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The quaternion-based three-dimensional beam theory [PDF]
, 2009 This paper presents the equations for the implementation of rotational quaternions in the geometrically exact three-dimensional beam theory. A new finite-element formulation is proposed in which the rotational quaternions are used for parametrization of ...
Saje, Miran, Zupan, Dejan, Zupan, Eva
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The quaternionic determinant [PDF]
The Electronic Journal of Linear Algebra, 2000 The determinant for complex matrices cannot be extended to quaternionic matrices. Instead, the Study determinant and the closely related $q$-determinant are widely used. We show that the Study determinant can be characterized as the unique functional which extends the {\em absolute value} of the complex determinant and discuss its spectral and linear ...
Stefano De Leo, Nir Cohen
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Quaternionic Integrability [PDF]
Journal of Nonlinear Mathematical Physics, 2021 Standard (Arnold–Liouville) integrable systems are intimately related to complex rotations. One can define a generalization of these, sharing many of their properties, where complex rotations are replaced by quaternionic ones, and more generally by the action of a Clifford group.
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Hyper-Dual Leonardo Quaternions
Journal of New TheoryIn this paper, hyper-dual Leonardo quaternions are defined and studied. Some basic properties of the hyper-dual Leonardo quaternions, including their relationships with the hyper-dual Fibonacci quaternions and hyper-dual Lucas quaternions, are analyzed ...
Tülay Yağmur
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About special elements in quaternion algebras over finite fields
, 2016 In this paper we study special Fibonacci quaternions and special generalized Fibonacci-Lucas quaternions in quaternion algebras over finite fields.Comment: This is a preliminary form of the ...
Savin, Diana
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The vector algebra war: a historical perspective [PDF]
, 2016 There are a wide variety of different vector formalisms currently utilized in engineering and physics. For example, Gibbs' three-vectors, Minkowski four-vectors, complex spinors in quantum mechanics, quaternions used to describe rigid body rotations and ...
Abbott, Derek +3 more
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Integrating Rotations Using Nonunit Quaternions
IEEE Robotics and Automation Letters, 2018 In this letter, we propose and demonstrate a method for integration of rotations using nonunit quaternions. Unit quaternions are commonly used to represent rotation, in which case the rotation operation involves the conjugate of the unit quaternion ...
Caleb D. Rucker
semanticscholar +1 more source
On fourth-order jacobsthal quaternions
Journal of Mathematical Sciences and Modelling, 2018 In this paper, we present for the first time a sequence of quaternions of order 4 that we will call the fourth-order Jacobsthal and the fourth-order Jacobsthal-Lucas quaternions. In particular, we are interested in the generating function, Binet formula,
Gamaliel Cerda-morales
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Biquaternion (complexified quaternion) roots of -1
, 2005 The roots of -1 in the set of biquaternions (quaternions with complex components, or complex numbers with quaternion real and imaginary parts) are studied and it is shown that there is an infinite number of non-trivial complexified quaternion roots (and ...
Sangwine, Stephen J.
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