Month: July 2023

Video: Circular velocity and acceleration with geometric algebra

July 31, 2023 math and physics play , , , ,

Months ago, I used Manim to create a outline a geometric algebra treatment of the derivation of the circular velocity and acceleration formulas that you would find in a first year undergrad physics course.  I never published it, since overlaying audio and getting the timing of the audio and video right is hard (at least for me.)  I’m also faced with the difficulty of not being able to speak properly when attempting to record myself.
Anyways, I finally finished the audio overlays (it was sitting waiting for me to record the final 10s of audio!), and have posted this little 11 minute video, which includes:
  • A reminder of what circular coordinates are.
  • A brief outline of what is meant by each of the circular basis vectors.
  • A derivation of those basis vectors (just basic geometry, and no GA.)
  • A brief introduction to geometric algebra, and geometric algebra for a plane, including the “imaginary” \( i = \Be_1 \Be_2 \), and it’s use for rotation and polar form.
  • How to express the circular basis vectors in polar form.
  • Application of all the ideas above to compute velocity and acceleration.
  • Circular coordinate examples of velocity and acceleration.
It probably doesn’t actually make sense to try to pack all these ideas into one video, but oh well — that’s what I did.
You can find the video on google’s censorship-tube, and on odysee.

Cleaning the exhaust vents on my NUCs

July 3, 2023 electronics , , , , ,

My NUC needed an SSD brain transplant, which presented a good opportunity to clean the dust out of the fan exhaust vents.  It was almost completely clogged:

I vacuumed it out, which didn’t work too well, since the dust was a little greasy, so I hauled out the carpentry tools (my compressor and blower attachment),

and gave it a good blast.  Check out the after picture for the vents:

Here it is, reassembled

Ready to be my little workhorse once again.  I also blew the dust out of my older non-skull canyon NUC, which I had abandoned (switching to a backup) when it started emitting a strong burnt electronics smell.  That unit is now fully functional again too, and doesn’t smell like burnt electronics anymore!

These NUCs are nice little machines, but are really susceptible to dust clogs, as the vent spacing is really tight.  Once those gets clogged, there’s basically no airflow possible.

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