Thanks a lot, it really helped. I would have one more question as I went further into the proof. If ##r## changes in time, why does it say that we use a notation ##L=r^2*\frac{d\theta}{dt}## and ##L## is constant? Why is it constant if ##r## changes in time?
So, first of all, why and how are we taking the derivative of the vector r or s as d/dt if t is not a parameter of the equations?
Second question is what is the difference between d/dt(r) and d(theta)/dt(r) and also between d/dt(s) and d(theta)/dt(s)? Like, both of these appear at the bottom of...