On Calculation of Relativistic Effects in Numerical Prediction of the Artificial Satellite Motion

Bordovitsyna, T. V.; Sharkovsky, N. A.

doi:10.1007/978-94-009-4602-6_39

Cited by 4 publications

(5 citation statements)

References 2 publications

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“…Moreover, they are close (in the presence of perturbations) to linear equations. In particular, Stiefel and Scheifele [37] , Bordovitsyna [38] , and Bordovitsyna and Avdyushev [39] showed that regular equations in the KS variables allow to increase the accuracy of numeric solutions for a number of problems in celestial mechanics and astrodynamics (e.g., the problem of the perturbed motion of an Earth's artificial satellite along high-eccentricity orbits) by three to five orders compared with the solutions obtained with the classical (Newtonian) equations. Fukushima [40][41] also wrote, "The KS regularization resulted in a very efficient integration scheme, improving the accuracy and speed of numerical integration.…”

Section: Ks Regularization Of the Perturbed Spatial Two-body Problem Equationsmentioning

confidence: 99%

“…The right parts of Eqs. ( 37) and (38) do not depend on time t. Time t can be calculated by additionally integrating dt/dτ = r.…”

Section: Problem Of Motion Of An Artificial Satellite In the Earth's Gravitational Fieldmentioning

confidence: 99%

“…Stiefel and Scheifele [37] , Bordovitsyna [38] , Bordovitsyna and Avdyushev [39] , Fukushima [40][41] , Pelaez et al [42] , Bau et al [43] , Amato et al [44] , and Bau and Roa [45] demonstrated the results of comparing the numerical solutions to the equations of orbital motion of celestial and cosmic bodies in the KS variables, Euler parameters, and other variables. These results prove the efficiency of the KS variables and Euler parameters in celestial mechanics and astrodynamics.…”

Section: Introductionmentioning

confidence: 99%

“…The KS regular equations of the perturbed spatial two-body problem in four-dimensional KS variables in scalar and matrix forms were presented by Kustaanheimo [51] , Kustaanheimo and Stiefel [52] , and Stiefel and Scheifele [37] . Primary analytical and computational advantages of these equations were described by Stiefel and Scheifele [37] , Brumberg [53] , Bordovitsyna [38] , Bordovitsyna and Avdyushev [39] , and Fukushima [40][41] . Section 2 also describes regular equations for the twobody problem in Cartesian coordinates by Bohlin [54] , in which the advantages and disadvantages are pointed out, and the development of Bohlin's idea in the works by Burdet [55][56] is also mentioned.…”

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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Section: Ks Regularization Of the Perturbed Spatial Two-body Problem Equationsmentioning

confidence: 99%

“…The right parts of Eqs. ( 37) and (38) do not depend on time t. Time t can be calculated by additionally integrating dt/dτ = r.…”

Section: Problem Of Motion Of An Artificial Satellite In the Earth's Gravitational Fieldmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Quaternion methods and models of regular celestial mechanics and astrodynamics

Chelnokov

2022

Appl. Math. Mech.-Engl. Ed.

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“…The problem of high accuracy interpretation of observations of solar system bodies is closely connected with the problem of the accurate prediction of the motion of these objects. This paper presents a brief summary of results obtained by the authors (Bordovitsyna 1984;Shefer 1989;Bordovitsyna et al 1989) forthe development and investigation of effective algorithms for the numerical prediction of the motion of minor bodies of the solar system. Research on the efficiency of the set of regularizing and stabilizing methods in the problem of numerical prediction of the motion of celestial bodies was carried out by the authors.…”

mentioning

confidence: 98%