  We exploit a special, less-common, variational principle in analytical
mechanics (the Hertz' principle of least curvature) to develop a variational
analogue of Euler's equations for the dynamics of an ideal fluid. We apply this
variational formulation to the classical problem of the flow over an airfoil.
The developed variational principle reduces to the Kutta-Zhukovsky condition in
the special case of a sharp-edged airfoil, which challenges the accepted wisdom
that lift generation is a viscous phenomenon wherein the Kutta condition is a
manifestation of viscous effects. Rather, it is found that lift arises from
enforcing a necessary condition of momentum preservation of the inviscid flow
field. Moreover, the developed variational principle provides a closure
condition for smooth shapes without sharp edges where the Kutta condition is
not applicable. The presented theory is validated against Reynolds-Averaged
Navier-Stokes simulations. Finally, in the light of the developed theory, we
provide a simple explanation for lift generation.
