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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 ]
In vector calculus, the curl, also known as rotor, is a vector operator that describes the infinitesimal circulation of a vector field in three-dimensional Euclidean space. The curl at a point in the field is represented by a vector whose length and direction denote the magnitude and axis of the maximum circulation. [ 1 ]
Rotation in mathematics is a concept originating in geometry. Any rotation is a motion of a certain space that preserves at least one point . It can describe, for example, the motion of a rigid body around a fixed point.
The rotors in a space of dimension + have () / + degrees of freedom, the same as the number of degrees of freedom in the rotations and translations combined for an -dimensional space. This is the case in Projective Geometric Algebra (PGA), which is used [ 33 ] [ 34 ] [ 35 ] to represent Euclidean isometries in Euclidean geometry (thereby ...
In geometry, various formalisms exist to express a rotation in three dimensions as a mathematical transformation.In physics, this concept is applied to classical mechanics where rotational (or angular) kinematics is the science of quantitative description of a purely rotational motion.
In mathematics, the group of rotations about a fixed point in four-dimensional Euclidean space is denoted SO(4). The name comes from the fact that it is the special orthogonal group of order 4. In this article rotation means rotational displacement .
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Such non-standard orientations are rarely used in mathematics but are common in 2D computer graphics, which often have the origin in the top left corner and the y-axis down the screen or page. [ 2 ] See below for other alternative conventions which may change the sense of the rotation produced by a rotation matrix.