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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 .
In mathematics, a translation of axes in two dimensions is a mapping from an xy-Cartesian coordinate system to an x'y'-Cartesian coordinate system in which the x' axis is parallel to the x axis and k units away, and the y' axis is parallel to the y axis and h units away.
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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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 ...
1. Luring “This is where you have a treat in your hand and you use it to guide your dog into specific positions,” explains DeWillems. “Luring can be pretty easy for most people and dogs to ...
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In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure, shape or space by the same distance in a given direction. A translation can also be interpreted as the addition of a constant vector to every point, or as shifting the origin of the coordinate system. In a Euclidean space, any translation is ...