Are there any good sources to understand the physics behind a rolling sphere down an incline plane?
What specifically don't you understand?
See page 69: http://www.astro.uwo.ca/~houde/courses/PDF files/physics350/Lagrange.pdf
There is always more to say!
I ran through the slides and was overloaded with information. Not sure if it was the slides with information that was scattered but it was just a lot of information.
I was hoping there might be a good source from which I can weave the entire mathematical reasoning together in a systematic fashion rather than having to read through a slide with information scattered.
Just p. 69 - assuming you understand analytical mechanics.
Or if you want Newtonian mechanics, try this:
Or with pictures:
Or you can tell us what it is you know, and what you don't understand.
Separate names with a comma.