How do I get the group of symmetries and the constant of motion of $L=\frac{\dot{x}^2}{2}m+V(x+ct)$ where c is a constant?
When I tried to solve it, it was to look for shifts in $x$ and $ct$ under which $L$ is invariant. I did $$x\rightarrow x+A,$$ $$ct\rightarrow ct+B.$$ $\therefore A+B=0$ so that invariance is satisfied.
But I don't know what to do from here.
