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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 …

$\begingroup$ 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) = …

Oct 19, 2010 · 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 …

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。

I can't see the page in Google Books, but what you apparently have there is the logarithm of a unit quaternion $\mathbf q$, which has scalar part $\cos(\theta)$ and vector part …

Dec 11, 2017 · Then a general quaternion (a constant times a unit quaternion) can be thought of as representing a linear transformation which is a combination of a rotation and a scaling, and …

where log/exp are the quaternion logarithm/exponential. If you can convert between rotation vectors (where the direction is the rotation axis and the magnitude is the angle) and …

May 24, 2016 · First: note we are dealing only with the unit quaternions as a representation of attitude. The full quaternions don't really have a role here. I should also note up front that the …

In the quaternion case, reduced means that instead of taking this as the norm, you take its square root. Since the quaternions are 4-dimensional over $\Bbb R$, the reduced norm defines a …