Decomposition of functions for elliptic orbits

DOI10.1007/BF00693322zbMath0822.70008OpenAlexW136504019MaRDI QIDQ1805473

Carlos Osácar, Jesús F. Palacián

Publication date: 17 October 1995

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

Full work available at URL: https://doi.org/10.1007/bf00693322

zbMATH Keywords

Lie derivativerecursive rulesdilogarithmic functionmean anomalyalgebra of functionsKeplerian flow

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Computational methods for problems pertaining to mechanics of particles and systems (70-08) Two-body problems (70F05)

Related Items (15)

The Keplerian regime of charged particles in planetary magnetospheres ⋮ Numerical evaluation of the dilogarithm of complex argument ⋮ From the circular to the spatial elliptic restricted three-body problem ⋮ Dynamics of a satellite orbiting a planet with an inhomogeneous gravitational field ⋮ Symplectic coordinates on \(S^2\times S^2\) for perturbed Keplerian problems: application to the dynamics of a generalised Størmer problem ⋮ Solution to the main problem of the artificial satellite by reverse normalization ⋮ Closed-form normalizations of perturbed two-body problems. ⋮ ATESAT: A symbolic processor for artificial satellite theory ⋮ Exploring the long-term dynamics of perturbed Keplerian motion in high degree potential fields ⋮ Asymptotic invariant tori of perturbed two-body problems ⋮ Normalization through invariants in \(n\)-dimensional Kepler problems ⋮ A new radial, natural, higher-order intermediary of the main problem four decades after the elimination of the parallax ⋮ Brouwer's satellite solution redux ⋮ Normal forms for perturbed Keplerian systems. ⋮ Complete zonal problem of the artificial satellite: generic compact analytic first order in closed form

Uses Software

• Mathematica

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A note on first-order normalizations of perturbed Keplerian systems
• Mean values of particular functions in the elliptic motion
• Elimination of the perigee in the satellite problem
• Simplify or perish
• The elimination of the parallax in satellite theory
• Third-Order Solution to the Main Problem in Satellite Theory
• Canonical transformations depending on a small parameter
• Delaunay normalisations

This page was built for publication: Decomposition of functions for elliptic orbits