A special perturbation method in orbital dynamics

Peláez, Jesús; Hedo, J. M.; Andrés, Pedro Rodríguez de

doi:10.1007/s10569-006-9056-3

Cited by 63 publications

(77 citation statements)

References 7 publications

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“…Dromo is the method presented in Peláez et al (2007); Dromo(P) is the improved version of Dromo for taking advantage of forces that are derived from disturbing potentials (Baù et al 2013); the Dromo(PL) and Dromo(PC) schemes are based on the seven generalized orbital elements of Dromo(P) supplied by, respectively, the linear and constant time elements, ζ 0 and τ 0 , developed in this paper. The Dromo(P) schemes are implemented with the total energy ε in place of ζ 3 (Equation (19)) as the dependent variable.…”

Section: Benchmark Problems and Compared Methodsmentioning

confidence: 99%

“…The method, called Dromo(P), represents a generalization of the original formulation published by Peláez et al (2007) for taking advantage of perturbations deriving from a potential. The state of the propagated particle is described by means of the physical time and seven generalized orbital elements that are strictly related to the variables of the B-F linearization, namely the inverse of the orbital radius and the unit vector of the position.…”

Section: Introductionmentioning

confidence: 99%

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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: Benchmark Problems and Compared Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Time Elements for Enhanced Performance of the Dromo Orbit Propagator

Baù

Bombardelli

2014

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“…The performance of the original Dromo scheme (Pelaez et al, 2007;Urrutxua et al, 2013) is compared against the new versions Dromo-I and Dromo-II. Cowell's method, the solution from the Kustaanheimo-Stiefel transformation (Kustaanheimo and Stiefel, 1965), and the Sperling-Burdet regularization (Burdet, 1968) are integrated as reference solutions.…”

Section: So So Errormentioning

confidence: 99%

“…Palacios and Calvo (1996) advanced on Deprit's work and proposed a regularization of the equations of motion based on ideal frames. These concepts and the introduction of the fictitious time motivated Pelaez et al (2007) to derive a special perturbation method, called Dromo. Dromo first introduces a Hansen ideal reference frame that describes the motion of the orbital plane.…”

Section: Introductionmentioning

confidence: 99%

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Singularities in Dromo formulation. Analysis of deep flybys

Roa

Sanjurjo-Rivo

Peláez

2015

Advances in Space Research

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The singularities in Dromo are characterized in this paper, both from an analytical and a numerical perspective. When the angular momentum vanishes, Dromo may encounter a singularity in the evolution equations. The cancellation of the angular momentum occurs in very specific situations and may be caused by the action of strong perturbations. The gravitational attraction of a perturbing planet may lead to rapid changes in the angular momentum of the particle. In practice, this situation may be encountered during deep planetocentric flybys. The performance of Dromo is evaluated in different scenarios. First, Dromo is validated for integrating the orbit of Near Earth Asteroids. Resulting errors are of the order of the diameter of the asteroid. Second, a set of theoretical flybys are designed for analyzing the performance of the formulation in the vicinity of the singularity. New sets of Dromo variables are proposed in order to minimize the dependency of Dromo on the angular momentum. A slower time scale is introduced, leading to a more stable description of the flyby phase. Improvements in the overall performance of the algorithm are observed when integrating orbits close to the singularity.

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Quaternion methods and models of regular celestial mechanics and astrodynamics

Chelnokov

2022

Appl. Math. Mech.-Engl. Ed.

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This paper is a review, which focuses on our work, while including an analysis of many works of other researchers in the field of quaternionic regularization. The regular quaternion models of celestial mechanics and astrodynamics in the Kustaanheimo-Stiefel (KS) variables and Euler (Rodrigues-Hamilton) parameters are analyzed. These models are derived by the quaternion methods of mechanics and are based on the differential equations of the perturbed spatial two-body problem and the perturbed spatial central motion of a point particle. This paper also covers some applications of these models. Stiefel and Scheifele are known to have doubted that quaternions and quaternion matrices can be used efficiently to regularize the equations of celestial mechanics. However, the author of this paper and other researchers refuted this point of view and showed that the quaternion approach actually leads to efficient solutions for regularizing the equations of celestial mechanics and astrodynamics.This paper presents convenient geometric and kinematic interpretations of the KS transformation and the KS bilinear relation proposed by the present author. More general (compared with the KS equations) quaternion regular equations of the perturbed spatial two-body problem in the KS variables are presented. These equations are derived with the assumption that the KS bilinear relation was not satisfied. The main stages of the quaternion theory of regularizing the vector differential equation of the perturbed central motion of a point particle are presented, together with regular equations in the KS variables and Euler parameters, derived by the aforementioned theory. We also present the derivation of regular quaternion equations of the perturbed spatial two-body problem in the Levi-Civita variables and the Euler parameters, developed by the ideal rectangular Hansen coordinates and the orientation quaternion of the ideal coordinate frame.This paper also gives new results using quaternionic methods in the perturbed spatial restricted three-body problem.

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A special perturbation method in orbital dynamics

Cited by 63 publications

References 7 publications

Time Elements for Enhanced Performance of the Dromo Orbit Propagator

Time Elements for Enhanced Performance of the Dromo Orbit Propagator

Singularities in Dromo formulation. Analysis of deep flybys

Quaternion methods and models of regular celestial mechanics and astrodynamics

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