Results 1 to 10 of about 2,080 (316)

A Review on the Applications of Dual Quaternions [PDF]

Machines
This 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, Edson De Pieri, Daniel Martins   +2 more
doaj   +5 more sources

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, Fatih Yılmaz, Mustafa Çalışkan   +2 more
doaj   +7 more sources

Dual Quaternion Functions and Its Applications [PDF]

Journal of Applied Mathematics, 2013
A dual quaternion is associated with two quaternions that have basis elements e0, e1, e2, e3, and ε. Dual numbers are often written in the form z=ζ+εζ*, where ε is the dual identity and has the properties ε2=0  (ε≠0).
Su Jin Lim, Kwang Ho Shon
doaj   +6 more sources

Dual third-order Jacobsthal quaternions [PDF]

Proyecciones (Antofagasta), 2018
In 2016, Yüce and Torunbalcı Aydın (18) defined dual Fibonacci quaternions. In this paper, we defined the dual third-order Jacobsthal quaternions and dual third-order Jacobsthal-Lucas quaternions.
Cerda-Morales, Gamaliel
core   +5 more sources

Spacecraft Robot Kinematics Using Dual Quaternions

Robotics, 2018
In recent years, there has been a growing interest in servicing orbiting satellites. In most cases, in-orbit servicing relies on the use of spacecraft-mounted robotic manipulators to carry out complicated mission objectives.
Alfredo Valverde, Panagiotis Tsiotras
doaj   +4 more sources

Quaternions and Dual Quaternions: Singularity-Free Multirobot Formation Control [PDF]

Journal of Intelligent and Robotic Systems: Theory and Applications, 2016
Cluster space control is a method of multirobot formation keeping that considers a group of robots to be a single entity, defining state variables to represent characteristics of the group, such as position, orientation, and shape.
Ignacio Mas, Christopher Kitts
exaly   +4 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, Gülsüm Yeliz Şentürk, Salim Yüce   +2 more
doaj   +3 more sources

On Dual Hyperbolic Narayana and Narayana-Lucas Hybrid Quaternions

Universal Journal of Mathematics and Applications
In this present communication, we introduce the novel concepts of dual hyperbolic Narayana quaternions and dual hyperbolic Narayana-Lucas quaternions within the framework of hybrid numbers.
Pankaj Kumar, Shilpa Kapoor
doaj   +3 more sources

Dual-Quaternion-Based SLERP MPC Local Controller for Safe Self-Driving of Robotic Wheelchairs [PDF]

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, Wenjing Cao, Atsuo Takanishi   +2 more
doaj   +2 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, Çiğdem Zeynep Yılmaz   +1 more
doaj   +2 more sources