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  2. Rotation (mathematics) - Wikipedia

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

    Rotation can have a sign (as in the sign of an angle): a clockwise rotation is a negative magnitude so a counterclockwise turn has a positive magnitude. A rotation is different from other types of motions: translations , which have no fixed points, and (hyperplane) reflections , each of them having an entire ( n − 1) -dimensional flat of ...

  3. Rotation of axes in two dimensions - Wikipedia

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

    In the new coordinate system, the point P will appear to have been rotated in the opposite direction, that is, clockwise through the angle . A rotation of axes in more than two dimensions is defined similarly. [2] [3] A rotation of axes is a linear map [4] [5] and a rigid transformation.

  4. Clockwise - Wikipedia

    en.wikipedia.org/wiki/Clockwise

    For example, the daily rotation of the Earth is clockwise when viewed from above the South Pole, and counterclockwise when viewed from above the North Pole (considering "above a point" to be defined as "farther away from the center of earth and on the same ray"). The shadow of a horizontal sundial in the Northern Hemisphere rotates clockwise

  5. Rotation matrix - Wikipedia

    en.wikipedia.org/wiki/Rotation_matrix

    corresponds to a 90° planar rotation clockwise about the origin. ... In Euclidean geometry, a rotation is an example of an isometry, ...

  6. 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 ...

  7. Euler angles - Wikipedia

    en.wikipedia.org/wiki/Euler_angles

    Euler angles can be defined by elemental geometry or by composition of rotations (i.e. chained rotations).The geometrical definition demonstrates that three composed elemental rotations (rotations about the axes of a coordinate system) are always sufficient to reach any target frame.

  8. Rotation - Wikipedia

    en.wikipedia.org/wiki/Rotation

    A sphere rotating (spinning) about an axis. Rotation or rotational motion is the circular movement of an object around a central line, known as an axis of rotation.A plane figure can rotate in either a clockwise or counterclockwise sense around a perpendicular axis intersecting anywhere inside or outside the figure at a center of rotation.

  9. Rotations and reflections in two dimensions - Wikipedia

    en.wikipedia.org/wiki/Rotations_and_reflections...

    In the new coordinate system, the point P will appear to have been rotated in the opposite direction, that is, clockwise through the angle . A rotation of axes in more than two dimensions is defined similarly. [2] [3] A rotation of axes is a linear map [4] [5] and a rigid transformation.

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