One possible starting point to create a physical theory is the Lagrangian $L$. There we assume that the variation of the action $\delta S = \delta \int\_{-\infty}^\infty dt \ L = 0$.

In classical theories we usually only use $q$ and $\dot{q}$ in the Lagrangian. But there are also effects like the [Abraham-Lorentz force](http://en.wikipedia.org/wiki/Abraham%E2%80%93Lorentz_force), which describes a force $F(q) = \alpha \dddot{q}$, where $\alpha$ is a constant and $q$ is the location of a particle. This would require a higher order derivatives in the Lagrangian.

Now I wondered if it is even possible to write down a Lagrangian for such a force, that contains a third derivative in time?

Maybe a similar question is if it is possible to get a Lagrangian that results in a friction force $m\ddot{q} = - \gamma\dot{q}$?