Quaternion regularization in celestial mechanics, astrodynamics, and trajectory motion control. III

Chelnokov, Yu. N.

doi:10.1134/s0010952515050044

Cited by 14 publications

(6 citation statements)

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“…Besides, Eq. (32) for the case of the unperturbed Keplerian motion takes the form of harmonic oscillator motion equation, while Eq. ( 23) for r for this case stays highly nonlinear.…”

Section: Systems Of Quaternion Regular Equations Of the Perturbed Central Motionmentioning

confidence: 99%

“…which has to be complemented with the generalized Binet equation (32) for the variable ρ and the above-stated relations for the quaternion Q, which describes acting perturbances.…”

Section: Systems Of Quaternion Regular Equations Of the Perturbed Central Motionmentioning

confidence: 99%

“…The equations in elements α, β, and c 2 are complemented with the generalized Binet equation (32), which for the Newtonian central field of gravity (when the potential Π(r) = −mµr −1 = −mµρ) takes the form of the perturbed oscillator, or with the equations in osculating elements, derived from the generalized Binet equation and related to the variable ρ = 1/r, and also the time element equation.…”

Section: Equations In Quaternion Osculating Elementsmentioning

confidence: 99%

“…Chelnokov [30,32] also considered regularization of the models of celestial mechanics and astrodynamics, derived within the context of the perturbed spatial two-body problem and the perturbed central motion of a point particle. The fundamental regular quaternion models in celestial mechanics and astrodynamics, which are free from singularities induced by gravitation and other central forces, are presented.…”

Section: Optimal Control Of Orbital Motion Of a Spacecraft Inertial Navigationmentioning

confidence: 99%

“…Various aspects of quaternion regularization of differential equations of the perturbed spatial two-body problem by using the KS variables have been studied by Velte [1] , Vivarelli [2][3][4] , Shagov [5] , Deprit et al [6] , Vrbik [7][8] , Waldvogel [9][10] , Saha [11] , Zhao [12] , Roa et al [13][14] , Roa and Pelaez [15] , Breiter and Langner [16][17][18] , Ferrer and Crespo [19] , and also by the author of this paper, Chelnokov [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36] .…”

Section: Introductionmentioning

confidence: 99%

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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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“…Besides, Eq. (32) for the case of the unperturbed Keplerian motion takes the form of harmonic oscillator motion equation, while Eq. ( 23) for r for this case stays highly nonlinear.…”

Section: Systems Of Quaternion Regular Equations Of the Perturbed Central Motionmentioning

confidence: 99%

“…which has to be complemented with the generalized Binet equation (32) for the variable ρ and the above-stated relations for the quaternion Q, which describes acting perturbances.…”

Section: Systems Of Quaternion Regular Equations Of the Perturbed Central Motionmentioning

confidence: 99%

Section: Equations In Quaternion Osculating Elementsmentioning

confidence: 99%

Section: Optimal Control Of Orbital Motion Of a Spacecraft Inertial Navigationmentioning

confidence: 99%