Time elements in rectangular coordinates

Kwok, Johnny H.; Nacozy, P. E.

doi:10.1007/bf01229558

Cited by 4 publications

(1 citation statement)

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“…Because the definition given by Nacozy stems from Kepler's equation in its classic form, the differential equations result in cumbersome expressions that contain the semi-major axis, eccentricity, and the anomalies. By writing Kepler's equation in terms of the state vector and the Keplerian energy (as done in Stiefel & Scheifele 1971), Kwok & Nacozy (1981) obtain much more compact derivatives of the Nacozy's time elements wherein the position and velocity appear explicitly. One order of magnitude in the accuracy of the position is gained by the three time elements with respect to the integration of Equation (1).…”

Section: Introductionmentioning

confidence: 99%

Time Elements for Enhanced Performance of the Dromo Orbit Propagator

Baù

Bombardelli

2014

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We propose two time elements for the orbit propagator named Dromo. One is linear and the other constant with respect to the independent variable, which coincides with the osculating true anomaly in the Keplerian motion. They are defined from a generalized Kepler's equation written for negative values of the total energy and, unlike the few existing time elements of this kind, are free of singularities. To our knowledge it is the first time that a constant time element is associated with a second-order Sundman time transformation. Numerical tests to assess the performance of the Dromo method equipped with a time element show the remarkable improvement in accuracy for the perturbed bounded motion around the Earth compared to the case in which the physical time is a state variable. Moreover, the method is competitive with and even better than other efficient sets of elements. Finally, we also derive a time element for a null and positive total energy.

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Section: Introductionmentioning

confidence: 99%