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  2. Rotation of axes in two dimensions - Wikipedia

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

    A point P has coordinates (x, y) with respect to the original system and coordinates (x′, y′) with respect to the new system. 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.

  3. 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.

  4. Rotation (mathematics) - Wikipedia

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

    Rotation of an object in two dimensions around a point O. 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. Rotation can have a sign (as in the sign of an angle ): a clockwise ...

  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 (geometry) of an axis of rotation, and an angle of rotation θ describing the magnitude and sense (e.g., clockwise) of ...

  6. Direct-quadrature-zero transformation - Wikipedia

    en.wikipedia.org/wiki/Direct-quadrature-zero...

    Direct-quadrature-zero transformation. The direct-quadrature-zero ( DQZ or DQ0 [1] or DQO, [2] sometimes lowercase) transformation or zero-direct-quadrature [3] ( 0DQ or ODQ, sometimes lowercase) transformation is a tensor that rotates the reference frame of a three-element vector or a three-by-three element matrix in an effort to simplify ...

  7. Right-hand rule - Wikipedia

    en.wikipedia.org/wiki/Right-hand_rule

    Right-hand rule. In mathematics and physics, the right-hand rule is a convention and a mnemonic, utilized to define the orientation of axes in three-dimensional space and to determine the direction of the cross product of two vectors, as well as to establish the direction of the force on a current-carrying conductor in a magnetic field.

  8. Rotations and reflections in two dimensions - Wikipedia

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

    A point P has coordinates (x, y) with respect to the original system and coordinates (x′, y′) with respect to the new system. 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.

  9. Spherical coordinate system - Wikipedia

    en.wikipedia.org/wiki/Spherical_coordinate_system

    In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a given point in space is specified by three numbers, ( r, θ, φ ): the radial distance of the radial line r connecting the point to the fixed point of origin (which is located on a fixed polar axis, or zenith direction axis ...

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