Uniform formulation for orbit computation: the intermediate elements

Baù, Giulio; Roa, Javier

doi:10.1007/s10569-020-9952-y

Cited by 16 publications

(2 citation statements)

References 49 publications

(76 reference statements)

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“…Roa et al [34] analyzed the singularities posed by deep flybys and then proposed the re-formulation H-DROMO, not sensitive to a vanishing angular momentum. The latest updates involve the study of the evolution of an intermediate frame [35]. The interest on universal variables, capable of managing either closed, open or even rectilinear trajectories is introduced.…”

Section: Introductionmentioning

confidence: 99%

Kustaanheimo–Stiefel Variables for Planetary Protection Compliance Analysis

Masat

Romano

Colombo

2022

Journal of Guidance, Control, and Dynamics

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Planetary protection in trajectory design aims to assess the impact probability of space mission disposed objects based on their initial uncertain conditions, to avoid contaminating other planetary environments. High precision dynamical models and propagation methods are required to reach high confidence levels on small estimated impact probabilities. These requirements have so far confined planetary protection analyses to robust Monte Carlo-based approaches, using the Cartesian formulation of the full force problem dynamics. This work presents the improvements brought by adopting the Kustaanheimo-Stiefel (KS) formulation of the dynamics. The KS formulation is combined with reference frame switch procedures and adaptive non-dimensionalization upon detection of close encounters. The fibration property of the KS space, namely the parametrizable locus of point arising when mapping to a higherdimensional space, is exploited to minimize the computational time, because of the minimized numerical stiffness of the system. Impact probability estimation tasks become more efficient than the single simulation case, since the regularization of the dynamics removes the singularity of gravitational potentials for distances approaching zero. Despite an almost halved computational burden for Monte-Carlo analysis, the precision of the single simulations is increased by nearly one order of magnitude, setting a new performance benchmark for planetary protection tasks.

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Section: Introductionmentioning

confidence: 99%

Kustaanheimo–Stiefel Variables for Planetary Protection Compliance Analysis

Masat

Romano

Colombo

2022

Journal of Guidance, Control, and Dynamics

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“…Finally, Refs. [20][21][22][23][24][25][26][27][28][29][30] have further developed parameterizations using quaternions for orbital motion.…”

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confidence: 99%

Nonsingular Euler Parameterizations for Motion of a Point Mass in Atmospheric Flight

Miller¹,

Rao²

2021

Preprint

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Three parameterizations are developed for modeling translational motion of a point mass in atmosphere flight over a central rotating body. Unlike well-known parameterizations such as spherical coordinate parameterizations, where position and velocity are parameterized using a magnitude an an Euler angle rotation sequence, the method presented in this research employs Euler parameters. Consequently, singularities and trigonometric functions are eliminated from the differential equations of motion. As a result, the new parameterizations presented in this paper offer computational advantages over standard parameterizations that employ Euler angle sequences. Finally, an example is studied where an atmospheric vehicle moves while in vertical flight, demonstrating the nonsingular nature of the formulations developed in this paper.

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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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Uniform formulation for orbit computation: the intermediate elements

Cited by 16 publications

References 49 publications

Kustaanheimo–Stiefel Variables for Planetary Protection Compliance Analysis

Kustaanheimo–Stiefel Variables for Planetary Protection Compliance Analysis

Nonsingular Euler Parameterizations for Motion of a Point Mass in Atmospheric Flight

Quaternion methods and models of regular celestial mechanics and astrodynamics

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