- #1

Sciencemaster

- 105

- 17

- TL;DR Summary
- I've been told that the infinitesimal change in coordinates x and y takes the form δx=wy and δy=wx, and I was hoping someone could help me figure out why.

I've been told that the infinitesimal change in coordinates x and y as you rotate along a hyperbola that fits the equation b(dy)^2-a(dx)^2=r takes the form δx=bwy and δy=awx, where w is a function of the angle of rotation (I'm pretty sure it's something like sinh(theta) but it wasn't clarified for me so I'm not 100% sure). However, I'm not sure why this is the case, and I was hoping someone could show me how you get these infantesimal transformations and how they preserve the invariant r.