Cyclic angular momentum in a rotational metric
= Cyclic angular momentum in a rotational metric
{title2=$J=f(r)^2\dot\phi$}
For the affinely parametrized <geodesic Lagrangian> $\mathcal L=(\dot r^2+f(r)^2\dot\phi^2)/2$, the conserved cyclic momentum is $J=f(r)^2\dot\phi$. Its <Euler-Lagrange equations> are $\ddot r-ff^{\prime}\dot\phi^2=0$ and $\ddot\phi+2f^{\prime}\dot r\dot\phi/f=0$.