On not understanding circular motion.

I never did really understand circular motion, even in Newtonian Mechanics. I never got the more complex aspects of the mathematics, nor how the equations are derived. As a result I never understood simple harmonic motion, which is mathematically similar, and because I never understood that I never understood waves either.

And now, I'm stuck on the question I was going to tackle last weekend, of which ultrarelativistic and relativistic circular motion is a big part.

If you have any good resources on the matter please post them in the comments. Just a good explanation of how things are derived in Newtonian mechanics would help, then I might be able to follow the same derivation but relativistically.

For now, one of the best sources I've come across is a series of video lectures from the 80s called The Mechanical Universe. Unfortunately they're prohibitively expensive to buy because they're not sold in editions for personal use, only for showing in schools and stuff. They can, however, be readily obtained by copyright-infringing means.

Normal service will be resumed once I've sussed the physics.