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

Spatial rotations in three dimensions can be parametrized using both Euler angles and unit quaternions. This article explains how to convert between the...

The algebra of quaternions is often denoted by H (for Hamilton), or in blackboard bold by H . {\displaystyle \mathbb {H} .} Quaternions are not a field...

3-sphere S3 and can be understood as the group of versors (quaternions with absolute value 1). The connection between quaternions and rotations, commonly...

angles Davenport chained rotations Euler's rotation theorem Gimbal lock Quaternion Quaternions and spatial rotation Rotation formalisms in three dimensions...

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

isoclinic rotations. Laplace–Runge–Lenz vector Lorentz group Orthogonal group Orthogonal matrix Plane of rotation Poincaré group Quaternions and spatial rotation...

unit quaternions, but the extension loses the fixed execution-time of the slerp algorithm. Circular interpolation Quaternions and spatial rotation Spherical...

some other way. This could be as a rotation matrix, a quaternion (see quaternions and spatial rotation), or a similar orientation representation that treats...

of three squares of integers) Prouhet–Tarry–Escott problem Quaternions and spatial rotation Taxicab number R. Spira, The diophantine equation x2 + y2 +...

from the demand for a unit quaternion, we find that nonzero quaternions act as homogeneous coordinates for 3 × 3 rotation matrices. The Cayley transform...

two individual rotations represented as quaternions using a quaternion product Like rotation matrices, quaternions must sometimes be renormalized due to...

possibility to represent a rotation of three-dimensional Euclidean vectors are quaternions described below. Unit quaternions, or versors, are in some ways...

can be found in the article on quaternions and spatial rotation. This game serves to clarify the notion that rotations in space have properties that cannot...

above. When q is used to describe spatial rotations (cf. quaternions and spatial rotations), it describes a rotation about τ through an angle of 2ψ. For...

representing an axis, and an angle of rotation about it; A quaternion q of length 1 (cf. Versor, quaternions and spatial rotation, 3-sphere), the components...

Spin(3) group can be represented by unit quaternions, also known as versors. Quaternions and spatial rotation Candle dance US 3586413, Adams, Dale A.,...

multiplicative group of unit quaternions. (For a description of this homomorphism see the article on quaternions and spatial rotations.) The binary cyclic group...

1870s. Peter Guthrie Tait carried the quaternion standard after Hamilton. His 1867 Elementary Treatise of Quaternions included extensive treatment of the...

four spatial dimensions, called quaternions, was defined by William Rowan Hamilton in 1843. Soon after, tessarines and coquaternions were introduced as...

a quaternion. While the quaternion described above does not involve complex numbers, if quaternions are used to describe two successive rotations, they...

to and from matrices. When used to represent orientations, rotation quaternions are typically called orientation quaternions or attitude quaternions. The...

"Review of Quaternions and Elliptic Space by Georges Lemaître". Mathematical Reviews. MR0031739 (requires subscription) "Quaternions: Rotation representation"...

gyroscope dynamics. Rotation formalisms in three dimensions Quaternions and spatial rotation Versor Spinors in three dimensions SO(4) 3D rotation group Beltrami–Klein...

subgroup of the versors, which are the quaternions of norm one. For more information see Quaternions and spatial rotations. Explicitly, the binary icosahedral...

counterclockwise rotation through an angle α about an axis given by a unit vector v; z is the same rotation; see quaternions and spatial rotation. This is not...

method for representing spatial rotations – see quaternions and spatial rotation. However, it is often desirable to represent rotations by a set of three numbers...

and this coincidence corresponds to the covering map homomorphism from SU(2) × SU(2) to SO(4) given by quaternion multiplication; see quaternions and...

Minkowski space Biquaternions Indefinite orthogonal group Quaternions and spatial rotation Special relativity Symmetry in quantum mechanics Note that...

(For a description of this homomorphism see the article on quaternions and spatial rotations.) Explicitly, the binary tetrahedral group is given as the...