Relevant bibliographies by topics / Quaternions algebra

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Quaternions algebra'

Author: Grafiati
Published: 7 June 2025
Last updated: 16 July 2025

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Journal articles on the topic "Quaternions algebra"

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ATA, Erhan, and Ümit Ziya SAVCI. "Generalized Quaternions and Matrix Algebra." Afyon Kocatepe University Journal of Sciences and Engineering 23, no. 3 (2023): 638–47. http://dx.doi.org/10.35414/akufemubid.1182145.

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In this paper, we established the connection between generalized quaternion algebra and real (complex) matrix algebras by using Hamilton operators. We obtained real and complex matrices corresponding to the real and complex basis of the generalized quaternions. Also, we investigated the basis features of real and complex matrices. We get Pauli matrices corresponding to generalized quaternions. Then, we have shown that the algebra produced by these matrices is isomorphic to the Clifford algebra Cl(E_αβ^3) produced by generalized space E_αβ^3.
 Finally, we studied the relations among the sy
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ABRATE, MARCO. "QUADRATIC FORMULAS FOR GENERALIZED QUATERNIONS." Journal of Algebra and Its Applications 08, no. 03 (2009): 289–306. http://dx.doi.org/10.1142/s0219498809003308.

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In this paper we derive explicit formulas for computing the roots of a quadratic polynomial with coefficients in a generalized quaternion algebra over any field 𝔽 with characteristic not 2. We also give some example of applications for the derived formulas, solving equations in the algebra of Hamilton's quaternions ℍ, in the ring M2(ℝ) of 2 × 2 square matrices over ℝ and in quaternion algebras over finite fields.
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Jiang, Tongsong, Dong Zhang, Zhenwei Guo, Gang Wang, and V. I. Vasil’ev. "Algebraic Techniques for Canonical Forms and Applications in Split Quaternionic Mechanics." Journal of Mathematics 2023 (November 7, 2023): 1–13. http://dx.doi.org/10.1155/2023/4599585.

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The algebra of split quaternions is a recently increasing topic in the study of theory and numerical computation in split quaternionic mechanics. This paper, by means of a real representation of a split quaternion matrix, studies the problem of canonical forms of a split quaternion matrix and derives algebraic techniques for finding the canonical forms of a split quaternion matrix. This paper also gives two applications for the right eigenvalue and diagonalization in split quaternionic mechanics.
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Colombaro, Ivano. "Exterior-algebraic formulation of quaternions with applications." Journal of Physics: Conference Series 3027, no. 1 (2025): 012020. https://doi.org/10.1088/1742-6596/3027/1/012020.

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Abstract The purpose of this paper is to describe the formulation of quaternion algebra by means of exterior algebra and calculus, in a three dimensional time-like spacetime. A formal structure is provided, corroborating the equivalence with existing concepts and formulas known in literature. A first application is thus presented by depicting the description of rotations expressed with exterior-algebraic quaternionic notation. Secondly, a formal equivalence between exterior-algebraic quaternions and the classical theory of electromagnetism is recovered, too.
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Dargys, Adolfas, and Artūras Acus. "Exponential and logarithm of multivector in low-dimensional (n = p + q < 3) Clifford algebras." Nonlinear Analysis: Modelling and Control 27, no. 6 (2022): 1129–49. http://dx.doi.org/10.15388/namc.2022.27.29528.

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The aim of the paper is to give a uniform picture of complex, hyperbolic, and quaternion algebras from a perspective of the applied Clifford geometric algebra. Closed form expressions for a multivector exponential and logarithm are presented in real geometric algebras Clp;q when n = p + q = 1 (complex and hyperbolic numbers) and n = 2 (Hamilton, split, and conectorine quaternions). Starting from Cl0;1 and Cl1;0 algebras wherein square of a basis vector is either –1 or +1, we have generalized exponential and logarithm formulas to 2D quaternionic algebras Cl0;2, Cl1;1, and Cl2;0. The sectors in
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Dai, Songsong. "Quaternionic Fuzzy Sets." Axioms 12, no. 5 (2023): 490. http://dx.doi.org/10.3390/axioms12050490.

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A novel concept of quaternionic fuzzy sets (QFSs) is presented in this paper. QFSs are a generalization of traditional fuzzy sets and complex fuzzy sets based on quaternions. The novelty of QFSs is that the range of the membership function is the set of quaternions with modulus less than or equal to one, of which the real and quaternionic imaginary parts can be used for four different features. A discussion is made on the intuitive interpretation of quaternion-valued membership grades and the possible applications of QFSs. Several operations, including quaternionic fuzzy complement, union, int
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Cao, Wensheng. "Quadratic Equation in Split Quaternions." Axioms 11, no. 5 (2022): 188. http://dx.doi.org/10.3390/axioms11050188.

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Split quaternions are noncommutative and contain nontrivial zero divisors. Generally speaking, it is difficult to solve equations in such an algebra. In this paper, by using the roots of any split quaternions and two real nonlinear systems, we derive explicit formulas for computing the roots of x2+bx+c=0 in split quaternion algebra.
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Eri̇şi̇r, Tülay, Gökhan Mumcu, Sezai̇ Kiziltuğ, and Funda Akar. "A New Construction of Rectifying Direction Curves for Quaternionic Space Q." WSEAS TRANSACTIONS ON MATHEMATICS 24 (March 14, 2025): 114–25. https://doi.org/10.37394/23206.2025.24.13.

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Our article focuses on the study of quaternions topic introduced by Hamilton. Quaternions are a generalization of complex numbers and have multiple applications in mathematical physics. Another application of quaternions is robotics because what generalizes the imaginary axis is the family i, j, k modeling Euler angles and rotations in space. The first part of the article we recall the different definitions of how the algebra of quaternions is well constructed. The main results are given in the third part and concern: spatial quaternionics rectifying-direction (sqRD) curves and and spatial qua
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Eri̇şi̇r, Tülay, and Mehmet Ali̇ Güngör. "On Fibonacci spinors." International Journal of Geometric Methods in Modern Physics 17, no. 04 (2020): 2050065. http://dx.doi.org/10.1142/s0219887820500656.

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Spinors are used in physics quite extensively. Basically, the forms of use include Dirac four-spinors, Pauli three-spinors and quaternions. Quaternions in mathematics are essentially equivalent to Pauli spin matrices which can be generated by regarding a quaternion matrix as compound. The goal of this study is also the spinor structure lying in the basis of the quaternion algebra. In this paper, first, we have introduced spinors mathematically. Then, we have defined Fibonacci spinors using the Fibonacci quaternions. Later, we have established the structure of algebra for these spinors. Finally
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Pogorui, Anatoliy, and Tamila Kolomiiets. "Some algebraic properties of complex Segre quaternoins." Proceedings of the Institute of Applied Mathematics and Mechanics NAS of Ukraine 33 (December 27, 2019): 158–59. http://dx.doi.org/10.37069/1683-4720-2019-33-13.

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This paper deals with the basic properties the algebra of Segre quaternions over the field of complex numbers. We study idempotents, ideals, matrix representation and the Peirce decomposition of this algebra. We also investigate the structure of zeros of a polynomial in Segre complex quaternions by reducing it to the system of four polynomial equations in the complex field. In addition, Cauchy-Riemann type conditions are obtained for the differentiability of a function on the complex Segre quaternionic algebra.
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Dissertations / Theses on the topic "Quaternions algebra"

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GÜNAŞTI, Gökmen. "Quaternions Algebra, Their applications in Rotations and Beyond Quaternions." Thesis, Linnéuniversitetet, Institutionen för datavetenskap, fysik och matematik, DFM, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-20267.

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The theory of quaternions was discovered in the middle of nineteenth century and they were commonly used to represent rotations.This thesis is written to review the basic properties of quaternions algebra and their applications in representing rotation of a body in 3-dimensional Euclidean space. Also, last sections in this thesis explore why the use of quaternions are more advantages than Euler angle sequences and can quaternions themselves be further generalized to another number systems?
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Lopes, Wilder Bezerra. "Geometric-algebra adaptive filters." Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/3/3142/tde-22092016-143525/.

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This document introduces a new class of adaptive filters, namely Geometric- Algebra Adaptive Filters (GAAFs). Those are generated by formulating the underlying minimization problem (a least-squares cost function) from the perspective of Geometric Algebra (GA), a comprehensive mathematical language well-suited for the description of geometric transformations. Also, differently from the usual linear algebra approach, Geometric Calculus (the extension of Geometric Algebra to differential calculus) allows to apply the same derivation techniques regardless of the type (subalgebra) of the data, i.e.
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Rodríguez, Ordóñez Hugo. "Topological study of nonsingular bilinear maps /." view abstract or download file of text, 2006. http://proquest.umi.com/pqdweb?did=1251841791&sid=5&Fmt=2&clientId=11238&RQT=309&VName=PQD.

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Thesis (Ph. D.)--University of Oregon, 2006.<br>Typescript. Includes vita and abstract. Includes bibliographical references (leaves - ). Also available for download via the World Wide Web; free to University of Oregon users.
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Silva, Julio César Conegundes da 1986. "G2 e as álgebras normadas." [s.n.], 2012. http://repositorio.unicamp.br/jspui/handle/REPOSIP/305803.

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Orientador: Luiz Antonio Barrera San Martin<br>Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica<br>Made available in DSpace on 2018-08-21T14:02:28Z (GMT). No. of bitstreams: 1 Silva_JulioCesarConegundesda_M.pdf: 1171316 bytes, checksum: 4e6e6eb2a3f1c066ac73e86495c06428 (MD5) Previous issue date: 2012<br>Resumo: ...Observações: Por apresentar basicamente fórmulas, o resumo, na íntegra, poderá ser visualizado no texto completo da tese digital<br>Abstract: ...Note: The complete abstract is available with the full electronic
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Floderová, Hana. "Geometrické struktury založené na kvaternionech." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2010. http://www.nusl.cz/ntk/nusl-229021.

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A pair (V, G) is called geometric structure, where V is a vector space and G is a subgroup GL(V), which is a set of transmission matrices. In this thesis we classify structures, which are based on properties of quaternions. Geometric structures based on quaternions are called triple structures. Triple structures are four structures with similar properties as quaternions. Quaternions are generated from real numbers and three complex units. We write quaternions in this shape a+bi+cj+dk.
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Freitas, José Roberto. "Equações algébricas nos quatérnios de Hamilton." Universidade Tecnológica Federal do Paraná, 2013. http://repositorio.utfpr.edu.br/jspui/handle/1/594.

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Capes<br>A descoberta dos quatérnios pelo matemático britânico William Rowan Hamilton (1805-1865) permitiu uma nova abordagem na resolução de equações algébricas, fornecendo uma estrutura algébrica mais geral onde buscar soluções. Generalizando o caso clássico (sobre os complexos) apresentamos neste trabalho um tratamento da equação algébrica geral com coeficientes quatérnios. Verificamos que o número de raízes pode ser maior que o grau, e muitas vezes, pode mesmo ser infinito. Damos ênfase ao caso da equação quadrática, obtendo fórmulas para as raízes. Também nos detemos na obtenção de uma ra
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Resende, Adriana Souza. "Introdução elementar às álgebras Clifford 'CL IND.2' 'CL IND. 3'." [s.n.], 2010. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306698.

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Orientador: Waldyr Alves Rodrigues Junior<br>Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matemática, Estatistica e Computação Cientifica<br>Made available in DSpace on 2018-08-15T23:09:32Z (GMT). No. of bitstreams: 1 Resende_AdrianaSouza_M.pdf: 17553204 bytes, checksum: a66cefe30e9957cc4351e03d3aec35b2 (MD5) Previous issue date: 2010<br>Resumo: O presente trabalho tem a intenção de apresentar por intermédio de uma linguagem unificada alguns conceitos de cálculo vetorial, álgebra linear (matrizes e transformações lineares) e também algumas idéias elem
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Vieira, Vandenberg Lopes. "Grupos fuchsianos aritmeticos identificados em ordens dos quaternios para construção de constelações de sinais." [s.n.], 2007. http://repositorio.unicamp.br/jspui/handle/REPOSIP/261079.

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Orientadores: Reginaldo Palazzo Jr., Mercio Botelho Faria<br>Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação<br>Made available in DSpace on 2018-08-08T06:25:10Z (GMT). No. of bitstreams: 1 Vieira_VandenbergLopes_D.pdf: 990187 bytes, checksum: 2212b8074f5503f78aa813ce4422cc4b (MD5) Previous issue date: 2007<br>Resumo: Dentro do contexto de projetar sistema de comunicação digital em espaços homogêneos, em particular, em espaços hiperbólicos, é necessário estabelecer um procedimento sistemático para construção de reticulados O, como element
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Parcollet, Titouan. "Quaternion neural networks A survey of quaternion neural networks - Chapter 2 Real to H-space Autoencoders for Theme Identification in Telephone Conversations - Chapter 7." Thesis, Avignon, 2019. http://www.theses.fr/2019AVIG0233.

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Au cours des dernières années, l’apprentissage profond est devenu l’approche privilégiée pour le développement d’une intelligence artificielle moderne (IA). L’augmentation importante de la puissance de calcul, ainsi que la quantité sans cesse croissante de données disponibles ont fait des réseaux de neurones profonds la solution la plus performante pour la resolution de problèmes complexes. Cependant, la capacité à parfaitement représenter la multidimensionalité des données réelles reste un défi majeur pour les architectures neuronales artificielles.Pour résoudre ce problème, les réseaux de ne
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Lesesvre, Didier. "Arithmetic Statistics for Quaternion Algebras." Thesis, Sorbonne Paris Cité, 2018. http://www.theses.fr/2018USPCD040.

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Les formes automorphes sont des objets centraux en théorie des nombres. En dépit de leur omniprésence, elles demeurent mystérieuses et leur comportement est loin d'être entièrement compris. Considérer ces formes automorphes au sein de familles a un effet régularisant, et ouvre la voie aux résultats en moyenne : voilà l'esprit des statistiques arithmétiques. La famille de toutes les représentations automorphes d'un groupe réductif donné, appelée famille universelle du groupe, est particulièrement importante. Dans le cas des formes intérieures de GL(2), autrement dit les groupes d'unités d'algèb
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Books on the topic "Quaternions algebra"

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P, Ward J. Quaternions and Cayley numbers: Algebra and applications. Kluwer Academic Publishers, 1997.

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Ward, J. P. Quaternions and Cayley Numbers: Algebra and Applications. Springer Netherlands, 1997.

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Conway, John Horton. On quaternions and octonions: Their geometry, arithmetic, and symmetry. AK Peters, 2003.

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Chuang, Chih-Yun. Brandt matrices and theta series over global function fields. American Mathematical Society, 2015.

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Behrns, Vernon N. An introduction to the algebra of hypernumbers. Dorrance Publishing Co., 2007.

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Paşa, Hüseyin Tevfik. Hüseyin Tevfik Paşa ve "Linear algebra". İstanbul Teknik Üniversitesi Bilim ve Teknoloji Tarihi Araştırma Merkezi, 1988.

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Dixon, Geoffrey M. Division algebras: Octonions, quaternions, complex numbers, and the algebraic design of physics. Kluwer Academic Publishers, 1994.

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Voight, John. Quaternion Algebras. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-56694-4.

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Wolfgang, Sprössig, Gürlebeck Klaus, and Volkswagenstiftung, eds. Proceedings of the symposium: Analytical and numerical methods in quaternionic and Clifford analysis : Seiffen 1996. s.n., 1996.

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Fragoulopoulou, Maria. Tensor products of enveloping locally C*-algebras. Mathematisches Institut der Universität Münster, 1997.

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Book chapters on the topic "Quaternions algebra"

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Gorodentsev, Alexey L. "Quaternions and Spinors." In Algebra I. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-45285-2_20.

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Goldman, Ron. "The Algebra of Quaternion Multiplication." In Rethinking Quaternions. Springer International Publishing, 2010. http://dx.doi.org/10.1007/978-3-031-79549-7_4.

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Goldman, Ron. "Summary—Formulas From Quaternion Algebra." In Rethinking Quaternions. Springer International Publishing, 2010. http://dx.doi.org/10.1007/978-3-031-79549-7_10.

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Vince, John. "Quaternion Algebra." In Quaternions for Computer Graphics. Springer London, 2011. http://dx.doi.org/10.1007/978-0-85729-760-0_5.

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Vince, John. "Quaternion Algebra." In Quaternions for Computer Graphics. Springer London, 2021. http://dx.doi.org/10.1007/978-1-4471-7509-4_6.

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Kantor, I. L., and A. S. Solodovnikov. "Quaternions and Vector Algebra." In Hypercomplex Numbers. Springer New York, 1989. http://dx.doi.org/10.1007/978-1-4612-3650-4_4.

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Goldman, Ronald. "Algebra." In Dual Quaternions and Their Associated Clifford Algebras. CRC Press, 2023. http://dx.doi.org/10.1201/9781003398141-3.

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Vince, John. "Number Sets and Algebra." In Quaternions for Computer Graphics. Springer London, 2011. http://dx.doi.org/10.1007/978-0-85729-760-0_2.

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Ward, J. P. "Fundamentals of Linear Algebra." In Quaternions and Cayley Numbers. Springer Netherlands, 1997. http://dx.doi.org/10.1007/978-94-011-5768-1_1.

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Kamberov, George, Peter Norman, Franz Pedit, and Ulrich Pinkall. "Chapter 3. Spinor Algebra." In Quaternions, Spinors, and Surfaces. American Mathematical Society, 2002. http://dx.doi.org/10.1090/conm/299/03.

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Conference papers on the topic "Quaternions algebra"

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Purwar, Anurag, and Q. J. Ge. "Polar Decomposition of Unit Dual Quaternions." In ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/detc2012-70882.

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This paper seeks to extend the notion of polar decomposition from matrix algebra to dual quaternion algebra. The goal is to obtain a simple, efficient and explicit method for determining the polar decompositions (PD) of spatial displacements in Euclidean three-space that belong to a special Euclidean Group known as SE(3). It has been known that such a decomposition is equivalent to the projection of an element of SE(3) onto SO(4) that yields hyper spherical displacements that best approximate rigid-body displacements. It is shown in this paper that a dual quaternion representing an element of
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Terze, Zdravko, Andreas Mueller, and Dario Zlatar. "Redundancy-Free Integration of Rotational Quaternions in Minimal Form." In ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/detc2014-35118.

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Redundancy-free computational procedure for solving dynamics of rigid body by using quaternions as the rotational kinematic parameters will be presented in the paper. On the contrary to the standard algorithm that is based on redundant DAE-formulation of rotational dynamics of rigid body that includes algebraic equation of quaternions’ unit-length that has to be solved during marching-in-time, the proposed method will be based on the integration of a local rotational vector in the minimal form at the Lie-algebra level of the SO(3) rotational group during every integration step. After local rot
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Condurache, Daniel. "Dual Lie Algebra Representations of Rigid Body Motion With Dual Cayley Maps: An Overview." In ASME 2024 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2024. http://dx.doi.org/10.1115/detc2024-143707.

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Abstract The main objective of this research is to develop a new minimal parameterization technique for the displacement and motion of rigid bodies using hypercomplex dual algebra. Our study is based on the properties of dual tensors and dual quaternions, more precisely, their Lie groups and algebras. Based on the higher-order modified fractional Cayley transforms, for the first time, a complete and unitary parameterization framework, which gives the possibility of developing direct unitary solutions for the calculation of the leading entities of kinematic representation of displacement and mo
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Ge, Q. J. "On the Matrix Algebra Realization of the Theory of Biquaternions." In ASME 1994 Design Technical Conferences collocated with the ASME 1994 International Computers in Engineering Conference and Exhibition and the ASME 1994 8th Annual Database Symposium. American Society of Mechanical Engineers, 1994. http://dx.doi.org/10.1115/detc1994-0221.

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Abstract This paper describes a matrix algebra presentation of Clifford’s theory of biquaternions. We examine 4 × 4 skew-symmetric matrices and use their exponentials to relate quaternions to equal-angle double rotations in Euclidean four-space E4. We show how double rotations in E4 expressed in terms of plane coordinates lead to elliptic biquaternions in both Plücker and Study forms and present the fundamental Plücker and Study conditions that govern the biquaternions. Finally, we show that a spatial displacement in E3 in terms of parabolic biquaternions (or dual quaternions) is a limiting ca
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Yu, Zihan, Qiaode Jeffrey Ge, and Mark P. Langer. "Construction of Confidence Regions for Uncertain Spatial Displacements With Dual Rodrigues Parameters." In ASME 2024 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2024. http://dx.doi.org/10.1115/detc2024-143410.

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Abstract This paper follows our recent work on the computation of kinematic confidence regions from a given set of uncertain spatial displacements with specified confidence levels. Dual quaternion algebra is used to compute the mean displacement as well as relative displacements from the mean. In constructing a 6D confidence ellipsoid, however, we use dual Rodrigue parameters resulting from dual quaternions. The advantages of using dual quaternions and dual Rodrigues parameters are discussed in comparison with those of three translation parameters and three Euler angles, which were used for th
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Agrawal, O. P. "Quaternions, Hamilton Operators, and Kinematics of Mechanical Systems." In ASME 1987 Design Technology Conferences. American Society of Mechanical Engineers, 1987. http://dx.doi.org/10.1115/detc1987-0095.

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Abstract In this paper, quaternions are briefly reviewed and their associated matrix algebra is developed. Two Hamilton operators are defined and some of their properties are studied. The properties of these operators are then applied to find kinematic relations of a body undergoing spatial rotation and to find a recursive relation for intermediate-axes. The formulation presented provides an easy approach to kinematic analysis of spatial mechanical systems.
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Benger, Werner. "Illustrating Geometric Algebra and Differential Geometry in 5D Color Space." In WSCG 2023 – 31. International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision. University of West Bohemia, Czech Republic, 2023. http://dx.doi.org/10.24132/csrn.3301.1.

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Geometric Algebra (GA) is popular for its immediate geometric interpretations of algebraic objects and operations. It is based on Clifford Algebra on vector spaces and extends linear algebra of vectors by operations such as an invertible product, i.e. divisions by vectors. This formalism allows for a complete algebra on vectors same as for scalar or complex numbers. It is particularly suitable for rotations in arbitrary dimensions. In Euclidean 3D space quaternions are known to be numerically superior to rotation matrices and already widely used in computer graphics. However, their meaning bey
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Saldias, Daniel P., Luiz A. Radavelli, Carlos R. M. Roesler, and Daniel Martins. "Kinematic synthesis of the passive human knee joint by differential evolution and quaternions algebra: A preliminary study." In 2014 5th IEEE RAS & EMBS International Conference on Biomedical Robotics and Biomechatronics (BioRob). IEEE, 2014. http://dx.doi.org/10.1109/biorob.2014.6913759.

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Nelson, Donald D., and Elaine Cohen. "User Interaction With CAD Models With Nonholonomic Parametric Surface Constraints." In ASME 1998 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/imece1998-0260.

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Abstract User manipulation of assembly models can provide insight during the early, formulative design stages into kinematic and dynamic characteristics of a mechanism. We present the advantages of kinematic representation of constraint equations in fully Cartesian coordinates, a departure from standard practice for interactive mechanical assembly at interactive rates. Formulations of a surface rolling contact constraint equation and its Jacobian, defined as a joint between two NURBS surfaces via position, tangency and velocity constraint relations, are derived for use in dynamic simulation an
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Müller, Andreas, Zdravko Terze, and Viktor Pandza. "A Non-Redundant Formulation for the Dynamics Simulation of Multibody Systems in Terms of Unit Dual Quaternions." In ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/detc2016-60191.

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Abstract:
Quaternions are favorable parameters to describe spatial rotations of rigid bodies since they give rise to simple equations governing the kinematics and attitude dynamics in terms of simple algebraic equations. Dual quaternions are the natural extension to rigid body motions. They provide a singularity-free purely algebraic parameterization of rigid body motions, and thus serve as global parameters within the so-called absolute coordinate formulation of MBS. This attractive feature is owed to the inherent redundancy of these parameters since they must satisfy two quadratic conditions (unit con
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