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  2. Rotation matrix - Wikipedia

    en.wikipedia.org/wiki/Rotation_matrix

    The case of θ = 0, φ ≠ 0 is called a simple rotation, with two unit eigenvalues forming an axis plane, and a two-dimensional rotation orthogonal to the axis plane. Otherwise, there is no axis plane. The case of θ = φ is called an isoclinic rotation, having eigenvalues e ±iθ repeated twice, so every vector is rotated through an angle θ.

  3. Kabsch algorithm - Wikipedia

    en.wikipedia.org/wiki/Kabsch_algorithm

    Let P and Q be two sets, each containing N points in .We want to find the transformation from Q to P.For simplicity, we will consider the three-dimensional case (=).The sets P and Q can each be represented by N × 3 matrices with the first row containing the coordinates of the first point, the second row containing the coordinates of the second point, and so on, as shown in this matrix:

  4. Active and passive transformation - Wikipedia

    en.wikipedia.org/wiki/Active_and_passive...

    A rotation of the vector through an angle θ in counterclockwise direction is given by the rotation matrix: = (⁡ ⁡ ⁡ ⁡), which can be viewed either as an active transformation or a passive transformation (where the above matrix will be inverted), as described below.

  5. Ansys - Wikipedia

    en.wikipedia.org/wiki/Ansys

    Ansys, Inc. is an American multinational company with its headquarters based in Canonsburg, Pennsylvania. It develops and markets CAE / multiphysics engineering simulation software for product design, testing and operation and offers its products and services to customers worldwide.

  6. Rodrigues' rotation formula - Wikipedia

    en.wikipedia.org/wiki/Rodrigues'_rotation_formula

    In the theory of three-dimensional rotation, Rodrigues' rotation formula, named after Olinde Rodrigues, is an efficient algorithm for rotating a vector in space, given an axis and angle of rotation. By extension, this can be used to transform all three basis vectors to compute a rotation matrix in SO(3) , the group of all rotation matrices ...

  7. Rotordynamics - Wikipedia

    en.wikipedia.org/wiki/Rotordynamics

    Rotordynamics (or rotor dynamics) is a specialized branch of applied mechanics concerned with the behavior and diagnosis of rotating structures. It is commonly used to analyze the behavior of structures ranging from jet engines and steam turbines to auto engines and computer disk storage.

  8. 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 ...

  9. Rotation of axes in two dimensions - Wikipedia

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

    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 .