Solution
= Solution
$L^2=J^2-(q\beta)^2=J^2\sin^2\alpha$. Splitting <kinetic energy> into radial and angular parts therefore gives $E=\tfrac12m\dot r^2+J^2\sin^2\alpha/(2mr^2)+V(r)$, proving the stated <effective potential>.
= Solution
$L^2=J^2-(q\beta)^2=J^2\sin^2\alpha$. Splitting <kinetic energy> into radial and angular parts therefore gives $E=\tfrac12m\dot r^2+J^2\sin^2\alpha/(2mr^2)+V(r)$, proving the stated <effective potential>.