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Real world uses of Quaternions? - Mathematics Stack Exchange The quaternion algebra shows there as a way of disentangling two Alamouti coded signals transmitted by a pair of antennas The advantages come from the fact that even if the signal from one antenna is lost for a particular receiver (due to sitting in a node for that particular radio wave), then the signal from the other antenna saves the day
How can one intuitively think about quaternions? Here is the intuitive interpretation of this Given a particular rotation axis $\omega$, if you restrict the 4D quaternion space to the 2D plane containing $ (1,0,0,0)$ and $ (0,\omega_x,\omega_y,\omega_z)$, the unit quaternions representing all possible rotations about the axis $\vec \omega$ form the unit circle in that plane
Understanding quaternions - Mathematics Stack Exchange Of course adding two quaternions gives a quaternion, so algebraically this is clear I don't really think it's clear geometrically, however, and with good reason: this is a very exceptional accident that occurs in precisely four dimensions, and no other dimensions
Concise description of why rotation quaternions use half the angle The idea of Hamilton was to find some generalization of this formula for three-dimensional rotations The quaternions can do such a generalization identifying a $3D$ -vector with a pure imaginary quaternion $\mathbf {v}$ and using a pure imaginary versor $\mathbf {u}$ to identify the axis of rotation
Combining rotation quaternions - Mathematics Stack Exchange If I combine 2 rotation quaternions by multiplying them, lets say one represents some rotation around x axis and other represents some rotation around some arbitrary axis The order of rotation ma
How to convert a quaternion from one coordinate system to another I am trying to find a way of converting a quaternion from an arbitrary coordinate system to a fixed coordinate system that is used in my application I have two different coordinate systems, one is
四元数 (Quaternions) 数学背景 四元数变换 (Quaternion Transforms) 连接两个四元数 矩阵和四元数相互转换 球面线性插值 从一个向量旋转到另一个向量)Rotation from One Vector to Another 1 数学背景 (Mathematical Background) 四元数定义: 一个四元数 可以被定义以下形式，相互等价。 其中， 为四元数
linear algebra - Conversion of rotation matrix to quaternion . . . One of the quaternion elements is guaranteed to have a magnitude of greater than 0 5 and hence a squared value of 0 25 We can use this to determine the "best" set of parameters to use to calculate the quaternion from a rotation matrix