## Archive of posts on Dec 22, 2023

### The duality between two plane trajectories related by a conformal map

The conformal map $\fc wz$ transforms the trajectory with energy $-B$ in potential $\fc Uz\ceq A\v{\d w/\d z}^2$ into the trajectory with energy $-A$ in potential $\fc Vw\ceq B\v{\d z/\d w}^2$. I will prove this beautiful result and show some implications of it.

- Categories: physics
- Tags: complex, classical mechanics, canonical transformation, kepler problem, mathematical physics, vector analysis, long paper