problem solved, typo in Goldstein
Many thanks to Ravinder Abrol for solving this problem. There is a typo in the most current printing of Goldstein, the correct equation should be
\theta = \pi - 4 s \int_{0}^{1} \frac{\rho d\rho}{\sqrt{r_{m}^{2} (1 - V(r)/E) - s^{2} (1-\rho^{2})^{2}}}...
Hi everyone, could anyone give me a hint on Goldstein derivation 3.4? Starting from
\theta = \pi - 2 \int_{r_{m}}^{\infty} \frac{s / r^{2} dr}{\sqrt{1 - V(r)/E - s^{2}/r^{2}}}
they do a change of variables to get
\theta = \pi - 4 s \int_{0}^{1} \frac{\rho d\rho}{\sqrt{r_{m}^{2} (1...