Generalized angular momentum in a radial monopole field (source code)

= Generalized angular momentum in a radial monopole field
{title2=$\mathbf L=m\mathbf r\times\dot{\mathbf r}-\mu\widehat{\mathbf r}$}

For a radial conservative force plus the magnetic-type force $\dot{\mathbf r}\times(\mu\mathbf r/r^3)$, the torque equals $\mu\,d\widehat{\mathbf r}/dt$. Subtracting $\mu\widehat{\mathbf r}$ from ordinary <angular momentum> therefore produces a constant vector. Its dot product with $\widehat{\mathbf r}$ is $-\mu$, so motion lies on a cone about that vector. At $\mu=0$, ordinary planar <central force> motion is recovered. This is the classical radial <magnetic monopole> angular-momentum correction.