here and there

content/blog/2023-11-23-pid.md

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+---
+title: PID
+description: Getting from here to there
+date: 2023-11-23
+tags:
+  - math
+draft: true
+extra:
+  auto_center_images: true
+  excerpt: A post about PID controllers
+  uses:
+    - mermaid
+aliases:
+  - /blog/pid
+---
+
+
+We are here.
+
+<img src="/images/posts/pid/here.svg" style="margin: 2em auto;" />
+
+And we want to go there.
+
+<img src="/images/posts/pid/here_there.svg" style="margin: 2em auto;" />
+
+## Figuring out how to get there
+
+The first step in getting from *here* to *there* is knowing where *there* *isn't*.
+
+I suppose a good place to start is checking to see if *here* and *there* are in fact the same place.
+
+Are we there?
+
+<img src="/images/posts/pid/are_we_there.svg" style="margin: 2em auto;" />
+
+*Nope.*
+
+Well, let's say we want to go *there* from *here* (because we do).. Which way do we have to go?
+
+<img src="/images/posts/pid/this_way.svg" style="margin: 2em auto;" />
+
+I think we can do that. How far will we have to travel?
+
+<img src="/images/posts/pid/how_far.svg" style="margin: 2em auto;" />
+
+Great!
+
+## Getting there
+
+So,  we know where we are, we know where we aren't, and we know the distance and direction we'll have to travel. What's next?
+
+Unfortunately, as the answer tends to be, physics is next.
+
+We can't exactly just *go* there. We have to *get* there. And that means we have to spend some time 'twixt *here* and *there*.

content/blog/2023-11-24-tank-tracks.md

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+---
+title: Tank Tracks
+description: 
+date: 2023-11-24
+tags:
+  - math
+draft: true
+extra:
+  auto_center_images: true
+  excerpt: A post about the math behind tank tracks
+  uses:
+    - mermaid
+aliases:
+  - /blog/tank-tracks
+---
+
+$$
+  f(\vec{v}) = 
+    \vec{v} +
+    \begin{bmatrix}
+      0 & 1 \\\\
+      -1 & 0
+    \end{bmatrix}
+    \vec{v}
+$$

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