00011566

zbMATH Keywords

circular restricted three-body problemplanar equilateral triangle circular solutionthree-body problemvariational minimization solution

Mathematics Subject Classification ID

Three-body problems (70F07) Variational methods for problems in mechanics (70G75)

Related Items (16)

Geometric characterizations for variational minimizing solutions of charged 3-body problems ⋮ Periodic solutions for planar four-body problems ⋮ Periodic solutions for circular restricted \(N+1\)-body problems ⋮ New periodic solutions for 2\(n\)-body problems in \(R^{3}\) ⋮ The variational minimization solutions of 3-body problems with 2 fixed centers ⋮ Rose solutions with three petals for planar 4-body problems ⋮ Periodic solutions for the generalized anisotropic Lennard-Jones Hamiltonian ⋮ New periodic solutions for some planar \(N + 3\)-body problems with Newtonian potentials ⋮ New periodic solutions for planar \((N+2)\)-body problems ⋮ Geometric characterization for variational minimization solutions of the 3-body problem with fixed energy ⋮ Variational minimizing solutions for the 2-fixed center problems ⋮ Saari's Conjecture for Elliptical Motions and Minimizing Solutions of the N-body Problem ⋮ Action-minimizing solutions of the one-dimensional \(N\)-body problem ⋮ Action minimizing orbits in the 2+2- and 3+2-body problems with 2 fixed centers ⋮ Morse index and stability of elliptic Lagrangian solutions in the planar three-body problem ⋮ Variational minimizing parabolic orbits for 2-fixed center problems

Cites Work

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• Periodic solutions for N-body type problems
• Collisionless periodic solutions to some three-body problems
• Periodic solutions of singular Lagrangian systems
• A class of periodic solutions of the \(N\)-body problem
• Symmetries and noncollision closed orbits for planar N-body-type problems
• A Minimizing Property of Keplerian Orbits
• Introduction to Hamiltonian dynamical systems and the \(N\)-body problem

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