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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 ]
Because of this property of rotating within a square, the Reuleaux triangle is also sometimes known as the Reuleaux rotor. [ 5 ] The Reuleaux triangle is the first of a sequence of Reuleaux polygons whose boundaries are curves of constant width formed from regular polygons with an odd number of sides.
A.M. – arithmetic mean. AP – arithmetic progression. arccos – inverse cosine function. arccosec – inverse cosecant function. (Also written as arccsc.) arccot – inverse cotangent function. arccsc – inverse cosecant function. (Also written as arccosec.) arcexc – inverse excosecant function. (Also written as arcexcsc, arcexcosec.)
Rotation formalisms are focused on proper (orientation-preserving) motions of the Euclidean space with one fixed point, that a rotation refers to.Although physical motions with a fixed point are an important case (such as ones described in the center-of-mass frame, or motions of a joint), this approach creates a knowledge about all motions.
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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.
A federal research agency that tracks the progress of America’s students is being hit with almost $900 million in cuts after Elon Musk’s Department of Government Efficiency found no need for ...