>>12451072>Read what I said.Evidently I did, since I seem to have correctly apprehended your dumbass notion in
>>12451060. I just wanted to make sure since it is a little bit mind-boggling. Anyway, your whole line of thinking is misguided. What does
>the Lagrangian is only defined up to a time derivativereally mean? Are you talking about a rigorous mathematical definition of a Lagrangian in general? The statement that Lagrangians in general are only defined up to a time derivative is trivially untrue from a formal perspective, since you can go ahead and define whatever Lagrangians you want. You have to realise what Lagrangian means in the context, which is "the Lagrangian that can be defined for a given physical system". In this context, where a hypothetical physical system comes first, Landau's "theorem" is true. Technically, Landau argues that time derivatives in L don't affect the physics (i.e. the equations of motion), but the converse is obviously true i.e. knowing the equations of motion allows you to define a Lagrangian, but only up to an arbitrary time derivative.
