I am aware of questions/answers that address the question of space around the equal-sign (e.g. this one or this other question).
However, my question is related to a situation where I make use of \underbrace:

The text in \underbrace causes a shift to the right of everything outside of the braces.
I do not want to introduce a linebreak in the text, nor do I want to extend the underbrace - I just do not like the large gap in the equation.
I have tried \! without significant effect.
How do I move the portion to the right of the braces so that it is partially above the text?
(Have I missed something in the mathtools package documentation?)
This portion of code reproduces the equation above:
\begin{equation}
\underbrace{\left(\frac{\vec{\omega}\cdot\vec{v}}{\vec{v}\cdot\vec{v}}\right)}_%
{\text{projection of }\vec{\omega}\text{ on }\vec{v}}\vec{v}=%
\frac{\xi_{\text{s}}}{v_{\text{s}}}\vec{v}
\end{equation}
