Hello I am using Landau's mechanics Vol I for classical mechanics. On page 4 he mentions for Lagrangian of a system composed of two systems A and B which are so far away so that their interactions can be neglected. then for the combined system we have L = LA + LB I'm trying to understand how this additivity implies only simultaneous multiplication of LA and LB by an arbitrary constant. I think to establish it we might have to consider the difference in Lagrangian when A & B are close by and when they are far away. Please guide. Any help will be appriciated.