A Unified Approach: Split Quaternions with Quaternion Coefficients and Quaternions with Dual Coefficients [PDF]
Mathematics, 2020 This paper aims to present, in a unified manner, results which are valid on both split quaternions with quaternion coefficients and quaternions with dual coefficients, simultaneously, calling the attention to the main differences between these two ...
Emel Karaca +2 more
doaj +7 more sources
A Review on the Applications of Dual Quaternions
MachinesThis work explores dual quaternions and their applications. First, a theoretical construction begins at dual numbers, extends to dual vectors, and culminates in dual quaternions.
João Gutemberg Farias +2 more
doaj +4 more sources
On Dual Quaternions with $k-$Generalized Leonardo Components
Journal of New Theory, 2023 In this paper, we define a one-parameter generalization of Leonardo dual quaternions, namely $k-$generalized Leonardo-like dual quaternions. We introduce the properties of $k$-generalized Leonardo-like dual quaternions, including relations with Leonardo,
Gülsüm Yeliz Saçlı +1 more
doaj +2 more sources
Investigating generalized quaternions with dual-generalized complex numbers [PDF]
Mathematica Bohemica, 2023 We aim to introduce generalized quaternions with dual-generalized complex number coefficients for all real values $\alpha$, $\beta$ and $\mathfrak{p}$.
Nurten Gürses +2 more
doaj +3 more sources
3D kinematics using dual quaternions: theory and applications in neuroscience [PDF]
Frontiers in Behavioral Neuroscience, 2013 In behavioral neuroscience, many experiments are developed in 1 or 2 spatialdimensions, but when scientists tackle problems in 3-dimensions (3D), theyoften face problems or new challenges. Results obtained for lower dimensionsare not always extendable in
Guillaume eLeclercq +5 more
doaj +2 more sources
Dual Quaternions as Constraints in 4D-DPM Models for Pose Estimation [PDF]
Sensors, 2017 The goal of this research work is to improve the accuracy of human pose estimation using the Deformation Part Model (DPM) without increasing computational complexity.
Enrique Martinez-Berti +2 more
doaj +2 more sources
Robust Pose and Inertial Parameter Estimation of an Unknown Aircraft Based on Variational Bayesian Dual Vector Quaternion Extended Kalman Filter [PDF]
EntropyAccurately determining the parameters of an unmodeled spacecraft is crucial. Filtering methods that are resilient to uncertainty, employing dual quaternion frameworks to ascertain orientation and position, introduce a design for an extended Kalman filter
Shengli Xu, Yangwang Fang, Hanqiao Huang
doaj +2 more sources
A High-Precision Hand–Eye Coordination Localization Method under Convex Relaxation Optimization [PDF]
SensorsTraditional switching operations require on-site work, and the high voltage generated by arc discharges can pose a risk of injury to the operator. Therefore, a combination of visual servo and robot control is used to localize the switching operation and ...
Jin Hua +3 more
doaj +2 more sources
Application of slice regularity to functions of a dual-quaternionic variable
Karpatsʹkì Matematičnì Publìkacìï, 2021 In this paper, we present the algebraic properties of dual quaternions and define a slice regularity of a dual quaternionic function. Since the product of dual quaternions is non-commutative, slice regularity is derived in two ways.
Ji Eun Kim
doaj +1 more source
On a generalization of dual-generalized complex Fibonacci quaternions [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 In this study, we introduce a new class of generalized quaternions whose components are dual-generalized complex Horadam numbers. We investigate some algebraic properties of them.
Elif Tan, Umut Öcal
doaj +1 more source