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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 haveL = L_{A}+ L_{B}

I'm trying to understand how this additivity implies only simultaneous multiplication ofLand_{A}Lby an arbitrary constant._{B}

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.

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# Additivity of lagrangian and constraints on multiplication by arbitrary const

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