▁mass ▁is ▁the ▁same ▁as ▁the ▁cent roid ▁of ▁the ▁volume . ▁ ▁B ary cent ric ▁coordinates ▁ ▁The ▁coordinates ▁R ▁of ▁the ▁center ▁of ▁mass ▁of ▁a ▁two - part icle ▁system , ▁P 1 ▁and ▁P 2 , ▁with ▁masses ▁m 1 ▁and ▁m 2 ▁is ▁given ▁by ▁ ▁Let ▁the ▁percentage ▁of ▁the ▁total ▁mass ▁divided ▁between ▁these ▁two ▁particles ▁vary ▁from ▁ 1 0 0 % ▁P 1 ▁and ▁ 0 % ▁P 2 ▁through ▁ 5 0 % ▁P 1 ▁and ▁ 5 0 % ▁P 2 ▁to ▁ 0 % ▁P 1 ▁and ▁ 1 0 0 % ▁P 2 , ▁then ▁the ▁center ▁of ▁mass ▁R ▁moves ▁along ▁the ▁line ▁from ▁P 1 ▁to ▁P 2 . ▁ ▁The ▁percent ages ▁of ▁mass ▁at ▁each ▁point ▁can ▁be ▁viewed ▁as ▁project ive ▁coordinates ▁of ▁the ▁point ▁R ▁on ▁this ▁line , ▁and ▁are ▁term ed ▁b ary cent ric ▁coordinates . ▁Another ▁way ▁of ▁interpre ting ▁the ▁process ▁here ▁is ▁the ▁mechanical ▁bal ancing ▁of ▁moments ▁about ▁an ▁arbitrary ▁point . ▁The ▁numer ator ▁gives ▁the ▁total ▁moment ▁that ▁is ▁then ▁bal anced ▁by ▁an ▁equivalent ▁total ▁force ▁at ▁the ▁center ▁of ▁mass . ▁This ▁can ▁be ▁generalized ▁to ▁three ▁points ▁and ▁four ▁points ▁to ▁define ▁project ive ▁coordinates ▁in ▁the ▁plane , ▁and ▁in ▁space , ▁respectively . ▁ ▁Systems ▁with ▁periodic ▁boundary ▁conditions ▁For ▁particles ▁in ▁a ▁system ▁with ▁periodic ▁boundary ▁conditions ▁two ▁particles ▁can ▁be ▁neighb ours ▁even ▁though ▁they ▁are ▁on