Lagrangian Form

The Lagrangian is given by the difference of the kinetic and potential energy, $$L=T-V,$$ where for a continuum occupying a domain $\Omega$ we have $$T={\int }_{\Omega }\frac{1}{2}\rho \mathbf{v}\cdot \mathbf{v}d\Omega$$ and $V$ is problem dependent. For the quasi-static limit we can assume $T<<V$ and $L\approx -V$