High-order normal form stability estimates for co-orbital motion

DOI10.1007/s10569-013-9507-6zbMath1274.70047OpenAlexW2083832304MaRDI QIDQ375149

Christos Efthymiopoulos

Publication date: 28 October 2013

Published in: Celestial Mechanics and Dynamical Astronomy (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10569-013-9507-6

zbMATH Keywords

normal formseffective stabilityaveraged Hamiltonianelliptic restricted three body problemtrojans

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Orbital mechanics (70M20) Stability problems for problems in Hamiltonian and Lagrangian mechanics (70H14) Perturbation theories for problems in Hamiltonian and Lagrangian mechanics (70H09)

Related Items

Secondary resonances and the boundary of effective stability of Trojan motions ⋮ Explicit solution and resonance dynamics around triangular libration points of the planar elliptic restricted three-body problem ⋮ Trojan resonant dynamics, stability, and chaotic diffusion, for parameters relevant to exoplanetary systems

Cites Work

• On the stability of the Lagrangian points in the spatial restricted problem of three bodies
• Stability of co-orbital motion in exoplanetary systems
• Chaotic diffusion and effective stability of Jupiter Trojans
• Formal integrals and Nekhoroshev stability in a mapping model for the Trojan asteroids
• The observed Trojans and the global dynamics around the Lagrangian points of the Sun-Jupiter system
• Nekhoroshev-stability of \(L4\) and \(L5\) in the spatial restricted three-body problem
• Fast Lyapunov indicators. Application to asteroidal motion
• Symplectic mapping for Trojan-type motion in the elliptic restricted three-body problem
• A perturbative treatment of the co-orbital motion
• A semi-analytic algorithm for constructing lower dimensional elliptic tori in planetary systems
• High order normal form construction near the elliptic orbit of the Sitnikov problem
• A proof of Nekhoroshev's theorem for the stability times in nearly integrable Hamiltonian systems
• AN EXPONENTIAL ESTIMATE OF THE TIME OF STABILITY OF NEARLY-INTEGRABLE HAMILTONIAN SYSTEMS
• Solar System Dynamics
• Nonconvergence of formal integrals: II. Improved estimates for the optimal order of truncation
• On the construction of the Kolmogorov normal form for the Trojan asteroids