Stability, periodic solution and KAM tori in the circular restricted \((N+1)\)-body problem on \({\mathbb{S}}^3\) and \({\mathbb{H}}^3\)

DOI10.1007/S00332-023-09946-6zbMath1527.70011OpenAlexW4385416017MaRDI QIDQ6115829

D. E. Espejo, Jaime Andrade

Publication date: 10 August 2023

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

Full work available at URL: https://doi.org/10.1007/s00332-023-09946-6

zbMATH Keywords

linear stabilitynonlinear stabilityreduced HamiltonianGaussian curvatureaveraging theoryelliptic relative equilibriumconstant curvature surfaceperiodic orbit existence

Mathematics Subject Classification ID

(n)-body problems (70F10) Stability problems for problems in Hamiltonian and Lagrangian mechanics (70H14) Nearly integrable Hamiltonian systems, KAM theory (70H08)

Cites Work

• Unnamed Item
• Unnamed Item
• Relative equilibria of the curved \(N\)-body problem.
• The \(n\)-body problem in spaces of constant curvature. II: Singularities
• Invariant tori in the lunar problem
• Invariant tori in Hamiltonian systems with high order proper degeneracy
• Symmetric periodic solutions for the spatial Maxwell restricted \(N+1\)-problem with Manev potential
• Introduction to Hamiltonian dynamical systems and the \(N\)-body problem.
• Kepler's problem in constant curvature spaces
• On stability of an autonomous Hamiltonian system with two degrees of freedom under first-order resonance
• The restricted three body problem on surfaces of constant curvature
• On the stability of tetrahedral relative equilibria in the positively curved 4-body problem
• Mathematical aspects of classical and celestial mechanics. Transl. from the Russian by E. Khukhro.
• Relative equilibria in the 3-dimensional curved n-body problem
• On the singularities of the curved $n$-body problem
• The continuous transition of Hamiltonian vector fields through manifolds of constant curvature
• Central potentials on spaces of constant curvature: The Kepler problem on the two-dimensional sphere S2 and the hyperbolic plane H2
• Periodic Solutions in Hamiltonian Systems, Averaging, and the Lunar Problem
• The elimination of the parallax in satellite theory
• Periodic solutions of symmetric Kepler perturbations and applications
• Canonical transformations depending on a small parameter
• The main problem of artificial satellite theory for small and moderate eccentricities
• Introduction to Hamiltonian dynamical systems and the \(N\)-body problem

This page was built for publication: Stability, periodic solution and KAM tori in the circular restricted \((N+1)\)-body problem on \({\mathbb{S}}^3\) and \({\mathbb{H}}^3\)