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N3: F_12 = - F_21..........
regroup, et voila:
dP_1 / dt + dP_2 / dt = 0 = d(P total) / dt
conservation of linear momentum for the two interacting objects
.... momentum conservation is a Noether Current associated with
spatial translation invariance. Spatial translation invariance is a
very intuitive, natural and easy to swallow axiom. There's really
nothing strange or mystical about momentum conversation, it's simply
a reflection of symmetry.