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Статья

Abakumova, O.M.
Dual Quaternion Representation of Geometrical Motion in 3D Space / O.M.Abakumova, M.N.Gevorkyan, A.V.Korolkova, D.S.Kulyabov. – Text : electronic // Discrete and Continuous Models and Applied Computational Science. – 2026. – Vol. 34, No. 1. – P. 70-97. – URL: https://doi.org/10.22363/2658-4670-2026-34-1-70-97. – Bibliogr.: 22.

BackgroundIn a previous article we discussed the use of dual quaternions for modeling points, linesand planes and solving standard geometric problems. This article is a logical continuation and reveals the use ofdual quaternions to describe isometries of three-dimensional space.PurposeThe derivation of all necessaryformulas for the screw motion of points, straight lines and planes, as well as reflection relative to the plane.Refinement of notation and formalism.MethodThe algebra of dual numbers, quaternions and dual quaternionsis used, as well as elements of the theory of screws and sliding vectors.ResultsFormulas for rotation, translation,reflection, helical motion, and mirror rotation are obtained and systematized.ConclusionsDual quaternionscan serve as a full-fledged tool for describing helical motion in space. Due to the possibility of expressing dualquaternion operations in terms of standard vector and scalar products, the formulas obtained allow for effectivesoftware implementation.



Спец.(статьи,препринты) = С 138 - Геометрия. Риманова геометрия. Геометрия Лобачевского
Спец.(статьи,препринты) = С 17 и1 - Математическое моделирование
Спец.(статьи,препринты) = С 17 д - Численное решение дифференциальных и интегральных уравнений. Разностные методы
ОИЯИ = ОИЯИ (JINR)2026