- #1
Coffee_
- 259
- 2
Consider a Lagrangian: ##L(x,x',t)##
Define now: ##L'(x,x',t) = L + x ##
We have seen that Lagrangians can differ up to a total time derivative of some function ##F(x,t)## in such cases and give the same equation. When checking explicitly these two give different equations. Why would it be wrong then to say that ##x=x(t)## and say that this function ##F## is the primitive function of ##x(t)##?
Define now: ##L'(x,x',t) = L + x ##
We have seen that Lagrangians can differ up to a total time derivative of some function ##F(x,t)## in such cases and give the same equation. When checking explicitly these two give different equations. Why would it be wrong then to say that ##x=x(t)## and say that this function ##F## is the primitive function of ##x(t)##?