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quaternion    
n. 四个一组,四人一组,四元数

四个一组,四人一组,四元数

quaternion
四元数

quaternion
n 1: the cardinal number that is the sum of three and one [synonym:
{four}, {4}, {IV}, {tetrad}, {quatern}, {quaternion},
{quaternary}, {quaternity}, {quartet}, {quadruplet},
{foursome}, {Little Joe}]

Quaternion \Qua*ter"ni*on\, v. t.
To divide into quaternions, files, or companies. --Milton.
[1913 Webster]


Quaternion \Qua*ter"ni*on\, n. [L. quaternio, fr. quaterni four
each. See {Quaternary}.]
1. The number four. [Poetic]
[1913 Webster]

2. A set of four parts, things, or person; four things taken
collectively; a group of four words, phrases,
circumstances, facts, or the like.
[1913 Webster]

Delivered him to four quaternions of soldiers.
--Acts xii. 4.
[1913 Webster]

Ye elements, the eldest birth
Of Nature's womb, that in quaternion run. --Milton.
[1913 Webster]

The triads and quaternions with which he loaded his
sentences. -- Sir W.
Scott.
[1913 Webster]

3. A word of four syllables; a quadrisyllable.
[1913 Webster]

4. (Math.) The quotient of two vectors, or of two directed
right lines in space, considered as depending on four
geometrical elements, and as expressible by an algebraic
symbol of quadrinomial form.
[1913 Webster]

Note: The science or calculus of quaternions is a new
mathematical method, in which the conception of a
quaternion is unfolded and symbolically expressed, and
is applied to various classes of algebraical,
geometrical, and physical questions, so as to discover
theorems, and to arrive at the solution of problems.
--Sir W. R. Hamilton.
[1913 Webster]


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  • Quaternion Rotation formula - Mathematics Stack Exchange
    Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
  • Apply Quaternion Rotation to Vector - Mathematics Stack Exchange
    A quaternion can be thought of as a scalar plus a 3D vector (also known as real and imaginary parts) The product of a scalar and a 3D vector is the usual scalar multiplication The product of two vectors produces a quaternion with both scalar and vector components, given by (minus) the dot product and cross product respectively
  • 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
  • 四元数和旋转(Quaternion rotation) - 知乎
    四元数(quaternion)可以看作中学时学的复数的扩充，它有三个虚部。形式如下： ，可以写成 具有如下性质： 设 ， ，则 3 2 共 轭四元数 一个四元数 的共轭(用 表示)为 一个四元数和它的共轭的积等于该四元数与自身的点乘，也等于该四元数长度的平方。即，
  • Quaternions and spatial translations - Mathematics Stack Exchange
    $\begingroup$ The alternative is the dual quaternion, which Gerard mentioned (albeit not by name) - they are composed the same way, the "sandwich" (a)(bcb*)(a*) = (ab)c(ba) = (ab)c(ab)*, which means a long sequence on the LHS only needs to be conjugated after the fact to find the RHS So, you don't need to break a long sequence of quaternions
  • How to define a quaternion group of order 8
    $\begingroup$ Since you are in the happy position of working with a group of small order, I think you would be well served by writing out the elements of the group, and the product of each pair of elements (including things like a$^2$, and also remembering that ab need not = ba)
  • 如何形象地理解四元数？ - 知乎
    汉密尔顿定义了一种纯四元数（pure quaternion），其表达式为 qw=(0,wx,wy,wz) 。纯四元数第一项为零，它存在于四维空间的三维超平面上，与三维空间中的三维向量一一对应。
  • Understanding quaternions - Mathematics Stack Exchange
    Adding two unit quaternions generally does not yield a unit quaternion, so the answer is technically no as written, but the answer is yes if you say "rotating two separate planes by the same angle and rescales " Of course adding two quaternions gives a quaternion, so algebraically this is clear
  • How to use the quaternion derivative - Mathematics Stack Exchange
    There is that exponential form of a quaternion again, which we will continue to assume makes sense based on Euler identity intuition Thus at time t0+dt, q(t0+dt) = q(t0)*exp((1 2)*W*dt) which implies dq = exp((1 2)*W*dt) Performing the above operation is exactly the same as expressing w*dt as a quaternion through the axis-angle conversion
  • 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





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