
The position of the whole body CM can be computed from the positions of the segmental CMs. In Figure 1, let
where i = segment, R_{i} = the position of the segment CM, R = the position of the whole body CM, and r_{i} = the relative position of the segment CM to the whole body CM. The sum of the first mass moments of the segments is
where M = the whole body mass. The whole body center of mass is the balance point of the system and must suffice
From [2] and [3]:
where [x_{i}, y_{i}, z_{i}] = the coordinates of the segment CM. From [3]:
where v_{i} = the relative velocity of the segment CM to the whole body CM. Therefore:
where P = the whole body momentum, and V = the velocity of the whole body CM. As shown in [6], the whole body momentum is the whole body mass times the velocity of the whole body CM. 
© YoungHoo Kwon, 1998 