Difference between revisions of "Addition of quaternions"
From Robotics
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\begin{align} | \begin{align} | ||
q+p &= q_0+p_0 \oplus \vec{\mathbf{q}}+\vec{\mathbf{p}} | q+p &= q_0+p_0 \oplus \vec{\mathbf{q}}+\vec{\mathbf{p}} | ||
+ | \end{align} | ||
+ | </math> | ||
+ | Obviously addition of two quaternions is ''commutative'' and ''associative'': | ||
+ | :<math> | ||
+ | \begin{align} | ||
+ | q+p&=p+q \\ | ||
+ | (q+p)+r&=q+(p+r) | ||
\end{align} | \end{align} | ||
</math> | </math> |
Revision as of 17:20, 1 September 2015
← Back: Pure and unit quaternions | Overview: Quaternions | Next: Multiplication of quaternions → |
Two quaternions can easily be added by adding their components.
Assume two quaternions:
The quaternions and can just be replaced by these equations in their addition and then be summarized as the individual four components:
So the addition in vector notation can be written as:
Obviously addition of two quaternions is commutative and associative: