Dear Diary,

I hesitate to tell you that today I needlessly used up a couple sheets of paper trying to derive a general transformation from (x,y) coordinates to rotational coordinates. It sure made for an odd feeling. I'm in my 30s -- long out of school -- and couldn't remember the word for 'trigonometry.' I assume stubbornness kept me from trying to look it up. Or maybe I thought this would be a fun way to spend an early Saturday morning?

I did, however, remember that A squared plus B squared equals C squared, though Mr. P's theorem turned out to be a red herring (half a page worth of scribbles down the drain! You should be happy you're not made of paper, dear Diary, else I might have been tempted to scribble those notes in you).

What did the trick was punching in test cases into a calculator until I remembered how sine, cosine, tangent, and their variants work (ArcTangent I don't remember ever learning about, but it's brilliant!), and drawing up test cases until I realized what I was actually trying to do was to rotate the coordinate system through a certain angle (which would change over time based on position and velocity).

It turns out it works like this (for future reference, or in case you're interested, my bestest bookish friend):

Rotational Speed component = Sin(Angle-of-Motion - Position's-Angle-from-origin) * Speed-of-motion
Centripetal Speed component = Cos(Angle-of-Motion - Position's-Angle-from-origin) * Speed-of-motion

And that Angle-of-Motion is the ArcTan(vertical-speed-component/horizontal-speed-component)
And that Angle-from-origin is the ArcTan(vertical-position/horizontal-position)

Diary, am I proud of these accomplishments? Yes, of course. I only tell you this so you will love me more.

Yours, as always,
nobody.

p.s. - Why no superscript and subscript tags? This entry could have been so much spiffier.

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