Geometric characterization for variational minimization solutions of the 3-body problem with fixed energy

DOI10.1006/JDEQ.1999.3659zbMath0947.70009OpenAlexW1967746811MaRDI QIDQ1968704

Zhang, Shiqing, Long, Yiming

Publication date: 13 April 2000

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jdeq.1999.3659

zbMATH Keywords

three-body problemhomogeneous potentialsfixed energyfixed mean potential energyconstrained variational minimizationLagrange's solutionplanar equilateral triangle circular solutions

Mathematics Subject Classification ID

Three-body problems (70F07) Other variational principles in mechanics (70H30)

Related Items (11)

Periodic solutions for planar four-body problems ⋮ Nonconstant periodic solutions with any fixed energy for singular Hamiltonian systems ⋮ New periodic solutions for planar five-body and seven-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 ⋮ A noncollision periodic solution for \(N\)-body problems ⋮ Infinitely many non-constant periodic solutions with negative fixed energy for Hamiltonian systems ⋮ 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 ⋮ The realization of elementary configurations in Euclidean space ⋮ Geometric characterization for the least Lagrangian action of \(n\)-body problems

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