method of complex-coordinate rotation
1Rotation matrix — In linear algebra, a rotation matrix is a matrix that is used to perform a rotation in Euclidean space. For example the matrix rotates points in the xy Cartesian plane counterclockwise through an angle θ about the origin of the Cartesian… …
2Rotation representation (mathematics) — In geometry a rotation representation expresses the orientation of an object (or coordinate frame) relative to a coordinate reference frame. This concept extends to classical mechanics where rotational (or angular) kinematics is the science of… …
3Complex number — A complex number can be visually represented as a pair of numbers forming a vector on a diagram called an Argand diagram, representing the complex plane. Re is the real axis, Im is the imaginary axis, and i is the square root of –1. A complex… …
4Coordinate-measuring machine — A coordinate measuring machine (CMM) is a device for measuring the physical geometrical characteristics of an object. This machine may be manually controlled by an operator or it may be computer controlled. Measurements are defined by a probe… …
5Complex conjugate — Geometric representation of z and its conjugate in the complex plane In mathematics, complex conjugates are a pair of complex numbers, both having the same real part, but with imaginary parts of equal magni …
6Quaternions and spatial rotation — Unit quaternions provide a convenient mathematical notation for representing orientations and rotations of objects in three dimensions. Compared to Euler angles they are simpler to compose and avoid the problem of gimbal lock. Compared to… …
7Polar coordinate system — Points in the polar coordinate system with pole O and polar axis L. In green, the point with radial coordinate 3 and angular coordinate 60 …
8Cartesian coordinate system — Illustration of a Cartesian coordinate plane. Four points are marked and labeled with their coordinates: (2, 3) in green, (−3, 1) in red, (−1.5, −2.5) in blue, and the origin (0, 0) in purple. A Cartesian coordinate system specifies each point… …
9Wick rotation — In physics, Wick rotation, named after Gian Carlo Wick, is a method of finding a solution to a problem in Minkowski space from a solution to a related problem in Euclidean space, by analytic continuation.It is motivated by the observation that… …
10Direct stiffness method — As one of the methods of structural analysis, the direct stiffness method (DSM), also known as the displacement method or matrix stiffness method, is particularly suited for computer automated analysis of complex structures including the… …
