<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>This study discusses the use of quaternions and dual quaternions in the description of artificial fish kinematics. The investigation offered here illustrates quaternion and dual quaternion algebra, as well as its implementation in the software chosen. When it comes to numerical stability, quaternions are better than matrices because a normalised quaternion always shows the correct rotation, while a matrix more easily loses its orthogonality due to rounding errors and oversizing. Although quaternions are more compact than rotation matrices, using quaternions does not always provide less numerical computation and the amount of memory needed. In this paper, an algebraic form of quaternion representation is provided which is less memory-demanding than the matrix representation. All the functions that were used to prepare this work are presented, and they can be employed to conduct more research on how well quaternions work in a specific assignment.</p>
</abstract>

This study discusses the use of quaternions and dual quaternions in the description of artificial fish kinematics. The investigation offered here illustrates quaternion and dual quaternion algebra, as well as its implementation in the software chosen. When it comes to numerical stability, quaternions are better than matrices because a normalised quaternion always shows the correct rotation, while a matrix more easily loses its orthogonality due to rounding errors and oversizing. Although quaternions are more compact than rotation matrices, using quaternions does not always provide less numerical computation and the amount of memory needed. In this paper, an algebraic form of quaternion representation is provided which is less memory-demanding than the matrix representation. All the functions that were used to prepare this work are presented, and they can be employed to conduct more research on how well quaternions work in a specific assignment.

Dual Quaternions for the Kinematic Description of a Fish–Like Propulsion System

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

This study discusses the use of quaternions and dual quaternions in the description of artificial fish kinematics. The investigation offered here illustrates...

Dual Quaternions for the Kinematic Description of a Fish–Like Propulsion System

Data publikacji: 23 cze 2023

Zakres stron: 171 - 181

Otrzymano: 01 sie 2022

Przyjęty: 01 lut 2023

DOI: https://doi.org/10.34768/amcs-2023-0013

Słowa kluczowe
quaternions, dual quaternions, artificial fish, underwater vehicle, undulating propulsion system

© 2023 Zygmunt Kitowski et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Dual Quaternions for the Kinematic Description of a Fish–Like Propulsion System

Data publikacji: 23 cze 2023

Zakres stron: 171 - 181

Otrzymano: 01 sie 2022

Przyjęty: 01 lut 2023

DOI: https://doi.org/10.34768/amcs-2023-0013

Słowa kluczowequaternions, dual quaternions, artificial fish, underwater vehicle, undulating propulsion system

© 2023 Zygmunt Kitowski et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Słowa kluczowe
quaternions, dual quaternions, artificial fish, underwater vehicle, undulating propulsion system