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Functional Calculus for Dual Quaternions
Advances in Applied Clifford Algebras, 2023 We give a formula for $f(η)$, where $f :\mathbb C \to \mathbb C$ is a continuously differentiable function satisfying $f(\bar z) = \overline{f(z)}$, and $η$ is a dual quaternion. Note this formula is straightforward or well known if $η$ is merely a dual number or a quaternion.
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Solution of an inverse kinematics problem using dual quaternions
International Journal of Applied Mathematics and Computer Science, 2020 The paper proposes a solution to an inverse kinematics problem based on dual quaternions algebra. The method, relying on screw theory, requires less calculation effort compared with commonly used approaches.
Chen Lei +3 more
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Dual-Quaternion Fourier Transform
CoRR, 2023 Fourier transform (FT) plays a crucial role in a broad range of applications, from enhancement, restoration and analysis through to security, compression and manipulation. The Fourier transform (FT) is a process that converts a function into a form that describes the frequencies.
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Quaternion modeling of the helical path for analysis of the shape of the DNA molecule
Вавиловский журнал генетики и селекции, 2018 The threedimensional shape of a DNA molecule is a key property influencing its functional specificity and the nature of its molecular interactions. The characteristic shape into which a DNA molecule folds under certain conditions is a manifestation of ...
A. F. Muterko
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Dual-Quaternion-Based SLERP MPC Local Controller for Safe Self-Driving of Robotic Wheelchairs
Robotics, 2023 In this work, the motion control of a robotic wheelchair to achieve safe and intelligent movement in an unknown scenario is proposed. The primary objective is to develop a comprehensive framework for a robotic wheelchair that combines a global path ...
Daifeng Wang +2 more
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A Full-Body Relative Orbital Motion of Spacecraft Using Dual Tensor Algebra and Dual Quaternions
Mathematics, 2023 This paper proposes a new non-linear differential equation for the six degrees of freedom (6-DOF) relative rigid bodies motion. A representation theorem is provided for the 6-DOF differential equation of motion in the arbitrary non-inertial reference ...
Daniel Condurache
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Quaternionic and Dual Quaternionic Darboux Ruled Surfaces
Turkish Journal of Mathematics and Computer Science, 2021 In this paper, firstly the ruled surface drawn by the Darboux vector is expressed as a quaternion. Then, the spatial quaternionic definition of the striction curve is given and the integral invariants of the surface are calculated. Finally, the ruled surface which corresponds to a dual curve drawn by a dual Darboux vector is derived with the help of ...
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Dual quaternion representation of geometrical motion in 3D space
Discrete and Continuous Models and Applied Computational Science\emph {Background} In a previous article we discussed the use of dual quaternions for modeling points, lines and planes and solving standard geometric problems.
Olesya M. Abakumova +3 more
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Dual quaternion representation of points, lines and planes
Discrete and Continuous Models and Applied Computational ScienceBackground. The bulk of the work on dual quaternions is devoted to their application to describe helical motion. Little attention is paid to the representation of points, lines, and planes (primitives) using them. Purpose. It is necessary to consistently
Migran N. Gevorkyan +4 more
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Helmert Transformation Problem. From Euler Angles Method to Quaternion Algebra
ISPRS International Journal of Geo-Information, 2020 The three-dimensional coordinate’s transformation from one system to another, and more specifically, the Helmert transformation problem, is one of the most well-known transformations in the field of engineering.
Stefania Ioannidou, George Pantazis
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