Revisiting Hansen’s Ideal Frame Propagation with Special Perturbations—1: Basic Algorithms for Osculating Elements

Author:

Lara Martin1ORCID,Urrutxua Hodei2ORCID

Affiliation:

1. Scientific Computation & Technical Innovation Center, Universidad de La Rioja, C. Madre de Dios, 53, 26006 Logroño, La Rioja, Spain

2. Fuenlabrada Engineering School, Universidad Rey Juan Carlos, Camino del Molino, 5, 28943 Fuenlabrada, Madrid, Spain

Abstract

A review of the basic Hansen’s ideal frame algorithms for accurate numerical integration of perturbed elliptic motion is carried out. The fundamental approaches rely on the use of nonsingular variables and differ in the ways in which the ellipse in the orbital plane is determined. It is well known that the accuracy of the propagation of the orbit geometry is notably increased when using time-regularization techniques to transform the independent variable. However, this is at the expense of adding a differential equation to compute the time, which gathers the Lyapunov-type instabilities that are removed from the coordinates. The asynchronism resulting from errors in the numerical integration of the time may be palliated with the use of time elements, to which end a constant and a linear nonsingular time element are presented, which are new to our knowledge.

Publisher

MDPI AG

Subject

General Physics and Astronomy

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