Physics/A/String vibration/Energy (advanced)

energy density using Rowland's notation:

$$u= \tau_0 \left( \xi' + \tfrac 1 2 \eta '^2\right)$$

If $$\ell=1$$, I think I get:

$$u= \kappa_T \left( \xi' + \tfrac 1 2 \eta '^2\right)$$