In geometry, various formalisms exist to express a rotation in three dimensions as a mathematical transformation. In physics, this concept is applied to...

space is equivalent to a pure rotation about a single fixed axis. It is one of many rotation formalisms in three dimensions. The axis–angle representation...

is not a rotation but a screw operation. Rotations about the origin have three degrees of freedom (see rotation formalisms in three dimensions for details)...

of three dimensions. For example, any three skew lines in PG(3,q) are contained in exactly one regulus. 3D rotation Rotation formalisms in three dimensions...

number of rotations Rotation around a fixed axis Rotation formalisms in three dimensions Rotating locomotion in living systems Top – spinning toy Wormeli, R...

direction Directional statistics Oriented area Plane of rotation Rotation formalisms in three dimensions Signed direction Terms of orientation Triad method...

dual quaternions to 2D geometry Elliptic geometry Rotation formalisms in three dimensions Rotation (mathematics) Spin group Slerp, spherical linear interpolation...

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

rotation theorem Rodrigues' rotation formula Plane of rotation Axis–angle representation Rotation group SO(3) Rotation formalisms in three dimensions...

control of an aircraft's attitude Rotation formalisms in three dimensions, various mathematical descriptions of three-dimensional attitude Attitude (TV...

In mathematics and mechanics, the Euler–Rodrigues formula describes the rotation of a vector in three dimensions. It is based on Rodrigues' rotation formula...

equivalent to a pure rotation about a single fixed axis. It is one of many rotation formalisms in three dimensions. The simplest case of rotation around a fixed...

theory. Euler angles Euler–Rodrigues formula Rotation formalisms in three dimensions Angular velocity Rotation around a fixed axis Matrix exponential Axis–angle...

In mathematics, the special orthogonal group in three dimensions, otherwise known as the rotation group SO(3), is a naturally occurring example of a manifold...

with poststratification, used in opinion polling Modified Rodrigues parameters, in rotation formalisms in three dimensions Machine-readable passport Media...

dynamics and control (spacecraft) Euler's rotation theorem Gyroscope Triad Method Rotation formalisms in three dimensions Geographic coordinate system Astronomical...

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

quantity that changes sign with improper rotation Rotation formalisms in three dimensions – Ways to represent 3D rotations Right-hand rule – Mnemonic for understanding...

a rotation by angle φ. In 3 Euclidean dimensions, the single spinor representation is 2-dimensional and quaternionic. The existence of spinors in 3 dimensions...

following table gives a summary of what to consider. Rotation formalisms in three dimensions Geodetic coordinates Geodetic system Plane coordinates Gade...

Euler filtering is available in a number of 3D animation packages. Charts on SO(3) Rotation formalisms in three dimensions http://fliponline.blogspot...

Polychoron Rotations in 4-dimensional Euclidean space Fourth dimension in art Fourth dimension in literature 5 dimensions Kaluza–Klein theory 8 dimensions Octonion...

coordinate axes in three dimensions. William Rowan Hamilton, recognized for his development of quaternions, a mathematical system for representing three-dimensional...

The geometric interpretation of curl as rotation corresponds to identifying bivectors (2-vectors) in 3 dimensions with the special orthogonal Lie algebra...

inertia. Angular momentum and rigid-body rotation in two and three dimensions Lecture notes on rigid-body rotation and moments of inertia The moment of inertia...

have high rotational rates. In general, conservation limits the possible motion of a system, but it does not uniquely determine it. The three-dimensional...

In physics, spacetime, also called the space-time continuum, is a mathematical model that fuses the three dimensions of space and the one dimension of...

In physics, a Wick rotation, named after Gian-Carlo Wick, is a method of finding a solution to dynamics problems in n {\displaystyle n} dimensions, by...

particle moves can be described in terms of three velocity components, each in reference to the three dimensions of space. So, if the time evolution of the...

In such a formulation, along with ordinary space dimensions x, y, z, ..., there are also "anticommuting" dimensions whose coordinates are labeled in Grassmann...