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

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)...

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

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...

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

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...

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

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 not around a...

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...

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

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

Altitude, a distance measurement, usually in the vertical or "up" direction Rotation formalisms in three dimensions This disambiguation page lists articles...

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

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

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

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

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...

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...

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

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

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

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...

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...

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

and twistor theory, where it appears in the context of 2-spinors. In three dimensions, the Levi-Civita symbol is defined by: ε i j k = { + 1 if  ( i ,...

\end{aligned}}} The Hodge star relates the exterior and cross product in three dimensions: ⋆ ( u ∧ v ) = u × v ⋆ ( u × v ) = u ∧ v . {\displaystyle {\star...

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

formulated in the context of a four-dimensional theory, some theorists have explored their consequences in n dimensions. The equations in contexts outside...

the Terrestrial Planets: N-Body Integrations of Planetary Embryos in Three Dimensions". Icarus. 136 (2): 304–327. Bibcode:1998Icar..136..304C. CiteSeerX 10...