Generalized elliptic anomalies

DOI10.1007/BF01235849zbMath0652.70007OpenAlexW3048327118MaRDI QIDQ3798310

Maria L. Sein-Echaluce, Sebastián Ferrer, José Manuel Ferrándiz

Publication date: 1987

Published in: Celestial Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01235849

zbMATH Keywords

elliptic functionsperturbed Kepler problemsKeplerian systemsconservative functionsgeneralized elliptic anomalytwo-parameter time transformation

Mathematics Subject Classification ID

Computational methods for problems pertaining to mechanics of particles and systems (70-08) Two-body problems (70F05)

Related Items (8)

A note on the use of the generalized Sundman transformations as temporal variables in celestial mechanics ⋮ Geometrical definition of a continuous family of time transformations generalizing and including the classic anomalies of the elliptic two-body problem ⋮ Geometrical definition of a continuous family of time transformations on the hyperbolic two-body problem ⋮ CMMSE: Study of a new symmetric anomaly in the elliptic, hyperbolic, and parabolic Keplerian motion ⋮ A study about the integration of the elliptical orbital motion based on a special one-parametric family of anomalies ⋮ A note on the use of generalized Sundman anomalies in the numerical integration of the elliptical orbital motion ⋮ Length of arc as independent argument for highly eccentric orbits ⋮ Computational tools to construct semi-analytical planetary theories

Cites Work

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• Triple collision in the collinear three-body problem
• Numerical calculation of elliptic integrals and elliptic functions
• Regularization and linearization of the equations of motion in central force-fields
• Linearization in special cases of perturbed Keplerian motions
• On the radial intermediaries and the time transformation in satellite theory
• Time elements in Keplerian orbital elements
• A method of regularizing the equations of motion in the central force-field
• Notions of analytic vs numerical stability as applied to the numerical calculation of orbits
• Linearization of dynamical systems using integrals of the motion
• The intermediate anomaly
• Time transformations and Cowell's method

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