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  2. Rotation formalisms in three dimensions - Wikipedia

    en.wikipedia.org/wiki/Rotation_formalisms_in...

    The Rodrigues vector (sometimes called the Gibbs vector, with coordinates called Rodrigues parameters) [3] [4] can be expressed in terms of the axis and angle of the rotation as follows: = ^ ⁡ This representation is a higher-dimensional analog of the gnomonic projection , mapping unit quaternions from a 3-sphere onto the 3-dimensional pure ...

  3. Phasor - Wikipedia

    en.wikipedia.org/wiki/Phasor

    Phasor notation (also known as angle notation) is a mathematical notation used in electronics engineering and electrical engineering.A vector whose polar coordinates are magnitude and angle is written . [13] can represent either the vector (⁡, ⁡) or the complex number ⁡ + ⁡ =, according to Euler's formula with =, both of which have magnitudes of 1.

  4. Rotation matrix - Wikipedia

    en.wikipedia.org/wiki/Rotation_matrix

    To find the angle of a rotation, once the axis of the rotation is known, select a vector v perpendicular to the axis. Then the angle of the rotation is the angle between v and Rv. A more direct method, however, is to simply calculate the trace: the sum of the diagonal elements of the rotation

  5. Angular velocity - Wikipedia

    en.wikipedia.org/wiki/Angular_velocity

    The addition of angular velocity vectors for frames is also defined by the usual vector addition (composition of linear movements), and can be useful to decompose the rotation as in a gimbal. All components of the vector can be calculated as derivatives of the parameters defining the moving frames (Euler angles or rotation matrices).

  6. Minkowski addition - Wikipedia

    en.wikipedia.org/wiki/Minkowski_addition

    For Minkowski addition, the zero set, {}, containing only the zero vector, 0, is an identity element: for every subset S of a vector space, S + { 0 } = S . {\displaystyle S+\{0\}=S.} The empty set is important in Minkowski addition, because the empty set annihilates every other subset: for every subset S of a vector space, its sum with the ...

  7. 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 ...

  8. Quaternions and spatial rotation - Wikipedia

    en.wikipedia.org/wiki/Quaternions_and_spatial...

    The circle defined by this slice will be very small, corresponding to the small angle of the rotation. As the rotation angles become larger, the slice moves in the negative z direction, and the circles become larger until the equator of the sphere is reached, which will correspond to a rotation angle of 180 degrees. Continuing southward, the ...

  9. Vector notation - Wikipedia

    en.wikipedia.org/wiki/Vector_notation

    In green, the point with radial coordinate 3 and angular coordinate 60 degrees, or (3,60°). In blue, the point (4,210°). The two polar coordinates of a point in a plane may be considered as a two dimensional vector. Such a vector consists of a magnitude (or length) and a direction (or angle).