= Axial angular-momentum current of an elastic string
{title2=$L_x=\int\rho(\psi_y\dot\psi_z-\psi_z\dot\psi_y)\,dx$}
Rotating the two transverse displacement components around the string axis gives density $\ell_x=\rho(\psi_y\dot\psi_z-\psi_z\dot\psi_y)$ and flux $\mathcal J_x=-F(\psi_y\psi_z'-\psi_z\psi_y')$. The pair of <wave equations> yields $\partial_t\ell_x+\partial_x\mathcal J_x=0$. The total charge is physical <angular momentum> about the axis; it is conserved only when the net endpoint <torque> flux vanishes.
Back to article page
