On the stability of the Lagrangian homographic solutions in a curved three-body problem on \(\mathbb{S}^2\)

DOI10.3934/DCDS.2013.33.1157zbMath1263.70010OpenAlexW2316331411MaRDI QIDQ1946346

Carles Simó, Regina Martínez

Publication date: 19 April 2013

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2013.33.1157

zbMATH Keywords

stability of solutionspractical stabilitycurved 3-body problemhomographic orbits

Mathematics Subject Classification ID

Three-body problems (70F07) Characteristic and Lyapunov exponents of ordinary differential equations (34D08) Stability problems for finite-dimensional Hamiltonian and Lagrangian systems (37J25) Periodic and almost periodic solutions for problems in Hamiltonian and Lagrangian mechanics (70H12)

Related Items (22)

Equilibrium points in restricted problems on S2 and H2 ⋮ Central configurations of the curved \(N\)-body problem ⋮ Rotopulsators of the curved \(N\)-body problem ⋮ All the Lagrangian relative equilibria of the curved 3-body problem have equal masses ⋮ The curved \(N\)-body problem: risks and rewards ⋮ Stability of regular polygonal relative equilibria on \(\mathbb{S}^2\) ⋮ Three-body relative equilibria on \(\mathbb{S}^2\) ⋮ On the \(n\)-body problem on surfaces of revolution ⋮ Hyperbolic relative equilibria for the negative curved \(n\)-body problem ⋮ Relative equilibria for the positive curved \(n\)-body problem ⋮ On the stability of tetrahedral relative equilibria in the positively curved 4-body problem ⋮ Some results on the existence and multiplicity of Dirichlet type solutions for a singular equation coming from a Kepler problem on the sphere ⋮ The curved symmetric 2- and 3-center problem on constant negative surfaces ⋮ Stability of fixed points and associated relative equilibria of the 3-body problem on \({\mathbb {S}}^1\) and \({\mathbb {S}}^2\) ⋮ The N-body problem in spaces with uniformly varying curvature ⋮ Relative equilibria of the restricted three-body problem in curved spaces ⋮ Regular polygonal equilibria on \(\mathbb{S}^1\) and stability of the associated relative equilibria ⋮ Relative equilibria in the 3-dimensional curved n-body problem ⋮ Continuation of relative equilibria in the \(n\)-body problem to spaces of constant curvature ⋮ An intrinsic approach in the curved \(n\)-body problem: the negative curvature case ⋮ Relative Equilibria in curved restricted 4-body problems ⋮ Bifurcations of the Lagrangian orbits from the classical to the curved 3-body problem

Uses Software

• PARI/GP

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