# Tag Info

If you just give the mass an explicit time-dependence, $$L = \frac12 m(t) \dot{x}^2 - U(x)$$ then the Euler-Lagrange equation is $$\frac{d}{dt} (m \dot{x}) = \dot{m} \dot{x} + \dot{m} \ddot{x} = - \frac{dU}{dx}.$$ It's unclear to me why you think "we simply cannot use" this result. It isn't Galilean invariant, but once you let $m(t)$ have arbitrary time-...