\(F\) and \(G\) Taylor series solutions to the Stark and Kepler problems with Sundman transformations

DOI10.1007/s10569-014-9538-7zbMath1294.70007OpenAlexW2026349714MaRDI QIDQ740339

Ryan P. Russell, Vivek Vittaldev, Etienne Pellegrini

Publication date: 2 September 2014

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

Full work available at URL: https://doi.org/10.1007/s10569-014-9538-7

zbMATH Keywords

Taylor seriesTaylor series methodsKepler problemlow-thrustStark problemF\&G seriesgeneralized Sundman transformationtrajectory propagation

Mathematics Subject Classification ID

Two-body problems (70F05)

Related Items (4)

Sundman transformation and alternative tangent structures ⋮ Infinitesimal time reparametrisation and its applications ⋮ On the solution to every Lambert problem ⋮ Two direct low thrust trajectory optimization techniques

Uses Software

• ADOL-C
• ADIFOR
• FADBAD++
• Taylor center
• Taylor

Cites Work

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• The accelerated Kepler problem
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• A Software Package for the Numerical Integration of ODEs by Means of High-Order Taylor Methods
• Transformations of the perturbed two-body problem to unperturbed harmonic oscillators
• On the Szebehely-bond equation generalized Sundman's transformation for the perturbed two-body problem
• Notions of analytic vs numerical stability as applied to the numerical calculation of orbits
• Trajectory optimization by making use of the closed solution of constant thrust-acceleration motion
• The intermediate anomaly
• An approximate method for nonlinear ordinary differential equations
• Remarks on numerical integration of Keplerian orbits
• A problem of orbital dynamics, which is separable in KS-variables
• Solution of theN-body problem with recurrent power series
• Numerical stabilization of the differential equations of Keplerian motion

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