Bruh, it's \(j\), not \(i\):
\[
X(\omega) = \int_{-\infty}^{+\infty} x(t) e^{-jwt}\ dt
\]
This is what we #ElectricalEngineers say, when we're looking for a fight. This inevitably ends in us getting smacked down by muscular #Mathematicians and pumped #Physicists, but ya know....
@AmenZwa
Yeah! We'll work with quaternions if we feel like it!
Alternately, "No, we refuse to agree on notation!"
@dougmerritt 🤣 Nailed it!
I'd say CSs are better at wrangling quaternions than EEs. And EE notational consistency—boy....
@AmenZwa
You think? I have no feel for that.
There was a guy back in the day (Doug Sweetser) who was super fond of them, and wrote an online textbook redoing all of Physics 101 in terms of quaternions.
Good for him, on the one hand. On the other hand, web physicists we all know agreed that it was vast overkill, and they are mostly useful in only a small subset of physics problems. Avoiding gymbal lock with Euler angles in 3d problems or 3d computer graphics, especially.
@dougmerritt The only exposure to quaternions I got (which was skimpy), was through CS 3D CG in the context of rigid-body simulation and visualisation. And, with due respect to Rev. Hamilton, they aren't even used in ordinary 3D CG work, neither in polygonal nor in volumetric—as far as my experience went in those fields. But then, that's just me. But I do know a few CS guys who eat only in "quarters", and they all work for the Naval Research Lab.🤣
@AmenZwa
> And, with due respect to Rev. Hamilton, they aren't even used in ordinary 3D CG work, neither in polygonal nor in volumetric—as far as my experience went in those fields. But then, that's just me
Well, I'm really just an onlooker myself, but since graphics is a cool area, I've been trying to pay attention this entire time.
My first reaction is that I think that quaternions are in heavy use in the disguised form of matrix transformations.
@dougmerritt @AmenZwa hey! Quaternions are actually used directly fairly commonly too, and converted into matrices as the last step before use. One place they are used directly is in skeletal animation.
@demofox @dougmerritt @AmenZwa They are definitely commonly used in attitude control systems on, e.g., spacecraft. In fact, it's so common that people sometimes speak of "quaternions" and the "describing attitude" part is just understood to be implied.
@internic @demofox @dougmerritt @AmenZwa I can say with certainty that replacing all the axis-angle and matrix representations with quaternions cut the calculate time for missile test data analysis by about 40%, mainly because the sandwich product can be reduced to a much smaller number of multiplications than it would appear at first glance.
@internic @demofox @AmenZwa
That makes intuitive sense for attitude control. Thanks.