Mass-independent shapes for relative equilibria in the two-dimensional positively curved three-body problem

DOI10.1007/S00332-024-10065-ZMaRDI QIDQ6599773

Toshiaki Fujiwara, Ernesto Perez-Chavela

Publication date: 6 September 2024

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

zbMATH Keywords

relative equilibriacotangent potentialEuler configurations

Mathematics Subject Classification ID

Three-body problems (70F07) Celestial mechanics (70F15) (n)-body problems (70F10)

Cites Work

• Relative equilibria of the curved \(N\)-body problem.
• The \(n\)-body problem in spaces of constant curvature. II: Singularities
• Homographic solutions of the curved 3-body problem
• Two-body problem on a sphere. Reduction, stochasticity, periodic orbits
• Reduction and relative equilibria for the two-body problem on spaces of constant curvature
• On the stability of the Lagrangian homographic solutions in a curved three-body problem on \(\mathbb{S}^2\)
• Relative equilibria of the restricted three-body problem in curved spaces
• Almost all 3-body relative equilibria on \(\mathbb{S}^2\) and \(\mathbb{H}^2\) are inclined
• The spatial problem of 2 bodies on a sphere. Reduction and stochasticity
• Computing planar and spherical choreographies
• An intrinsic approach in the curved \(n\)-body problem. The positive curvature case
• Eulerian relative equilibria of the curved 3-body problems in 𝐒²
• Polygonal homographic orbits in spaces of constant curvature
• Euler-type Relative Equilibria and their Stability in Spaces of Constant Curvature
• Libration points in spaces \(S^2\) and \(L^2\)

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