Problem3.22
Kornpob Bhirombhakdi
February 2, 2017
Problem3.22
From the previous calculation, we obtained \[ \Omega^2(x)=\frac{V^2}{x^2a^2}(1-\frac{\arctan(x)}{x}) \] \[ \kappa^2(x)=2 \times (\frac{V^2xa\Delta}{2}+\Omega^2) \] where \(x=\frac{r}{a}\) and \(\Delta=\frac{-2}{x^3a^3}-\frac{1}{x^3a^3} \times \frac{1}{1+x^2}+\frac{3a}{x^4a^4}\arctan(x)\).
