Normal forms for perturbed Keplerian systems.

DOI10.1006/jdeq.2001.4068zbMath1098.70014OpenAlexW2054826158MaRDI QIDQ1599268

Jesús F. Palacián

Publication date: 2002

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

Full work available at URL: https://doi.org/10.1006/jdeq.2001.4068

Mathematics Subject Classification ID

Two-body problems (70F05) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Celestial mechanics (70F15) Perturbation theories for problems in Hamiltonian and Lagrangian mechanics (70H09) Normal forms for nonlinear problems in mechanics (70K45)

Related Items (15)

The Keplerian regime of charged particles in planetary magnetospheres ⋮ Closed-form perturbation theory in the restricted three-body problem without relegation ⋮ Exact Delaunay normalization of the perturbed Keplerian Hamiltonian with tesseral harmonics ⋮ From the circular to the spatial elliptic restricted three-body problem ⋮ Dynamics of a satellite orbiting a planet with an inhomogeneous gravitational field ⋮ Regular and singular reductions in the spatial three-body problem ⋮ Rigorous estimates for the relegation algorithm ⋮ Symplectic coordinates on \(S^2\times S^2\) for perturbed Keplerian problems: application to the dynamics of a generalised Størmer problem ⋮ Relegation-free closed-form perturbation theory and the domain of secular motions in the restricted three-body problem ⋮ Nekhoroshev estimates for the orbital stability of Earth's satellites ⋮ Influence of planetary oblateness on Keplerian dynamics in magnetospheres and existence of invariant tori ⋮ Asymptotic invariant tori of perturbed two-body problems ⋮ Invariant manifolds of an autonomous ordinary differential equation from its generalized normal forms ⋮ Normalization through invariants in \(n\)-dimensional Kepler problems ⋮ Bifurcation of frozen orbits in a gravity field with zonal harmonics

Uses Software

• Mathematica

Cites Work

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