mathematics, the dual quaternions are an 8-dimensional real algebra isomorphic to the tensor product of the quaternions and the dual numbers. Thus, they...

In mathematics, the quaternion number system extends the complex numbers. Quaternions were first described by the Irish mathematician William Rowan Hamilton...

Unit quaternions, known as versors, provide a convenient mathematical notation for representing spatial orientations and rotations of elements in three...

the dual quaternion algebra to 2D geometry are discussed. At this present time, the article is focused on a 4-dimensional subalgebra of the dual quaternions...

subspace. As K-algebras, they generalize the real numbers, complex numbers, quaternions and several other hypercomplex number systems. The theory of Clifford...

axis appears in the dual quaternion formulation of a spatial displacement D = ([A], d). The dual quaternion is constructed from the dual vector S = (S, V)...

Split-biquaternions when the coefficients are split-complex numbers. Dual quaternions when the coefficients are dual numbers. This article is about the ordinary biquaternions...

worked with are dual numbers, dual quaternions, and split-biquaternions, all being associative algebras over R. Study's work with dual numbers and line...

In mathematics, quaternions are a non-commutative number system that extends the complex numbers. Quaternions and their applications to rotations were...

including the axis–angle representation of rotations, the quaternion and dual quaternion representations of rotations and translations, the plücker representation...

In abstract algebra, the split-quaternions or coquaternions form an algebraic structure introduced by James Cockle in 1849 under the latter name. They...

of error is significantly reduced. By formulating the matrices as dual quaternions, it is possible to get a linear equation by which X is solvable in...

dynamics. This is in part because of the relationship between screws and dual quaternions which have been used to interpolate rigid-body motions. Based on screw...

dualer Quaternionen auf Kinematik", Annales Academiae Scientiarum Fennicae (1958), 1-13; Gesammelte Werke, volume 2, Applications of dual quaternions...

University of Tasmania, Hobart, Tasmania. He was also a proponent of dual quaternions, which he termed "octonions" or "Clifford biquaternions". McAulay was...

split-biquaternions, while H ⊗ N {\displaystyle H\otimes N} forms dual quaternions. The algebra of dual quaternions is used to express screw displacement, a common mapping...

of space science experimental payloads. Hybrid Global Finite-Time Dual-Quaternion Observer and Controller for Velocity-Free Spacecraft Pose Tracking...

{\textbf {q}}^{0}} denote a unit dual quaternion. A homogeneous dual quaternion may be written as a pair of quaternions, Q ^ = Q + ε Q 0 {\displaystyle...

TriAx Weight Maps, where many other industry platforms were using Dual Quaternion. This changed in Genesis 3 to allow Daz 3D figures to be more compatible...

In algebra, the dual numbers are a hypercomplex number system first introduced in the 19th century. They are expressions of the form a + bε, where a and...

of quaternion algebras over a field. The biquaternions of William Rowan Hamilton (1844) and the related split-biquaternions and dual quaternions do not...

representing a rotation as numbers in a computer, some people prefer the quaternion representation or the axis+angle representation, because they avoid the...

analysis of movement in machines: Burmester theory Clifford algebra Dual quaternion Euler's rotation theorem Gear ratio Ideal machine Instantaneous center...

September 2010). "Simultaneous robot-world and hand-eye calibration using dual-quaternions and Kronecker product" (PDF). International Journal of the Physical...

algebra of quaternions and the non-commutative Hamilton product. In particular, when the Hamilton product of two vectors (that is, pure quaternions with zero...

group PSL(2, Z). Ring homographies have been used in quaternion analysis, and with dual quaternions to facilitate screw theory. The conformal group of spacetime...

unit quaternions. Multiplication of rotation matrices is homomorphic to multiplication of quaternions, and multiplication by a unit quaternion rotates...

map homomorphism from SU(2) × SU(2) to SO(4) given by quaternion multiplication; see quaternions and spatial rotation. Thus SO(4) is not a simple group...

of lattices, the dual lattice is a construction analogous to that of a dual vector space. In certain respects, the geometry of the dual lattice of a lattice...

coefficients of a quaternion; the scalar parameter a is the real part, the vector parameters b, c, d are the imaginary parts. Thus we have the quaternion q = a +...