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2. Rotation (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Rotation_(mathematics)

   The rotation group is a Lie group of rotations about a fixed point. This (common) fixed point or center is called the center of rotation and is usually identified with the origin. The rotation group is a point stabilizer in a broader group of (orientation-preserving) motions. For a particular rotation: The axis of rotation is a line of its ...

3. Rotation of axes in two dimensions - Wikipedia

   en.wikipedia.org/wiki/Rotation_of_axes_in_two...

   In mathematics, a rotation of axes in two dimensions is a mapping from an xy-Cartesian coordinate system to an x′y′-Cartesian coordinate system in which the origin is kept fixed and the x′ and y′ axes are obtained by rotating the x and y axes counterclockwise through an angle .

4. Rotor (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Rotor_(mathematics)

   A rotor is an object in the geometric algebra (also called Clifford algebra) of a vector space that represents a rotation about the origin. [1] The term originated with William Kingdon Clifford, [2] in showing that the quaternion algebra is just a special case of Hermann Grassmann's "theory of extension" (Ausdehnungslehre). [3]

5. Axis–angle representation - Wikipedia

   en.wikipedia.org/wiki/Axis–angle_representation

   The angle θ and axis unit vector e define a rotation, concisely represented by the rotation vector θe.. In mathematics, the axis–angle representation parameterizes a rotation in a three-dimensional Euclidean space by two quantities: a unit vector e indicating the direction of an axis of rotation, and an angle of rotation θ describing the magnitude and sense (e.g., clockwise) of the ...

6. Quaternions and spatial rotation - Wikipedia

   en.wikipedia.org/wiki/Quaternions_and_spatial...

   3D visualization of a sphere and a rotation about an Euler axis (^) by an angle of In 3-dimensional space, according to Euler's rotation theorem, any rotation or sequence of rotations of a rigid body or coordinate system about a fixed point is equivalent to a single rotation by a given angle about a fixed axis (called the Euler axis) that runs through the fixed point. [6]

7. Plane-based geometric algebra - Wikipedia

   en.wikipedia.org/wiki/Plane-based_geometric_algebra

   Rotations and translations do preserve handedness, which in 3D Plane-based GA implies that they can be written as a composition of an even number of reflections. A rotations can thought of as a reflection in a plane followed by a reflection in another plane which is not parallel to the first (the quaternions, which are set in the context of PGA ...